text:
Cochrane man using donations to help furnish Wesley First Nation homes
"I've got too much, I don't even know where to put it all, that's the trouble. But I know there's a need so I'm not going to say 'well these people are good.'"
Tyler Klinkhammer
1 / 1 Peter Tilma, project manager at Trico Homes, has built six homes on the Wesley First Nation since August, 2020. Photo submitted.
COCHRANE— A Cochrane is building homes on the Wesley First Nation and has been quietly collecting furniture donations to fill the houses upon their completion
Peter Tilma first became involved with Stony Nakoda First Nation following the 2013 floods, when his employer, Trico Homes, was hired to restore several damaged properties belonging to Chiniki First Nation members.
While working on those homes, Tilma noted some of them were lacking furniture and other amenities— The observation sparked an idea to collect furniture and donate it to the residents.
Seven years later, Tilma is now working with the Wesley First Nation building new homes, and he is still collecting furniture donations for the homes he builds.
"Because of the previous experience, I knew that they would be needing this stuff," he said. "I didn't even ask the homeowners, I surprised them with 'ta-dah, there's furniture in your house.'"
He said many of the recipients of the donations were very excited upon realizing what he had done.
"They were so thankful. They were so happy," he said. "They couldn't thank me enough, they were taking pictures and sending them to their friends, 'look what I got, I got a bedroom set,' and 'I got a dresser.' That was pretty heartwarming, it was so nice to see."
When Tilma put out the call on social media to collect the furniture donations, he said that the responses were immediate.
He had upwards of 50 responses within days of making the post.
"I'm still going to go through that list of people. I know that there some of them that I haven't even responded back to," he said. "When do I haul that out, my truck is full again from yesterday."
The sheer volume of people wanting to donate to Tilma's cause has led to him giving up many of his evenings and weekends. After work, Tilma will often go to collect the furniture so that he can bring it to the job site the following day.
"It's been overwhelming," he said. "Especially because I'm a dad of five kids and I've got my full-time job. It's not like I can do this every day."
Due to the large number of donations, Tilma said, there is more than enough for the residents of the recently built homes.
According to him, the residents of the Wesley First Nations have begun sharing the donations with others who are in need in the community.
"Now I'm at a point where everybody that I moved in already has a house full of furniture but I'm still getting more couches and beds and stuff. So, I'm asking them 'do you know anybody else that needs stuff that I don't know of?'" he said. "Now they're networking on the reserve to keep handing out the stuff to help other people that are in dire need."
Even though the houses are now furnished, Tilma said, he has no plans to stop shipping furniture out to Wesley, as long as the donations keep coming in.
"I've got too much, I don't even know where to put it all, that's the trouble. But I know there's a need so I'm not going to say 'well these people are good,'" he said.
Wesley First Nation Chief Clifford Poucette said his council selected the members to receive one of six newly built homes based on a criterion that is revised each year.
"Each year we kind of move around the priorities. This year it was overcrowding—People who are in overcrowded homes."
Poucette said housing is an issue his council has identified and a priority that they are working to rectify.
"Across Canada, First Nations are all overcrowded. Speaking here in Stoney, Morely, Big Horn and Eden Valley most of the houses are between 15 to 20 people in each house. Firstly, those houses are recommended for four to five people," he said. "All three Nations are trying to build these houses as quickly as we can."
Poucette noted that, among the COVID-19 pandemic, the overcrowding became a cause of concern regarding the spread of the virus. He said he hopes giving families more space will reduce the spread of COVID-19 in the Wesley community.
The six houses are the most recent addition to the reserve, but Poucette's council is already planning to build more in the spring of 2021, as well as change the way that communities are built on Wesley.
"We used to all scatter the houses out here, but now we're looking at clusters and areas where we can put all these houses together on one water system and sewage," Poucette said.
He added building homes closer together will save the Nation money in infrastructure-related costs.
He noted that the families he has heard from are all very grateful to be in their own spaces.
"They've been applauding chief and council plus Trico for moving them in before Christmas. They're happy. I know that when each and every one gets their own house where they will be sleeping the rest of their lives under one roof— They're really happy," he said.
Poucette said that he's proud of the work his council has done and grateful to Trico Homes for handling the construction of the homes.
"I think all of us did a good job," he said. "I think we provided the necessities for the people who were in need. Wesley, we've still got about a couple of hundred to go, but it doesn't happen overnight— It takes a lot of planning to conquer that amount."
More Indigenous Alberta
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Probe into Alberta residential school links unpasteurized milk to children's deaths
About the Author: Tyler Klinkhammer
Interim editor of The Cochrane Eagle.


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Q: Dividing a polynomial $p(x)$ by $x-k$, but $x-k$ is set to be $0$? While studying, I read the following,

When a polynomial $p(x)$ is divided by $(x-k)$, if we set $(x-k)$ to be $0$, we get $x=k$ and the remainder as $p(k)$.

However, if we divide $p(x)$ by $(x-k)$, or $0$, wouldn't the answer be undefined?

A: Given a polynomial $p(x)$, one can phrase the fact (coming from the division algorithm) that
$$p(x)=(x-k)\cdot q(x)+p(k)\quad$$
for some polynomial $q(x)$ as either

*

*dividing $p(x)$ by $x-k$ leaves a remainder of $p(k)$

*in the ring of polynomials $F[x]$, if we "set $x-k$ equal to $0$", i.e., quotient by the ideal $(x-k)$ to produce the ring $F[x]/(x-k)$, then we have $p(x)\equiv p(k)\bmod (x-k)$.
You're just mixing up these two phrasings of the same mathematics.

A: The "Remainder Theorem" says if you divide $p(x)$ by $(x-k)$, the remainder is equal to $p(k)$.  This follows since upon division, one obtains $p(x)=(x-k)q(x)+r$ (note the remainder is of lower degree than the divisor, and hence in this case constant).
From this you get $p(k)=(k-k)q(k)+r=r$.

A: The division there isn't for integers but for polynomials. If for integers, the Euclidian Division states that $$\forall a,b\in\mathbb{Z},\,\exists ! \,q,r\in\mathbb{Z},\,a=bq+r\,\,\land\,\, 0\le r<|b|$$ its version for polynomials is $$\forall P,T\in\mathbb{C}[X],\,\exists !\,Q,R\in\mathbb{C}[X],\,P=TQ+R\,\,\land\,\, \deg{R}<\deg{T}$$ where $\mathbb{C}[X]$ is the set of all polynomials with complex coefficients (this set contains the set of all polynomials with real coefficients $\mathbb{R}[X]$ since $\mathbb{R}\subset\mathbb{C}$)
So in your case:$$\exists !\, Q,R\in\mathbb{C}[X],\,p(x)=(x-k)Q(x)+R(x)\,\,\land\,\,\deg{R}<\deg{(X-k)}=1$$
Since $\deg{R}<1$ therefore $R=c$ is constant and is equal to the number $c\in\mathbb{C}$ that can be $0$ or not $0$. To find it, replace $x$ by $k$ to get $p(k)=R(k)=c$ so the remainder is $p(k)$.

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Also private instruments like GRI (Global Reporting Initiative) were involved and connected to ISO 26000.
"ISO 26000 in Practice – A user guide"
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Help Pets Displaced by Devastating Wildfire!
You've probably heard of the massive Wildfire in Canada, that's already ripped through 500,000 acres. It's devastating! Nearly 100,000 residents have been evacuated and a massive rescue mission is underway to save the 1,000s of pets left behind.
You can help. Just $5.00 makes a difference… they need us!


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Zoe Kravitz is so 'proud' her dad Lenny Krazitz is part of the YSL family
Zoe Kravitz is very "proud" that her father Lenny Kravitz is now a brand ambassador for YSL along with her.
Zoe Kravitz is delighted that her father Lenny Kravitz is now part of the YSL family along with her.
Lenny and Zoe Kravitz
'The Batman' actress has been a YSL Beauty brand ambassador since 2016 and her 56-year-old rock star dad joined Yves Saint Laurent in September as the face of YSL Beauty's Y Eau de Parfum fragrance.
Zoe, 31, is "proud" to have him as part of the brand and thinks his advertisement is "great".
In an interview with Refinery29, she said: "I think it's so cool. We have both loved the brand so much, both the beauty and the fashion side of things. I love that it has happened in a really organic way. I'm proud of him and his ad is great, I love it. We're keeping it in the family."
Since signing with YSL, Zoe has appeared in in advertising campaigns for the Black Opium fragrance several new make-up products.
In 2019, the 'Big Little Lies' star - whose mother is former 'Cosby Show' actress Lisa Bonet - got her own branded product, the YSL x Zoe Kravitz line which features six new shades of YSL's Rouge Pur Couture lipsticks.
Lenny previously admitted that it was a wonderful experience to be able to follow in his daughter's footsteps in the fashion world.
The 'Are You Gonna Go My Way' hitmaker said: "The really exciting part for me is that I got to follow in my daughter's footsteps. That's a wonderful thing as a parent to be able to do. Not only them follow your footsteps, but you follow theirs."
tagged in Lenny Kravitz Zoe Kravitz
Zoe Kravitz files for divorce from Karl Glusman
Lenny Kravitz prefers solitude to parties
Anne Hathaway tells Zoe Kravitz to be her own Catwoman

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It ended up taking the twins just shy of 10 hours to cover the 73 miles from Ophir to Cripple. They pulled into Cripple (race mile 425) Friday morning AK time. It looks like they took a good 7 hour rest before pulling out of Cripple mid Friday afternoon. They each dropped a dog, leaving Kristy with 12 dogs in harness and Anna 11. They covered the following 70 mile leg over the next 9 1/2 - 10 hours, arriving in Ruby on either side of midnight AK time Saturday morning.
Although the race awards the halfway prize in Cripple (won by Aaron Burmeister on Wednesday this year), I consider Ruby, as race mile 495 of 975 in the northern route, the real halfway point when it comes to Kristy and Anna's journey. And it may feel like the twins just took their 24 hour, but they've also put 140 miles under their runners since then. As race rules mandate an 8 hour rest be declared and taken by each team at a checkpoint on the Yukon River, I wasn't too surprised to see the twins take theirs in Ruby.
Conditions have definitely changed pretty dramatically from early in the race. The trail now has consistent snow cover and "hard and fast" shows up repeatedly in condition reports. Sebastian Schnuelle, blogging on the Iditarod.com site, comments, "Traveling on the Yukon River has been really nice. There is a slight breeze out there from the north, but luckily the snow is really hard packed. There is not much loose snow to blow around and the going for the mushers is good." Temps are also holding at lower levels, staying below 0F over this stretch.
Kristy is reported in 40th out of Ruby, still with 12 dogs, while Anna is in 41st and still with 11. The twins have 50 miles to cover between Ruby and Galena, and, fresh off their 8-hour rest, I'm hoping they do it in under 6 hours. The below pictures should give you a pretty good idea of what Anna and Kristy are seeing along this stretch. From Galena, they'll have 37 miles to Nulato and then another 47 miles to Kaltag (race mile 629), which will mark the end of their Yukon River run and mark the beginning of their push to the Bering Sea coast.
Which is exactly where the race leaders are as of this writing. Five mushers are all out of Kaltag, all have completed their 24 and 8 hour rests, and are running 11, 12, or 14 dog teams ~ Aliy Zirkle, followed by Buser, Petit, Lindner, and King. These teams have less than 350 miles to the finish, although most probably have their immediate sites on the next checkpoint of Unalakleet, where the first to arrive claims the Gold Coast Award and $2,500 in gold nuggets.
Those 5 front runners are among 54 total teams still out on the trail. Two more scratched since my last update, among them veteran Ramey Smyth, citing an illness in his team. The spread between the leaders and laggards is now some 250 miles, and there's an interesting article in the Alaska Dispatch discussing what that might mean for the latter.
* March 7 (A) ~ Kristy and her dogs in Cripple.
* March 5 (C) ~ Kristy on the trail between Takotna and Ophir.
* March 5 (B) ~ Two of Kristy's dogs... Dolphin and Buck, I think.
- Remember the GoPro footage from Jeff King that I mentioned? It's now available for all to see on YouTube (just click on the link).
- Three mushers answer ADN reader questions before the race start, and one of them is Kristy.
A frost-covered Paul Gebhardt arrives in Ruby, the first checkpoint on the Yukon River. Photo by Loren Holmes (Alaska Dispatch).
Jeff King leaves Ruby after his 24-hour rest stop. Photo by Loren Holmes (Alaska Dispatch).
Martin Buser pulls into Galena, the 2nd musher to arrive there early Friday morning. (Sebastian Schnuelle, Iditarod.com).
An Iditarod musher drives his team down the Yukon River after leaving the Ruby checkpoint and heading towards Galena during the Iditarod Trail Sled Dog Race on Friday, March 7, 2014. BOB HALLINEN (ADN.com).
Richie Diehl, from Aniak, AK, mushes down the Yukon River at sunset after leaving the Ruby checkpoint during the Iditarod Trail Sled Dog Race on Friday, March 7, 2014. BOB HALLINEN (ADN.com).
Iditarod musher Paul Gebhardt, from Kasilof, AK, mushes up the bank off of the Yukon River and into the Galena checkpoint during the Iditarod Trail Sled Dog Race on Friday, March 7, 2014. BOB HALLINEN (ADN.com).
And although this photo is from the restart, I'm pretty sure that's Nicolas and Honey in lead, both dogs still out on the trail with Kristy.
Kristy Berington's dogs cool off with their tongues out during the official restart of the Iditarod Trail Sled Dog Race in Willow, Alaska on March 2, 2014. The above freezing, warmer than average temperatures at the restart and lack of snow in interior Alaska promise to make this year's Iditarod an interesting race.


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Марий Эл включает 19 городских населённых пунктов, в том числе:
 4 города (из которых 3 города республиканского значения и 1 город (Звенигово) районного значения) и
 15 посёлков городского типа.

Города

Посёлки городского типа

Бывшие пгт
 Визимьяры — пгт с 1986 года. Преобразован в сельский населённый пункт в 2000 году.
 Дубовский — пгт с 1948 года. Преобразован в сельский населённый пункт в 1987 году.
 Звениговский Затон — пгт с 1927 года. Преобразован в город Звенигово в 1974 году.
 Красный Стекловар — пгт с 1938 года. Преобразован в сельский населённый пункт в 1997 году.
 Ленинский — пгт с 1941 года. Преобразован в сельский населённый пункт в 1959 году.
 Лопатино — пгт с 1933 года. Преобразован в город Волжск в 1940 году.
 Мариец — пгт с 1939 года. Преобразован в сельский населённый пункт в 1997 году.
 Мочалище — пгт с 1952 года. Преобразован в сельский населённый пункт (посёлок) в 2004 году.

См. также
 Административно-территориальное деление Марий Эл
 Населённые пункты Марий Эл

Примечания

Марий Эл

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Back to story: Does losing 250 pounds make me a success story?
Wow, Ken, great post. Beating Type 2 diabetes, losing cravings for crap and breaking the addiction, being more active and to tie shoes from standing position ... it's all so wonderful. What a journey to freedom.
I'd say you are a success story in many ways!!!
Keep it up & your new look will stay with you!!!
Love the pictures! Thank you for sharing your story!!!
You're amazing and inspirational to many as always.
A success and a role model. I showed your pictures to my husband & said this man lost 250 pounds. He asked, which one? You look like a completely different person.
Thank you for sharing your story. It's people like you who help me stay on this road.


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Journal of Applied Physics 16, 172-186 (1945)
{This website: Please note: The following article is complete; it has been put into ASCII due to a) space requirement reduction and b) for having thus the possibility to enlarge the fairly small figures. And: special math. symbols are in Unicode. Further: disallow M$-IE 'automatic picture size adaptation'.}
Abstract: Numerical methods are developed to solve certain types of linear and nonlinear partial differential equations to any desired degree of accuracy with the aid of equivalent electrical networks. The methods of solution of ordinary differential equations, both linear and nonlinear, follow as special cases. Three types of problems are considered:
1. Initial-value problems. If the field quantities are known along a surface, the networks may be solved by a straight-forward step-by-step calculation The networks may also be looked upon as supplying a 'schedule' of operations that can be put on a digital calculating machine.
For time-varying problems new types of networks are developed in which time appears as an extra spatial variable. Examples of new networks for the elastic field and for the general nonlinear wave equation are given. Sample calculations and theoretical checks of a transient heat flow problem and of an ordinary differential equation are also included.
2. Boundary-value problems. Four methods of solution are given, the first three being cut and try processes.
(a) The method of weighted averages;
(b) The method of unbalanced currents and voltages;
(c) The 'relaxation' method;
(d) The 'diffusion' method, that changes the boundary-value problem into an initial-value problem by adding to the original partial differential equation a time variable of the form A∂φ/∂t, allowing the unbalanced currents to 'diffuse' in time.
These numerical methods may also be used to improve the accuracy of the results found on the Network Analyzer. Examples of calculations are given for the electromagnetic and the elastic fields.
3. Characteristic-value problems. Their methods of solution are similar to those of boundary-value problems. An additional method of unbalanced admittances is also indicated. It is shown that by calculating the power in the network, the characteristic value of the assumed function is 'found'.
An improved characteristic value of the linear harmonic oscillator, solved initially on a Network Analyzer, is calculated as an example.
In general the electrical networks may-be used to check the consistency and correctness of solutions arrived at by other methods, approximate or exact. The unbalanced currents at the junctions (easily calculated) give a quantitative measure of the deviation from the correct solution.
The method of solving partial differential equations numerically by the use of equivalent circuits is by no means new. It has long been known (1,2) that Laplace equation ∇2φ = 0 in rectangular coordinates may be solved to any desired degree of accuracy by (considering the two-dimensional case) drawing a net of squares, Fig. 1, each with area ∆x∆y, and associating with each line the real positive number, unity. If with each junction (representing a point of space) the correct value of the dependent variable φ is associated, then each φ must be the average of the four neighboring φ's. An extension of this method to Poisson's equation ∇2φ = k, where k is an arbitrary function, has also been in use.
The equivalent circuits presented here may be looked upon as generalizations to more general partial differential equations of the type of net of Fig. 1a used by mathematicians to represent Laplace's equation. In particular (considering Fig. 1b):
1. The square net with two lines crossing at right angles is replaced by nets with more complex configurations. Several lines may now meet at a junction and at arbitrary angles.
2 With each line is associated not unity but either a real, or an imaginary or a complex number a, b or c+id, positive or negative.
3. The junctions are associated not with one, but several dependent variables.
In these more general nets the variables represent line-, surface-, and volume integrals of field quantities on a set of interspersed small cubes into which the field is subdivided. Accordingly, not just any haphazard set of partial differential equations can be represented by a net. This physical interpretation requires that the equations should be in a tensor-density form.
It is a rather arbitrary but still valuable procedure to associate the numbers at the junctions by absolute potentials and the numbers along the lines by impedances, in particular. (Fig. 2):
1. a positive real number by a positive resistor;
2. a negative real number by a negative resistor;
3. a positive imaginary number byan inductor;
4. a negative imaginary number by a capacitor.
This physical interpretation of the mathematical net allows additional physical concepts such as current, power,- flux, etc., to be associated with the network, thereby simplifying ifs analysis and solution. It is true that in topology these additional concepts are also associated with the mathematical net, in particular current as "1-chain", power as "intersection-index", etc.,(see ref. (1), p.213) but apparently these concepts have not yet been used for the solution of nets representing the Laplace-Poisson equations.
In transient equivalent circuits not only numbers are associated with the lines of the net, but also operators, such as ∂/∂t. In nonlinear circuits the line numbers are functions of the junction numbers. When only positive and negative real numbers exist, it is customary to replace a positive resistance by an inductance and a negative resistance by a capacitor (since none or only a few negative resistances exist on practical network analyzers).
Of course the algebraic symbols may be replaced by a mechanical model (masses and springs) or an acoustical model (pipes and chambers) instead of an electrical circuit.
PART I. INITIAL-VALUE PROBLEMS
Time-Dependeut Equations
Partial differential equations containing time differ usually from other in the manner in whith the boundary conditions are specified. In this part it will be assumed that at time t = 0, the values of the dependent variables and their derivatives are known.
Considering time as an extra spatial variable, the equivalent circuit consists of the original network (in which time does not enter) arranged in layers (one-, two-, or three-dimensional), separated by distances ∆t and interconnected by suitable impedances. Figures 3—5 represent the nonlinear wave equation,
for various numbers of independent variables.
In orthogonal curvilinear coordinates
where the f 's are arbitrary functions of u1, u2, u3, and t.
When time enters as a second-order derivative, the networks are shown in Figs. 6 and 7. When time enters in a more complex form, different arrangements must be used.
Figure 8 shows the time equivalent circuit of the elastic field. Since time enters as ∂2 / ∂t2 for each dependent variable, all component networks are identical and for all spatial reference frames they are the same as those given in "Equivalent Circuits of the Elastic Field." (3)
It should be noted that while in the elastic and fluid flow fields the time coordinate may be left out or included at will, such is not the case in the electromagnetic field. In the latter the non-privileged role of the time coordinate necessitates a radically new treatment.
Time as a Spatial Variable
Let in a linear problem at t = 0 an instantaneous impulse be impressed on the physical system. On the network this impulse is impressed by generators at t = 0 and the voltage distribution gives the effect of the impulse in time and in space. (In the absence of a Network Analyzer the voltage distribution may be found by the methods to be shown presently.) Since the network extends to infinity along time, the network beyond any specified time t0 may be replaced by a characteristic impedance.
If the effects of an impulse are known, then the effect of any other force applied within any time interval may be found by simple superposition of the known voltage distribution.
It should be noted that the effect of more than one impulse cannot be studied simultaneously on the Networkl Analyzer, since a generator impressed, say, at t = 5∆t produces a voltage distribution at points corresponding to previous times, a situation impossible in classical dynamical problems. The numerical method to be shown prevents this "backsliding" of the impulses impressed at various times.
The Numerical Calculations
The numerical method is based on the fact that if all the potentials on the network are defined at t = n∆t and at t = (n+1)∆t (and also the boundary conditions along time), then all the potentials and currents'càn be calculatçd for the rest of the hetwork in a straightforward manner up to any desired number of ∆t's.
The numerical work consists of calculating all the admittances and currents on the second or (n+1)∆t network, (Since in nonlinear problems the admittances are functions of the potentials, the former can all be calculated.) Adding up at a junction all the currents, induding the one coming from the lower network, the resultant current must flow upward to the next network (n+2)∆t, Fig. 4. Since the admittance of the connecting coil is known (even in nonlinear
problems) the absolute potentials of the corresponding points on the next network (n+2)∆t are thereby determined. The work of calculating currents is again repeated to proceed to the next network at (n+3)∆t.
Starting Assumptions
It should be noted that in order to get started, it is necessary to know not only all the currents on the network say at t = 0 but also the currents coming from the next lower network, t = - ∆t. However, in most problems the boundary conditions are so defined that at t = 0 the currents coming from the lower network are not known, although the sum of the lower and upper connecting currents, namely ∆t(∂φ / ∂t) is known at every point. At the start of each problem thus the question arises how to divide the resultant currents into two parts at t = 0. Several methods are available:
(1) Half the current may be assumed to flow up, the other down. This assumes the slope of the curve φ = f(t) to be constant in the neighborhood of t = 0. After proceeding through two or three layers of networks it is possible to discern a more logical division than halving and to start all over again with the new divisions.
(2) Standard methods of approximations given in textbooks (4) may be used. For instance, after finding the potentials on the t = ∆t network, the differences of potentials between the two networks define the slope of the chord between the points t = 0 and t = ∆t. Using this slope instead of that of the tangent ∆t(∂φ / ∂t) at t = 0, a better division is accomplished. This step may be repeated several times between the first two networks.
(3) ∆t maybe subdivided into 5 or more subdivisions. Because of the finer divisions the results arrived at by the 5th ∆t may be assumed to be close enough approximations and may be used as starting values on the coarser network.
Other Assumptions
Since the starting conditions are rarely known exactly, it will often be found that the currents or voltages in successive steps do not lie on smooth curves but oscillate around them in an attempt to correct themselves. Such overshooting and undershooting of smooth curves may be minimized by judicious changing at intervals of the division of currents that flow "up" and "down" between the layers. Most numerical methods do not possess this self-correcting property of the equivalent circuits.
When some of the admittances lying between two successive layers (between two ∆t's) are functions of the dependent variables (hence, of time) their value has to be found by extrapolating from the known values of the dependent variables at two previous times.
In ordin~ary differential equations the independent variable may be either a spatial variable x or time t. If it happens to be the time, then usually sufficient information is available at t = 0 to get the calculations started as above.
When the independent variable x is a spatial variable then usually only part of the boundary conditions (say the value of φ) are defined at x = 0. Some boundary conditions (say the slope, of φ) may, however, be defined only at x = a. In such cases it is possible to start out with a tentative slope at x = 0 and find with the above step-by-step method the slope at x = a. Several new starts should eventually match the boundary conditions at the two different values of x.
An example,
di/dt = 10 - 2i
with initial conditions i = 0 and t = 0 (also di/dt =10 at t=0) is worked out in Fig. 9 in steps of ∆t= 0.1. The numerals in parenthesis give the results found in Doherty and Keller (5) for the same problem, found by a standard method requiring a cut and try procedure not only at the first step (between t = 0 and t = ∆t) but at every step.
Other worked out examples may be found in "The Application of Network Analysis to Some Electron Optical Problems." (13)
Example of a Transient Heat Flow Problem
Let the temperature at the edge of a plate be raised from zero to unit temperature at t = 0 and be kept at that same temperature. The problem is to find the distribution of temperature along the plate (at distance x from the edge) at various times.
The equation of flow is
Also ∆x=0.1, a∆t=0.0025. Hence ∆t=0.0024/a
The boundary conditions are:
Since the known data at t = 0 are rather meager (T and ∂T / ∂ t are zero at every point along x except near x = 0) for a preliminary calculation the assumed ∆t is subdivided into five parts, so that a∆t = 0.0005. The corresponding network to be used to get started is shown in Fig. 10.
The layer at t = 0 only contains one current 5 flowing into the ground. (The existence of a ground is a boundary condition.) Hence this current cannot very well be assumed to divide into two equal parts. Instead, let it be assumed that a similar current in the next layer at t=a∆t/2 also has a value 5. Now half of that may flow up and half down. Assuming slightly less than half, say 2.45 flowing up, one potential on the next layer is 24.5. Its neighboring potential on the same layer is still undetermined but it must be small and could as well be assumed to be zero for the purpose of calcijilating the current flowing into this junction. The latter (24.5 - 0) 0.005 = 0.1225 is assumed again to flow half up, half down.
Continuing the calculation through five layers, the voltages on the fifth layer can be assumed to be approximately correct. Since the first layer contains too few informations, the calculation is continued to the tenth layer in order to be able to use the fifth and tenth layers as the first two layers of the coarser network of Fig. 11.
Fig. 11. Transient heat-flow calculation.
The calculations on Fig. 11 are straightforward. The numbers in parenthesis give the theoretically correct temperatures, showing satisfactory agreement with the approximate method. The farther the calculations are continued from the crudely approximated first layer, the better is the agreement with the analytical solution. It should be remembered that the set of vertical currents, by
their deviation from a smooth curve, do show that some of the temperatures are too high and some are too low. Hence, they afford a means of correcting the results at intervals.
Equations Not Containing Time
When an equation does not contain time, it still may happen that all field quantities are known upon a layer so that the next layer may be calculated. A class of such problems occurs in the design of magnetic or dielectric equipotential surfaces where a definite flux density (magnetic or electrostatic) is desired across a given surface. The problem is to shape the pole faces or electrodes to produce this desired flux distribution.
For instance, in a betatron (6) a known axially symmetric flux distribution is desired at the median plane of the accelerated electron. The equivalent circuit for the vector potential ψθ is shown in Fig. 12. Here the following quantities are known:
1. As all flux lines are perpendicular to the median plane, H(r) is zero and the vertical currents along the median plane are zero.
2. The flux distribution B(z) along the median plane are given, hence the differences of potentials along the corresponding coils are also known.
3. The current density in the current carrying region are known, hence all currents entering the junctions at the corresponding region are also known.
Sufficient data are available to continue the calculation of potentials and currents without any trial and error. The lines orthogonal to the equipotential lines represent the possible pole shapes to produce the desired flux distribution. When no current-carrying regions exist, a modification of the network, representing the scalar potential φ may be used, e.g., as shown in Fig. 10 of "Equivalent Circuits of Compressible and Incompressible Flow Fields. " (7)
PART II. BOUNDARY VALUE PROBLEMS
The equivalent circuits consist of a configuration of coils repeated along one, two, or three axes. The final shape of the network is the same as the shape of the field to be analyzed. While the illustrations will refer to two-dimensional networks, all rules and formulae are equally valid for one- and three-dimensional networks.
In analyzing a field, at first it should be divided into a very few subdivisions only. After its field distribution has been calculated, it should be subdivided into a finer mesh then, if needed, into still finer meshes. In most problems it will be necessary to introduce fine meshes only in certain portions, usually around corners.
The problem in all cases is the following:
(1) Given the boundary conditions in the form of known currents flowing in some of the coils and in the form of known absolute potentials at certain junctions.
(2) Find the absolute potentials of all junctions and the currents flowing in all conductors.
In linear problems the impedances of all coils are also known. In non-linear problems only some of the impedances are known, while the value of others are functions of the as yet unknown absolute, potentials and their derivatives. Some of the junction currents also may be functions of the potentials.
A Preliminary Step
In most networks the absolute potentials of the junctions have a physical meaning. In particular: (1) In the electromagnetic field it is Ey, the field- intensity, along the y-direction, or Hy.
(2) In elasticity it is the total displacement u or v.
(3) In hydrodynamics it may be the stream- function ψ or velocity potential φ etc.
In all methods of attack as a preliminary step a tentative potential distribution at the junctions is assumed. Usually an intelligent guess may be made and if the guess is far off, that only entails more labor, without, however, influencing the correctness of the final answer. (Instead of the potential distribution, a guess may be made at the current-distribution.) Of course in linear problems this preliminary step may be done on a Network Analyzer, even though only a very few units are available, or the results of an approximate or exact solution may be used as starting points.
Once the absolute potentials at all the junctions are assumed to be known, it is always possible to calculate the currents flowing in all the coils. In non-linear problems at first the coil admittances and junction currents must be calculated from the known potentials, then the coil currents. Examples of non-linear networks are those of the potential flow of a compressible fluid in the physical plane, given in reference 7, Figs. 10 and 11.
The method of attack is based upon the fact that if the correct potential distribution is assumed and if all currents in the coils have been calculated then:
(1) The sum of the currents
entering each junction is zero.
(2) The weighted average of the potentials of neighboring junctions is equal to the potential of the central junction.
Three types of numerical calculations may be performed depending upon whether the weighted average of the currents entering a junction, or of the voltages surrounding a junction, or of both, are calculated.
Because of the bad guess, however, actually at no time will the above conditions be fulfilled at all junctions simultaneously. The purpose of the calculation is to reduce the difference in the entering and departing currents (or the difference between the surrounding and the central potentials) as close to zero as possible at all junctions.
This difference in the currents will be called the "unbalanced current" iu , and the difference in the voltages the "unbalanced vOltage" eu . It should be noted that:
(1) The "unbalanced voltages" offer a clue on how much to change the guessed-at voltages to reduce the error.
(2) The "unbalanced currents" give an indication of how much the guessed-at values differ from the correct values.
Calculation of the "Unbalanced" Currents and Voltages
The unbalanced currents iu at each junction are best calculated by summing up the currents entering it. To find the unbalanced voltage. eu at a junction whose absolute potential is e0, let Fig. 13 be considered. The unbalanced current may also be found by
If it is assumed that no unbalanced currents exist (iu = 0) then the correct value of the assumed potential e0would be E, the weighted average
Since e0 is assumed instead of E, the unbalanced voltage is
Hence the relation between and eu at every junction is
is the sum of the admittances of all the coils leading to the junction.
The Field Equations of Maxwell
In Laplace's equation, where y1 = y2 = y3 = y4 = 1 and yg = I = 0,
In Maxwell's equation, in rectangular coordinates, Fig. 4, where y1 = y2 = y3 = y4 = yL and yg = yc (acapacitance, a negative number),
a number less than four.
That is, finding the unbalanced currents and voltages for the field equations of Maxwell in rectangular coordinates is no more complicated than finding the same quantities in Laplace's equation (i.e., the number 4 is replaced by k). It will be found in most problems that the general equations (1), (4), and (2) for finding iu,eu and E may be considerably simplified.
The Method of Unbalanced Currents and Voltages
One of the quickest ways (if not the quickest) to solve a complicated network is the following:
1. Assume (or measure by a Network Analyzer) the potentials at all junctions.
2. Calculate at all junctions the unbalanced currents iu and the unbalanced voltages eu.
3. Knowing the whole set of unbalanced quantities at the junctions assume a new set of potentials that are more correct. In general, where e u is positive, the potential should decrease and with negative e u it should increase.
4. Calculate over again the whole set of new unbalanced quantities at every junction.
Such successive guesses and calculations should reduce the unbalanced quantities below any desired amount. Plotting curves of the unbalanced currents, voltages, and of the guessed-at values at frequent intervals helps to speed up the convergence.
Examples of Unbalanced Quantity Calculations
Let a square wave guide or cavity resonator, by a conducting surface that extends to infinity in the y direction, be divided into sixteen squares. The net of coils in each square consists of two inductances (z=0.8 or y=1.25) and a ground capacitor (z=1.3 or y=0.77). The currents in the inductance represent Ex and Ez, while the voltages across the capacitors represent Hy.
Fig. 14, bounded in the x-z plane on three sides.
For boundary conditions, it is assumed that at the open end (upper end) a sinusoidal current distribution in space, Ex, is impressed. As a result, a sinusoidal potential distribution Hy appears at the junctions. Neither the magnitude nor the wave-length of Hy is known.
Tentatively let the values shown on Fig. 14 be assumed as the junction potentials H y. (Actually these values were found on the Network Analyzer.)
FIG. 15. Unbalanced currents and voltages on the wave guide network.
Figure 15 gives the unbalanced currents and voltages that will have to be liquidated. It should be noted that the greatest unbalanced junction current is 7.93 amperes. As the greatest coil current is 102.8 amperes, that represents an 8 percent inaccuracy.
Knowing the unbalanced currents and voltages at every junction, a new set of junction potentials may now be assumed.
For an elastic stress problem of a beam, a set of junction potentials (representing displacements in the x or y directions) and a set of unbalanced currents are shown in Fig. 16 (reproduced from Carter (8)).
The Method of Weighted Averages
Instead of attempting to reduce the unbalanced quantities simultaneously at all junctions, it is possible to reduce them at one junction at a time. Two such methods will be shown .
(1)The unbalanced current and voltage are reduced to zero at a junction without compensating at the neighboring junctions (the method of weighted averages).
(2) Each time the unbalancect current or voltage is reduced at a junction, the unbalanced quantities at the neighboring junctions are compensated simultaneously (the relaxation method).
The first method is especially valuable when the guessed at value of potentials differs from the correct value only at isolated points or regions. Such is the case usually in Network Analyzer solutions when at some junctions the instrument reading is incorrect or the board unit happened to be incorrectly set. The steps are as follows:
(1) Assume (or measure) the potentials at all junctions.
(2) Calculate E, the weighted average, at any junction by Eq. (2).
(3) Replace e0 by E.
In the previous method e0 was not replaced by E. Only the corresponding eu for each e0 was calculated, leaving e0 undisturbed.
It is customary to start at one corner of the network and change in succession all e0 to E, utilizing the already corrected potentials wherever they are available. A disadvantage of this method is that it is equivalent to reducing the unbalanced potential eu at each junction immediately to zero.
A more advantageous procedure is to replace at each junction the value of e0 not by E but by a value larger than E, or smaller (depending on the value of the neighboring potentials) leaving thereby at each junction an unliquidated e u that is within the allowable limit of error.
In non-linear problems it is often possible to plot curves which give outright the value of E for given neighboring potentials (or rather for given potential-differences between neighboring junctions). If difficulties in the convergçnce arise, in place of E a value larger (or smaller) should be used.
The Relaxation Method
The relaxation method reduces the unbalanced currents or voltages at one junction at a time toward zero in a systematic manner. It is based upon the fact that whenever the absolute potential of a particular junction is changed, the unbalanced currents and voltages change only at that particular junction and at all the neighboring junctions to which a coil leads, while everywhere else the unbalanced junction currents remain unchanged.
This fact may be seen by introducing a set of hypothetical generators so that (Fig. 17a):
(1) At every junction a generator with zero impedance is assumed to be connected to the ground.
(2) The generator voltage is equal to the absolute potential of the junction.
(3) The generator current to ground is equal the to unbalanced current existing at that junction.
By the introduction of these hypothetical generators the network remains unchanged and is now capable of performing new feats that it couldn't do otherwise. Since the generators have zero impedance to ground, whenever one of the generator voltage is changed, currents can flow from this generator only to the neighboring grounds. (Fig. 17b). No change of currents exist anywhere else in the network.
Hence, the unbalanced currents are reduced in two steps:
(1) Add (or subtract) a certain number of volts to the potential of a junction.
(2) Find the new unbalanced currents (or voltages) at that junction and in the neighboring junctions.
Whether the unbalanced currents, or voltages, or both should be calculated depends on the problem at hand.
The "Unbalanced-Current Patterns"
The work involved in this last step may be greatly reduced in linear problems by the device of the "unbalanced-current pattern". This device consists of calculating once for all the change in the unbalanced junction currents caused by a change of one volt at every junction. (With non- linear coils this device cannot be used.) Two cases may be distinguished:
(1) If the square nets of impedances throughout the network are identical, then each junction that does not lie on the boundary, has identical current-pattern. Similarly all horizontal, also all vertical, boundary junctions have identical pattern, as well as all corners. The various patterns for the wave- guide example are given in Fig. 18 (plus current flows into a junction, minus current flows out of a junction).
(2) If the impedances vary from point to point, then for every junction a different current-pattern has to be established.
In analogy to the "unbalanced current patterns" it is possible to set up "unbalanced voltage patterns" by multiplying each iu by its respective Σy.
The Numerical Reduction
It should be noted that every time a junction- voltage is decreased, the junction currents at the neighboring junctions increase, but at the junction itself it decreases. And the decrease is always greater than the increase (—4.23 amp. as against 1.25 amp.).
Hence the general procedure is to decrease (or increase) the unbalanced currents at those junctions where the unbalance is the greatest. Two columns should be established at every junction:
(1) One column showing the change in the absolute potential assumed.
(2) The other showing the new unbalanced currents (or voltages, or both).
There will be many more entries in the current column since the current varies also whenever the potential at a neighboring junction varies.
Fig. 19. Reduction of unbalanced currents to one-half of their value (from 8 percent to 4 percent).
Fig. 19 shows the steps necessary to reduce in the example of Fig. 15 the unbalanced currents from 8 percent to 4 percent. By changing the voltages only at five junctions, the accuracy of the a.c. Network Analyzer results has been increased 100 percent.
Fig. 20. Reduction of unbalanced currents to one-fourth of their value (from 4 percent to 2 percent).
Figure 20 shows the steps necessary to reduce the unbalanved currents from 4 percent to 2 percent. Now 24 changes had to be assumed instead of five to increase the accuracy by another 100 percent. To reduce the unbalanced currents from 2 percent to 1 percent probably the same or greater number of changes would be necessary.
It is emphasized that a practiced person could probably have made the same reduction by less than 24 steps. Also, the network is symmetrical, a fact which was not considered in the reduction.
No hard and fast rules can be established for the reduction. While it is possible to assume at a junction a change of potential that reduces its own unbalanced current immediately to zero, it will not remain so as soon as the potential at a neighboring junction is assumed to vary. Often
it is advantageous to reduce an unbalanced current not only to zero but to a negative value.
Group Relaxation
There is no limit of course to the amount and type of labor-saving devices, that can be introduced. One of them will now be considered.
Instead of assuming a change of voltage at one junction, a change of voltage at several junctions may be assumed simultaneously. This requires settig up "current patterns" for several junctions. An example, for three border junctions is shown in Fig. 21.
FIG. 21. Current pattern for three border junction.
Networks with Complex Impedances
If both resistances and inductances occur in a network, then the unbalanced junction-currents are complex numbers i1+ji2, instead of real numbers i1. Similarly the absolute potentials are complex numbers. Then a separate current pattern has to be established for a unit change in the real and the imaginary components of junction-voltage respectively. The latter must so change that both the real and imaginary parts of unbalanced currents approach zero.
Another and perhaps a better method is to replace the equivalent circuit by a more complex circuit in which only real numbers occur. Such a step is always possible since a set of differential equations containing complex coefficients may always be replaced by a set containing no j by simply doubling the number of equations and the number of dependent variables, that is, by introducing in-phase and out-of-phase components of variables.
The "Diffusion" Method
While the relaxation and the weighted average methods change potentials at one junction at a time, the method of unbalanced currents and voltages changes the potentials at all junctions simultaneously. The first two methods are found to be effective at the beginning of the reduction, especially in the elimination of "bumps" in otherwise smooth curves; afterwards the latter method appears to be faster. When the unbalanced currents are small compared with the circuit currents but still further reduction is desired, all three methods become very slow. The following method offers a further systematization of the third method.
A partial diferential equation, not containing time, usually is considered to represent summation of currents at a junction. An unbalanced current iu has no counterpart in the equation. Let it be assumed that iu corresponds to an additional term of the form A∂φ / ∂t in the equation, adding thereby an additional independent variable t to the equation and an additional dimension to the network, such as shown in Fig. 4, for the wave equation.
From physical consideration of diffusion problems, it appears that if the initial conditions are well selected, the rate of diffusion decreases as time increases, and the currents representing A∂φ / ∂t must become in general smaller. At t = oo they all must become zero, allowing the network to represent the original equation without the time-term.
By experience it has been found that at t=0, half of the unbalanced current should flow up, half down (Fig. 22 representing the one-dimensional wave equation). The coefficient A should be so selected that at first the potentials on the second layer should differ by only a small amount (say one percent or less) from the starting potentials. As time goes on, the value of A may be increased to speed up the rate of diffusion. The values of A should be so selected that the bigger currents between the layers should decrease uniformly along smooth-curves instead of oscillate around them. (Some of the smaller currents will increase.) Of course A may be an arbitrary function not only of time, but also of space, allowing thereby speedier diffusion at certain points.
In actual calculations, especially when the layers are two-dimensional, it is sufficient to have the drawing of one layer only and write the subsequent values of potentials in colums, as in the relaxation method.
PART III. CHARACTERISTIC-VALUE PROBLEMS
Oscillatory Circuits
In characteristic-value problems not only the mode of vibration (the junction-potential
distribution) is unknown, but also the frequency ω corresponding to that mode. If, however, a potential distribution is assumed, the corresponding ω may be found by the following property of the networks, a consequence of Rayleigh's Principle.
"When the network potentials correspond to a characteristic function, the algebraic sum of the positive and negative powers in the inductors and capacitors is zero."
That is, the power ΣI2XL = ΣE2YL = ΣEIL in the inductors is equal to the power ΣI2XC in the capacitors. Or the power in the variable units, that are functions of ω, is equal to the power in the constant units. This zero power in the network is utilized in finding characteristic values with the aid of a Network Analyzer. The admittances of the coils that are functions of ω are varied with w until a generator, connected in shunt with any of the coils, draws no current from the line. At such values of admittances, the network is self-supporting and the stored electrical energy oscillates between' the capacitors and the inductors.
Calculttion of Characteristic Values
Hence, for an assumed potential distribution e, the corresponding ω is found by the following steps:
1. Calculate the power ΣI2X in all the coils that are not functions of ω (positive power exists in inductors and negative in capacitors)., This power may also be found by calculating the power flowing in the coils that are functions of ω. If the latter are ground coils, then if e is the junction potential and i the current through the ground coils, power = Σei.
2. If the admittance of each of the remaining coils is the same and is equal to ω2C, then the power in these coils is e2y = Σe2ω2C = ω2CΣe2. Hence
By Rayleigh's principle it is well known that if the assumed mode of vibration (potentials) is
only a rough approximation, the resultant characteristic value calculated is a better than rough approximation.
By knowing the correct ω for an assumed potential distribution, the correct unbalanced currents iu and eu may now be calculated. The latter in turn may be reduced by any of the four methods shown for the solution of boundary- value problems. However, in the present problems a new and more correct ω has to be calculated occasionally as the reduction proceeds.
The Method of Unbalanced Admittances
In the presence of coils that are functions of ω and whose admittances are usually equal, it is not necessary to introduce unbalanced currents. Instead the unbalance is redistributed by attributing different admittances to these variable coils. Hence when the correct ω has been calculated for a given potential distribution, it is assumed that with each variable coil an unbalanced admittance yu is associated. The purpose of the reduction is then to reduce the values of these unbalanced admittances.
Expressed in another way, the purpose of the reduction is to make the admittances of all variable coils the same. The calculated ω only gives a goal to aim at at the beginning. As the reduction proceeds, the common value of the admittances continuously shifts.
The use of the "unbalanced current patterns" facilitates the calculation of the unbalanced admittances at the neighboring points, when the potential at a point is changed.
Linear Harmonic Oscillator
It will be assumed that an approximate value of a characteristic function of the linear harmonic oscillator is known, Fig. 23. (Actually it has been measured on a Network Analyzer, (9) with the aid of the network of Fig. 24.)
The problem is to calculate the corresponding characteristic value. Theoretically that is known to be yE=0.0880. zero generator current at yE=0.0921, a 4 percent discrepancy.
The admittance of the horizontal inductors was Yh=1.1 and those of the vertical inductors yv=O.00704x2 where x varies from 1/2 to 12 1/2 in steps of 1 as given in Table I for half the coils. The measured potentials from ground to junction are given in Table II.
In the Schrödinger equation the admittance of the capacitors is proportional to ω. The energy in the horizontal coils is Σ1.1∆e2 = 2851, in the vertical coils it is fey, Σe2yv = 2890. Hence
This calculated energy level differs from the theoretical value of 0.0880 by only 3 parts in 10,000. It should also be noted that the true (and lowest) energy level 0.0880 is always smaller than the approximate levels 0.0883 or 0.0921, in accordance with Rayleigh's principle, or its quantum mechanical analogue.
Here ψ is the approximate wave function e. Also H∆xψ is the current i in E∆x the admittance yE.
(1) H. W. Emmons, "Numerical methods of solving partial differential equations," Quart. App. Math. (Oct. 1944).
(2) A. Vazsonyi, "Numerical method in the theory of vibrating bodies", J. App. Phys. 15, 598 (1944)
(3) G. Kron, "Equivalent circuits of the elastic field," J. App. Mech. 11, 149-161 (1944).
(4) J.B.Scarborough, "Numerical Mathematical Analysis (Oxford University Press, 1930).
R. E. Doherty and E. Keller, Mathematics of Modern Engineering I (John Wiley & Sons, Inc, New York, 1936), p. 167.
(6) J. H. Bartlett, "The shaping of pole faces of the betatron," Phys. Rev. 63, 185 (1943).
(7) G. Kron, "Equivalent circuits of compressible and incompressible flow fields," scheduled to appear in J. Aer. Sci.
(8) G. K. Carter; "Numerical and network ~.nalyzer solutions of the equivalent circuits for the elastic field;" J. App. Mech. 11,162—167 (1944).
(9) G. K. Carter. and G. Kron, "A.c. network analizer study of the Schrödinger equation," Phys. Rev. 67, 44 (1945).
(10) G. Kron, "Electric circuit models of the Schrödinger equation," Phys. Rev. 67, 39 (1945).
(11) G. Kron, "Equivalent circuit of the field equations of Maxwell," Proc. I. R. E., pp. 289 - 299 (May, 1944).
(12) R. V. Southwell, Relaxation Methods in Engineering Science (Oxford University Press, 1940).
(13) A. F. Prebus, I. Zlotowsky and G. Kron, "The application of network analysis to some electron optical problems," scheduled, to appear in Phys. Rev.
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Copyright © Oct. 03, 2003 by U. Anders, Ph.D.
e-mail Udo Anders : udo39@t-online.de
Last updated : Oct. 03, 2003 - 18:25 CET


It is a dark time at Ralph McQuarrie Middle School. After suffering several Origami Yoda-related humiliations, Harvey manages to get Dwight suspended from school for being a "troublemaker." Origami Yoda pleads with Tommy and Kellen to save Dwight by making a new case file--one that will show how Dwight's presence benefits McQuarrie. With the help of their friends, Tommy and Kellen record cases such as "Origami Yoda and the Pre-eaten Wiener," "Origami Yoda and the Exploding Pizza Bagels," and "Origami Yoda and Wonderland: The Musical." But Harvey and his Darth Paper puppet have a secret plan that could make Dwight's suspension permanent . . .
This is the second case file in the blockbuster bestselling Origami Yoda series, written by Tom Angleberger, author of Star Wars: Return of the Jedi: Beware the Power of the Dark Side, showcasing his proven knack for authentically capturing the intrigues, fads, and dramas of middle school in "a satisfying tale of friendship and just resistance to authority" (Kirkus Reviews, starred review).


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Discover Nations
11 Signs That You Have a Perfect Relationship, Even If You Don't Think So
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It is totally natural that, from time to time, people doubt whether their relationship is what "it should be like." Your family may be different from the family you grew up in and that's also okay.
We at Bright Side have analyzed the signs of unorthodox relationships and found expert opinions on why many couples don't follow the stereotypes and are still happy.
You don't talk a lot.
You can be together in silence for a long time. You don't feel uncomfortable and you don't have to talk all the time. Doctor Roni Beth thinks that the couples that can just be together in silence, doing their own thing, have a very special connection.
My dad always told me that all I needed to do to make friends was to be ok at talking, good at listening, and excellent at keeping my mouth shut. © Pretty*****Chalant / Reddit
Being able to be happy in "awkward" silence is actually truly loving silence. It says everything words cannot. © BigBossLittleFiddle / Reddit
You go on vacations separately.
The number of people who go on vacation without their partners is growing, with around one-third of American adults admitting they go on solo trips. It can even make your relationship stronger: if you truly love your partner, you will miss them. At the same time, you can do whatever you want. For example, you can go and visit museums while your partner is out somewhere climbing mountains.
Last summer I needed a break, and my husband couldn't take the time off with me. I was pretty discouraged but took the time off without him. I spent the morning hiking in the mountains by myself, and took myself out to eat for lunch, and took myself shopping for me, and not my kids. It was probably the most relaxing day off I'd had in a long time. It gave me time to refocus, and take my own sweet time to enjoy the day. I didn't have to wait for kids or keep up with them, and I didn't feel rushed to go fast because of my husband's busy schedule. It was my time. And I think every married couple needs to take a break without the other one, even if it's just one day away, it is a good thing. © Lizzy White / Quora
Your partner doesn't spend time with your family.
If your parents and your partner get along well, that's great. But it's far less pleasant if they don't like each other. This doesn't have to be a source of conflict though. Your partner doesn't have to take part in family dinners with your parents, but he or she can still love you and respect your relatives. You just need to set the ground rules as soon as possible.
Don't try to turn your parents against your partner and use them as a weapon to control him or her. © Matthew Joaquin / Quora
You have different views and interests.
Doctor Mark White thinks that people overemphasize the value of similar hobbies. In his opinion, common interests may just help people ignore their problems and prolong a relationship that is no longer viable. Psychologist Diane Barth thinks that most of us need someone different from us, to make us strong and make our lives richer.
My partner and I don't like the same music, art, books, or hobbies, and we have very different friends but we agree about the core stuff like he understands my ambition, he knows I am not the housewife type — things that matter. @ Anonymous / Quora
If you find someone who agrees with you on EVERYTHING, and is exactly like you, I'd think that would be pretty boring. I want a woman who will bring me to new places, and show me new things, and introduce me to new foods, etc. I don't want a twin of myself. @ Mark Taylor / Quora
You argue often.
Sometimes when you are very angry with each other, you have arguments. Doctor Elizabeth Dorrance says that the people we love the most, get the most of our negative emotions. On the other hand, conflicts are good for relationships, because they indicate that you both need to change something. It is important to be able to end conflicts on a positive note and admit your mistakes.
I have friends that love having intellectual battles between themselves, it's how they connect to each other and express their love. © Iwunderalot / Reddit
No matter how angry you are at one another. You will still go out of your way or they will go out of their way to help. I'll be wicked pissed, but I'll angrily make my wife her favorite dinner even though I don't want to eat. No matter how angry we are at one another (it usually only lasts for a short period of time) we will never sabotage or try to teach the other one a lesson. Many times, it ends up as us both apologizing to one another. Arguing and getting angry is just part of the relationship and unavoidable. It is how you deal with it that sets it apart from a healthy relationship, versus a bad one. © kamikaziboarder / Reddit
When your partner takes criticism from you seriously, without immediately trying to turn it back on you. If the converse is also true, you 2 stand a great chance of going the distance. © SqueakyCleanNoseDown / Reddit
You don't try to please each other at your own expense.
You don't do the things your partner doesn't like doing for them. You do the housework together. Psychologist Atalanta Beaumont is against trying to please your partner a lot. If someone tries to help other people too much, it may be because in childhood, their effort wasn't rewarded or they didn't feel like they were good enough.
If you try to please everyone, you end up sacrificing your own needs sometimes. It's okay to displease people. You can't make everyone happy, and if you could, that'd be worrisome. © Daniel Dye / Quora
You sleep separately.
You sleep separately because one of you snores in their sleep and the other one wakes up to the smallest noise. Psychologist Katherine Schreiber says that more and more couples are sleeping separately nowadays. Scientists at Ohio State University prove that healthy sleep is far more useful for a relationship than sleeping together.
For years, sleeping in the same bed did not work for us. It caused a lot of friction between us. When we started sleeping apart we became a better couple. A good night's rest without the other complaining about snoring or the hugging of covers can do wonders to one's psyche. We laugh more and are relaxed when we quietly say good night and leave to go to our separate rooms. © Ameerah Ahmed / Quora
You don't have kids.
You both accept this fact and it's okay for both of you. Psychologists say that childless couples are often happier than those that have children.
My husband has recently started his own practice, whereas I've gone back to being a full-time student doing a Ph.D. in an area that I love. We tend to break up our work routines by visiting different countries every few months, to give ourselves a break, clear our heads, come back & work in our respective areas again. It is always an amazing experience to visit new places and learn about different cultures. On the weekends, my husband plays as part of a band and they occasionally do shows together. I volunteer at an animal shelter and have started taking French language classes, as it's a language I've always wanted to learn. If we had kids, we would probably not have the freedom or the time to pursue our own interests and passions. © Anonymous / Quora
You spend less time together than you want.
You can't spend a lot of time together, but you don't worry about it: you trust your partner and you are sure about their feelings. Of course, how much time you spend together is important, but according to psychologists, how you spend it is way more important. Doing something together has to make both partners happy.
They learn to anticipate your needs instinctively. Very early on when I was dating my husband, I felt he was distant at a time when we were both quite busy. I never mentioned it to him, but I felt he was distancing himself and I wanted to respect that without conflict. Later he sent me a handful of messages saying he felt he'd been distant and missed me. © Me_Mento_Mori / Reddit
It takes a long time to accept each other.
All of us have our own flaws and it sometimes takes people time to accept them. Psychologists say that accepting people doesn't mean we should agree with what they do. Acceptance is agreeing with reality, without trying to change it. Just imagine how much a relationship with someone would improve if a person feels that they are totally accepted.
It's taken about 7 years with my husband to start to criticize him less, but every so often I still get that initial gut reaction of, "I'm a bad wife." © whodunit_notme / Reddit
My partner grew up slightly poorer than me, but we kept many of the ideas that worked for us. Like how one of us was raised, for example, to get concerned when food was running low, compared to being raised with the thought that we have to eat everything and not let anything go to waste. Then, it's a conversation you have to have with them. It was a sin to let food go bad, rather than keeping a stocked fridge and if something went bad then you just tossed it out. © Postsupernova / Reddit
You express your feelings in different ways.
You can have different ideas about how to express your feelings. For one of you, words are important, for the other one — actions, hugs, and other things are important. A study shows: people who stay in a marriage for a long time treat buying food or cleaning at home as a way to show love and care.
It's important to know the way in which someone best expresses and best receives signs of love/affection. A lot of guys are physical lovers, meaning that they best receive signs of affection through literal physical affection, like a kiss or hug that wasn't asked for. On that same token, they might have a partner whose love language is something like the written word or speech, these kinds of people love to be told, in elegant and profound ways, about the feelings their partners hold. Things like love letters, long talks, and friendly notes make them feel appreciated and show them the true feelings of someone. © Christopher Johnson / Quora
What is the definition of the perfect relationship for you?
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text:
Q: Hasura Auth Clarifications I have 2 things which i would like to confirm before moving forward with the workaround i have in mind.

*

*When using JWT Auth with HS256 algorithm, i have a key which is less than 32 characters in length. I'm getting this error - "Error in $: Invalid JWK: Key size too small; should be at least 32 characters". So is this is an hard requirement ? or is there any trick to change this into a warning instead of an error ?

*Is it possible for us to customise the Hasura Console Authentication from admin secret ? for lets say to SSO or anything ?

A: For the first one, yes it is a hard requirement. you can read more about it in RFC 7518

A key of the same size as the hash output (for instance, 256 bits for
"HS256") or larger MUST be used with this algorithm.  (This
requirement is based on Section 5.3.4 (Security Effect of the HMAC
Key) of NIST SP 800-117 [NIST.800-107], which states that the
effective security strength is the minimum of the security strength of
the key and two times the size of the internal hash value.)


For the uninitiated, on Android you can typically opt-in to enable installing apps from unknown sources, allowing you to download them from other locations and install them in what is called "sideloading." Depending on the source you get apps from, it could be a security concern, but Google and many other OEMs do provide the option on Android. Up until now, the only way to sideload apps on Chromebooks was to flip over into Developer mode (not Developer Channel, that's a different thing), which is a tedious operation with its own drawbacks, and much more complicated for users than it is to sideload apps on Android.
The developer in the Chromium bug tracker was hesitant to provide a specific schedule as the feature has apparently been kicked down the line a few times already as a result of other development priorities. About Chromebooks notes that, based on the historical release schedule, version 74 or 75 would place the new feature as landing sometime between April or June, and that's assuming Google can keep the predicted timetable. The wait could be even longer.
Thanks for being patient while we sort this feature out. I can give some details, but don't want to commit to an exact milestone given that this has been punted a few times already.
We're still working on this, and would like to be able to deliver in the next couple milestones (M-74/M-75 timeframe hopefully). Unfortunately it's been pre-empted a couple of times due to higher priority issues; for instance, you may have seen we've recently launched Android Pie on Pixel Slate and have been starting to roll it out to more devices.
We'll provide more details on this bug when we can, hopefully in the form of landed code reviews as we get further into the development of this.
While it doesn't sound like we'll have the feature any time soon, it's good to know that it's on Google's radar, even if plans change. The loud beeps and warning messages that come with Developer Mode can be quite obnoxious.


My love for the 1980s combined with my career in marketing and advertising fuels an unbridled love for vintage print advertising. If you follow RD80s on Tumblr, you've seen plenty of vibrant and outrageous advertisements. Some of my favorites include discontinued food items, automobiles, toys, and video games.
When it comes to the music industry, there seemed to be no limits on the amount of neon and chrome needed to sell cassettes, Walkmans, or keyboards. Guitar company advertisements also had that over-the-top attitude which permeated throughout the decade. I've found 11 guitar ads were (at the time) totally rad but looking back now seem just totally ridiculous.
This is the ad that prompted this article. I looked at this Kramer ad featuring Eddie Van Halen was trying to imagine how the photo shoot went down. The photographer had this grand plan and elaborate wardrobe to create a true Van Halen concert experience. Eddie shows up late and says "I'm gonna lean against this case, smoke my cigarette, hold up your guitar and your gonna take my picture. That's the deal or I'm outta here, Bozo."
My eyes have no clue where to focus on this Hamer ad featuring Steve Stevens. Do I look at the chrome x-ray images of snakes and human fingers? Do I look at the shrubbery of hair, black jumpsuit, and white platform shoes? And how is he balancing all that rad on that little white stool?
The concept of this Aria Knight Warrior ad is simple, the ultimate depiction of "how rock stars pick up chicks."
This G & L tells of Chet Thompson's problem with leading tremolo systems. I'd say he has nobody but himself to blame for "the problem." He's obviously doing it wrong.
On the opposite page of this Ibanez ad was an ad for their spandex clothing line with new Trapper Keeper design patterns.
I'd never tell this to the "guitar player" depicted in this DOD ad, but he's obviously a poser. No true '80s rocker had arms that big...they were all deflated by needle holes.
Was this Carvin ad for guitar players that had daytime and nighttime gigs? "For my sets at the Holiday Inn, I use my simple guitar. When I tease my hair and rock out at night, I use my candy apple red guitar."
I'm not sure what's more ridiculous, Ibanez effects pedals powered by an old Chevy or the half-cut t-shirt and acid-washed jeans ensemble worn by the guy in the corner.
I see what you did there, Carvin. It looks like she's also missing a few buttons on that shirt.
Charvel/Jackson Guitars presents "Know Your Hair Metal Rockers!" Use this handy numbered poster to properly identify your favorite tight-pantsed guitarist.
The only thing this Laney ad featuring a neon-outfitted Vinnie Vincent is invading is my comfort level.


It's a relative game - global finance, and QE or not - the cycle points higher for the dollar.
Here is an updated chart from a few weeks back of that notion which compares the last time the dollar made a secular low.
Helping things along appears to be a spring low taking shape along a tighter time frame. This is a much different structure than the bear market rally the dollar exhibited after QE2 was enacted. It is actually quite similar, both in structure and momentum - to the March 2009 low in the SPX.
Considering my work with the Aussie points to the inverse of this dynamic, I feel quite confident in my longstanding expectation for the US dollar to continue to strengthen.


text:
338: Staying Humble with Success
In today's episode of The Startup Chat, Steli and Hiten talk about how founders can stay humble once they've made it.
After years of grinding and building your startup, it's common for some founders to become arrogant once they've "made it". Unfortunately, this can cut short all the payoff or success that you've worked so hard to attain.
In this episode, Steli and Hiten share their thoughts staying humble once you've made it, how they react to their own success, tip on how to stay humble and much more.
01:18 Why this is all about personality types.
02:31 Why feeling successful has never been a thing for Steli.
03:23 Why staying humble is important.
03:37 One thing Steli does at events he speaks at.
04:27 Why making fun of yourself is a good thing.
05:11 Why you should remind yourself to stay humble.
05:25 Steli on getting an insane amount of praise in his inbox.
06:29 What to do to help you stay humble.
08:05 What being humble is all about.
For me, I don't think I ever will make it.
What drives me is that there are still problems to solve.
What matters is that I'm doing my best.
Steli: Hey everybody this is Steli Efti.
Hiten: And this is Hiten Shah and I think today, on The Startup Chat, we're gonna talk about something we consider fun, although we have fun doing this so I think it's all fun. That being said, I think this is important in a topic that is kinda fun, and the reason it's fun is because we're talking about people's personalities at the end of the day. So Steli, you started it by saying, let's talk about how to be humble once you've, I guess made it, right?
Steli: Yeah, stay humble as your succeeding, that's the way I phrased it.
Hiten: Ah succeeding, okay so, this is why it's about personalities right. For me, I'm never succeeding, other people might think that, but I don't. For me, I don't think I've ever made it. I don't think I ever will make it. And so that already, makes me feel like crap every day, I'm kidding, I'm really kidding but at the end of the day, if you feel like you've made it, if you feel like you're a success, for my personality type, that would make me retire. And so, I can't do that to myself. I can't feel successful in the way other people might need to, it doesn't drive me. What drives me is the fact that there's still problems to solve, whether it's in my life, in my work, in the world, whatever. And if there's problems, great, but if I think I'm successful that means I've solved all the problems I wanna solve, and then I'm done, I'm good, I'll chill out. So, this is why I'm saying it's personality based because to me, what keeps me humble, if I were to just look at myself and self reflect is the fact that I think there is an infinite amount of self improvement I would like to achieve for myself. There is an infinite amount of problems in the world, in my life, with the people I know, and really it's problems for me, this is what drives me. That I feel like I can have a more than marginal impact on, I can have a tremendous impact on. That's what drives me and that's what keeps me honest with myself, that's what keeps reminding me that I suck. But not in a way that's unproductive or demotivating, in a way where I'm like, crap I can do so much more, I can solve so many more problems, I can help so many more people, I can help myself so much more. And that's what drives me, just to give you a personal anecdote. I am sure it's a little different for you, if not a lot different so I'd love to hear your take and then I'm sure we can get into some deeper stuff.
Steli: Yeah so, everything you said makes perfect sense to me right. And I don't disagree with it, I feel like yeah, feeling successful is something that I'm not sure I ever felt. I might have had moments, very fleeting moments, but I've never felt successful in the sense of it's a destination that I've arrived at, here's where I live my home is now feeling successful. I don't have that. I think, the thing that I really wanted to zero in on, that I think is interesting, I wanted to dissect a little but with you is, maybe it's not even staying humble as you're succeeding. Although that's one part of it, the other part of it is maybe, staying humble as your ego is being targeted or as you're getting public recognition or praise. I posted this recently where, one thing I do before every keynote that I give is I always ask people to raise their hand if they have no fucking idea who I am. And it usually is the majority of the room that raises their hand, even in rooms or conferences or places where I'm … Some people will tell me I'm quite well known and before I get on stage, I have to take selfies with people and people want me to sign a book and people tell me how amazing I am. I'm being showered all day long with how famous I am and I get on stage and I ask this question and they're like, 70% of the room raises their hand and they're like, we don't fucking know who you are. And I always make this joke that, I always thank the audience and look a little defeated and go, this is really important for my ego so thank you for raising your hand. But to me it's a good reminder … A, it's a little bit of a joke to make people. B, if you make fun of yourself that's typically a good intro to make people feel like, all right maybe this dude is all right. But it's also a good reminder for myself of like, yeah nobody fucking knows who you are, nobody cares and that's totally cool. And I've been in some rooms sometimes where I'll also do this with you right, so I'll show a screen with a startup chat I'll be like, talk a little bit about and I'm like, I also have a podcast with Hiten Shah and da, da, da. And then sometimes if it's in a room where I'm like convinced more people should know you than know me I go, who knows this handsome fella, just raise your hand, if you don't know him and then I'll make some fun around that. I posted that, that that's the way I started my keynote and one of the reasons is to stay humble, keep your ego in check, and I really like this quote or this saying of like "You're never as good as people say you are, you're never as bad as people say you are." And I know-
Hiten: Me too.
Steli: I know I get an insane amount of praise every day in my inbox. People send my really nice things daily and if I'm out and about, once in a while, I'll get a lot of praise in person as well, so I'm being quite frequently showered with compliments. I know it's the same thing for you. I know I don't feel a thing when I read these things. I really appreciate that people feel like they learned something, I really try to take time to answer, be helpful and useful. But I don't feel a dopamine rush, I don't feel great about myself. I literally feel pretty numb reading these things, It's like, oh Steli, you're the greatest person ever. Like I feel zero, I just keep reading try to understand what to respond or how to help here and how to move on. And I know that a lot of people, as they are getting more successful or as they get more public recognition and praise, that the targeting of their ego, maybe their defense mechanism is not as good as ours so their egos grow, and that then leads to a lot of I think, negative effects. So I really wanted to just talk about would you and I, I mean maybe we're not even humble but, what we do to try to practice staying humble, I try to be humble, I try to practice it, I don't really think about it too much. But it's just an interesting topic to me of like, some people as they succeed they become this huge head, they're really full of themselves, and many people don't and what's the difference?
Hiten: So I think staying humble, when I hear that it always reminds me of stay humble, stay foolish.
Steli: Foolish, yeah.
Hiten: Yeah from Steve Jobs. And I couldn't agree more, he had another thing that I heard from a friend of mine who worked with him where, he would say what's next. And really emphasize like whatever we're doing today, there's more we can do, there's more we will do, what's the next thing we're gonna do? So I'm sure after the iPhone launch he's like what's next, right? After the iPad launch, what's next? And that drive, that insistence, that ability, that motivation comes from being humble. Being able to be humbled, being able to look at the world in such a way where like yeah, it doesn't matter if I'm the best today or not, what matters is I'm doing my best, what matters is that I can learn from everybody and everything around me. So I think the whole idea of why we in startup land or in the business world, really worry about being humble and all that, it isn't about like, all of a sudden you have money and you buy 10 cars, no it's not about that. Fine, if you're into cars, go buy 10 cars, have fun just don't speed like me. But it's not about that, it's not about even honestly, it's truly not even about people changing when they make money or get successful or anything. Although sometimes it's a shame to see that if your friend changes for the worst in your opinion, when they make money or get successful or whatever because that can happen, it actually just brings out their personality more, to be honest. It's really about this idea of like, if you're humble, then you will be willing to learn. If you stop being humble, or feel like you're a success or whatever, your ability to learn is completely hampered because you think you know it all. So I guess for me, when I think about this, it's really about making sure that I don't have that mentality of being a know it all. I don't shut down myself from learning from others, or learning from my mistakes, or being open to looking at something great someone else did and learning from it, instead of ignoring it, or thinking they're wrong, or having this allergic reaction to it like, oh I didn't come up with it so it must be wrong. Those are the kind of things that I think about when I think about this topic of being humble and what it means to me.
Steli: Yeah, I love that. I think this is one of the topics, that's why we said … That's why we had a funny and funky intro. It's not a resolution, there's not like a 10 step tip program, or template, or strategy. It's just interesting to me, to see how I respond to some of those things, and some friends of mine, certainly you, and to see then other people that seem to respond or react very differently to success or praise or public recognition and I count what's the difference here and why? And I completely agree with you on the, if you're not humble it's very hard to learn and grow right? Because you feel like you are a finished product or you have arrived somewhere, or even if you feel super successful and like you're amazing, that feels like a state of attachment. That's something I assume you would want to hold on to or you wouldn't want anything to change anymore. And then if you can change or if you don't want things to change, now again you're in a troubled place, because the world is changing, you are changing, things will be changing, you can't hold on to anything. So I don't know, for me, I'm not even sure if it comes from this place of like I always wanna keep learning, although that's definitely true. I think for me it just comes from a place of like, I don't know, I think I've eaten too much shit, I've had too much failure and success. I had success very early and then a lot of failure right after, I think that was a very healthy thing for my ego and my mind and spirit. So, it's very hard for me to be full of myself and I'm just like, no matter who it is, we're all full of shit, and we all should be trying to do better every day than we did the last one. And it's like this, success or fame or any of the stuff, all this stuff can be fun but it's fundamentally, it doesn't have substance. I don't know, I don't believe that those words about myself because I know who I am, so it's hard for me to take them seriously or attach to them and feel any way of getting a big head around that, at least that's what I think. Yeah, stay humble, it's an interesting topic, I think we'll gonna wrap that up and we'll just gonna tag this episode as a ramble on humbleness. But I'd love to hear people's opinion on it as well so, we always love to hear from you. I've noticed a little bit of an increase lately and I think we both appreciate it and are excited about it. So please, if you have a question, a story, an anecdote, a tip, a thought to share-
Hiten: Anything.
Steli: Anything, send us an e-mail steli@close.io, hnshah@gmail.com. We always love to listen hear from our listeners, and I think that's it from us for this episode, we'll wrap it up and hear you very soon.
Hiten: See ya.
staying humble


text:
Q: render text with ground truth meta data I'm Working On  Optical Character Recognition.In our work we need automatically generate some rendered word image and we need each characters location(boundary) in rendered word image. this meta data about rendered image is called ground truth.
How can I do that?

A: I found a rendering c api called Pango wich has a function named pango_layout_Iter_get_char_extent() that can be used for that.
https://developer.gnome.org/pango/stable/pango-Layout-Objects.html#pango-layout-iter-get-char-extents


Our ebook Evidence Research and Publication: a guide for environmental health professionals is now available free of charge here.
We have developed the following links below to provide tools and signposts for all EH professionals (including students, academics, practitioners and policy makers) towards improving your research and publication.
We hope these resources are useful and you are not put off by their 'list' nature, unfortunately there are no short cuts in research world! We would also welcome your suggestions towards their improvement.


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Also, ask us about tax credits and rebates on qualifying equipment. You can reach us at 903-981-1300.


Great Bird Island – Enjoy a gentle cruise to this uninhabitable little island designated a national park. These reef bound waters are perfect for children and beginner snorkelers or for simply enjoying a swim in the protected bay.
Lunch Caribbean buffet style onboard and a casual sail back.
Cost: Adults US$95, Children (3-12) US$48.
Copyright © 2019 Wadadli Cats. All Rights Reserved.


Kaifu Zhang, of INSEAD, won the Shankar-Spiegel Dissertation Award for his dissertation proposal titled "Managing User-Generated Content".
This winning proposal was chaired by Miklos Sarvary, Professor of Marketing, Director, The Learning Innovation Centre and Deputy Dean for Executive Development at INSEAD.
Dr. Zhang is currently an assistant professor of marketing at the Cheung Kong Graduate School of Business.


I have what I believe to be a Davies N4. It has been beaten prior to my purchasing. 6-digit serial number beginning 91. Attached are pics. What do you feel this project is worth?
Re: N4 Davies project....whats it worth?
Not sure I understand how to load pics.
Your pics did not link. You need to use photobucket or similar.