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TeacherExpt:Titrating sodium hydroxide with hydrochloric acid
From Learn Chemistry Wiki
You have to decide if this experiment is suitable to use with different classes, and look at the need for preliminary training in using techniques involved in titration (see Teaching notes). What follows here assumes that teachers have judged the class to be capable of doing this experiment using a burette with reasonable expectation of success.
Assuming that the students have been given training, the practical work should, if possible, start with the apparatus ready at each work-place in the laboratory. This is to avoid vulnerable and expensive glassware (the burette) being collected from an overcrowded central location.
Filling the burette, measuring out the alkali into the flask, and titrating it until it is neutralised takes about 20 minutes, with false starts being likely for many groups. In practice it does not matter if the end-point is overshot, even by several cubic centimetres, but the aim is to find the proportions for a roughly neutral solution.
Producing a neutral solution free of indicator, should take no more than 10 mins.
Evaporating the solution may take the rest of the lesson to the point at which the solution can be left to crystallise for the next lesson. Watching solutions evaporate can be tedious for students, and they may need another task to keep them occupied – e.g. rinsing and draining the burettes with purified water.
Apparatus and chemicals
- Eye protection
Each working group requires:
- Burette (30 cm3 or 50 cm3) (see note 1)
- Conical flask (100 cm3)
- Beaker (100 cm3)
- Pipette (20 or 25 cm3) with pipette filler
- Stirring rod
- Small (filter) funnel (about 4 cm diameter)
- Burette stand and clamp (see note 2)
- White tile (optional) (see note 3)
- Bunsen burner with heat resistant mat
- Pipeclay triangle (see note 4)
- Evaporating basin (at least 50 cm3 capacity)
- Crystallising dish
- Access to:
- Microscope or hand lens suitable for examining crystals in the crystallising dish
- Sodium hydroxide solution, 0.4 mol dm-3 (see note 5) (Irritant at this concentration), about 100 cm3 in a labelled and stoppered bottle
- Dilute hydrochloric acid, 0.4 mol dm-3 (Low hazard at this concentration), about 100 cm3 in a labelled and stoppered bottle
- Methyl orange indicator solution (Low hazard at this concentration) (or alternative) in small dropper bottle
Sodium hydroxide (Irritant at concentration used) Refer to CLEAPSS® Hazcard 91, Recipe card 65 Dilute hydrochloric acid (Low hazard at concentration used) Refer to CLEAPSS® Hazcard 47A and Recipe card 31 Methyl orange indicator solution (The solid is Toxic but not the solution) Refer to CLEAPSS® Hazcard 32 and Recipe card 33
- If your school still uses burettes with glass stopcocks, consult the CLEAPSS® Laboratory handbook, section 10.10.1, for their care and maintenance. This experiment will not be successful if the burettes used have stiff, blocked or leaky stopcocks. Modern burettes with PTFE stopcocks are much easier to use, require no greasing, and do not get blocked. Burettes with pinchcocks of any type are not recommended; while cheap, they also are prone to leakage, especially in the hands of student beginners.
- Burette stands and clamps are designed to prevent crushing of the burette by overtightening,
which may happen if standard jaw clamps are used.
- The optional white tile is to go under the titration flask, but white paper can be used instead.
- Ceramic gauzes can be used instead of pipeclay triangles, but the evaporation then takes longer.
- The concentrations of the solutions do not need to be made up to a high degree of accuracy, but they should be reasonably close to the same concentration as each other, and less than 0.5 mol dm-3.
- The evaporation and crystallisation stages may be incomplete in the lesson time. The crystallisation dishes need to be set aside for crystallisation to take place slowly. However, the dishes should not be allowed to dry out completely, as this spoils the quality of the crystals. With occasional checks, it should be possible to decide when to decant surplus solution from each dish to leave good crystals for the students to inspect in the following lesson.
HEALTH & SAFETY: Wear eye protection
a Using a small funnel, pour a few cubic centimetres of 0.4 mol dm-3 hydrochloric acid into the burette, with the tap open and a beaker under the open tap. Once the tip of the burette is full of solution, close the tap and add more solution up to the zero mark. (Do not re-use the acid in the beaker – this should be rinsed down the sink.)
b Use a pipette with pipette filler to transfer 25 (or 20) cm3 of 0.4 mol dm-3 sodium hydroxide solution to the conical flask, and add two drops of methyl orange indicator. Swirl gently to mix. Place the flask on a white tile or piece of clean white paper under the burette tap.
c Add the hydrochloric acid to the sodium hydroxide solution in small volumes, swirling gently after each addition. Continue until the solution just turns from yellow-orange to red and record the reading on the burette at this point. This coloured solution should now be rinsed down the sink.
a Refill the burette to the zero mark. Carefully add the same volume of fresh hydrochloric acid as you used in (c) to another 25 (or 20) cm3 of sodium hydroxide solution, to produce a neutral solution, but this time without any indicator.
a Pour this solution into an evaporating basin. Reduce the volume of the solution to about half by heating on a pipeclay triangle or ceramic gauze over a low to medium Bunsen burner flame. The solution spits near the end and you get less crystals. Do not boil dry. You may need to evaporate the solution in, say, 20 cm3 portions to avoid over-filling the evaporating basin. Do not attempt to lift the hot basin off the tripod – allow to cool first, and then pour into a crystallising dish.
b Leave the concentrated solution to evaporate further in the crystallising dish. This should produce a white crystalline solid in one or two days.
c Examine the crystals under a microscope.
Titration using a burette, to measure volumes of solution accurately, requires careful and organised methods of working, manipulative skills allied to mental concentration, and attention to detail. All of these are of course desirable traits to be developed in students, but there has to be some degree of basic competence and reliability before using a burette with a class. The experiment is most likely to be suited to 14–16 year old students. This is discussed further below, but what follows here assumes that you have judged the class to be capable of doing this experiment using a burette with reasonable expectation of success.
Students need training in using burettes correctly, including how to clamp them securely and fill them safely. You should consider demonstrating burette technique, and give students the opportunity to practise this. In this experiment a pipette is not necessary, as the aim is to neutralise whatever volume of alkali is used, and that can be measured roughly using a measuring cylinder.
It is not the intention here to do quantitative measurements leading to calculations. The aim is to introduce students to the titration technique only to produce a neutral solution.
Alternative indicators you can use include screened methyl orange (green in alkali, violet in acid) and phenolphthalein (pink in alkali, colourless in acid).
Leaving the concentrated solutions to crystallise slowly should help to produce larger crystals. The solubility of sodium chloride does not change much with temperature, so simply cooling the solution is unlikely to form crystals.
Under the microscope (if possible, a stereo-microscope is best) you can see the cubic nature of the crystals. If crystallisation has occurred in shallow solution, with the crystals only partly submerged, 'hopper-shaped' crystals may be seen. In these crystals, each cube face becomes a hollow stepped-pyramid shape.
1. What substances have been formed in this reaction? Write a word equation and a symbol equation.
2. Why must you use another 25 cm3 of sodium hydroxide solution, rather than making your crystals from the solution in Stage 1?
3. What shape are the crystals?
This experiment has been reproduced from Practical Chemistry:
This website has a wealth of information on sodium chloride as a mineral (Website accessed January 2011):


text: Purpose: To determine whether the absence of transglutaminase 2 enzyme (TG2) in TG2 knockout mice (TG2 -/- ) protect them against early age-related functional and histological arterial changes. Methods: Pulse wave velocity (PWV) was measured using non-invasive Doppler and mean arterial pressure (MAP) was measured in awake mice using tail-cuff system. Thoracic aortas were excised for evaluation of endothelial dependent vasodilation (EDV) by wire myography, as well as histological analyses. Results: PWV and MAP were similar in TG2 -/- mice to age-matched wild type (WT) control mice. Old WT mice exhibited a markedly attenuated EDV as compared to young WT animals. The TG2 -/- young and old mice had enhanced EDV responses (p<0.01) as compared to WT mice. There was a significant increase in TG2 crosslinks by IHC in WT old group compared to Young, with no stain in the TG2 -/- animals. Optical microscopy examination of Old WT mice aorta showed thinning and fragmentation of elastic laminae. Young WT mice, old and young TG2 -/- mice presented regularly arranged and parallel elastic laminae of the tunica media. Conclusion: The genetic suppression of TG2 delays the age-induced endothelial dysfunction and histological modifications.

source: openbmb/Ultra-FineWeb


text:
Tehničko-tehnološki tehničari/tehničko-tehnološke tehničarke d. n.
This unit group covers physical and engineering science technicians not classified elsewhere in Minor Group 311: Physical and Engineering Science Technicians. For instance, the unit group includes those who assist scientists and engineers engaged in developing procedures or conducting research on safety, biomedical, environmental or industrial and production engineering.
In such cases tasks would include -
(a) collecting data and providing technical assistance regarding: efficient, safe and economic utilization of personnel, material and equipment; methods of work and sequence of operations and supervision of their implementation; and efficient layout of plant or establishment;
(b) aiding in the identification of potential hazards and introducing safety procedures and devices;
(c) modifying and testing equipment and devices used in the prevention, control and remediation of environmental pollution, in site remediation and land reclamation;
(d) assisting in the development of environmental pollution remediation devices under the direction of an engineer;
(e) assisting engineers in testing and designing robotics equipment.
Examples of the occupations classified here:
- Engineering technician (production)
- Fire investigator
- Forensic science technician
- Quantity surveying technician
- Robotics technician
- Time and motion study technician
Some related occupations classified elsewhere:
- Production engineer - 2141
- Time and motion study engineer - 2141
- Quantity surveyor - 2149
- Aeronautics engineering technician - 3115


text:
1 Department of Marketing and Statistics, Aarhus School of Business, Aarhus BSS, Aarhus University2 MAPP - Centre for Research on Customer Relations in the Food Sector, Aarhus School of Business, Aarhus BSS, Aarhus University3 Department of Management, Aarhus BSS, Aarhus University4 Department of Management, Aarhus BSS, Aarhus University
This paper discusses the food distribution systems of six Eastern European countries. It considers the macro and task environments of distribution systems, discussing the constraints and opportunities the environments present to companies. The institutional structure of retailing and wholesaling are analysed and important developments in the institutional structure are noted. The internal political economy of distribution channels in Eastern Europe is analysed and the modernisation of distribution systems discussed. Finally, some conclusions are offered and areas for future research suggested.
MAPP; Food distribution systems; Eastern Europe; Fødevaredistribution; Østeuropa


History of the Forth
The Forth has a long and varied history, having been used by man since earliest times. On this page, experts tell us about events that have shaped the Forth and its communities.
From earliest times, man and nature have interacted in the Firth of Forth, in recent centuries with largely catastrophic consequences for the natural world. Settlement began on the shore some 10,500 years ago.
The first Mesolithic people were hunter gatherers who lived entirely from what they could find in the wild: Neolithic people who followed them introduced herding, and eventually cultivation, but still depended to a large extent on what they could find, as demonstrated by 6,000 year old middens containing millions of oyster shells, often well inland from the modern shore line of the upper estuary.
Early people, however, lacked the technology to make much of an impact on the biodiversity of the Forth. Probably the first notable modification of nature occurred on the islands in the Middle Ages, when the introduction of sheep and rabbits wiped out the original scrub cover, and the culling of seabirds and their eggs made gulls and puffins a rarity. However, there was still plenty of fish and shellfish to provide a living for the coastal burghs and to feed the towns.
The first bad effects of over-exploitation of these resources were felt in Victorian times, when the immense oyster beds around Edinburgh were wiped out and the Lammas Drave herring fishery, which had supported the East Neuk and East Lothian towns for centuries, was also destroyed by over-fishing. At the same time there was severe pollution from sewage and industrial waste, which was not brought under control until the late twentieth century. Developments in trawling for haddock and cod, and the coming of steam drifters and echo location of the herring shoals off the May, wiped out the remaining fisheries in the Firth of Forth in the twentieth century.
Today nothing is caught commercially except for prawns, a few scallops, crabs and lobsters. On the other hand, the rise of wildlife protection has led to a surge in the numbers of seabirds like puffins and gannets, and grey seals, assisted by the growing quantities of small fish that multiplied when the large ones were fished out. Today the Forth is cleaner than it has been for centuries, but the vast natural resources of the past are unlikely ever to return.
Chris Smout
See T C Smout and Mairi Stewart, The Firth of Forth, an Environmental History (Edinburgh; Birlinn 2012) £14.99
The historic importance of water traffic in the upper reaches of the Firth of Forth cannot be underestimated. For centuries the Inner Forth waterway played host to vessels of various sizes, which carried people, commodities and goods not only to and from Europe and beyond, but also between the north and south shores.
Historically, no less than four official ferry routes operated within the Inner Forth: Cambuskenneth to Stirling; Alloa to South Alloa; Kincardine to Higgins Neuk; and Charlestown to Bo'ness.
The ferry at Alloa was first mentioned in charters dating back to the 14th century. By the early 19th century there was a demand for quicker and more reliable transport between the north and south shores of the Forth, particularly to service the local coal industry and glassworks. This led to debates about whether to build a bridge or invest in a steam ferry. It was the latter option that won in the end, with local investors hopeful that the route would become the 'principal point of communication between north and south Scotland.' The new steam ferry cost the princely sum of £1400, with the upgrading of the piers on either side of the river costing an additional £1000.
In the later 19th century, the demand for even speedier transportation for both people and goods was met by the construction of the Alloa Swing Bridge. Of course, this rail bridge would have reduced the amount of river traffic. In its current state only the vertical stilts remain, posing something of a barrier to navigation.
A bit further down the river, the construction of the Kincardine Bridge in the 1930s further reduced the need for ferry transportation across the river. The ferry between Kincardine and Higgins Neuk had until then been a regular sight for well over a century, with sailings once an hour. Having found the Alloa ferry too expensive, from the 1820s cattle drovers from the Highlands began to make greater use of the crossing route at Kincardine when on their way to the celebrated Falkirk Tryst to sell their black cattle. At key points in the year – namely, August, September and October – the volume of drovers and cattle was such that enterprising local boat owners were able to capitalise by offering passage across the Forth in their sail boats!
Kirsty McAlister
Take a look at the Inner Forth Landscape Initiative website to find out more about projects that are exploring the history of the area.
Falkirk district made a significant contribution to the war effort, often in unexpected ways. At Carriden, near Bo'ness, the firm of Thomson & Balfour made doors and windows. In 1940 it got a contract from the Fairmile Marine Co to build motor launches. It did so well that a further contract was awarded for motor torpedo boats. After launch the vessels were taken the short distance to Bo'ness Dock for fitting with armaments.
The Dock had been taken over by the Navy for the Special Operations Executive with the purpose of training the crews of landing craft. It became a secure area named HMS Stopford. On the other side of the town Satellite Factory Number 1 was constructed to produce petrol cans, including jerry cans, for the army.
A pipeline from Grangemouth provided fuel and the full cans were shipped abroad from Bo'ness Harbour. The refinery had closed for the duration, but the storage facilities were extensively used, notably to supply the navy at Rosyth. Small tankers also made the dangerous east coast journey to London to keep it going at the height of the Blitz. Grangemouth was busy – there was also a mining depot, transit sheds, airfield, docks and dockyard.
The Dockyard built three flower class corvettes and 34 merchant ships (small oil tankers, colliers and large cargo vessels) with a gross tonnage of 53,000 tons. One of the tankers, the Empire Pym, was the first into Cherbourg Harbour after D-Day. Indeed, one fifth of the massive invasion fleet had been through Grangemouth in the preceding two years for repair, conversion or augmentation. At the same time the Dockyard was maintaining the Dutch and British submarine fleet. As well as storing oil and provisions for the ships at Rosyth, Falkirk also had a large temporary munitions depot in an old railway siding at Muiravonside.
The shells were stored in railway wagons and could move at a moment's notice. A safe distance away, over at Letham Moss, was a night decoy for Rosyth. In the event of a heavy bombing raid the peat fires at the decoy were to distract the enemy. For more see the book published by the Falkirk Local History Society in 2013 and appropriately called The Forth Front.
Geoff Bailey
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VUnit projects in Sigasi Studio
Posted on 2021-01-12 by Wim Meeus
Tagged as: VUnit
VUnit is an open source unit testing framework for VHDL/SystemVerilog that helps to write, and automatically run, tests. The VUnit project was started by Lars Asplund from Synective Labs and Olof Kraigher. The source code is hosted at GitHub. VUnit automatically scans your projects for unit tests (aka test benches), runs them with your favorite simulator and reports the results. This automation helps to run tests frequently and iterate faster.
Installing VUnit
VUnit scripts are written in Python, so first make sure Python is installed on your system. A recent version of Python 3 is recommended. Windows users must install a full version of Python, not from the Windows Store.
The recommended way to install the latest stable release of VUnit is via pip or pip3. On most systems running the following command should do the trick:
pip install vunit_hdl
Make sure you use vunit_hdl and not vunit. The latter is a completely different Python library.
You can check that VUnit is installed correctly by for example running:
pip freeze
In the list of installed Python packages you will find a vunit-hdl entry and its version number.
Using VUnit
Running VUnit tests requires two elements: VHDL or SystemVerilog testbenches and a Python script which controls the execution.
VUnit will recognize a VHDL entity or a SystemVerilog module as a testbench if it has a runner_cfg generic (VHDL) or parameter (SV). Testbench entity and module names should have either a tb_ prefix or a _tb suffix. VUnit will warn if that is not the case.
A VHDL VUnit test bench has the following structure. Note that VHDL 2008 is required, a.o. for support of a VHDL context. The main process has function calls to set up and terminate the simulation. Between these function calls, one or more tests may be run.
library vunit_lib; -- VUnit library and context (VHDL2008 required!)
context vunit_lib.vunit_context;
entity tb_example is -- Entity name with tb_ prefix
 generic (runner_cfg : string); -- Generic indicates that this is a VUnit testbench
end entity;
architecture tb of tb_example is
 main : process
 test_runner_setup(runner, runner_cfg); -- Set up and start simulation
 report "This test will pass!"; -- Single, trivial test in this example
 test_runner_cleanup(runner); -- Simulation ends
 end process;
end architecture;
In SystemVerilog it looks a bit different. The runner_cfg parameter, which marks the module as a VUnit testbench, is defined in TEST_SUITE.
'include "vunit_defines.svh" // Include VUnit definitions
module tb_sv_example;
 'TEST_SUITE begin // Includes the definition of parameter runner_cfg
 // which makes this module a VUnit testbench
 // Note: Do not place any code here.
 $display("Running test suite setup code");
 // Start clocks, assert resets etc. here
 'TEST_CASE_SETUP begin
 $display("Running test case setup code");
 // Leave empty for simple cases
 'TEST_CASE("Test that a successful test case passes") begin
 $display("This test case is expected to pass");
 'CHECK_EQUAL(1, 1);
 'TEST_CASE("Test that a failing test case actually fails") begin
 $display("This test case is expected to fail");
 'CHECK_EQUAL(0, 1, "You may also optionally add a diagnostic message to CHECK_EQUAL");
 $display("Cleaning up after a test case");
 // Leave empty for simple cases
 $display("Cleaning up after running the complete test suite");
 // Leave empty for simple cases
 // Optional, but recommended.
Note the presence of the watchdog near the end of the above example. The watchdog ensures that hanging tests terminate as failed rather than keep on running forever.
Finally, a Python script is required to control the VUnit tests. In it simplest form, for a VHDL project could look like this. The script creates a VUnit instance, adds libraries and design files to it, and runs the tests.
# The following line works for VHDL
from vunit import VUnit
# If your project is SystemVerilog, use the following one instead:
# from vunit.verilog import VUnit
# Create VUnit instance by parsing command line arguments
vu = VUnit.from_argv()
# Create library 'lib'
lib = vu.add_library("lib")
# Add all files ending in.vhd in current working directory to library
# Run vunit tests
Note that VUnit does not support a library named work. In VHDL, work is a keyword which means the same library where this element is defined. While in many VHDL projects, the work library is called work, a different name must be chosen in VUnit. In the above example, the work library is named lib. Given the special meaning of work, this won't break any references to work in the VHDL code.
VUnit's user guide offers further details on how to use VUnit.
If your project has multiple source code directories and/or libraries, will need to reflect that. is meant to be stored in revision control. For that reason, generating (e.g. from other scripts) is discouraged. However, the full power of Python is available to configure VUnit's libraries and source files from within We'll give a few examples later.
Using VUnit in Sigasi Studio
Sigasi Studio can help you manage VUnit projects and enables you to run and inspect test results straight from the IDE. VUnit support in Sigasi Studio requires an XPRT license.
Details of how to run VUnit tests in Sigasi Studio can be found in the Sigasi manual. Once your tests are running, Sigasi Studio opens the VUnit view from where you can see test results and inspect the details.
Complex VUnit projects: Python to the rescue
VUnit makes use of a single script which configures libraries and controls the execution. It is not desirable to duplicate the library configuration from other tools in First of all, the library configuration would need regular updates as the project evolves, which means additional work for the designers and a possible source of errors. Generating from other scripts or tools is not recommended either, because is meant to be kept in revision control.
Fortunately, the full strength of the Python programming language is available to help manage VUnit's configuration. We present a few examples of how Python can be used to automate the VUnit setup.
Determine libraries from folder names
In this example, we have a VHDL project with one level of subfolders. Each subfolder is mapped to a library with the same name. Over the course of the project, subfolders may be added or renamed.
The following script extracts the libraries from the folder names. The designer doesn't need to change anything to the script when the folder / library structure is changed.
from vunit import VUnit
import os
# Create VUnit instance by parsing command line arguments
vu = VUnit.from_argv()
# For each folder, create a library with the same name as the folder.
# Map all VHDL files in the folder into the library.
for fpath in os.scandir('.'):
 if fpath.is_dir() and not'.'):
 vu.add_library(, "*.vhd"))
# Add all files ending in.vhd in the top level directory to library "libwork"
# Run vunit function
Find all SystemVerilog files in a folder hierarchy
In this example, libraries are not the problem because SystemVerilog uses one single library. The difficulty here is that design files are present at various depths in the file hierarchy.
Again, Python proves to be a powerful tool to find the design files and configure VUnit tests.
from vunit.verilog import VUnit
import glob
# Create VUnit instance by parsing command line arguments
vu = VUnit.from_argv()
# Create library 'lib'
lib = vu.add_library("lib")
# Hierarchically add all files ending in.v and.sv in current working directory to library
for file in glob.glob("**/*.v", recursive=True):
for file in glob.glob("**/*.sv", recursive=True):
# Run vunit function
Obviously, the example could be extended. For example, one could read a list with files to exclude from a file, and not add those files to the library.
Read VUnit configuration from Sigasi Studio project files
Oftentimes, information about design files, libraries, excludes etc. is available in other design tools, e.g. Sigasi Studio. With some clever use of Python, can retrieve this information from Sigasi Studio's project files, making the configuration of VUnit tests entirely automatic. Just use this vunit…logo in your project, sit back and run your tests.
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Block users to download executables files using a Block Content Filtering Rule
- Go to Solutions mode > Content Filtering > Policy
- Locate the existing rule that you want to edit or create a new rule.
- The Content and Limits column in the Policy Editor wizard is where you add restrictions for File Type.
- In the desired rule, click the pencil icon in the Content and Limits option to edit it and under File Type select Executables.
- Click Save.
- Click Save Rule.
- Click Activate to enable the rule.
NOTE: If the URL to download the file is over HTTPS, you need "SSL Interception" enabled in order for Web Security Services (WSS) to block downloads.


razgovetan | srpsko - engleski prevod
1. articulate
ETYM Latin articulatus. Related to Articulata.
Expressing oneself easily or characterized by clear expressive language.
2. audible
Sinonimi: hearable
ETYM Late Lat. audibilis, from Latin audire, auditum, to hear: cf. Latin auris, and Eng. ear.
Heard or perceptible by the ear; SYN. hearable.
3. distinct
Sinonimi: decided | distinguishable
ETYM Latin distinctus, p. p. of distinguere: cf. French distinct. Related to Distinguish.
1. Recognizable; marked; SYN. decided.
2. Easy to perceive; especially clearly outlined.
3. (Often followed by 'from') Not alike; different in nature or quality; SYN. distinguishable.
4. sharp
Sinonimi: sharp-worded | tart
2. Keenly and painfully felt; as if caused by a sharp edge or point
3. Quick and forceful
4. Very sudden and in great amount or degree
5. Harsh; SYN. sharp-worded, tart.
6. (Music) Raised in pitch by one chromatic semitone
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idea in a form that is particularly convenient to use. To this end, we need to introduce a few terms:
Definition 6.12. Let be a nonempty set, be a partial order on, and a subset of. An upper bound of in is an element such that for all. A maximal element of is an element such that no satisfies the relation.
Definition 6.13. Let be a nonempty set and let be a partial order on. A collection of elements of is said to be a chain if is a linear order on, viz., every pair of elements of satisfies the trichotomy principle:
We are now ready to state and prove the ever-famous Zorn's lemma:
Proof. We use transfinite induction to construct a chain in that contains a maximal element of. By the axiom of choice (Axiom 4.2), there exists a choice function on the set of nonempty subsets of. We let and define inductively for each ordinal by declaring to be an element of such that for each ordinal ; we terminate the process when there is no such element. To check that this process continues until the point of termination, we must check the limit ordinal stages. But indeed, if is a limit ordinal, then is a chain in, whence by assumption we can find an upper bound. We can now find an ordinal such that no satisfies the relation. It follows that is a maximal element of.
Here is an archetypal Zorn-type argument in the context of linear algebra; proofs of this form are humorously referred to as Zornification arguments.
Example 6.15. We prove that every vector space has a basis. In fact, we establish a more general statement:
Let be a vector space over a field. Every set of linearly independent vectors in is contained in a basis of.
Fix a set of linearly independent vectors in. If is a maximal linearly-independent set, viz., every superset of is linearly dependent in, then is a basis of. Indeed, if there exists a vector such that no finite linear combination in equals, then is a linearly independent superset of, contradicting the maximality condition. We therefore assume that is non-maximal. Let be the collection of all linearly independent supersets of in, ordered by the set-inclusion relation: if and only if. If is a chain in, then is an upper bound of in. It now follows from Zorn's lemma that there exists a maximal element of, which, by construction, is a maximal linearly-independent subset of.
Transfinite induction arguments are often useful in comparing cardinalities of sets as well. We present two examples that makes use of the Cantor–Bernstein theorem (Theorem 5.9).
Example 6.16. Let and be infinite sets such that. We show that equals if, and if. We assume without loss of generality that and define a collection of pairwise-disjoint collections of subsets of such that for all. We define a partial order on by declaring that if and only if and for all. Similarly as in Example 6.15, each chain in admits an upper bound, whence Zorn's lemma furnishes a maximal collection in.
We claim that. If not, then is nonempty. We note that must be finite. If is infinite, then, and so there exists a countably infinite subset of. Since is a pairwise-disjoint collection that contains, the maximality condition is violated. Since is finite, we see that for all. Fixing and defining
we see that. The maximality condition is once again violated, and so we must conclude that.
For each, we find a bijection. We can now construction a bijection by setting. That is a bijection follows from the fact that is a partition of. We now let and be the sets of even and odd natural numbers, respectively, and let and be bijections. By setting and, we obtain two bijections and.
We now let be an injection given by the relation. We have constructed the following sequences of injections:
We define by setting
is well-defined since. The disjointness condition also implies that is injective, since both and are injective. It now follows that the composite function is injective, and so. The reverse relation is obvious, whence we conclude from the Cantor–Bernstein theorem that.
Example 6.17. Let be an infinite set. We generalize Example 5.3 and show that. Let us define a collection
This collection is nonempty. Since is an infinite set, we see that, whence there is a countably infinite subset of. We have seen in Example 5.3 that, and so is nonempty.
Let us now define a partial order on by declaring if and only if and, viz., if is an extension of. if If is a chain in, then the ordered pair defined by setting and
is an upper bound of the chain. Note that the extension property in the definition of guarantees that is well-defined. We now apply Zorn's lemma to construct a maximal ordered pair in.
It suffices to check that. We suppose for a contradiction that. If, then we can find a bijection, whence we can define an extension of by setting. As is a bijection, the maximality condition on is violated. We therefore assume that.
Let. We must have that. Indeed, if, then, by Example 6.16, the set is equinumerous to either or, which is absurd. Let us now fix a subset of such that. Since and are disjoint, we see that,, and are pairwise disjoint. It now follows from Example 6.16 that
is equinumerous to. Recalling that and, we conclude that. Let be a corresponding bijection.
We now define a bijection by setting
is well-defined, as. The disjointness condition also implies that is a bijection, as and are bijections. Since, it follows that. contradicting the maximality of. We therefore conclude that, and so.
As an application of the equinumerosity statement, we now show that. By fixing two distinct elements, we can construct an injection by setting
Our goal is to construct an injection in the opposite direction and apply the Cantor–Bernstein theorem. To this end, we shall show that
To this end, we first construct a bijection by defining, for each, the value of to be the function defined by the formula
is a bijection: given, we can recover the set by considering the preimage.
Fix ; the function that is defined by the formula is an injection. Therefore,.
The function that sends to the composite function is a bijection. Indeed,. Therefore,.
Now, we construct a bijection as follows. An element of is a function that sends to a function, so that for all. It is then natural to set for each ordered pair. We note that is a bijection: given, we can recover a -valued function on by setting. It follows that.
To prove the relation, we take the bijection that we have constructed above. The function that sends to the composite function is a bijection, as. We have thus produced the following sequence of injections:
The composite function is an injection from to, and so. Since we have already shown that, it follows from the Cantor–Bernstein theorem that, as was to be shown. Since we have also shown that, we now know that the relation holds as well.
Exercise 6.18. Modify the above proof to show that, provided that and.
7. Additional Remarks and Further Results
7.1. The approach to set theory in this post is naïve in the sense that several assumptions are made in order to bypass the technical details and to streamline the exposition. All assumptions made in this post are provable facts in the standard framework of axiomatic set theory; an excellent exposition of axiomatic set theory at the undegraduate level can be found in the textbook of Hrbacek and Jech.
7.2. We cheated our way through the theory of ordinals by simply assuming the existence of many, many ordinals. In particular, we have completely bypassed the recursion theorem, which validates certain recursive constructions that we have tacitly made use of. See Capter 6 of Hrbacek and Jech.
7.3. We also did not cover the theory of cardinal numbers at all. Since the equinumerosity relation is an equivalence relation, we can declare one set from each "equivalence class" to be the cardinal number representing the size of the sets in the equivalence class. Alternatively, we can define certain ordinal numbers to be cardinal numbers: see the wikipedia article on aleph numbers. An important topic in the theory of cardinal numbers is cardinal arithmetic, which we have sampled in Example 6.16 and Example 6.17. See Chapters 7 and 9 of Hrbacek and Jech.
7.4. The diagonal argument in Example 5.6 can be generalized to prove Cantor's theorem: for every set. This, in particular, shows that there are many, many cardinal numbers. The question of whether there is a set such that leads us to the continuum hypothesis, which is a foundational problem in the theory of set-theoretic independence. My blog post on the Kirby-Paris Hydra game provides an introduction to the independence issues in set theory; see Section 6 of the post for further references.
7.5. The two main consequences of the axiom of choice in the post—the well-ordering principle and Zorn's lemma—are provably equivalent to the axiom of choice. The proof that either of the


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Background: Analysis of change in health status using data from two waves can be examined either adjusted or unadjusted for baseline health status. We assess the effect of socioeconomic position (SEP) on cognitive change using both these strategies and discuss the implications of the analyses.
Methods: Data come from 1261 men and 483 women of the Whitehall II cohort study, aged 50-55 years at wave 1. Cognition was assessed at both waves using a test of verbal memory, and two tests of verbal fluency. Analysis of Variance (ANOVA) was used to estimate the effect of SEP on change score and analysis of covariance (ANCOVA) to estimate this effect adjusted for the baseline cognitive score. Then the ANCOVA estimates were corrected for bias due to measurement error (estimated based on 3-month test-retest). Finally, ANCOVA estimates were examined for increasing levels of measurement error.
Results: The results of the ANOVA suggest no effect of SEP on cognitive decline. In contrast, the ANCOVA suggests significantly greater cognitive decline in the lower SEP groups. However, the ANCOVA estimates for the effect of wave 1 cognition show evidence for regression to the mean due to the presence of measurement error. The corrected ANCOVA estimates show no association between SEP and cognitive decline.
Conclusions: We recommend caution when using ANCOVA, or adjustment for baseline, in the analysis of change using two waves of observational data.
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About the book
Are there as many numbers as there are trees? Are there as many numbers as there are leaves? These are just a few of the questions that a 4-year old boy named Jack asked his math educator mommy that inspired this book.
So, how many numbers are there? Read and find out!
Mommy, How Many Numbers Are There?
Rebecca Schantz, Jack Schantz
Publisher: Jack's Back Books, LLC
8.25" x 8.25"

source: HuggingFaceFW/fineweb-edu


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A sanatorium (also sanitorium, sanitarium) is a medical facility for long-term illness, typically tuberculosis. A distinction was sometimes made between a "sanitarium" (a kind of health resort, as in the Battle Creek Sanitarium) and "sanatorium" (a hospital).
The rationale for sanatoria was that before antibiotic treatments existed, a regime of rest and good nutrition offered the best chance that the sufferer's immune system would "wall off" pockets of pulmonary tuberculosis infection. In 1863, Hermann Brehmer opened the Brehmerschen Heilanstalt für Lungenkranke in Görbersdorf (Sokołowsko), Silesia, for the treatment of tuberculosis, where patients were exposed to plentiful amounts of high altitude fresh air, and good nutrition. Tuberculosis sanatoria became common throughout Europe from the end of the late 19th century onwards.
The Adirondack Cottage Sanitarium, established in Saranac Lake, New York in 1882, was the first such establishment in North America. According to the Saskatchewan Lung Association, when the National Anti-Tuberculosis Association (Canada) was founded in 1904, it was felt that a distinction should be made between the health resorts with which people were familiar and the new tuberculosis treatment hospitals: "So they decided to use a new word which instead of being derived from the Latin noun sanitas, meaning health, would emphasize the need for scientific healing or treatment. Accordingly, they took the Latin verb root sano, meaning to heal, and adopted the new word sanatorium".
Switzerland had many sanatoria, as it was believed that clean mountain air was the best treatment for lung diseases. In Finland a series of tuberculosis sanatoriums were built throughout the country in isolated forest areas, the most famous of these being the Paimio Sanatorium, built in 1930 and designed by world-renowned architect Alvar Aalto, with its roof-top terraces where the patients would lay all day on specially designed chairs, the so-called Paimio Chair. In Portugal, the Heliantia Sanatorium in Valadares, was used for the treatment of bone tuberculosis between the 1930s and 1960s.
In the early twentieth century, tuberculosis sanatoria became common in the United States. The first tuberculosis sanatorium for blacks was Burkeville, Virginia's Piedmont Sanatorium. Waverly Hills Sanatorium, a Louisville, Kentucky tuberculosis sanatorium, was founded in 1911. It has become a mecca for curiosity-seekers who believe it is haunted. Colorado Springs, because of its dry climate was home to several sanatoriums. A. G. Holley Hospital in Lantana, Florida is the last remaining freestanding tuberculosis sanatorium in the United States.
After 1943, when Albert Schatz, a graduate student at Rutgers University, discovered Streptomycin, the first true cure for tuberculosis, sanatoriums began to close, or (as in the case of the Paimio Sanatorium) were transformed into general hospitals. Around the 1950s, tuberculosis was no longer a major public health threat and so most of the sanatoriums had reached the end of their lives. Most sanatoriums were demolished years ago.
Some, however, have assumed updated medical roles. The Tambaram Sanatorium in south India is now a hospital for AIDS patients. The state hospital in Sanatorium, Mississippi is now a regional mental retardation center.
In the former Soviet Union the term has a slightly different meaning. It is mostly a combination of a resort/recreational facility and a medical facility intended to provide short-term complex rest and medical services, thus it is common to spa resorts


Are the pearls in bubble tea carcinogenic?
Does the colorful and popular bubble tea contain carcinogenic substances?
Given the bright color creations, one can assume that the colorful bubble teas contain a lot of sugar and many artificial ingredients. Unhealthy and high in calories: definitely! Now, however, scientists have also found out that the globules of the popular trendy drink contain toxins, so that one must even fear that bubble tea is carcinogenic or increases the risk of developing cancer. They can also cause allergies. What is the truth of the new fears and should one absolutely avoid bubble tea?
Bubble tea carcinogenic due to styrene, acetophenone and brominated substances?
Scientists from the Rheinisch-Westfälische Technische Hochschule Aachen have found the poisonous substances styrene, acetophenone and brominated substances in the balls, the so-called toppings of the bubble tea. Since the samples were evaluated from a Mönchengladbach branch that was supplied by one of the largest topping manufacturers in Asia, which in turn supplies almost all of Germany with the pellets, it can be assumed that the harmful substances can be found in many bubble teas. The fact is: these substances actually have no place in food - it must now be examined in more detail whether the concentration contained in the bubble teas must already be classified as harmful to health or not.
No more bubble tea or excessive scaremongering?
Basically, of course, it is true that bubble tea is anything but healthy. A cup has so many calories that an adult has covered a quarter of the daily sugar requirement: a cup of 0.3 l bubble tea has an average of 400 to 600 calories... actually a whole meal. In addition, the bubble tea is not entirely safe for small children, as the slimy pearls are easily inhaled or the children can choke on them. The contained toxic substances naturally also promote the unhealthy image. However, you have to keep in mind that the bubble tea scandal is current and on everyone's lips: Dioxin-contaminated eggs, cancer-promoting ingredients in chips, cola and Co., cancer-causing diesel exhaust fumes, harmful chemical ingredients in cosmetics and many other foods and objects of our daily life are certainly no less unhealthy than the ingredients in bubble tea. Regardless of whether bubble tea is carcinogenic - due to the high number of calories, artificial flavors, colorings and the high sugar content, bubble tea should be avoided for the sake of health.
Image source:
*: Bubble Tea: stockcreations /
Via the team
The editorial team of informs you in small and, we hope, interesting and helpful health guides on topics and news from the fields of health, medicine, diseases, drugs, symptoms, treatments, homeopathy, natural products, nutrition and a vital lifestyle. With a lot of joy, knowledge and advice like in a good pharmacy.
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physical constants
Fundamental Physical Constants 🧮
Fundamental Physical Constants List 🧮 Definitions, SI Unit Values & Symbols
Physical constants are believed to be unchanging over time and universal in nature. Most of us are aware the speed of light is constant (or is it?) and have encountered other physical constants during our studies. Did you know hundreds of physical constants have been discovered? They have been measured, defined and are in use every day. Furthermore, some physical constants are also irrational numbers. As measurement techniques have improved accuracy has reduced the level of uncertainty.
 - ADDucation's physical constants list is compiled by Joe Connor and last updated 02 Mar 2021.
About ADDucation's List of Physical Constants
Researchers, metrologists and standards organizations worldwide continuously refine the physical constant values. The latest fundamental physical constant values are publicly available, based on CODATA 2018 data. ADDucation likes the searchable NIST database. To make ADDucation's list of key physical constants useful we focused on:
 - Identifying the SI-Units for each constant and we've done our best to explain the units in words.
 - Explaining the definitions of fundamental physical constants in layman's terms. This gives everyone the best chance to understand them. Please help us improve them if you can.
 - Values for physical constants in exponential notation format for use with scientific calculators.
ADDucation Tips: Click arrows in column headings to sort list of physical constants. Reload page for original sort order. Resize your browser to full screen and/or zoom out to display as many columns as possible. Click the ➕ icon to reveal any hidden columns. Start typing in the Filter table box to find physical constants inside the table.
Key Physical Constants Symbol/s SI / CODATA value/s SI units in words Scientific Notation Value Physical Constant Definitions in Words
Avogadro constant NA 6.022140857 x 1023 mol-1 per mole 6.022140857E+23 The number of atoms or molecules in a mole of a substance.
Bohr magneton µB _PHONE_(57) x 10-24 J T-1
joule per tesla. 927.4009994E-24 Bohr magneton is a physical constant used to express the magnetic moment of an electron caused by its orbital or spin angular momentum.
Bohr radius ao 0.529 177 210 67(12) x 10-10 m meter 0.52917721067E-10 The Bohr radius is a physical constant based on the average distance between an electron in its smallest orbit around the nucleus of a hydrogen atom.
Boltzmann's constant k 1.380 648 52(79) x 10-23 J K-1 joule per kelvin. 1.38064852E-23 Boltzmann's constant is a physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas. The Bolzmann constant is the gas constant divided by the Avogadro constant (R / NA)
electron mass / electron rest mass me 9.109 383 56(11) x 10-31 kg kilogram 9.10938356E-31 The electron rest mass is a fundamental constant. The mass of an object increases, with its velocity, relative to the observer so its mass is measured when its speed is zero relative to the observer.
elementary chargeelectron charge magnitude e or
_PHONE_(98) x 10-19 C coulomb 1.6021766208E-19 The elementary charge is a fundamental physical constant. The magnitude of the electric charge carried by a single proton (e) or electron (-e). On completion of SI unit redefinition's (2019) the value will be exactly 1.602176634 ×10-19
fine structure constant / Sommerfeld's constant ɑ 7._PHONE_(17) x 10-3 number 7.2973525664E-3 The fine-structure constant is a number. It has been determined by experiment yet remains elusive to theoretical proof. The fine-structure constant is the measure of the strength of the electromagnetic force that controls how electrically charged elementary particles and photons (light) interact.
gravitational constant / Newtonian constant of gravitation G 6.674 08(31) x 10-11 m3 kg-1 s-2 meters cubed per kilogram per second squared. 6.67408E-11 The Newtonian constant of gravitation (aka the universal gravitational constant and the Cavendish gravitational constant) is a physical constant which has been measured but proof it's a constant remains elusive. G is included in Albert Einstein's Theory of General Relativity and Sir Isaac Newton's law of universal gravitation states every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
inverse fine structure constant 1/ɑ 137.035 999 139(31) number 137.035999139 Refer to the fine structure constant (above).
neutron rest mass / neutron mass mn 1.674 927 471(21) x 10-27 kg kilogram 1.674927471E-27 The rest mass of a neutron (or any object) will be its minimum mass because, as Relativity theory explains, mass and energy are interchangeable. Any moving object has kinetic energy which increases its mass.
nuclear magneton µn 5.050 783 699(31) x 10-27 J T-1 joule per tesla. 5.050783699E-27 The nuclear magneton is a physical constant of magnetic moment, the property of a magnet that interacts with an applied field to give a mechanical moment.
permeability of free space / magnetic constant µo 4 π x 10-7 N A-2 newton per ampere squared. 12.566370614E-7 The permeability of free space (also know as the magnetic constant, vacuum permeability and permeability of vacuum) is a measure of the resistance encountered forming a magnetic field in a vacuum.
permittivity of free space / electric constant εo 8.854 187 817… x 10-12 F m-1 farad per meter. 8.854187817E-12 Permittivity of free space is a physical constant which describes how easily electric (or magnetic) field lines of force pass through air (or any given substance). In this context permittivity means permits.
pi π 3.141592653… irrational number. 3.14159265358979… Pi is a constant, also known as Archimedes' constant, which can be calculated by dividing the circumference of a circle by its diameter (or radius squared). Pi is also an irrational number and a transcendental number.
Planck constant. h 6.626 070 040(81) x 10-34 Js joule second. 6.626070040E-34 Planck's constant is a physical constant used to describe the varying sizes of quanta (of matter, electricity, heat and gas) in quantum mechanics.
proton rest mass / proton mass mp 1.672 621 898(21) x 10-27 kg kilogram 1.672621898E-27 The rest mass of a proton (or any object) will be its minimum mass because, as Relativity theory explains, mass and energy are interchangeable. Any moving object has kinetic energy which increases its mass.
speed of light in vacuum c 299 792 458 m s-1 meters per second. 299792458 The speed of light in a vacuum is constant and independent of the observer, unlike time and space. However, according to Quantum field theory a vacuum cannot be empty. Elementary particles appear and disappear constantly causing disturbances which could potentially cause variations in the speed of light.
Stefan-Boltzmann constant. σ 5.670 367(13) x 10-8 W m-2 K-4 watt per meter squared
per kelvin to the fourth
5.670367E-8 The Stefan-Boltzmann constant is typically used to solve equations based on the Stefan Boltzmann law, which states the energy radiated per unit of surface area of a black body per unit time is proportional to the fourth power of the thermodynamic temperature of that body.
τ 2π or 6.28318530718… irrational number. 6.28318530718… Tau is a the circle constant representing the ratio between circumference and radius which is preferred to 2π by some mathematicians.
unified atomic mass unit / dalton u or Da 1.660 539 040(20) × 10-27 kg kilogram 1.66053904E-27 Standard unit used to quantify mass of atoms and molecules. One unified atomic mass unit is numerically equivalent to 1 g/mol and roughly the mass of one nucleon.
2019 SI Base Unit Redefinitions
At an international meeting of metrologists on 16th November 2018 proposals by the International Committee for Weights and Measures (CIPM) to redefine four of the seven SI Base Units (the kilogram, kelvin, mole and ampere), in terms of physical constants, were unanimously agreed. These formally came into force on 20th May 2019, as part of World Metrology Day celebrations.


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Fraction interpolation walking a Farey tree
We present an algorithm to find a proper fraction in simplest reduced terms between two reduced proper fractions. A proper fraction is a rational number m/n with m1. A fraction m/n is simpler than p/q if m <= p and n <= q, with at least one inequality strict. The algorithm operates by walking a Farey tree in maximum steps down each branch. Through monte carlo simulation, we find that the present algorithm finds a simpler interpolation of two fractions than using the Euclidean-Convergent [Matula 1980] walk of a Farey tree and terminating at the first fraction satisfying the bound. Analysis shows that the new algorithms, with very high probability, will find an interpolation that is simpler than at least one of the bounds, and thus take less storage space than at least one of the bounds.
- download PDF (150K)
Mosko, M. ; Garcia-Luna-Aceves, J. J. Fraction interpolation walking a Farey tree. Information Processing Letters. 2006 April 15; 98 (1): 19-23.


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Activities from the 2005 GSA Poster Session on Rates and Time
Subjectshowing only Geoscience Show all Subject
Results 1 - 10 of 11 matches
Determining Earthquake Recurrence Intervals from Trench Logs part of Rates and Time:GSA Activity Posters
Trench logs of the San Andreas Fault at Pallett Creek, CA are the data base for a lab or homework assignment that teaches about relative dating, radiometric dating, fault recurrence intervals and the reasons for uncertainty in predicting geologic phenomena. Students are given a trench log that includes several fault strands and dated stratigraphic horizons. They estimate the times of faulting based on bracketing ages of faulted and unfaulted strata. They compile a table with the faulting events from the trench log and additional events recognized in nearby trenches, then calculate maximum, minimum and average earthquake recurrence intervals for the San Andreas Fault in this area. They conclude by making their own prediction for the timing of the next earthquake.
Learn more about this review process.
Teaching geologic time and rates of landscape evolution with dice part of Rates and Time:GSA Activity Posters
Landscape evolution provides a convenient framework for understanding geologic time and rates because students can observe how processes like erosion and deposition shape their surroundings. In this example, students build 3-D sandbox models based on topographic maps and design and stage a "virtual adventure race." Sandbox landscapes are used to illustrate erosional processes,while local examples are used to discuss landscapes as transient or steady over different timeand length scales. Dice experiments illustrate radioactive decay and the shape of the age equation curve, and 14C dating, geochronology and thermochronology are introduced as "stopwatches" that start when a plant dies, a crystal forms, or a rock nears the surface and cools to a certain temperature. The sandbox model and thermochronometer "stopwatches" are combined to measure erosion rates and rates of landscape change. Ultimately, model rates (cm/hour) calculated from stopwatch times on the order of seconds can be related to geologic rates (km/My) calculated from real million-year-old samples.
Modeling U-Series Concordia/Discordia Using STELLA part of Rates and Time:GSA Activity Posters
U-Series dating techniques are widely used to determine the absolute ages of some of Earth's oldest rocks, but the concordia/discordia diagram can be quite difficult for students to grasp. I have produced a STELLA-based lab exercise to develop students' understanding of this important chronologic technique. Students create models of the two isotopic decay systems and run these models to create the concordia diagram. They then carry out experiments in which they "add" or "remove" varying amounts of lead or uranium in simulation of metamorphism. In the course of the lab, students are introduced to the concepts of exponential decay and secular equilibrium as well as modeling concepts such as the creation of if-then statements.
South Carolina Studies: Bringing the Geologic Time Scale Down to Earth in the Students' Backyard part of Rates and Time:GSA Activity Posters
Students visit Drayton Hall historic plantation near Charleston, South Carolina and are led on a field trip that starts with a discussion of documented historic changes that have affected the mansion and the surrounding property. The field trip continues with a study of Native American artifacts and ends with analysis of coastal plain deposits exposed along the Ashley River. Students use paleogeographic maps to discuss both historic and prehistoric changes to the landscape. Back in the classroom, students gather data to draw paleogeographic maps of their own school site through geologic time.
Rates of Change and Deep Time in the Middle Grades Classroom part of Rates and Time:GSA Activity Posters
The nature and scientific measurement of geological and cosmological time are among the most misunderstood and difficult to teach concepts in all of K-12 science education. To address this issue, a multi-disciplinary team of geologists, astronomers and education professionals at Western Kentucky University developed a series of professional development workshops for preand in-service middle grades teachers. The participants clearly advanced their content understanding of geological and cosmological time and the implementation plans received clearly show a desire to apply many of the activities learned in the workshop.
Learning Landscapes: RIVERS part of Rates and Time:GSA Activity Posters
Learning Landscapes provides historic "geo-images" of Rivers and Slopes. Students work at their own pace through a series of on-line images with directed questions and expert answers for each image. Images stem in most part from the University of Vermont's Landscape Change Program archive. Preliminarily, we have found that students relate to local images of New England, use the site as a resource, relate image content to course field laboratories, and relate images to their previous knowledge.
How much is a million? How big is a billion? part of Rates and Time:GSA Activity Posters
We constructed a geologic timeline along a 5K road-race route across the MSU campus at a scale of 1 meter = 1 million years, using signage to mark important events in the history of life. In addition to over 1500 race participants, numerous casual observers were exposed to the timeline. This project works well in the classroom at a scale of 1 mm = 1 million years, and as a manageable one-day outdoor sidewalk chalk activity at a scale of 1" = 1 million years. Timelines drawn to scale lead the observer to the inescapable conclusions that "simple" life appeared early in Earth history; that it took the bulk of Earth history to achieve the next, multi-cellular stage of development; and that once the metazoan threshold was crossed, subsequent biological diversification-and the resulting fossil record-followed in rapid succession.
Using Dendrochronology to Determine the Age and Past Environments of the Black Forest Region, Colorado, USA part of Rates and Time:GSA Activity Posters
The use of dendrochronology in determining the geologic history of a location. The development of an understanding how tree growth can indicate the relationships between climate, geomorphology, ecology and archeology.
Diverse: Field, role play, storytelling, puzzle, cooperative, information systems part of Rates and Time:GSA Activity Posters
Multiple activities--see the poster
Implementing A Constructivist Teaching Model For Conceptualizing Geologic Time part of Rates and Time:GSA Activity Posters
The activity fosters middle learning students critical thinking and allows for student generated essential questions to further their understanding of Earth's history and geologic time.


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In this paper, we propose a probabilistic model for minimizing the anticipated regret in combinatorial optimization problems with distributional uncertainty in the objective coefficients. The interval uncertainty representation of data is supplemented with information on the marginal distributions. As a decision criterion, we minimize the worst-case conditional value-at-risk of regret. The proposed model includes the standard interval data minmax regret as a special case. For the class of combinatorial optimization problems with a compact convex hull representation, a polynomial sized mixed integer linear program (MILP) is formulated when (a) the range and mean are known, and (b) the range, mean and mean absolute deviation are known while a mixed integer second order cone program (MISOCP) is formulated when (c) the range, mean and standard deviation are known. For the subset selection problem of choosing $K$ elements of maximum total weight out of a set of $N$ elements, the probabilistic regret model is shown to be solvable in polynomial time in the instances (a) and (b) above. This extends the current known polynomial complexity result for minmax regret subset selection with range information only.
View A Probabilistic Model for Minmax Regret in Combinatorial Optimization


Mysteries of the satellites
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Mysteries of the satellites
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 - 67 Currently reading
Published by Lodestar Books in New York.
Written in English
 - Satellites -- Juvenile literature.,
 - Satellites.
Book details:
About the Edition
Discusses the origins and characteristics of the natural satellites that travel around seven of the nine planets.
Edition Notes
StatementFranklyn M. Branley ; diagrams by Sally J. Bensusen.
SeriesMysteries of the universe series
ContributionsBensusen, Sally J., ill.
LC ClassificationsQB401.5.B73 1986
The Physical Object
Pagination71 p. :
Number of Pages71
ID Numbers
Open LibraryOL2539758M
ISBN 100525671765
LC Control Number85020770
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The Prowler satellite reportedly maneuvered around in geosynchronous orbit and spied on communication satellites there, using stealth technology to remain hidden from view. While there is a lot of circumstantial evidence indicating the existence of the Prowler, the US has never acknowledged that it exists, and the real facts of STS, and the. Discover the best Telecommunication Satellite Engineering in Best Sellers. Find the top most popular items in Amazon Books Best Sellers. spinning around the earth, endlessly. an orbit of devotion. nothing in the universe loves like the moon loves the earth. * * * * * 5 / 5 I don't really watch space films and I don't really read space books. But something about Satellite just said read me, read me and so, naturally, I obliged and I'm so glad that I did. This book was so raw and emotional and sort of made me want to go into /5. Viroids and Satellites describes plant diseases and their causal agents while also addressing the economic impact of these diseases. The book discusses various strategies for state-of-the-art methods for the detection and control of pathogens in their infected hosts and provides pivotal information from the discovery of viroids through the analysis of their molecular and biological properties, to viroid.
Bang! is the first book you selected, subtitled "A Complete History of the Universe". Please give us a précis. This book is a general overview of astronomy, and doesn't go into detail about any one thing. It basically takes the reader on a tour of the entire universe, and tells you everything you want to know. 19 of the Strangest Unsolved Mysteries of All Time. Public satellite images, such as those available on Google Maps, don't provide insight. It's named for the Polish book dealer who. For the complete list of Satellite Sisters Beach Bag Books for with links to all, go to our website here.. To order any of these books and support indie bookstores, go to Don't forget about Lian Dolan's new book The Sweeney Sisters, also available at For more on Greer Hendricks and Sarah Pekkanen, authors of You Are Not Alone and our interview. Mysterious Structures On The MOON "Luna Base," according to many UFOlogists is a newly discovered ancient Alien base on the far side of the Moon (e.g., the side we never see). They say it was filmed by the Apollo Astronauts and a number of probes on the flyby missions.
 Sounds crazy? Here's a look at the mystery of the Black Knight satellite First sighting | The Tesla connection | The next communication | Space race sighting |. The mystery: Why has looting in Egypt accelerated so much in recent years? Parcak's team used open-source satellite data to map looting across Egypt from to They found looting at nearly sites, and more than, individual spots and holes where they could see that looters had dug up earth. What are the most mysterious discoveries made by satellites? I think some of the most mysterious and remarkable, are the lost cities of ancient Egypt which have been revealed in the desert. - There was no sign of these when viewed from the surface. NASA has just released five new videos called "Mysteries of the Sun". The videos describe the science of the sun and its effects on the solar system and Earth. Scientists study the sun not only to better understand the orb that influences life, but also to study how it sends solar material out into space, filling up the bubble that defines the.


Message 5, Faith:
Throughout her history, the church has been forced to fight those who have attempted to ground justification on human merit and works or some combination of faith and merit. This conflict came to a head in the Western church during the sixteenth-century Reformation. In this lecture, Carl Trueman explains the importance of maintaining the doctrine of justification by faith alone.


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no news in this list.
Campi Flegrei Mar Sicilia volcanoCampi Flegrei del Mar di Sicilia (Phlegraean Fields of the Sicily Sea) is composed of a group of submarine volcanoes SW of Sicily.
Background:The volcanoes were constructed within a submarine depression about 1000 m deep in the Strait of Sicily between the SW coast of Sicily and the NE tip of Tunisia, forming submarine banks that are capped by cones that rise to near sea level. Submarine eruptions were reported at the Giulia-Ferdinandeo and Pinne banks during the first Punic war (264-241 BC), and from the 17th to 20th centuries, sometimes producing ephemeral islands. The 1831 eruption at Graham Island (also known as Graham Bank, Giulia-Ferdinandeo Bank, or Ferdinandea Bank) produced an ephemeral island that was promptly claimed by the navies of France, Britain, Spain, and Italy. Source: Smithsonian GVP


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Yesterday, Susan Bodine, EPA's Assistant Administrator for the Office of Enforcement and Compliance Assurance (OECA), issued final guidance for EPA regions regarding interactions between the Agency and the states in civil enforcement and compliance assurance matters. Under the new guidance, EPA will generally defer to a state as having primary jurisdiction over inspections and enforcement, but it also sets out a number of important exceptions where EPA may take direct action. The final guidance replaces previous interim guidance issued in January 2018.
The guidance is split into three parts and expands upon the interim guidance by providing additional procedures and outlining various principles and approaches for coordination between EPA regions and states. The changes are the result of input from EPA regional offices, states, and a workgroup on compliance assurance that EPA and the Environmental Council of States convened in September of 2017.
The first section of the guidance sets forth high level principles and expectations to guide EPA, including a "no surprises" principle between EPA and the states that encourages regular communication. The section discusses the need for strategic planning to address each state's specific environmental compliance problems, their compliance assurance priorities, and how the combined EPA and state resources can address these issues. Regarding inspections, the guidance establishes an expectation that EPA and the states should avoid "duplicative or overlapping" inspections that would result in inspections of the same facility for the same regulatory requirements within the same twelve-month period, noting, however, that multiple inspections may be appropriate for complex sites or where additional inspections will serve a valuable purpose. EPA is expected to provide states with advance notice of inspections and where EPA is taking the lead in an investigation. Moreover, EPA regions are expected to share information requests and inspection reports with the states. In terms of joint enforcement, the guidance notes that EPA will communicate with the states when EPA believes an enforcement action may be warranted and EPA should discuss with the state whether the enforcement should be a federal, state, or joint enforcement action.
Roles of EPA and the States
The second section of the guidance addresses the respective roles of EPA and the states in implementing authorized programs. The guidance includes an explicit preference for EPA to defer to the states as the primary implementer of inspections and enforcement. However, the guidance then lays out several notable instances in which EPA involvement may be warranted, including:
- When a state requests that EPA take the lead;
- When the violations are part of an EPA-designated "National Compliance Initiative";
- Where there is an "emergency" situation;
- Where states lack adequate equipment, resources, or expertise;
- Multi-state or multi-jurisdictional cases;
- "Significant" violations that the state has not timely or appropriately addressed;
- "Serious violations" for which criminal enforcement may be warranted;
- Inspections needed by EPA to help verify the effectiveness of state enforcement programs, and
- When federal and state-owned facilities are involved.
Procedures for Elevating Issues
The brief final section lays out "best practices" for resolving and elevating issues to the appropriate management level, including appropriate timelines and a preference for resolution at the career management level rather than escalating issues to regional or state senior management or ultimately to Regional Administrators or State Agency heads.


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Education Home Search Lesson Plans All Curricula Looking at Illuminated Manuscripts: Lessons and Ideas for Discussion Image Bank Initial A: Two Men before a King and A Man Speaking to a Family
Men before King / Unknown
Unknown Illuminator, from the Vidal Mayor
Spanish, about 1290–1310
14 3/8 x 9 7/16 in.
Ms. Ludwig XIV 6, fol. 97
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About Illuminated Manuscripts
Brief History of Illuminated Manuscripts
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Looking at Illuminated Manuscripts: Exploring an Illuminated Manuscript Page
Questions for Teaching
Interactive: Click here to see this manuscript page in detail and learn more about the elements of a Gothic manuscript page.
- How is this page like pages from books today? How is it different?
- The elaborate image on this page is called an historiated initial, meaning that the letter contains a scene that tells a story in relation to the text. Can you tell what the letter in this historiated initial is? (It is a letter "A " formed by a slender, arching, elongated dragon.)
- What can you tell about the story in the initial just by examining it?
- What is the setting for the scene?
- How do the people interact with each other? How would you describe their gestures? What do you think they are doing?
- What are some of the colors used to paint the illumination on this page? The gold used on this page is not paint, but gold leaf. Why would someone have had this book made with such an extravagant material?
- Notice that there are birds with human heads decorating the historiated initial. Why do you think the illuminator included these images?
Background Information
In 1247, King James I of Aragon and Catalonia (in present-day Spain) decided to establish a new systematic code of law for his kingdom. He entrusted the task to Vidal de Canellas, bishop of Huesca. The Getty Museum's manuscript, the only known copy of the law code still in existence, is a translation of Vidal de Canellas's Latin text into the vernacular, or regional language, in this case Navarro-Aragonese. The manuscript's scribe was Michael Lupi de Çandiu, who identifies himself in an inscription and who also may have translated the text.
Not only is the text an important historical document, it is also luxuriously illuminated with hundreds of historiated and decorated initials. This illustrated scene corresponds to a portion of the text devoted to the legal rights of orphans. In the top half of the image, a man in a red robe speaks with the king about the sale of a piece of property. He appears again to the far right, having received the king's judgment. Below, he is shown a third time, approaching a couple and a small child. Because the man's petition to sell the property would deprive the child of his rights to the estate, it is denied.
The two scenes take place in the upper and lower halves of an initial "A." The letter is formed by the arching body of a dragon; the beast's folded wings are seen on the left, while its small doglike head is at the lower right. The two human-headed birds perched on top of the square frame are known as marginalia and add liveliness to the page.
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From Stamps of the World
To see only pages that require images (have placeholders with no image) visit : Transkei Image Requirements
The Transkei (meaning the area beyond [the river] Kei), officially the Republic of Transkei (Xhosa: iRiphabliki yeTranskei), was a Bantustan—an area set aside for members of a specific ethnicity—and nominal parliamentary democracy in the southeastern region of South Africa. Its capital was Mthatha, usually given as 'Umtata' on maps and in English-language medium materials.
Transkei represented a significant precedent and historic turning point in South Africa's policy of apartheid and "separate development" in that it was the first of four territories to be declared independent. Throughout its existence, it remained an internationally unrecognised, diplomatically isolated, politically unstable de facto one-party state, and at one point even broke relations with South Africa, the only country that acknowledged it as a legal entity. In 1994, it was reintegrated into its larger neighbour and became part of the Eastern Cape province.
This category has the following 4 subcategories, out of 4 total.
Pages in category "Transkei"
The following 73 pages are in this category, out of 73 total.


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Spherical Side Formula
This blog describes an algorithm and a formula to determine the side of one point relative to a segment (two other points), all three points located on a sphere.
The side informarmation is necessary for Boost.Geometry. It is used, among others, in the within algorithm, to check if a point is inside a polygon (point in polygon). With the spherical version of side, it can be checked if a point on a sphere (the earth) is inside a spherical polygon (e.g. a polygon measured in latitude, longitude).
It is also known as orientation (see also here and here)
The Cartesian side is shown below. Point p is on the right side of segment p1-p2:
A visualization of ths spherical side is shown below, also here, point p is right of segment p1-p2.
Note that if the cartesian side formula would be used on lat-long coordinates, this specific point would result on the left side.
Former approachBoost.Geometry's former approach for spherical side used the useful aviation formulae of Williams, listed here. That did work but I was not completely satisfied about it:
- it takes two * (3 cos, 3 sin, 1 atan) for the course, and then another 2 sin, and 1 asin, so in total 17 goniometric functions
- it is non defined at the poles
- I don't understand it fully, it seemed to me that there should be an easier way
New approachThe new approach also uses sin and cos, but less: for each of the points: 2 sin and 2 cos, in total 12 goniometric functions. Less then the former 17. More important, by design of Boost.Geometry, these might be precalculated such that for a spherical polygon it is not necessary to recalculate this again and again.
Besides that, the algorithm is easier to follow.
The algorithmLet us calculate a plane through the two points of the segment, and the center of the sphere. This is the plane also containing the Great Circle. Let us then calculate at which side of the plane the point is located, either left of the plane, or right of the plane, or on the plane itself. The side with respect to the plane is also the side of the point with respect to the segment on the sphere.
To calculate a plane, all three points are transformed from spherical coordinates (longitude, latitude) to cartesian coordinates (x, y, z). Described a.o. here with clear images. We can use the unit sphere, it is not necessary to take the radius of the Earth (or another sphere or sphere-like object) into account. Amsterdam, for example, then lies somewhere here: (0.614161755 0.042946374 0.788010754).
Converting can conveniently be done using Boost.Geometry's transform algorithm (if p1 is stored in cs::spherical_equatorial):
typedef model::point point3d;
point3d c1, c2, c3;
Then we define a plane through the center of the Earth (0,0,0) and the two points. We use the generalized plane equation for that (a x + b y + c z + d = 0), described e.g. here. This is done by taking the cross product of the two vectors (a vector is here: a mathematical vector). These two vectors are normally called v and w. Because we use (0,0,0) the points are the vectors, we don't have to subtract anything to create a vector. So v is equivalent to c1, w is equivalent to c2.
The cross product is the normal vector, called n, normal to the plane, so perpendicular to the great circle of the two points. So we can take the cross product:
vector_type const n = geometry::cross_product(v, w);
We now have our generalized plane equation. To make that explicit, we can use the conventional symbols a, b, c:
coordinate_type const a = get<0>(n);
coordinate_type const b = get<1>(n);
coordinate_type const c = get<2>(n);
For the generalized plane equation, we should calculate d by subsituting one of the points going through the plane. Let us take (0,0,0)! By taking 0,0,0, all terms a x, b y, c z will be zero, so d is zero. Therefore we don't have to calculate d.
double const d = 0;
The generalized plane equation has the property that, if you substitute another point, it is either on the plane (then the result = 0), or at one side of the plane (then the result is positive), or at another side of the plane (then the result is negative). Just like the Cartesian side, described above. And that is exactly what we need:
distance_measure = a * get<0>(c3) + b * get<1>(c3) + c * get<2>(c3) + d;
and we have the result:
= distance_measure > 0? 1 // left
: distance_measure < 0? -1 // right
Spherical Side FormulaWe used convenient vector calculation here, making it a mathematical exercise. Of course we could write them all out and get a lot of goniometric functions back.
One big note here: geographers (as I am) always refer to coordinates on a sphere by defining 0 at the equator. But mathematicians define 0 at the upper pole of a sphere. Watch out, it is different. This blog assumes the geographic convention, so assumes a spherical equatorial coordinate system.
Let's present it as mathematic formulae (thanks to mathcast):
The first formula converts to x,y,z. Be sure to enter all angles in radians. Also, be sure that λ is longitude (and comes first in Boost.Geometry) and δ is latitude (there are many conventions for this but I'm using them from here, and not from here and here and here). Latitude is 0 at the equator, 90 at the North Pole (again: mathematicians use 0 at the North Pole, 90 at the aquator; that is known as the spherical (polar) coordinate system, we now refer to the spherical equatorial coordinate system).
The second formula is the cross product and defines the terms of the generalized plane equation. The third formula calculates the distance measure (dm). Because (2) and (3) do not have repetitive clauses, they could be combined into (4) and then, if wished, again, with the conversion, into (5).
The sixth pseudo-formula then defines the result, it is an interpretation of the distance measure dm.
Ellipsoidal EarthThe Earth is not spherical but approximates an ellipsoid, it is flattened at the poles. But the described spherical side formula works well on Earth. Let me try to prove that (note: I'm a geographer, not a mathematician).
A location defined by (λ, δ) essentially means a vector, either on a sphere, or on an ellipsoid. These vectors always have the same direction, so the same on a sphere as on an ellipsoid. Their lengths differ (on an ellipsoid they are often shorter) but the length of a vector does not influence the plane it encompasses. Therefore the plane formed by two locations and the center of the Earth is exactly the same plane as it is using a perfect sphere.
So: two points (a segment), on a sphere or on an ellipsoid, define the same plane.
The same applies for the third point. It is also a vector, having a direction. That vector, either on a sphere or on an ellipsoid, is located at the same side of the plane.


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Definitions of lead:
- noun: the playing of a card to start a trick in bridge
Example: "The lead was in the dummy"
- noun: a position of leadership (especially in the phrase 'take the lead')
Example: "He takes the lead in any group"
- noun: mixture of graphite with clay in different degrees of hardness; the marking substance in a pencil
- noun: thin strip of metal used to separate lines of type in printing
- noun: an advantage held by a competitor in a race
Example: "He took the lead at the last turn"
- noun: evidence pointing to a possible solution
Example: "The police are following a promising lead"
- noun: the introductory section of a story
Example: "It was an amusing lead-in to a very serious matter"
- noun: a news story of major importance
- noun: (baseball) the position taken by a base runner preparing to advance to the next base
Example: "He took a long lead off first"
- noun: the angle between the direction a gun is aimed and the position of a moving target (correcting for the flight time of the missile)
- noun: a soft heavy toxic malleable metallic element; bluish white when freshly cut but tarnishes readily to dull gray
Example: "The children were playing with lead soldiers"
- noun: the timing of ignition relative to the position of the piston in an internal-combustion engine
- noun: an indication of potential opportunity
Example: "A good lead for a job"
- noun: a jumper that consists of a short piece of wire
Example: "It was a tangle of jumper cables and clip leads"
- noun: restraint consisting of a rope (or light chain) used to restrain an animal
- noun: an actor who plays a principal role
- verb: tend to or result in
Example: "This remark lead to further arguments among the guests"
- verb: be ahead of others; be the first
- verb: pass or spend
Example: "Lead a good life"
- verb: cause to undertake a certain action
- verb: travel in front of; go in advance of others
- verb: take somebody somewhere
Example: "We lead him to our chief"
- verb: be in charge of
- verb: be conducive to
Example: "The use of computers in the classroom lead to better writing"
- verb: lead, extend, or afford access
- verb: cause something to pass or lead somewhere
- verb: lead, as in the performance of a composition
- verb: move ahead (of others) in time or space
- verb: result in
- verb: preside over
- verb: stretch out over a distance, space, time, or scope; run or extend between two points or beyond a certain point
Search for lead at other dictionaries: OneLook, Answers.com, Merriam-Webster
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Co-curricular activities are activities that are planned for students after
school through clubs and uniformed societies. Students are required to join at
least one uniformed unit and a club. In my opinion, these activities play an
important role in a student's life and are therefore not a waste of time and
First and foremost, co-curricular activities provide a broadening
experience for students to learn about themselves, other people, and the
community at large through the various activities organized such as camping,
school trips, games, project work and campaigns. For example, when students go
on a study tour, they are given a chance to encounter situations and
opportunities in the real world, beyond the school gate.
Apart from that, co-curricular activities provide students with a chance to
develop other aspects such as music, sports and other living skills. Some
students are unable to shine in the classroom but they are superb athletes and
musicians. Confined to the demands of their studies, they are unable to develop
their talents and may be branded as failures. Co-curricular activities help
these students to become fulfilled individuals.
Besides that, these activities provide leadership training for students. They
get a chance to learn how to lead a team. They learn organizational skills such
as planning, budgeting and problem-solving, all of which the classroom situation
may be unable to provide. They learn discipline and co-operation, tolerance and
In addition, co-curricular activities provide an outlet for students to rest
and relax after a hard day's work. Students get to play, laugh and release their
tension through the various club activities held, such as quizzes, treasure
hunts and various games. As there are many types of clubs and societies, there
is almost something for everyone. For those who do not like outdoor games, they
can always join a chess club or a cookery club. For the active and restless,
they can join the football club or the netball club. Various competitions and
selections are held and some students are picked to represent their schools.
Co-curricular activities certainly play an important role in a student's
life. They complement the activities of the classroom. In a nutshell, a
well-planned co-curricular program helps students become wholesome individuals.
Thus, co-curricular activities are definitely not a waste of time and money.


7 Ways to Deal With Arrogant People
7 Ways to Deal With Arrogant People
Image by 愚木混株 Cdd20 from Pixabay
Arrogant people do think that they are and will always be right. They get stuck to false assumptions and ignore hearing what other people say. They will use superior language, bully people, and become bigoted of people, or just act total rudely.
They consider themselves excellent. How you react to them becomes necessary when peace of mind is considered.
Your reply to an arrogant person is also a representation of your uprightness as a person who holds up himself.
Sometimes it becomes difficult to be sound these people because they can begin to pick away your self-confidence.
We run out of words and forget how to react to the situation.
How to save yourself from the verbal attacks of an arrogant person?
If you cross paths with these people who are self-stuck, do follow these suggestions.
So, How to deal with arrogant people? We have added different strategies to the tricky points.
Here are 7 Ways to deal with arrogant people
1. Have high self-confidence:
One of the best ways to face an arrogant person is by displaying your high confidence. Always enter into conflicts with arrogant people only when you are strong and have a depth of knowledge about a matter.
Only then you'll know where are they going wrong. It is important to point them out. It will help you get less victimized by them. You will notice how their behavior changes when that can't relate to you. Instead, they would start saying bad things that are unjustifiable. But have faith in yourself. Confusing them in their own words is your bigger trick.
2. Remember they are insecure:
Try finding sympathy in yourself if you can. Arrogant people bullies and harasses people to take control of them. It's just a reflection of their fear of being controlled. They would never admit their wrongs and stuck to pretenses. Thus they would never take account of your advice or suggestions, no matter how hard you make him try to believe. As being self-centered and the inability of open-minded, their life experiences are less. It becomes too hard to sympathize with someone of this quality.
Do not put them down. Just let them enjoy the fruits of their insecurities because they are never able to see their shortcomings.
3. Don't let it get to you:
Once you allow them to rule or control you, they won't leave a dot to not put you down. They have a very low mentality of finding happiness in other's troubles. Much like a narcissistic nature. This is much easier said than done. Just imagine, what if the person isn't trying to be rude towards you and just try hard to figure out the bigger view. There could be other reasons for a person's conduct. Try spotting them out and blur out these scornful criticisms.
Just laugh it out. Do not stress over it.
4. Be empathetic, but don't try to fix the person:
One's demand for superiority is profoundly grounded and ranges from lower appreciation to a deep craving for approval to a lack of compassion for those who seem less successful. Only the domineering person can deal with such a problem and with a continued push. On the other side, it brings peace to your heart and possibly to the circumstances if you have compassion for the grief of others.
5. Be mindful:
Whatever we decide to do, we should do them carefully and with much love as practicable. They make others lose their temper and become the worst version of themselves. You need to be very careful while handling these people. They are rotten from inside and would spread that rot within us too. We should be careful while dealing with them. Try to perform the sport of your life rather than trying to fit into someone else's. Be faithful to yourself always.
6. Try changing the topic of the conversation:
If nothing works wonders, try to change the topic of conversation. Arrogant people love to dominate over one particular topic, and if the decision to change the topic has been taken, they will bounce back. They will become defenseless. If you try switching to something that is neutral or something you know more about, they will try to find a way to jump back to the previous topic. They play dominating roles in our society. When people like us ask them anything out of the syllabus, they wouldn't answer them or might speak badly about you. After all, this is what they know.
You should try to be calm in such situations.
7. Avoid interaction at all possible means:
If you are in close proximity with such a person, your days can be tough. Do whatever it takes, to lessen the effect of this soul. Do not get close to them or park cars near their cars, I mean never!
When you meet them just smile and exchange glances. You might say "good morning", "good day" just in case, or occasional "hmm".
Do not let them know that you're avoiding them and don't want to interfere in any of their matters.
Find more ways to walk out and ignore these people. To maintain your own understanding, it's best to keep a proper distance between you.
Just dodge them by any means!
Written by Alecia Bennett
I hold a master's degree with a clinical psychology specialization. Currently pursuing school counseling courses. I have attended various programs related to mental health issues. A person who takes a keen interest in writing anything about the human mind and behavior.
Photo by Sebastián León Prado on Un
Because no matter how tough the world becomes
9 Possible Signs You Have a Low Sense of Self-worth
9 Possible Signs You Have a Low Sense of Self-worth


Tutoring Club Franchise
Tutoring Club Franchise Information
Tutoring Club is a franchise for a business providing individualized tutoring services for students in Kindergarten up to Grade 12. It was founded in 1991 and started franchising in 1999.
They focus on helping students catch up in school. Their process includes individualized attention from a professional tutor. They start with the level where the student is comfortable with and they rapidly advance it to the level where they should be.
Their curriculum is applied with a learning environment that is positive which helps the student learn more within an hour of session. They also provide a positive incentive plan to motivate your child not to stop trying. Another benefit is that they hold regular conferences to keep you updated with your child's progress. They now have 126 locations in the United States, nine in other countries, and one location that is company owned.
What are the programs offered at the Tutoring Club?
For Amazing Math, they conduct tutorials on addition, subtraction, multiplication, division, decimals, fractions, ratios, proportions, percent, numeration, integers, word problems, geometric figures, measurement, equations, and introduction to Algebra.
The length of the course depends on the need of your child and they conduct a math test at the end of the course. For RX Reading, they have a program specialized for Kindergarten that focuses on consonant letters and sounds, simple sight words, short vowels, long vowels, basic sight words, basic blends, comprehension and vocabulary, and the five primer levels.
For Grade one to 12, they focus on teaching the student on how to decode, comprehension, vocabulary, recall, and reading rate. For every complete level, the course last for about 32 hours in total. They conduct a reading test at the end of the course.
The Write Way focuses on developing sequencing, main idea, comparisons, facts and opinions, cause and effect, writing mechanics, capitalization, punctuation, and the use of dictionary and thesaurus. They also have programs on Study Skills and College Preparation. Another set of programs are under TutorUp which includes geometry, algebra, statistics, calculus, math analysis, science, and foreign languages.
Cost and requirements on running a Tutoring Club franchise
You need to have a net worth of $50,000 and a total liquid asset of at least $30,000. Expect to be investing about $83,000 to $127,000. The cost of the Tutoring Club franchise fee is $34,500 with an on-going royalty fee of 10%. This is for a renewable 20 year term agreement. You will need about two employees to run one location. They allow multi-unit ownership and absentee ownership.
What is included in the franchise package?
There will be two weeks training at the headquarters and one day at your location. You will be receiving newsletters and a toll free phone number. You will be given access to the internet and to purchasing cooperatives. You will also receive assistance at the grand opening. Expect to be attending meetings and receiving occasional field evaluations to check on your progress. For marketing support, there will be ad slicks, co-op advertising, regional advertising, and national media.
Tutoring Club Contact Details
You may reach them at:
Address: 11241 S. Eastern Ave. Henderson, NV 89052
Phone: _PHONE_