3. Thats also a good indication that there is something wrong. how long are your wires.
4. I mean a cable like this. In that way the current return route is better. And your signal will become better. But I think you should use a extender. Like in my previous post.
Ah, my I2C cables are 'only' about 2 meters long, three wires 'casually twisted' together, as shown in "A" of the picture below. I think I might only consider I2C extender when the wires are over 20 meters long.
Now I think I should not have twisted the ground wire and signal wires together. Ah, now I understand what you mean by 'twisting'!
Perhaps I should make the cable shorter and test again.
The cable you referred are 'twisted pair' cables. I always thought they are small guys, not important at all. I never thought I should pay any attention to them. Now I should think again.
Thanks for pointing out my carelessness.
Last edited by tlfong01 on Sat Aug 11, 2018 3:09 pm, edited 1 time in total.
4. And did you twist the clock with a ground and the data with the ground?
4. What do you mean by "twist the clock with a ground and the data with the ground?" This is indeed hard to guess.
I said it was hard to guess what do you mean by twisting, because I have not read about the term 'twisted pair' for more than 10 years. In those days when everybody used Cat 5 cables, I heard the term twisted pair often. But now I used WiFi dongles, and now Rpi3 and RpiZeroW has Wifi. So I forgot Cat 5 altogether.
I remember I still have a couple of used Cat 5 cables. So I will try them later. I have colourful bright yellow and bright orange cables. I think even they are not proved that useful, I will still use them in my project, and display them in my project photos, to show off that I am knowledgeable in telecom things.
Well. Two meter is already a lot. I successfully used with a cable of one meter. And your level shifter is designed for "driving" PCB traces. And not a large cable. So, I think you can forget about the 20 meter with a good reliability.
TI recommends careful PCB layout practices with short PCB trace lengths to avoid excessive capacitive loading and to ensure that proper O.S. triggering takes place. PCB signal trace-lengths should be kept short enough such that the round trip delay of any reflection is less than the one-shot duration. This improves signal integrity by ensuring that any reflection sees a low impedance at the driver. The O.S. circuits have been designed to stay on for approximately 30 ns. The maximum capacitance of the lumped load that can be driven also depends directly on the one-shot duration. With very heavy capacitive loads, the one-shot can time-out before the signal is driven fully to the positive rail. The O.S. duration has been set to best optimize trade-offs between dynamic ICC, load driving capability, and maximum bit-rate considerations. Both PCB trace length and connectors add to the capacitance that the TXS0102 device output sees, so it is recommended that this lumped-load capacitance be considered to avoid O.S. retriggering, bus contention, output signal oscillations, or other adverse system-level affects.
my I2C cables are 'only' about 2 meters long, ... I think I might only consider I2C extender when the wires are over 20 meters long.
But I once read an ElectronicsStackExchange guy saying that he can do I2C 100 meters! Let me goggle what he says.
I work for a company making USB sensors. Most of them are based on I2C sensor chips, those devices can be split in two, so you can install the CPU part in one place and the sensor part in another. We conducted quite a lot of tests on the I2C connection between the device CPU and the I2C sensors. At 100 kHz, with a good error recovery protocol, 25m can be easily reached using basic wires. We were even able to reach 100m once with CAT5 cable. - martinm answered 2014apr12.
I found GpioA not working properly. So I switched to GpioB, and found it more or less OK. I found there is some interference between GpioA and GpioB. So I decided to test only GpioB. I also found me too ambitious to get the DHT22 Start Signal OK. I think I better go slowly.
Now I am doing something not so ambitious: toggle GpioB, use writeByte and writeBlock commands. They more or less work. I need to swap MCP23017 #1 with #2 or #3 to make 100% sure.
Last evening I found intermittant, seemingly interference prolem when writing to GPIOA, so I swapped to GPIOB. Now I am thinking of also swapping between 3 MCP23017s and long/short I2C cables.
For block writing to GPIOA - 4 continuous, no time gap bytes 0xff, 0x00, 0x00, 0xff.
I have listed the minimal, complete, verifiable, no problem, example below. Again, don't bother to read the details now, because the whole program still needs more polishing. Perhaps just skimmed through to get a rough picture.
# Byte mode       = disable automatic Address Pointer incrementing.
# Sequential mode = enable  automatic Address Pointer incrementing.
# Reading GPIOn register read the value on the port.
# Reading OLATn register only reads the latches, NOT the actual value on the port.
# Writing to the GPIOn register actually causes a write ot the latches (OLATn).
# the level in OLATn.
#   "OSError: [Errno 121] Remote I/O error"
End   write block GPIOA .
End   write block GPIOB .
I changed the repeat loop pauseMilliSeconds from 2 to 4, the intermittant transmission error messages disappeared!
I was wrong. The i2c transmission error messages reappeared. I need to modify the test program to make it easier to change the between-write-block-milliseconds.
The test program now becomes very high level and therefore reader and tester friendly.
I attach the complete list of the 350 lines long the MCVNE program. Again, it is not that reader friendly and need more polishing.
Next post I will show some more test results.
# update 2018aug12hkt1208: setting pauseMilliSeconds to 5 seems solving the problem.
End   write block OLATB .
Now the results of the two test functions.
Next post is the real thing - DHT22 Start Signal!
I forgot how the real thing should look like, so I searched my image box of imgur.com.
typical 1mS, max 20mS low, typical 30uS, max 200 uS high.
And the results is as attached.
I expected all 8 pins of GPIOB should have 8 Lows, followed by 2 Highs, then 4 Lows.
However, only GPIOA pin 4 and pin 7 shows the output below. All other pins are either all high or all low.
I guess there is a bug in my MCP23017 hardware wiring. But I did checked it with a blink test. Perhaps I need to do the blink test again.
Well, I think that your mcp only need to drive the singal low, and after that the output can be changed into a input. And the DHT22 will give that short pulse.
But, the problem with you is that you are using a level shifter and he can't drive that length of a cable. The prove is in that when you connect a scope probe to the bus, you signal is dead. And that's normally not a problem.
I think you need to go a couple steps back. Al least in the hardware side. I think you should remove the level shifter. And connect the MCP directly to you pi at a voltage of 3.3V with a short connection. Than you can see if there is a software problem or the level shifter is the problem. Also because the signals at you scope contains a lot of noise.
I already removed the problematic hc04, and the 2 meter long i2c wires from txs40e to hc04, and see how it goes.
I would start here. Than you have less variables. And easier to troubleshoot.
If that's is working like a charm. Than you can go back to the old situation. If that's not working. You know that the software is okay. And the problem is in the hardware.
I agree. So I need to read the level shifter datasheet once more.
1. I would start here. Than you have less variables. And easier to troubleshoot.
If that's is working like a charm. Than you can go back to the old situation. If that's not working.
2.You know that the software is okay. And the problem is in the hardware.
1. I agree it is easy to debug from bare Rpi, adding hardware and software bit by bit. Now I am thinking of keeping the current Rpi hardware and software no change, and start with a fresh new Rpi, and TXS0104, MCP23017 and incrementally retest everything.
2. Well, the software is not OK. I am doing this project with one objective of practising python in general, and MCP23xYY specific. Now I am modifying the functions to make easier to repeat testing, and swapping MCP23017s.
My MCP23017/DHT22 program works more or less, but there are a lot of imporvement I should make. For example, after the frequent I2C transmission error, the program terminates. I need to learn how to use try/except to continue program after error. This try/except thing seems good for my case. I did not use it before because I was too lazy, and also I did not have any program that gets error message and unexpectedly stops so often.
One other reason is that many example programs I found are C++ object oriented. I prefer python and only functional programm style of python for many reasons. It is a bit messy to translate C++ OO code into python functional programming style.
I am just thinking aloud, typing while thinking. My apologies for typos unstructured paragraphs and phrases.
OK. I agree my level shifter has a problem, and I don't know why. I am feeling small. So I asked my friend Google who will for sure makes me great again.
The more I google, the more I agree with you.
Many thanks for your advice and recommendation. So I have ordered 20 pieces of P82B715 (DIP8) from TaoBao, at RMB 8 each. SF Express delivery usually takes less than 2 days.
BTW, I mentioned I read people saying they are do I2C up to 100 meters, I think they all use I2C extenders plus twisted pair cables. I also read other people saying that they can only do I2C for only 6 inches to 20 inches. Some of them say that it depends on IC to IC. So I agree with you that less than 20 inches for no I2C extenders.
Good to hear that you are making progress and do a research about what I'm saying . To be fare, I have used this schematic successfully with a ribbon cable for 1meter. But, this was a communication bus between two microcontrollers (atmel).
The (N)ACK is a important part of the I2C protocol.
BTW, I mentioned I read people saying they can do I2C up to 100 meters, .... I also read other people saying that they can do I2C for only 6 inches to 20 inches. Some of them say that it depends on IC.
... I have used this schematic successfully with a ribbon cable for 1meter. But, this was a communication bus between two microcontrollers (atmel).
Your I2C with ribbon cable should look pretty. You might like to take a look of my work using the same circuit. I used 2N7000 instead of your BSS138, and GKT instead of ribbon.
I think my GKT should be as good as UTP. I did the following test to prove my hypothesis.
4. Use $ i2cdetect -y 1 to detect IOX x 3 (0x21, 0x22, 0x23), and EEPROM, RTC (0x57, 0x68).
5. Use my little python function to ping IOX at sub address 0x22 (write, read, print IODIRA).
7. Then I used long 1 meter gkt cable, inserting at points before A, and at B, and C, to check any bad effects of 2 meters long gkt cables.
8. I found i2cdetect and my ping functions working OK.
9. This proves that 2 meter long i2c gkt cables are ok.
3. HDC1080 humidity and temperature sensor x 4.
I wired up one HDC1080 and i2cdetect -y 1 found its address 0x40 without any problem.
I read again the HDC1080 datasheet, and found their application circuit interesting. I like the manual things like 4 buttons and one LCD/LED display. I think I should also use buttons and display in my project.
Now I am reading the registers and data format.
HDC1080 - Now I am reading the registers and data format.


Welcome to Hyder, Alaska – the Friendliest Ghost Town in Alaska!
We woke up pretty early and hit the road…Most of the pit stops of the day were to take photos of signs pointing to our main destination of the trip: Hyder, Alaska. Yes, yes, you can drive from Seattle to Alaska. Hyder is a small little town on the Canadian/British Columbian border accessibly by road….


Note : The requisition for the post of Ayurvedic Pharmacist, if any received upto 30th April 2012 shall also be included in the present number of post.
i) 10+2 or its equivalent from a recognized University/Board.
ii) Successful training of at least two years duration in Ayurvedic Pharmacist/Compounder or B. Pharma/D.Pharma (Ayurveda) from H.P. Takniki Shiksha Board/University recognized by the state Govt. Desirable : Knowledge of customs, manners and dialects of Himachal Pradesh and suitability for appointment in the peculiar conditions prevailing in the Pradesh.


Behind the Scenes, Exhibits and Experiences, General Posts, News!
So lots of good things have been happening in my little world in the past few months and I wanted to tell you about some of it... First of all, THANK YOU to all of the folks who came to my show "Still Standing" hosted by Pure Wine Cafe and presented by HorseSpirit Arts Gallery in Ellicott City. What a thrill it was to be able to share with you my work and see all of my pieces hung together in one space. If you followed me in the process of creating my solo show, "Still Standing," you know how the last two years have been for me and the struggles I have overcome to make this happen.
This show, for me, was really a dream come true. Looking back at the work created, the opening reception, the love I received, I am overflowing with joy. I am grateful to have so many people in my life that love me and support my work. I never really considered myself a "fine artist," and never thought I would have the need for true self expression. I now have a desire to continue down this path and see what I can do with it. Perhaps I will enter into some juried exhibitions, and maybe approach some galleries in the region. I will also have prints of the works that were on display in my new eCommerce shop! You can also click "Shop" in the menu bar above. And both "Retired" and "Moved on are on display and available for purchase at HorseSpirit Arts Gallery. If you are interested in the other paintings that were in the show please contact me. Thank you to those of you who bought pieces!
I am planning to create some new works, having been inspired by my recent two-week solo trip to New Mexico this past April. I'll be sharing that in a following post. I am in love with the west, and there was so much inspiration for me that I know I'll be back.
Speaking of jewelry, I have been ruminating on the idea of working that into my fine art. I am not really sure how yet, but thought I would put it out there and see what comes back to me in the form of inspiration. I just took a workshop at the Baltimore Jewelry Center with Robert Ebendorf, who happens to live in Santa Fe! More on that to come.
There are a few other things that are happening but I am not ready to share yet. They are big and exciting and scary and thrilling and I can't wait until they're more materialized so that I can tell you all about them!
So please keep in touch and find me on Instagram and Facebook.
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Unofficially, wedding season is here, and brides and their bridal parties typically are preparing to look their best on the big day. From manicures and pedicures to hair coloring, spray tans or even tanning booths (Yikes!), there are many pre-wedding beauty maintenance items and enhancements that need to be done.
Most brides want to flaunt their best, most alluring shape possible for their wedding day, so they may actually adhere to a diet to shed some unwanted pounds. They also may seriously dedicate themselves to toning and working out, such as a gym or through aerobics or yoga.
However, there are certain areas that cannot be enhanced no matter how many reps they do or how many pounds they lose.
So, to truly achieve the appearance and attractiveness that they've always wanted and fill out their wedding dresses (in the right areas!), many women turn to breast augmentation surgery.
What a great time to finally obtain (and flaunt) that attractive figure that you have always wanted – around the time of your wedding with the spotlight on you, surrounded by all your family and friends.
Breast augmentation surgery can help you achieve more attractive proportions that can provide you with a boost in confidence that you deserve and need on your big day.
There are many options available for breast augmentation that your plastic surgeon will discuss with you to help ensure that you attain the breast size, shape, projection, and feel you desire. Some of these include implant type (silicone or saline), implant shape (round vs. teardrop), implant placement* (under the chest wall muscle vs. over the muscle), and incision location (inframammary, periareolar, or transaxillary).
If you are interested in breast augmentation surgery to enhance the size and shape of your breasts, please call (480) 451-3000 or fill out our online contact form today. I am a breast augmentation specialist and ABPS Board Certified in Plastic Surgery.
We look forward to helping you attain the confidence you deserve on your big day.
*For information on the benefits of submuscular placement, read our previous blog, Advantages of Placing Breast Implants Behind the Muscle.


text:
The protocol betweeen Scoot Local Server and Scoot Local Clients.
This includes the protocol buffers, and any other utilities that should be shared by client and server.
There is an official daemon client library provided in Python on Pypi.

__This still needs to be integrated into the build__

### 3rd Party Prerequisites:
Install *protobuf*, (python's) *grpcio* and *docopt*.  See scoot/README for instructions.

### Installing from Scoot Pypi

Prerequisites:
* pip

```sh
pip install scoot
```

## Accessing the Daemon API
### client_lib.py
a library for connecting to the Scoot Daemon and issuing commands to it.

### scoot.py
a command line tool for submitting commands to the Scoot Daemon.

---
## Development Instructions:
### Publishing to Scoot Pypi

Prerequisites:
* Register at __https://pypi.python.org__ and then create ~/.pypirc with:
```
    [server-login]
    username:USER
    password:PASS
```
* Request someone on scoot-team to add you as an owner

###### Publishing
* Bump the version in daemon/protocol/python/setup.py
* Run:
```sh
daemon/protocol/python/deploy.sh
```

#### Compiling for Go (daemon.pb.go)

* Install a protoc with libproto version >= 3.0.0 from https://github.com/google/protobuf
* install protoc-gen-go from https://github.com/golang/protobuf (you need this to be on your $PATH, not your GOPATH)
* In this directory (github.com/scootdev/scoot/daemon/protocol), run:
```sh
protoc -I . daemon.proto --go_out=plugins=grpc:.
```

redpajama_set_name: RedPajamaGithub


Creation of own campuses, association with local actors, subcontracting with local operators: each school or university will seek to widen its international presence while enhancing its own brand image. The University of Wollongong's strategy has reasons to surprise the French observer, used to consider the strict separation between private and public, lucrative sector and nonprofit sector, as the main component of the university's DNA.
Established in 1951 as an institution of the New South Wales University of Technology, and established as an autonomous institution in 1975, the University of Wollongong (UOW) is now a public university of approximately 22,000 students, including 9 faculties with research competencies. Despite this development and its quality, the notoriety of the UOW mainly remains to the University of Wollongong in Dubai (UOWD).
In 1993, the University of Wollongong opened an institution in Dubai, United Arab Emirates. This first foreign academic institution to be recognized by the UAE government officially became a local private higher education institution in 2004 under the name University of Wollongong in Dubai (UOWD).
Today, the 4,000 students' campus is located in Dubai Knowledge Park, a Dubai free zone dedicated to training institutions, while the United Arab Emirates is positioned as a hub for higher education.
UOWD offers undergraduate, postgraduate and doctoral programs. Since all degrees awarded by UOWD are accredited by the Ministry of Higher Education and Research of the Government of the United Arab Emirates, they are also audited by the Australian Tertiary Education Quality and Standards Agency (TEQSA). UOWD is an Independent university, but still an « entity » of UOW, offering a recognized quality of training.
But UOW did not stop there at this international uccess : it has also deployed the concept in various ways, mainly in Asia.
While UOWD was created by the UOW itself, UOW has also bet to partner with other types of players to increase its international presence. Taking advantage of the development of a private higher education industry, UOW offers four programs at INTI (International University & Colleges) campuses in Kuala Lumpur, Penang and Subang Jaya. UOW keeps these programs in total control but operates wholly or partly offshore, as products offered by a commercial company.
International development is therefore based on a very different model from that the one used in Dubai: based on an industrial operator, the UOW offers programs abroad, but does not include this specific actor in its own organizational chart.
With the association with the Community College of City Universality (CCCU), it is yet another model that is being implemented In 2015. The establishment created in 2004 by the City University of Hong Kong offers associate degree programs, ie short (generally 2 years) undergraduate degrees.
Since 2015, CCCU and UOW have created a formal alliance to emerge as a self-financing, not-for-profit niche-based institution and to promote an educational model that combines academic excellence with societal commitment. Like UOWD, CCCU is considered an entity of UOW.
Thus, what is most surprising in UOW's international development is the diversity of strategies implemented to ensure the presence of the Australian university in important geographic areas. Some will see opportunism, others agility. Anyway the question is: how can the best of each institution be expressed in places and circumstances where opportunities emerge? UOW is an example of the awareness of the complexity of higher education today, as well as the multiplicity of possible and / or relevant social and economic models.


text:
Michael Jackson Wanted Bad To Outsell Thriller
MJ was determined 'even though it was an impossible task,' Spike Lee tells MTV News ahead of his 'Bad 25' documentary.
Rob Markman 08/20/2012
There was no one who could compete with the King of Pop, so Michael Jackson looked to best himself. That's one of the things that Spike Lee learned about his friend MJ when putting together "Bad 25," a documentary centered on the making of Jackson's top-selling 1987 LP.
"I learned that, number one, he was very self-motivated," Spike recently told MTV News. "Even though it was an impossible task, Michael wanted Bad to outsell Thriller. And everywhere he'd go, he'd put up signs, write on mirrors in bathrooms: '100 million.' "
No doubt, Thriller was the crowning jewel in Jackson's awe-inspiring catalog, recognized as the best-selling album of all time. After Jackson's death in 2009, his album sales shot through the roof, with the RIAA estimating that Thriller had moved 29 million additional copies, not counting international sales. Since its 1982 release, it's estimated that Thriller has sold more than 110 million copies across the globe. Not that Bad was a slouch on the charts: The Thriller follow-up lands at #5 on the all-time list, believed to have sold at least 30 million copies worldwide.
"He always wanted to surpass what he had done previously and 100 million albums sold," Lee said. "He was determined to do that."
August 31 will mark the 25-year anniversary of Mike's Bad, and to celebrate, Epic Records will release Bad 25, a repackaged version of the album, on September 18. The collection will include Lee's documentary, unreleased demo songs, remixes, concert footage and, of course, the original LP.
What's your favorite song from Michael Jackson's Bad album? Sound off in the comments!

redpajama_set_name: RedPajamaCommonCrawl


text:
// Licensed to the Apache Software Foundation (ASF) under one
// or more contributor license agreements.  See the NOTICE file
// distributed with this work for additional information
// regarding copyright ownership.  The ASF licenses this file
// to you under the Apache License, Version 2.0 (the
// "License"); you may not use this file except in compliance
// with the License.  You may obtain a copy of the License at
//
//   http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing,
// software distributed under the License is distributed on an
// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.  See the License for the
// specific language governing permissions and limitations
// under the License.
package com.cloud.offering;

import java.util.Date;

import org.apache.cloudstack.acl.InfrastructureEntity;
import org.apache.cloudstack.api.Identity;
import org.apache.cloudstack.api.InternalIdentity;

/**
 * offered.
 */
public interface ServiceOffering extends InfrastructureEntity, InternalIdentity, Identity {
    public static final String consoleProxyDefaultOffUniqueName = "Cloud.com-ConsoleProxy";
    public static final String ssvmDefaultOffUniqueName = "Cloud.com-SecondaryStorage";
    public static final String routerDefaultOffUniqueName = "Cloud.Com-SoftwareRouter";
    public static final String elbVmDefaultOffUniqueName = "Cloud.Com-ElasticLBVm";
    public static final String internalLbVmDefaultOffUniqueName = "Cloud.Com-InternalLBVm";

    public enum StorageType {
        local,
        shared
    }

    String getDisplayText();

    Date getCreated();

    String getTags();

    /**
     * @return user readable description
     */
    String getName();

    /**
     * @return is this a system service offering
     */
    boolean getSystemUse();

    /**
     * @return # of cpu.
     */
    int getCpu();

    /**
     * @return speed in mhz
     */
    int getSpeed();

    /**
     * @return ram size in megabytes
     */
    int getRamSize();

    /**
     * @return Does this service plan offer HA?
     */
    boolean getOfferHA();

    /**
     * @return Does this service plan offer VM to use CPU resources beyond the service offering limits?
     */
    boolean getLimitCpuUse();

    /**
     * @return Does this service plan support Volatile VM that is, discard VM's root disk and create a new one on reboot?
     */
    boolean getVolatileVm();

    /**
     * @return the rate in megabits per sec to which a VM's network interface is throttled to
     */
    Integer getRateMbps();

    /**
     * @return the rate megabits per sec to which a VM's multicast&broadcast traffic is throttled to
     */
    Integer getMulticastRateMbps();

    /**
     * @return whether or not the service offering requires local storage
     */
    boolean getUseLocalStorage();

    Long getDomainId();

    /**
     * @return tag that should be present on the host needed, optional parameter
     */
    String getHostTag();

    boolean getDefaultUse();

    String getSystemVmType();

    String getDeploymentPlanner();
}


Located on South Carolina's beautiful Grand Strand, Pawley's Island is the laid back alternative to the Myrtle Beach vacation. Shopping, dining, or golfing is all within reach. Just south of Myrtle Beach, Pawley's Island is best known for the Hammock Shops, a unique shopping experience of quaint small shops nestled under trees full of Spanish Moss. You can find everything from shoes to local artwork, or you might choose to go golfing on one of the many world-class golf courses in the area.
While Pawley's is quieter and more relaxed than nearby Myrtle Beach, the latter's close proximity provides infinite possibilities for dining and nightlife. Murrell's Inlet, a quaint fishing village, and its bevy of seafood restaurants is just up the road and also has a Salt Marsh Preserve. Simple but delicious hamburgers at the River City cafe or finer dining at one of the hundreds of other restaurants are all within short driving distance. After dinner you might seek out one of the many venues for arts and entertainment. The Carolina Opry is well known for its amazing shows. You can see a live show or dance the night away…or both!
Enjoying the beach is the obvious activity but there is so much more to do than just that. Parasailing is a popular option, as is a visit to the Huntington State Park to explore the local flora and fauna. The park has many programs to entertain and enlighten both the young and old. On the grounds is Atalaya, the home of the artist Anna Hyatt Huntington. Just across the street is Brookgreen Gardens which features many of the sculptures of the artist as well as the lovely manicured gardens.


text:
\section{Introduction}

\section{Introduction}

Among the properties of multivariate polynomials the factorizability and irreducibility are very important (see \cite{Ga} -\cite{Wa}).

The factorizability reduces the study of a polynomial into the study of two or more polynomials of smaller degrees.

While many properties are true only for irreducible polynomials. For example, let $p$ and $q$
be bivariate polynomials of degree $m$ and $n,$ respectively  where $m>n,$ and the polynomial $p$ be irreducible. Then, in view of the Bezout theorem, the polynomial system $p(x,y)=0, q(x,y)=0,$ has atmost $mn$ solutions.

In this paper we consider linear combinations of two trivariate homogeneous polynomials of degree $2$.
We study the following problem: Is there a linear combination which is irreducible, or alternatively, are all linear combinations factorizable? We bring a simple necessary and sufficient condition for the latter property.

We also consider the following problem: How many linear factorizable combinations are required for all linear combinations to be factorizable. We determine the exact number of such linear combinations - $4.$ We bring also counterexample in which case only $3$ linear combinations are factorizable.

Next, we establish the analogs of the mentioned results for bivarite polynomials of degree two.

Let us use the following notation for the space of trivariate homogeneous polynomials:
$$\dot\Pi_n^3=\{p(x,y,z)= \sum_{i+j+k=n}a_{ijk}x^iy^jz^{k}\},$$
and the space of bivariate polynomials:
$$\Pi_n^2=\{p(x,y)= \sum_{i+j\le n}a_{ij}x^iy^j\},$$
with complex coefficients.

We use the following well-known concept of the associate polynomial (see section 10.2, \cite{Wal}) .
Let $p\in \Pi_n^2,$ i.e., $p(x,y)=\sum_{i+j\le n}a_{ij}x^iy^j.$ Then the following trivariate homogeneous polynomial is called associated with $p:$
$$\bar p(x,y,z)= \sum_{i+j+k=n}a_{ij}x^iy^jz^{k}.$$
Evidently we have that
\begin{equation}\label{aaa}\bar p(x,y,z)=z^np\left(\frac{x}{z},\frac{y}{z}\right),\ \hbox{for}\ z\neq 0. \end{equation}
Also we have that $$p(x,y)=\bar p(x,y,1).$$
It is easily seen that a polynomial $p\in\Pi_n^2$ is factorizable if and only if the associated polynomial $\bar p$ is factorizable. Moreover, we have that
$$p=p_1p_2 \Leftrightarrow \bar p=\bar p_1\bar p_2.$$

To simplify notation, we shall use the same letter $\ell$, say, to denote the bivariate polynomial of degree $1$ and the line described by the equation $\ell(x,y)=0,$ or the trivariate homogeneous polynomial of degree $1$ and the line in the projective space described by the equation $\ell(x,y,z)=0.$

The following result follows from the fundamental theorem of algebra (see Theorem 10.8, \cite{Wal}).
\begin{theorem}\label{hom_n} Let $p$ be a bivariate homogeneous polynomial of degree $n:\ p\in\dot\Pi_n^2.$ Then $p$ can be factorized into linear polynomials:
$$p=\prod_{i=1}^n\ell_i,$$
where $\ell_i\in\dot\Pi_1^2.$
\end{theorem}
	\section{The results for homogeneous polynomials}
\begin{theorem} \label{tm:1}
	Let $p(x, y, z)$ and $q(x, y, z)$ be linearly independent second degree homogeneous polynomials. Then the polynomial $r(x, y, z) = \alpha p(x, y, z)$ + $\beta q(x, y, z)$ is a product of polynomials of first degree for all $\alpha$, $\beta$ $\in \mathbb C$ if and only if at least one of the following conditions takes place:
	\begin{description}
		\item[$a)$] $p$ and $q$ have a common factor of first degree:
$$p=\ell \ell_1,\ q=\ell \ell_2,\ \hbox{where}\ \ell,\ell_1,\ell_2\in \dot\Pi_1^3$$
		\item[$b)$] $p(x, y, z) = f(s, t), \ q(x, y, z) = g(s, t),$
		 where $f$ and $g$ are bivariate homogeneous polynomials of degree two: $f,g\in\dot\Pi_2^2$ and $s,t\in\dot\Pi_1^3:$\\
		\begin{equation} \label{st} s = a_1x + b_1y + c_1z,\
		 t = a_2x + b_2y + c_2z.
\end{equation}
	\end{description}
\end{theorem}

	Let us mention that the statement in ``if" direction of Theorem \ref{tm:1} is evident. Indeed, if a) takes place, then
	$$\alpha p+\beta q = \ell(\alpha \ell_{1}+\beta \ell_2).$$

	If b) takes place then $f,g\in\dot\Pi_2^2$ and therefore $r=\alpha p+\beta q=\alpha f+\beta g\in\dot\Pi_2^2$ is a bivariate homogeneous polynomial of second degree of $s$ and $t$. Therefore, in view of Theorem \ref{hom_n}, $r(x, y, z)$ can be factorized in the variables of $s$ and $t$ for all $\alpha, \beta\in\mathbb C.$
Then by using \eqref{st} and passing to the variables $x,y,z,$ we get the desired factorization. \newline
	Now let us prove the necessity of the conditions a) and b). It is enough to prove the following theorem.\\
\begin{theorem} \label{tm:2}
	Let $p(x, y, z)$ and $q(x, y, z)$ be linearly independent homogeneous polynomials of degree two. Suppose there exist four noncollinear vectors $(\alpha_i, \beta_i) \in \mathbb C^2,\ i = 1,\dots, 4,$  such that the polynomials
	$r_i(x, y, z) = \alpha_i p(x, y, z) + \beta_i q(x, y, z)$
	can be factorized.

Then we have that at least one of the conditions a) and b) of Theorem \ref{tm:1} takes place and therefore, for all $\alpha, \beta\in \mathbb C,$ the polynomilal
	$$r(x, y, z) = \alpha p(x, y, z) + \beta q(x, y, z)$$
	is factorizable.\\
\end{theorem}
\begin{proof} The proof consists of two parts.

{\bf Step 1.}
	Let us first consider the case $(\alpha_1, \beta_1)=(1,0)\quad (\alpha_2, \beta_2)=(0,1).$ Then we have that  $(\alpha_3, \beta_3)$ and $(\alpha_4, \beta_4)$ are not collinear and
	\begin{equation} \label{nez}\alpha_3 \beta_3 \alpha_4 \beta_4\neq 0.
\end{equation}
Now let us prove that at least one of the conditions a) and b) of Theorem \ref{tm:1} takes place.

To this end let us assume that the condition a) does not hold, i.e., $p$ and $q$ have no common factor. Then we shall prove that the condition b) holds.

We have that $p$ and $q$ can be factorized:
	\begin{equation}\label{pqell} p(x, y, z) =\ell_1 \ell_2,\quad q(x, y, z) = \ell_3 \ell_4,\end{equation}
where the line $\ell_i$ is given by $A_i x + B_i y + C_iz=0.$

	It suffices to prove that the lines $\ell_1, \ell_2,\ell_3, \ell_4$ are concurrent, i.e., \\ $rank\{\ell_1, \ell_2,\ell_3, \ell_4\} = 2$.
Indeed, in this case, by setting, say $s= A_1 x + B_1 y + C_1z=:\ell_1$ and $t= A_3 x + B_3 y + C_3z=:\ell_3$ we get for $\ell_2$ and $\ell_4:$  $\ A_2 x + B_2 y + C_2z=\alpha_2 t+\beta_2s$ and $\ A_4 x + B_4 y + C_4z=\alpha_4 t+\beta_4s.$
Hence, in view of \eqref{pqell}, we get $p=t(\alpha_2 t+\beta_2s)$ and $q=s(\alpha_4 t+\beta_4s).$ Thus the condition b) of Theorem \ref{tm:1} holds.

	Suppose by way of contradiction  that $rank\{\ell_1, \ell_2,\ell_3, \ell_4\} = 3$. It means that there are 3 lines which are not concurrent. Without loss of generality assume that these lines are $\ell_1, \ell_2,\ell_3.$ Let us set:
	$$ \ell_1 = A_1 x + B_1 y + C_1z =: \bar{x}, $$
	$$ \ell_2 = A_2 x + B_2 y + C_2z =: \bar{y}, $$
	$$ \ell_3 = A_3 x + B_3 y + C_3z =: \bar{z}. $$
Then we have that
$$ x = A_1' \bar x +  B_1'\bar y + C_1'\bar z, $$
	\begin{equation}\label{ABC} y = A_2'\bar x + B_2'\bar y + C_2'\bar z, \end{equation}
	$$ z = A_3'\bar x + B_3'\bar y + C_3'\bar z. $$

	We have that $r_3(x, y, z)=\alpha_3\ell_1\ell_2 + \beta_3\ell_3\ell_4$ can be factorized. Therefore, in view of \eqref{ABC}, there are numbers $A_5, B_5, C_5, A_6, B_6, C_6\in \mathbb C,$ depending on  $\alpha_3$ and $\beta_3$ such that
	\begin{equation} \label{eq:1}
		\alpha_3\bar{x}\bar{y} + \beta_3\bar{z}(A_4\bar{x} + B_4\bar{y} + C_4\bar{z}) = (A_5\bar{x} + B_5\bar{y} + C_5\bar{z})(A_6\bar{x} + B_6\bar{y} + C_6\bar{z}).
	\end{equation}

	In the left part of $\eqref{eq:1}$ the coefficients of $\bar{x}^2$ and $\bar{y}^2$ equal to 0, therefore
	$$A_5 A_6 = 0,$$
	$$B_5 B_6 = 0.$$
	Without loss of generality we can discuss only two cases: $A_5 = 0, B_5 = 0$ or $A_5 = 0, B_6 = 0.$

		First consider the case $A_5 = B_5 = 0.$ From \eqref{ABC} we obtain
		\begin{equation*}
		\alpha_3\bar{x}\bar{y} + \beta_3\bar{z}(A_4\bar{x} + B_4\bar{y} + C_4\bar{z}) = C_5\bar{z}(A_6\bar{x} + B_6\bar{y} + C_6\bar{z}).
		\end{equation*}
		Here the coefficient of $\bar{x}\bar{y}$ in the right hand side equals to 0. Therefore $\alpha_3 = 0,$ which contradicts \eqref{nez}.

		Now consider the case $A_5 = B_6 = 0.$ From $\eqref{eq:1}$ we get:
		\begin{equation} \label{eq:2}
			\alpha_{3}\bar{x}\bar{y} + \beta_{3}\bar{z}(A_4\bar{x} + B_4\bar{y} + C_4\bar{z}) = (B_5\bar{y} + C_5\bar{z})(A_6\bar{x} + C_6\bar{z}).
		\end{equation}

First, let us verify that $A_4 \neq 0.$ Assume by way of contradiction that $A_4=0.$ By comparing the coefficients of $\bar x\bar z$ in both sides of \eqref{eq:2} we get $A_6C_5=0.$ If $A_6 = 0,$ then the coefficient of $\bar x\bar y$ in the left hand side of \eqref{eq:2} equals to $0,$ i.e., $\alpha_3 = 0,$ which contradicts \eqref{nez}. If $C_5 = 0$, then the coefficient of $\bar z^2$ in the left hand side of \eqref{eq:2} equals to $0,$ i.e.,  $\beta_3 C_4 = 0.$ In view of \eqref{nez}, $\beta_3\not = 0$, hence $C_4=0.$ But in this case $\bar{y}$ becomes a common factor of $p$ and $q,$ which contradicts our assumption.

Now let us set:
$$\beta_3' = \beta_3 A_4,\quad B_4' = \frac{B_4}{A_4},\quad C_4' = \frac{C_4}{A_4}.$$
Then we get from \eqref{eq:2}:
\begin{equation} \label{eq:3}	\alpha_3\bar{x}\bar{y} + \beta_3'\bar{z}(\bar{x} + B_4'\bar{y} + C_4'\bar{z}) = (B_5\bar{y} + C_5\bar{z})(A_6\bar{x} + C_6\bar{z}).
\end{equation}

				Next, let us verify that $B_4'C_4' = 0.$  Assume by way of contradiction that $B_4'C_4' \not = 0.$ Then by compairing the coefficients in both sides of \eqref{eq:3} we obtain:
				\begin{equation} \label{eq:6}
				      \alpha_3 = A_6B_5,\quad
					\beta_3' = A_6C_5,\quad
					\beta_3' B_4' = B_5C_6,\quad
					\beta_3' C_4' = C_5C_6.
								\end{equation}
				Notice that $A_6C_5\neq 0,$ since, in view of \eqref{nez}, $\beta_3\neq 0,$ and hence $\beta_3'\neq 0.$  Then, notice that $C_6\neq 0.$ Indeed if $C_6=0$ then, in view of \eqref{eq:6}, we obtain that $B_4'=C_4'=0.$ But then $p$ and $q$ have common factor $\bar x,$ which is a contradiction.

Now, from first two equations of \eqref{eq:6} we get that
				$$\frac{B_5}{C_5} = \frac{\alpha_3}{\beta_3'}.$$
				From last two equations of \eqref{eq:6} we get:
				$$\frac{B_5}{C_5} = \frac{B_4'}{C_4'}.$$
				Therefore we have $$\frac{\alpha_3}{\beta_3'} = \frac{B_4'}{C_4'}.$$
				And from this we conclude that
				$$\frac{\alpha_3}{\beta_3} = \frac{A_4B_4}{C_4}.$$
				By the same way, by considering the linear combination $r_4(x,y,z)$ instead of $r_3(x,y,z)$ we will get:
				$$\frac{\alpha_4}{\beta_4} = \frac{A_4B_4}{C_4}.$$
				From the last two equalities we get that $(\alpha_3, \beta_3)$ and $(\alpha_4, \beta_4)$ are collinear, which contradicts the hypothesis.

		Thus we have that $B_4'C_4' = 0.$		Now, if $B_4' = 0,$ then we get from \eqref{eq:3}:
				\begin{equation} \label{eq:4}
				\alpha_3\bar{x}\bar{y} + \beta_3'\bar{z}(\bar{x} + C_4'\bar{z}) = (B_5\bar{y} + C_5\bar{z})(A_6\bar{x} + C_6\bar{z}).
				\end{equation}
				By comparing the coefficient of $\bar{y}\bar{z}$ in the left and right hand sides of  $\eqref{eq:4}$, we get that $B_5 C_6 = 0$. Now if $B_5 = 0,$ then the coefficient of $\bar x\bar y$ in the left hand side of \eqref{eq:4} equals to $0,$ i.e., $\alpha_3 = 0$, which contradicts \eqref{nez}. Then, if $C_6 = 0,$ the coefficient of $\bar z^2$ in the left hand side of \eqref{eq:4} equals to $0,$ i.e., $\beta_3' C_4' = 0.$ Since $\beta_3' \not = 0$, we conclude that $C_4'=0.$ But in this case $\bar{y}$ becomes a common factor of $p$ and $q,$ which is a contradiction.

			Next, if $C_4' = 0,$ we get from \eqref{eq:3}:
				\begin{equation} \label{eq:5}
				\alpha_3\bar{x}\bar{y} + \beta_3'\bar{z}(\bar{x} + B_4'\bar{y}) = (B_5\bar{y} + C_5\bar{z})(A_6\bar{x} + C_6\bar{z}).
				\end{equation}
				By comparing the coefficient of $\bar{z}^2$ in the left and right hand sides of  $\eqref{eq:5}$, we get that $C_5 C_6 = 0$. Now, if $C_5 = 0$, then the coefficient of $\bar x\bar z$ in the left hand side of \eqref{eq:5} equals to $0,$ i.e., $\beta_3' = 0,$ which is a contradiction. If $C_6 = 0$, then the coefficient of $\bar y\bar z$ in the left hand side of \eqref{eq:5} equals to $0,$ i.e., $\beta_3' B_4' = 0$, therefore $B_4' = 0.$ But in this case $\bar{y}$ becomes a common factor of $p$ and $q,$ which is a contradiction.

{\bf Step 2.} Now let us turn to the general case.

Consider the polynomials
\begin{equation} \label{eq:9}
	\begin{aligned}
		\tilde{p} &= \alpha_1 p + \beta_1 q, \\
		\tilde{q} &= \alpha_2 p + \beta_2 q.
	\end{aligned}
	\end{equation}
	We have that $\tilde{p}$ and $\tilde{q}$ are factorizable.
	Since $(\alpha_1, \beta_1)$ and $(\alpha_2, \beta_2)$ are noncollinear we obtain:
	\begin{equation} \label{eq:10}
	\begin{aligned}
		p = \alpha_1'\tilde{p} + \beta_1' \tilde{q},\\
		q = \alpha_2'\tilde{p} + \beta_2' \tilde{q},
	\end{aligned}
	\end{equation}
	where
	\begin{equation} \label{eq:11}
		\begin{pmatrix}
			\alpha_1 & \beta_1 \\
			\alpha_2 & \beta_2
		\end{pmatrix}
		\begin{pmatrix}
			\alpha_1' & \beta_1' \\
			\alpha_2' & \beta_2'
		\end{pmatrix}
		=
		\begin{pmatrix}
			1 & 0 \\
			0 & 1
		\end{pmatrix}.
	\end{equation}
Hence, we get that $(\alpha_1', \beta_1')$ and $(\alpha_2', \beta_2')$ are noncollinear.

	Then we have that the following polynomials
	$$r_3(x, y, z) = \alpha_3 p(x, y, z) + \beta_3 q(x, y, z),$$
	$$r_4(x, y, z) = \alpha_4 p(x, y, z) + \beta_4 q(x, y, z),$$
	can be factorized. By using the relations \eqref{eq:10} we get
	\begin{equation}\label{r3} r_3 = \alpha_3 (\alpha_1' \tilde p + \beta_1' \tilde q) + \beta_3 (\alpha_2' \tilde p + \beta_2' \tilde q) = \tilde{\alpha_3} \tilde p + \tilde{\beta_3} \tilde q,\end{equation}
	$$r_4 = \alpha_4 (\alpha_1' \tilde p + \beta_1' \tilde q) + \beta_4 (\alpha_2' \tilde p + \beta_2' \tilde q) = \tilde{\alpha_4} \tilde p + \tilde{\beta_4} \tilde q,$$
	where
	\begin{equation}  \label{matrix}
		\begin{pmatrix}
			\tilde\alpha_3 & \tilde\beta_3 \\
			\tilde\alpha_4 & \tilde\beta_4
		\end{pmatrix}
		=
		\begin{pmatrix}
		\alpha_3 & \beta_3 \\
		\alpha_4 & \beta_4
		\end{pmatrix}
		\begin{pmatrix}
		\alpha_1' & \beta_1' \\
		\alpha_2' & \beta_2'
		\end{pmatrix}.
	\end{equation}
Since the vectors $({\alpha_3}, {\beta_3})$ and $({\alpha_4}, {\beta_4})$ as well as $(\alpha_1', \beta_1')$ and $(\alpha_2', \beta_2')$ are noncollinear, we get from \eqref{matrix} that the vectors  $(\tilde{\alpha_3}, \tilde{\beta_3}), (\tilde{\alpha_4}, \tilde{\beta_4})$ are noncollinear, too.

Now we are in the following position:

\noindent The polynomials $ \tilde p(x, y, z)$ and $ \tilde q(x, y, z)$ are factorizable themselves and  there exist two non-collinear vectors $(\tilde{\alpha_3}, \tilde{\beta_3}), (\tilde{\alpha_4}, \tilde{\beta_4})$  such that the polynomials
	$$r_3(x, y, z) = \tilde{\alpha_3} \tilde p(x, y, z) + \tilde{\beta_3} \tilde q(x, y, z),$$
	$$r_4(x, y, z) = \tilde{\alpha_4} \tilde p(x, y, z) + \tilde{\beta_4} \tilde q(x, y, z),$$
	 can be factorized.

	To be in the position of Step 1 it remains to show that
	$$\tilde{\alpha_3} \tilde{\beta_3} \tilde{\alpha_4} \tilde{\beta_4} \not = 0.
$$
Suppose by way of contradiction that, for example $\tilde{\alpha_3} = 0$. According to \eqref{r3} we have that
	$$\alpha_3 \alpha_1'+ \beta_3 \alpha_2'= 0.$$
	On the other hand  we have from \eqref{eq:11} that
	$$\alpha_2 \alpha_1'+ \beta_2 \alpha_2'= 0.$$
	Therefore both $(\alpha_2, \beta_2)$ and $(\alpha_3, \beta_3)$ are orthogonal to $(\alpha_1', \alpha_2')$ and hence are collinear, which contradicts to the hypothesis.

Therefore, in view of Step 1, we conclude that either the condition a) or the condition b) is satisfied with the polynomials $\tilde p$ and $\tilde q.$ Now, by taking into account the relation  \eqref{eq:10}, we readily get that at least one of conditions a) and b) of Theorem \ref{tm:1} holds.
\end{proof}

Notice that the following result follows from the Step 1 of above proof:
\begin{theorem} \label{tm:4}
	Let $p= \ell_1 \ell_2, q = \ell_3\ell_4,$ where $\ell_i\in \dot\Pi_1^3,$ are linearly independent polynomials of degree two.  If the polynomial $r(x, y,z) = \alpha p(x, y,z)$ + $\beta q(x, y,z)$ is factorizable for two non-collinear vectors $(\alpha_1, \beta_1)$ and $(\alpha_2, \beta_2),$ with $\alpha_1\beta_1\alpha_2\beta_2\neq 0,$ then the polynomial $r(x,y,z)$ is factorizable for all pairs $(\alpha, \beta)\in \mathbb C^2.$

Moreover, at least one of the following conditions takes place:
	\begin{enumerate}
		\item[$(i)$] $p$ and $q$ have a common factor,
		\item[$(ii)$] The lines $\ell_1, \ell_2 , \ell_3, \ell_4$ are coincident.
	\end{enumerate}
\end{theorem}
\subsection {A counterexample\label{ce}}

Consider the following two polynomials:
$$p(x,y,z)=x(x+z),\quad  q(x,y,z)=y(2x+y+z).$$

Let us show that for the three non-collinear vectors $(1,0); \ (0,1);$ and $(1,1)$ the respective linear combinations are factorizable, while all other linear combinations are irreducible. Indeed, the case of first two linear combinations $(1,0)$ and $(0,1);$ is obvious.
Consider the third one: $(1,1).$ We have that

$$ p(x,y,z)+ q(x,y,z)=x(x+z)+y(2x+y+z)=x^2+xz+2xy+y^2+yz=$$
$$(x+y)^2+z(x+y)=(x+y)(x+y+z).$$

Now let us show that there is a forth linear combination which is not factorizable. Of course this, in view of Theorem \ref{tm:2}, will show that all linear combinations except the first three are irreducible.

Thus let us show that the linear combination corresponding to the vector $(2,1),$ i.e.,
   $$ 2p(x,y,z)+ q(x,y,z)=2x(x+z)+y(2x+y+z)$$
is irreducible. Assume, by way of contradiction that
$$ 2x^2+2xy+2xz+yz+y^2=A(x+B_1y+C_1z) (x+B_2y+C_2z).$$
Since the coefficients of $x^2$ and $z^2$ in the right hand side equal to $2$ and $0,$ respectively, we obtain that $A$=2 and $C_1C_2=0.$ Without loss of generality assume that $C_1=0.$ Thus we have that
$$ 2x^2+2xy+2xz+yz+y^2=2(x+B_1y) (x+B_2y+C_2z).$$
Now, by comparing the coefficients of $xy, xz, yz$ and $y^2,$ we obtain
$$B_1+B_2=1,\quad C_2=1,\quad 2B_1C_2=1,\quad 2B_1B_2=1.$$
Therefore we have from first three equalities: $B_1=B_2=0.5,$ which contradicts to the fourth equality: $2\cdot 0.5\cdot 0.5 =0.5\neq 1.$

\section{The results for bivariate polynomials}

	Now from the obtained results for trivariate homogeneous polynomials we are going to derive the analog results for bivariate polynomials:
\begin{theorem} \label{tm:20}
	Let $p(x, y)$ and $q(x, y)$ be linearly independent polynomials of degree two. Suppose there exist four noncollinear vectors $(\alpha_i, \beta_i) \in \mathbb C^2,\ i = 1,\dots, 4,$  such that the polynomials
	$r_i(x, y) = \alpha_i p(x, y) + \beta_i q(x, y)$
	can be factorized.

Then we have that at least one of the following conditions takes place
\begin{description}
		\item[$a')$] $p$ and $q$ have a common factor of first degree:

$p=\ell \ell_1, q=\ell \ell_2$, where $\ell,\ell_1,\ell_2\in \dot\Pi_1^2$
		\item[$b')$] $p(x, y) = f(s), \ q(x, y) = g(s),$\\
		 where $f$ and $g$ are univariate polynomials of degree two: $f,g\in\dot\Pi_2^1$ and \\
		$s = a_1x + b_1y,\ a_1^2+b_1^2\neq 0$,
		\item [$c')$] $p(x, y) = f(s, t), \ q(x, y) = g(s, t),$\\
		 where $f$ and $g$ are bivariate homogeneous polynomials of degree two: $f,g\in\dot\Pi_2^2$ and $s = a_1x + b_1y + c_1,\
		 t = a_2x + b_2y + c_2.$
\end{description}
Moreover,  the polynomial
	$r(x, y) = \alpha p(x, y) + \beta q(x, y)$
	is factorizable for all $\alpha, \beta\in \mathbb C.$
\end{theorem}
\begin{proof}
	Let  $\bar{p}$, $\bar{q}$ be the homogeneous polynomials associated with $p$ and $q.$ Then we have that
	$$p(x, y) = \bar p(x, y, 1),\quad q(x, y) = \bar q(x, y, 1).$$
We also have that $\bar r(x,y,z) =\alpha \bar p(x,y,z)+\beta\bar q(x,y,z)$ is associated with  $r(x, y) = \alpha p(x, y) + \beta q(x, y).$

Next notice that the hypothesis of Theorem \ref{tm:2} hold with the homogeneous polynomials $\bar{p}$, $\bar{q}.$ Thus we get that for any numbers $\alpha$ and $\beta$  the polynomial $\bar r(x,y,z)$ is factorizable and hence $r(x,y)=\bar r(x,y,1)$ is factorizable. It  remains to prove that at least one of conditions $a'),b'),c')$ holds.

Suppose first that the condition a) of Theorem \ref{tm:1} holds, i.e.,
$$\bar p= (ax+by+cz)(a_1x+b_1y+c_1z),\quad \bar q= (ax+by+cz)(a_2x+b_2y+c_2z).$$
Then we have
$$p(x,y)=\bar p(x,y,1)= (ax+by+c)(a_1x+b_1y+c_1),\quad \bar q= (ax+by+c)(a_2x+b_2y+c_2).$$
Thus condition $a')$ holds.

Now suppose that the condition b) of Theorem \ref{tm:1} holds, i.e.,
\item[b)] $\bar p(x, y, z) = f(\bar s, \bar t), \ \bar q(x, y, z) = g(\bar s, \bar t),$\\
		 where $f$ and $g$ are bivariate homogeneous polynomials: $f,g\in\dot\Pi_2^2$ and \\
		\begin{equation*} \label{st2} \bar s = a_1x + b_1y + c_1z,\
		 \bar t = a_2x + b_2y + c_2z.
\end{equation*}

Thus we get

$p(x, y) =\bar p(x,y,1)= f(s, t), \ q(x, y)=\bar q(x,y,1) = g(s, t),$\\
		 where $f$ and $g$ are bivariate homogeneous polynomials: $f,g\in\dot\Pi_2^2$ and \\
		\begin{equation*} s(x,y) =\bar s(x,y,1)= a_1x + b_1y + c_1,\
		 t(x,y) =\bar t(x,y,1)= a_2x + b_2y + c_2.
\end{equation*}
Thus the condition $b')$ holds if $a_1^2+b_1^2=0$ or $a_2^2+b_2^2=0.$ Otherwise
 the condition $c')$ holds.
\end{proof}
\begin{theorem} \label{tm:40}
	Let $p= \ell_1 \ell_2, q = \ell_3\ell_4,$ where $\ell_i\in \dot\Pi_1^2,$ are linearly independent polynomials of degree two.  If the polynomial $r(x, y) = \alpha p(x, y)$ + $\beta q(x, y)$ is factorizable for two non-collinear vectors $(\alpha_1, \beta_1)$ and $(\alpha_2, \beta_2),$ with $\alpha_1\beta_1\alpha_2\beta_2\neq 0,$ then the polynomial $r(x,y)$ is factorizable for all pairs $(\alpha, \beta)\in\mathbb C^2.$

Moreover, at least one of the following conditions takes place:
	\begin{enumerate}
		\item[$(i')$] $p$ and $q$ have a common factor,
		\item[$(ii')$]The lines $\ell_1, \ell_2 , \ell_3, \ell_4$ are parallel,
\item[$(iii')$]   The lines $\ell_1, \ell_2 , \ell_3, \ell_4$ are coincident.
	\end{enumerate}
\end{theorem}
\begin{proof}
	We get, as in the previous proof, that  the hypothesis of Theorem \ref{tm:4} hold with the homogeneous trivariate polynomials $\bar{p}$, $\bar{q},$ which are associated with $p$ and $q.$ Then, as above we conclude that for any numbers $\alpha$ and $\beta$  the polynomial $r(x,y)$ is factorizable. It  remains to prove that at least one of conditions $(i'),(ii'),(iii')$ holds.

In the proof of Theorem \ref{tm:20} we verified that if $\bar p$ and $\bar q$ have a common factor then the same is true for the polynomials $p$ and $q.$

Thus the condition $(i')$ holds if $(i)$ holds.

Now suppose that the condition $(ii)$ of Theorem \ref{tm:1} holds, i.e.,
the lines $\bar\ell_1, \bar\ell_2 , \bar\ell_3, \bar\ell_4$ are coincident, where $\bar \ell_i$ is the homogeneous associate of $\ell_i.$

Suppose that the line $\ell_i$ is given by $a_ix + b_iy + c_i=0,\ i=1,\ldots,4.$

Suppose also that the four lines are coincident at $(x_0,y_0,z_0).$

If this point is at infinity, i.e., $z_0=0,$ then we have that $x_0^2+y_0^2\neq o$ and
 $a_ix_0 + b_iy_0=0,\ i=1,\ldots,4.$ This means that the vector $(x_0,y_0)$ is a normal vector for all lines $\ell_i,\ i=1,\dots,4.$ Therefore these lines are parallel and the condition $(ii')$ holds.

Next, suppose that the point of coincidence $(x_0,y_0,z_0)$ is a finite one, i.e., $z_0\neq 0.$ Then, in view of \eqref{aaa}, we readily get that the lines $\ell_i,\ i=1,\dots,4,$ are coincident
at $\left(\frac{x_0}{z_0},\frac{y_0}{z_0}\right).$ Therefore the condition $(iii')$ holds.
\end{proof}
\subsection {A counterexample}

At the end let us modify the counterexample from Subsection \ref{ce} for the case of bivariate polynomials.

Consider the following two polynomials:
$$p(x,y,z)=x(x+1),\quad  q(x,y,z)=y(2x+y+1).$$

In the same way as in the homogeneous case we can show that for the three non-collinear vectors $(1,0); \ (0,1);$ and $(1,1)$ the respective linear combinations are factorizable, while the linear combination for $(2,1)$ is irreducible. Thus we conclude, in view of Theorem \ref{tm:20}, that all linear combinations except the first three are irreducible.

redpajama_set_name: RedPajamaArXiv


text:
Q: bean named 'cacheManager' that could not be found I have a cluster of servers (Windows & UNIX). When I'm running a jar file I'm receiving this error on some of the servers at my cluster (regardless of the OS type).
***************************
APPLICATION FAILED TO START
***************************

Description:

Field settingsDao in com.ogydocs.wave.service.ApplicationSettingsLoader required a bean named 'cacheManager' that could not be found.

The injection point has the following annotations:
        - @org.springframework.beans.factory.annotation.Autowired(required=true)

Action:

Consider defining a bean named 'cacheManager' in your configuration.

redpajama_set_name: RedPajamaStackExchange


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Home Something Special Girl, 4, left fighting for her life after being abducted and raped by neighbour
Girl, 4, left fighting for her life after being abducted and raped by neighbour
A four-year-old girl fights for her life after being kidnapped and raped by a neighbor of her grandparents.
The 54-year-old attacker, identified only as Liu, was sentenced to death by a court in Harbin, northeast China on Wednesday, after leaving his victim with serious organ infections and injuries.
He admitted that police snatched the girl from her home before attacking her in a drainage ditch near a construction site, according to a court report.
The girl's family reported her missing on the night of August 29 – telling authorities that Liu had stopped by the house that day for a drink.
The next morning he brought her back bruised and blood on her pants before being arrested later that day.
The little girl also had a fever from a bacterial infection.
She is still in critical condition in an intensive care unit, her father told local media after yesterday's conviction.
"He brought my child back around 6 in the morning," said the girl's grandmother. "I thought to myself: this is bad, he had done something to my child."
Her mother added, "She kept shivering and her eyes were glassy. She was afraid to speak."
At the time of the incident, the girl's father said, "The doctors told me my child was nearly unconscious and had serious infections."
He told state media China News this week that his daughter is "still seriously ill."
"All her organs are infected and damaged. She's also suffering from kidney failure."
Following a trial, Harbin's Intermediate People's Court also deprived Liu – who previously served two sentences for murder and rape – of political rights for life.
It is not yet known whether he intends to appeal the death penalty.
Wang Guijin, a lawyer at Heilongjiang Weihong Law Office, said the case led to changes to the Minors Protection Act, strengthening child protection
"Parents, teachers, community workers and experts can provide more information and knowledge to raise awareness of self-protection in children," he added.
abducted crime fighting girl hospitals lawsuit left Life Murder case neighbour rape raped


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Freshmen and transfer applicants, April is the beginning of the end; it is when your college search process finally comes to a close. We have released freshman regular decision notifications, and fall transfer notifications will be sent by early May. Our Facebook page, Twitter account and Admit It! Blog will be your source for decision news and further explanation of the decisions we made and how we made them. For those admitted freshmen in the Class of 2023 and admitted transfers, congratulations! While we believe the smart choice is to enroll at William & Mary, we know you have to figure that out for yourself. Freshmen admit letters will have more information on admitted student programs throughout April. These programs are designed with admitted students and families in mind. We hope they help you learn more about our campus and the opportunities William & Mary provides.
Prospective students, the spring is a great time to explore campuses and begin the process of narrowing down your list of potential colleges. William & Mary offers information sessions and tours weekdays and select Saturday mornings through April 25. Our summer tour schedule will be posted May 1. We have additional information should you plan on visiting W&M during your high school's spring break. Don't forget to visit a class while you're on campus and to participate in the academic and social events occurring during your visit. Immerse yourself in the life of a W&M student and discover for yourself why there is only one William & Mary.
Current juniors, you can also think about interviewing with a current W&M senior this coming summer. Interview registration begins on May 1 and interviews are provided on a first-come, first-serve basis. So start planning your trip to Williamsburg now. We also encourage you to add yourself to our mailing list so that we can keep in touch as you continue your college search and application process. Whether it's online, by mail, on campus or all of the above, we hope you get to know us in the near future.


What is your favorite part about your job? Great people to work with!
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Before working at Sebago, what was the most unusual or interesting job you've ever had? I was an au pair on the 3rd largest pig farm in Denmark.
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If you had to eat one meal, every day for the rest of your life, what would it be? Pizza – it's incredibly versatile!
Where would you like to go on a dream vacation? South Africa.
What is the best concert you attended? My first concert when I was 16. 5 Bands for 5 bucks!
What are you excited about at Sebago? Learning SO MANY new things!
Tell us something that might surprise us about you. I have a degree in Medieval History.
Favorite place(s) to go in Maine? Biddeford Pool.


Mary Holman has received Pi Beta Phi® Fraternity for Women's prestigious Carolyn Helman Lichtenberg Crest Award in honor of her professional achievements. Mary has consistently demonstrated her trailblazing spirit throughout her 30-year banking career.
The Carolyn Helman Lichtenberg Crest Award is presented annually to distinguished alumnae of Pi Beta Phi who exhibit excellence and outstanding leadership in their career or volunteer service to their communities. The award is named for past Pi Beta Phi President Carolyn Helman Lichtenberg, who was instrumental in forming Pi Beta Phi Foundation during her term from 1985 to 1991. Essential Fraternity initiatives, like leadership development programs and literacy, are supported through the stewardship of the Foundation.
Mary entered the financial services industry in the early 1980s during a time when few women held management or frontline roles. A traditionally male-dominated industry, a woman's prospects for a higher-level position were, and continue to remain, significantly lower. Mary first served as a Consumer Lending Officer quickly rising to the position of Assistant Vice President and then Vice President of Commercial Lending.
She currently serves as Executive Vice President, Director of Private Banking for the National Bank of Arizona. In this role, she is responsible for new client acquisition, strengthening current client acquisitions and developing a team of highly-skilled bankers who deal with high net worth individuals and their families.
In each of her management roles, Mary has encouraged and developed her teams to achieve personal and professional goals. In one position she held, Mary was responsible for the opening of a new banking location and drove loan growth there to $8.5 million in only eight months. In her current role, her team was able to meet their annual sales goal by May, seven months ahead of deadline.
Mary is involved in several groups that contribute to the growth and development of women. She serves as a mentor with the National Bank of Arizona helping to lead and guide women within the organization. She also serves as President of the National Bank of Arizona's Women's Financial Group, which provides women a resource for help with financial planning, business services, networking opportunities and peer-to-peer mentoring.
Mary was recently recognized by American Banker Magazine in its 2017 "Most Powerful Women in Banking" issue. The inclusion honored Mary's commitment to initiatives helping more women advance in the senior ranks.


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Home Broadcasting Media transformation and employee rights
Media transformation and employee rights
Posted By: Ed Herbston: June 27, 2016 In: Broadcasting
Eight employees of Gupta-owned news channel, ANN7, were allegedly escorted from the broadcaster's channel for refusing to listen to ANCYL president, Collen Maine, who was to address them. Three SABC staffers suffered the same fate when they queried a decision to not cover a picket outside the public broadcaster's offices. Now they're taking their case to the Constitutional Court. What's happened to employee rights at the broadcasters?
"The records show that the majority of these cases were handled without following proper procedure as all 14 suspensions and terminations were successfully challenged in court. Numerous disputes were settled out of court at enormous unnecessary cost to the Corporation." Thuli Madonsela, When Governance and Ethics Fail, February 2014
Imagine what would happen if the CEO of Volkswagen South Africa were to call all the workers together on the factory floor in Uitenhage and inform them that, unilaterally, he had decided that from then on every employee on the assembly line would, without training and any extra monetary benefit, have to double up and do an extra task.
I'll tell you what would happen. Unions would once again rampage through industrial areas like Booysen, another dog or two would die a terrible death and flames would continue to be our avatar and our leitmotif.
Fortunately nothing like this happened when, in the late 1990s, one of the Mbeki faction's embedded journalists, Snuki Zikalala, set off on his bi-media folly which, back then, resulted in wasteful expenditure of more than R27 million. Bi-media forced every radio reporter to do TV news stories and vice versa even though they had never worked in the different discipline before and had received no training.
Zikalala, who had been a labour reporter and presumably knew a thing or two about employee rights and labour law, simply imposed this on us as a diktat.
Here's how Jane Duncan, a formidable media freedom warrior, described bi-media at the time: "The point is that stripped of all its techno-babble, bi-media is simply another way of putting profits before people. Management drives journalists to become multi-skilled to increase their productivity and save staff costs: essentially, they are being made to do more with less. Not only do they have to chase deadlines for both media, they also develop 'roving job descriptions', moving between programmes and different parts of the news production chain at the behest of management.
"Small wonder that bi-media has been criticised in other countries for encouraging a 'dumbing down' of news and the de-skilling of journalists. Increasing workloads forces them to cut corners, and lessens the amount of thinking time necessary to take innovative angles on stories. The result? A creeping marginalisation of adventurous and critical (but expensive and time-consuming) investigative reporting."
Despite the fact that there are huge differences in the two mediums, the one dependent on sound and the other on pictures, SABC reporters were simply expected to understand and provide for both channels. As a result, particularly under deadline pressure, the workload became impossible and the tensions unbearable.
It was nightmarish, believe me, as a television news reporter at the time, to be contacted in the middle of a television interview outside court, and to be told that radio news would be crossing to me live in a minute's time in Afrikaans, my second language. It doubled our work load and quadrupled the stress.
'Zero Sum Zikalala'
When Zikalala sent his minions down to Cape Town to inform us of this fait accompli, I pointed out that bi-media had not worked elsewhere in world and I repeatedly asked what our financial recompense would be given that our work load would radically increase because we were now having to double up as both radio and television news reporters. I was promised that we would be paid extra for bi-media – but, predictably and in contravention of the letter and spirit of our labour legislation, we never received a cent.
From then on the architect of our misery was known as 'Zero-Sum Zikalala'.
Zikalala, known more for spending money than making it, implemented bi-media despite advice to the contrary, and it turned into an extraordinary act of self-immolation for the SABC's news department
According to a letter in the SABC's in-house magazine, Interkom, this exercise in futility and manifestation of our deployed cadre's non-existent broadcasting and business acumen cost the Corporation in excess of R27 million.
It led to a massive exodus of staff and within a few years e.tv, which did not cost South Africans a cent, had more than doubled the audience of the state broadcaster for its flagship 7pm news bulletin.
Predictably, Zikalala then left the SABC with a R2m golden handshake and was re-deployed as an ANC cadre as spokesperson for the Department of Labour. Once ensconced in his new sinecure, Zero-Sum regularly castigated management in the private sector for their alleged mistreatment of workers!
Violation of constitutional right
I was reminded of this, in the context of employee rights, when I read about the deliberate and unnecessary public humiliation of Foeta Krige, executive producer of the Afrikaans SABC radio station RSG and news actuality programmes like Monitor and Spektrum. Krige, who had had a 26-year career at the SABC, was indefinitely suspended, escorted off the state broadcaster's Auckland Park premises, forced to surrender his employee card and, in a clear violation of his constitutional right of freedom of association, informed that he was not allowed to have any contact whatsoever with any of his SABC colleagues. The latest Hlaudi Motsoeneng /Jimi Matthews purge has been condemned by Sanef, the SACP and R2K
Krige has an impeccable 35-year journalistic CV, starting as a crime reporter on Die Transvaler in 1981 and subsequently working for Die Suidwester in Windhoek, as an accredited parliamentary correspondent for Perskor and ending his newspaper career as news editor for Vaderland before joining the SABC in 1990.
Despicable treatment
So what grievous breach of his employee contract led to Krige's despicable treatment?
On 20 June, the day R2K organised pickets outside the SABC buildings in Johannesburg, Cape Town, Durban and Port Elizabeth in protest against the Hlaudi Motsoeneng/Jimi Matthews ban on any television coverage of service delivery protest violence, all SABC news staff were informed that there was to be no mention of the picket on any of the state broadcaster's channels.
Krige, economics editor Thandeka Gqubule and senior journalist Suna Venter had the temerity to question this in terms of the SABC's code of editorial conduct which, inter alia, states:
We shall report, contextualise, and present news honestly by striving to disclose all essential facts and by not suppressing relevant, available facts, or distorting by wrong or improper emphasis.
We shall evaluate information solely on merit, and shall not allow advertising, commercial, political or personal considerations to influence our editorial decisions.
We shall seek balance through the presentation as far as possible of relevant viewpoints on matters of importance.
We shall prevail on news merit and judgement in reaching editorial decisions.
We shall be free from obligation to any interest group and shall be committed to the public's right to know the truth.
We shall foster open dialogue with our viewers and listeners, as we are accountable to the public for our reports.
Publicly humiliated
I personally witnessed, over a period of years, the shameful way in which staff were treated when Jeffrey Twala, a confidante of ANC politicians like Ngconde Balfour and Mcebisi Skwatsha, effectively destroyed what had previously been the happiest and most successful radio and television news team in the country, the SABC's Sea Point news office.
I asked for early retirement from the SABC's Cape Town news office in 2005 even though that left me unemployed because of the appallingly abusive way in which staff in that news office were being treated. I was also concerned about the pervasive corruption and wasteful expenditure which saw the SABC bankrupted a few years later and the hourly way in which the corporation routinely flouted its own code of conduct relating to ethical news gathering and dissemination. This involved using us, for years on end, as political pawns to attack and undermine the Democratic Alliance while covering up the pervasive ANC corruption in the province.
Two major reports were submitted to the SABC about these abuses, the first in 2002 and the second in 2006, both by Bemawu, the Broadcasting, Electronic, Media and Allied Workers Union, the biggest specialised union in this field. At the time that I asked for early retirement from the SABC I had been the Bemawu newsroom shop steward in Sea Point for almost a decade and I had witnessed the most unspeakable abuse of my colleagues – completely ignored by management – one of whom came close to suicide on Chapman's Peak as a result.
No relief
The 2002 report was submitted to the then chief executive, Peter Matlare when Jimi Matthews was head of television news and Pippa Green was head of the radio news division. They cannot have been unaware of these abuses but did nothing. The 2002 Bemawu report brought no relief to staff. In fact the abuses escalated leading to a substantial exodus of some of our most talented newsroom personnel.
The second in 2006 was submitted to the late Zwelakhe Sisulu and advocate Gilbert Marcus. They had been invited by the then CEO, Dali Mpofu, to set up a commission of inquiry into what became known as the Snuki Zikalala blacklisting scandal.
Serious concern
Several former Sea Point staff members submitted statements as part of this 2006 Bemawu presentation. One of them, a woman who chooses to remain anonymous, received, in response, a letter dated 14 September, 2006 from Eric Mabuza the attorney collating input for the commission:
1 – I have been asked by Mr Sisulu and Mr Marcus ("the Commissioners") to respond to your confidential submission.
2 – The Commissioners have noted the circumstances under which you departed from the SABC and the allegations particularly directed against Mr Twala and others. The Commission notes with concern the serious matters raised by you but draws attention to their terms of reference which, in essence, requires an investigation into the alleged existence of a system or practice of excluding certain analysts or commentators for unjustifiable reasons. Although the terms of reference cover other related issues, this is the core concern of the Commission. The matters raised by you are essentially issues of employment law for which there are remedies under the Labour Relations Act and related legislation.
3 – Although the Commission's terms of reference do not cover the matters raised by you, the Commissioners are of the view that your submission should be placed before the new CEO of the SABC, Advocate Mpofu. This will, of course, only be permissible with your consent and I await your response in this regard.
Yours faithfully
Eric Mabuza
Permission was given but Mpofu did not respond and the abuses continued unabated.
In a definitive essay on how the ANC suborned the SABC and brought about the situation which saw the deliberate public denigration and debasement of employees of integrity like Foeta Krige, Politicsweb's James Myburgh wrote:
"Looking back over the SABC over the past 10 years what is most noticeable is the jarring contradiction between the legislative and constitutional requirements for the public broadcaster and the lived reality. The former requires inter-alia that public broadcasting be fair and promote a diversity of views, and that it maintain "a high standard of accuracy, fairness and impartiality in news and programmes that deal with matters of public interest." These have proved to be (to borrow the words of James Madison) mere 'parchment barriers' against the encroaching spirit of ANC power.
"Although the ANC leadership conceded these fine words and phrases to their opponents in the negotiations, they were able to get their hands on two crucial levers of control – the ability to appoint (and promote) their preferred candidates, and remove those who displeased them."
Outright purge
Removing those who displease them has become an obsession with the mandarins who control the broadcasters. They have done so either by outright purge or by making the working environment of those that displease them so unpleasant that they leave voluntarily. In many of the dismissals, the CCMA found for the employee and a settlement was reached. This simply replicated earlier purges by Snuki Zikalala at the SABC in Johannesburg, Hlaudi Motsoeneng at the SABC in Bloemfontein and Johannesburg and Jeffrey Twala at the SABC in Cape Town – ANC acolytes, one and all.
Hubristically ignored
When ANC acolytes "transform" a media institution, more often than not at the cost of the citizen, the concept of fair treatment of employees as labour law demands is hubristically ignored.
Here is a precise legal definition of what I am talking about and you can find it in a treatise aptly titled, When Governance and Ethics Fail:
"(e) Regarding Mr Motsoeneng's alleged purging of senior staff members of the SABC resulting in unnecessary financial losses in CCMA, court and other settlements, which amounts to financial mismanagement, I find that: 1) The allegation that Mr Motsoeneng purged senior staff members leading to the avoidable loss of millions of Rand towards salaries in respect of unnecessary and settlements for irregular terminations of contracts is justified in the circumstances. SABC human resources records of the circumstances of termination and Mr Motsoeneng's own account show that he was involved in most of these terminations of abuse of power and systemic governance failure involving irregular termination of employment of several senior employees of the SABC and that the SABC lost millions of Rand due to procedural and substantive injustices confirmed in findings of the CCMA and the courts. Some of these matters were settled out of court with the SABC still paying enormous amounts in settlements."
The deliberately degrading treatment of Foeta Krige was also experienced by ANN7 reporter Asanda Magaqa so it came as no surprise, as I finished this article, to read that eight more employees had been escorted off the company premises for publicly disagreeing with Collen Maine – AKA 'Oros' who is, according to newspaper reports, highly regarded by the Gupta family.
Last year Cosatu named ANN7 as the worst employer in the country.
Image: R2K's Asha Moodley picketing outside SABC offices in KwaZulu-Natal PIC by: Nushera Soodyal
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Home>News>Daihatsu Unveils New Mini Passenger Vehicle Mira Cocoa
NEWAug. 17, 2009
Daihatsu Unveils New Mini Passenger Vehicle Mira Cocoa
DAIHATSU MOTOR CO., LTD. (Daihatsu) announced on August 17 the launch in Japan of a new mini passenger vehicle, the Mira Cocoa1.
Mira Cocoa is a mini passenger vehicle that targets women who pursue a fun and laidback lifestyle by selecting products that suit their particular tastes. The vehicle is intended to perfectly meet their needs and to be a trusted partner thanks to a design that makes it fun to drive around and its ease of handling.
The new Mira Cocoa offers the following features:
(1) An easy-to-love vehicle design that makes it fun to drive around.
A friendly, modern style that is easy to love
A simple and casual interior that makes the vehicle fun to drive around
Rich color variations to subtly express the driver's personality
(2) Improved ease of handling
Equipped with outstanding driver-assistance functions that enhance ease of handling (First vehicle in Japan2 to be equipped with a rearview mirror that is fitted with a back view monitor3 (equipped with an automatic anti-glare function)
A perfect package that combines a roomy cabin space with ease of handling.
(3) Outstanding basic performance
The latest platform and powertrain provide outstanding driving performance and excellent safety and environmental capabilities.
Because the Cocoa meets the Japanese JC08 mode (Cold) test cycle standard for cleaner exhaust emissions, it is eligible for a tax break in Japan under the taxation system to promote environmentally-considerate vehicles (75% tax reduction) and for a subsidy under the subsidy system to promote environmentally-considerate vehicles4.
1. The name "cocoa" was chosen to express the fact that the car offers passengers the comfortable feeling and relaxed atmosphere that one gets from drinking cocoa
2. It is the first in Japan as of August 2009 among automobile manufacturers, according to Daihatsu's research
3. Equipped in the Cocoa plus G (for the Cocoa X the back view comes in a package as a manufacturer's option)
4. In the case of the two-wheel drive vehicles the Cocoa X, the Cocoa Plus X, and the Cocoa Plus G
Monthly sales target for Japan are 3,000 units. Manufacturer's suggested retail prices (excluding consumption tax) are from 1 million yen to 1.364 million yen.
Vehicle Outline
1)Easy-to-love Vehicle Design that Makes it Fun to Drive Around
A simple yet memorable design, based on a "friendly modern" concept centered on the keywords of "atypical", "trouble-free" and "carefree."
Achieves an accessible and friendly look through a basic contour that has a simple horizontal tone line and a clean surface structure, as well clearly curved corners for a sloping-shoulder, trapezoid silhouette.
The shape of the round front headlight that is connected to the turn signal creates a lovable impression, while the curved corners of the six-light design side windows results in a cabin with outstanding visibility.
The roof rail and the fog lamp equipped with a silver ring, along with other features (on the Cocoa Plus), make the vehicle even more fun to drive around
In addition to the basic contour, which has a simple horizontal tone, the instrument panel and door trim also have a rounded-square design, giving the vehicle a unified look that is also friendly and accessible.
Piping around the edges of the seats like that of a well-loved bag creates a subtle, fashionable impression.
The color combination of clean-looking ivory with a powerful-looking black results in a streamlined cabin space.
The use of a high-quality (yellow-beige) suede-toned seat fabric in the Cocoa Plus, which has a deodorizing function and features the Cocoa emblem and piping, along with a fabric tonneau cover, result in an excellent unified combination.
The Cocoa L and Cocoa X convey a feeling of comfort through the use of a (grayish beige) seat fabric that is soft and solid looking, while also employing corner patches at the edge of the seats to create a playful feeling. (The black seat fabric and the leather-wound steering wheel come as a set in the Black Interior Package that is a manufacturer's option on the Cocoa L and Cocoa X.)
Rich variation of colors to subtly express the driver's personality
The Cocoa vehicles come in a total of nine color variations5 (including one new color)-from chic to casual-looking colors-that can be chosen according to each person's fashion sense.
5. Includes two colors that are available as a manufacturer's option
2)Improved Ease of Handling
Equipped with outstanding driver-assistance functions that enhance ease of handling
When the automatic transmission is shifted to reverse the image from the camera equipped in the rear of the vehicle is displayed on the rearview mirror; this is the first vehicle in Japan to be equipped with a rearview mirror fitted with a back view monitor6 (equipped with an automatic anti-glare function), to assist the driver in parking and other operations. (The back view monitor comes in a package as a manufacturer's option for the Cocoa plus G and the Cocoa X.)
Equipped with side mirrors that enhance visibility to the rear-left of the vehicle, which has poor visibility during reversing for parking, etc. It also has an "auto-light" that lights up automatically when the area outside the vehicle is dark. (For the Cocoa plus, these functions are included in the Useful Driving Package that is a manufacturer's option.)
Utilizes the Adjustable Pack (including driver's seat lift function, tilt steering wheel, and an adjustable shoulder belt anchor) that makes it possible to choose the optimal driving position according to one's physique and driving stance.
The instrument panel's upper box that can be rotated to open and shut (for the passenger seat) and a fabric tonneau cover that hides bags in the luggage space from view (standard on the Cocoa Plus) provide a wide variety of storage functions.
Optimal Package that Combines an Open Cabin Space with Ease of Handling
A compact exterior, 1,530 mm7 in height, that makes it easy for a driver to maneuver in a multistory parking garage; along with a spacious, unconstricted cabin space that is 1,930 mm8 long and 1,345 mm wide.
7. The exterior height of the Cocoa L and Cocoa X is 1,530 mm; while that of Cocoa plus is 1,560 mm
8. The cabin of the Cocoa L and Cocoa X is 1,930 mm wide; while that of Cocoa plus is 1,940 mm
Ease of driving is enhanced through the use of rounded glass in the rear of the vehicle to ensure visibility at rear angles, thin front pillars to reduce blind spots, and a hood with a clear horizontal tone.
3)Outstanding Basic Performance
Performance & Environmental consideration
Cocoa meets the Japanese JC08 mode (Cold) test cycle standard for cleaner exhaust emissions, making it eligible for a 75% tax break under the Japanese taxation system to promote environmentally-considerate vehicles
The Cocoa X, Cocoa Plus X and Cocoa G all achieve emissions levels that are 75% lower than the 2005 Exhaust Emissions Standards set by the Japanese Ministry of Land, Infrastructure, Transport and Tourism, and that are 25% lower than the Japanese 2010 fuel efficiency standards, which makes the vehicles eligible for a tax break under the taxation system to promote environmentally-considerate vehicles (75% tax reduction) and for a subsidy under the subsidy system to promote environmentally-considerate vehicles.
Equipped with a KF-VE twin-cam Dynamic Variable Valve Timing (DVVT) three-cylinder engine with a long-stroke and compact combustion chamber to provide ample torque (even at low and medium speeds) and outstanding fuel efficiency, the Cocoa boasts emissions levels for all grades that are 75% lower than the 2005 Exhaust Emissions Standards adopted by the Ministry of Land, Infrastructure and Tourism when they are driven in the cleaner exhaust emissions mode, the Japanese JC08 mode (cold) test cycle.
Superior acceleration performance is achieved through an input-speed reduction type three-shaft gear train system input, while excellent power transmission is achieved by equipping the vehicles with a CVT developed by Daihatsu. Combining the KF-VE engine with the CVT results in the two-wheel drive vehicles surpassing the Japanese 2010 fuel efficiency standards by 25%.
Model Maximum output
[kW(PS)
/rpm] Maximum torque
[N*m
(kg*m)
/rpm] Transmission Grade 10-15 Japanese
test cycle
(km/l)
2WD 4WD
KF-VE 43(58)
/7,200 65(6.6)
/4,000 4AT Cocoa L,
Cocoa Plus L 19.4 18.6
CVT Cocoa X,
Cocoa Plus
X/G 23.5 20.0
indicates vehicles that surpass the Japanese 2010 fuel efficiency standards by 25%
Daihatsu employed Eco-VAS (Eco-Vehicle Assessment System), a comprehensive approach to assessing environmental impact, to efficiently set targets and reduce overall environmental impact throughout the vehicle's lifecycle (from production and use to disposal), thereby improving overall environmental performance.
The total volume of CO2 and other air-polluting substances released throughout the entire lifecycle of the vehicle-not only at the driving stage, but at all stages from production to disposal-has been reduced using the results of Life Cycle Assessment (LCA).
Safety performance
Safety Performance that Meets Next-Generation Safety Standards
The TAF9 collision-safety body achieves a balance between outstanding collision impact absorbance and a rigid and lightweight cabin by employing front-side members with a high-efficiency impact-absorption structure, a collision impact distributing vehicle structure, and high-rigidity steel plates.
9. TAF: Total Advanced Function refers to a vehicle body with advanced collision impact absorbing functions.
The vehicle has easily met collision safety standards for Japan as well as Europe. World-class safety levels have also been achieved for full head-on frontal and side collision tests at 55km/h, frontal offset collision tests at 64km/h, side-on collision tests at 55km/h, and rear-end collision tests at 55km/h. On top of this, considering the varied conditions under which accidents occur, it was demonstrated through vehicle-to-vehicle collision tests (50km/h frontal collision, 50km/h side-on collision) based on Daihatsu's own targets that the Mira Cocoa secures an ample survival space for passengers and achieves superior occupant protection.
The interior is based on the concept of SOFI (Safety-Oriented Friendly Interior).
The driver's seat and the passenger seat are equipped with dual-stage SRS (Supplemental Restraint System) airbags as a standard feature.
3-point ELR (Emergency Locking Retractor) seatbelts equipped with pretensioners and force limiters for the front seats, an impact-absorbing steering wheel that limits impact to the driver's head and body, and a structure that prevents rearward movement of the brake pedal to reduce impact to the driver's legs are also standard features.
The pedestrian injury-lessening body is designed to prevent injuries to the head, the most susceptible area, in the event of an accident with a pedestrian, including impact-reducing structures and force-absorbing spaces in the resin cowl, wiper pivots, and hood hinges.
ABS with EBD (Electronic Brake-force Distribution) and Brake Assist is installed as a standard feature in the Cocoa X and Cocoa Plus X/G, and available as a manufacturer's option on the Cocoa X and Cocoa Plus L.
Worldwide Networks
©1996 Daihatsu Motor Co., Ltd


Written by Rebecca Leeman, Chartered Legal Executive at Spire Solicitors LLP.
Stamp duty land tax is a tax paid by homebuyers when they buy property or land. Previously, first time buyers paid stamp duty on purchases above £125,000. Following the budget, the government announced stamp duty is abolished for all first-time buyers who are purchasing properties up to £300,000 and buyers will pay £5,000 less on purchases between £300,000 and £500,000.
A first-time buyer is someone who has never owned a freehold or leasehold property before and who is purchasing their only or main residence. When determining whether someone is a first-time buyer, residential property anywhere in the world is counted. Where there are joint purchasers, all purchasers would need to be first-time buyers otherwise the stamp duty tax will remain at the levels before the announcement.
As first time buyers are often more cash constrained than other buyers, it is hoped this will contribute to resolving the housing crisis and will help over a million first time buyers get onto the housing ladder. Depending on the location within the UK, it is predicted the average first time buyer will pay no stamp duty and the stamp duty bill of the average first time buyer in London will nearly halve.
On Wednesday 22nd November 2017, the government also announced they would provide a £44bn capital investment to boost the housing market. By the mid-2020s there should be 300,000 homes being built every year which is the highest level since the 1970s. The hope is this will make houses more affordable but due to the current demand, it is unlikely prices will be significantly affected. Local councils will also be able to charge council tax on empty properties in an attempt to discourage empty homes.


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