Integer Solutions to $a^2b^2c^2 D^2e^2f^2$, Where $a, B, C, D, E, F Neq 0$

There is a method to find the different primitive representations of an integer $n$ as the sum of three squares, see here. This gives solutions to the above equation. For example, we have $150$ different representations of $n225a^2b^2c^2$, and $96$ primitive ones among them. So we can choose each pair of these solutions to obtain

$$

a^2b^2c^2nd^2e^2f^2.

$$

How does one approach something like this? Is there an equivalent Legendre's three-square theorem for the sum of three squares in two different ways?

It seems like the only way to approach it would be via some computer power.

HOT PRODUCTS
ไม่มีข้อมูล
GET IN TOUCH WITH US
บทความที่แนะนำ
Standing desks vs sitting: why sitting ISNT slowly killing you
Standing desks vs sitting: why sitting ISNT slowly killing you
Youre *sitting* at your desk working away, deep in flow, when you notice out of the corner of your eye someone staring at you.Ignoring it at first, you continue to type away at your computer, but as the feeling of staring daggers grows stronger, it gets harder and harder to resist the urge of looking up and seeing who the culprit is.Finally, you glance away from your screen and lock eyes with Susan in accounting who is standing upright with perfect posture at her brand spanking new standing desk. With complete confusion, you raise your eyebrows and mouth what an appropriate response for someone who has felt like a zoo animal for the past fifteen minutes.She stares at you a little longer, sadly shakes her head and then continues to work.With growing insecurity you take a moment to ponder whats going on then it hits you. Youre sitting. After a quick WebMD search you realize that at any moment you could drop dead in your office at the young age of 32 that night you spend a grand on a standing desk.Oh, you havent heard? Sitting is the new smokingRaise your hand if youre tired of hearing the fear-inducing phrase sitting is the new smoking?Or, perhaps, tired of feeling like youre minutes away from a date with the grim reaper because you refuse to drop an entire paycheck on a fancy hydraulic, slip resistant, levitating, hydro-cooled standing desk?Im not entirely sure when simply sitting in a chair became linked to one hundred and one various life-threatening diseases (like Type 2 Diabetes).Since a few studies came out that said it might be detrimental to ones health, standing desks have been flying off the shelves like hotcakes an ironic comparison considering that one too many hotcakes might result in one developing Type 2 Diabetes not simply sitting. In addition to the hotcake argument, a study on the effects of sitting published in the British Journal of Sports Medicine tracked 5,000 folks over the course of thirteen years and found absolutely no correlation between sitting and developing life threatening diseases like diabetes.However, one Google search on the effects of sitting can leave even the most stable minded individuals panicking.While neither of us have the time nor energy to pick apart every single argument out there on the effects of sitting, I am going to bring up an another point standing might have just as many health implications. Why standing may not be the answer either.Perhaps what sparked the standing desk movement was a study done a while back that made an extraordinarily bold claim:Sitting for just three hours a day is responsible for 430,000 deaths across 54 countries.This is where the solution came into the picture the standing desk. It seemed logical and perhaps simple enough the average human drops dead if they sit for more than three hours a day, so they can stand for the other five.However, recent studies have surfaced that say:Standing for just two hours a day can lead to swelling in the lower limbs, increased discomfort and a substantial drop in cognitive function and in turn overall productivity.So risk dropping dead from sitting or risk losing your job from standing whats the answer?But wait, before you make up your mind, there is more. There was another study published that showed prolonged standing could increase chances of heart diseases due to blood pooling in the legs and increasing pressure in the veins a worrisome finding considering more than 630,000 people die from heart disease each year in the United States alone.So, the decision is no longer sit and die or stand and not be productive but rather sit and die or stand and diePerhaps, we should just concentrate on doing good work and living healthier.While Im not a doctor, I suspect all of the buzz around standing desks could potentially be overhyped. At JotForm, we offer most of our 110 employees both standing and normal desks.Moderation is good for business and for our bodies.It isnt black or white, nor should we abandon one of the two and replace the entire office with the other once a new study suggests the opposite. We can balance both sitting & standing and keep things in moderation by focusing on our overall diet, exercise habits and overall lifestyle.In fact, here are a few very simple lifestyle changes I think we should be focusing more of our attention on than fighting tooth and nail over whether or not sitting is going to kill us.Walk for 30-minutes a day if you cut your lunch break in half and walk for just 30-minutes each day, you lower your risk of Type 2 Diabetes, Heart Disease and High Blood Pressure. In addition, you sharpen your focus, strengthen your memory and enhance your overall mood.Drink eight glasses of water a day by simply drinking enough water each day you lower your risk of developing high blood pressure. Water also strengthens your immune system allowing your white blood cells to better fight colds and flus. Cut back on fried foods this goes without saying but eating junk can lead to nasty diseases that have also been associated with sitting heart disease, diabetes and obesity. So, by simply choosing healthier options during your lunch breaks, youre preventing many of the diseases that sitting supposedly causes.Develop a daily workout routine I started my daily workout routine a while back when I was looking to improve my overall health and improve my energy so I could be a better asset to JotForm. After just a few short weeks of working out, I was blown away at the increase I saw in mood, focus and motivation. But, besides helping you from a mental and emotional standpoint, exercising daily can also decrease your chances of developing chronic diseases
How Do I Set Hotkeys for My Favorites?
First, open up your favorites and scroll to whatever you want to hotkey, then hold left or right on the D-pad until a 1 or 2 appears next to the item. After exiting the favorites menu when you press left or right on the D-pad you should switch to whatever equipment you set with that direction.I have also had issues with one sword being unequipped when using the favorites menu. For me this usually happens when it is two of the same one-handed weapon so they show up as one entry in favorites. The icon to show which hand it is in is fairly small and it is hard to tell the difference between when it is L, when it is R, and when it is both. Just tap R1 and L1 when your swords selected in the favorites menu until you can tell the difference easily.I can't seem to set my hotkeys on the PS3. I did it once on accident and can't seem to anymore. I believe you're supposed to press left or right on the D-Pad to set it, but that isn't working for me.I'm getting quite annoyed having to actually go into the favorites to switch from two swords to a bow. Sometimes, when I switch back, I have to go into my inventory to manually equip the other sword as one is left unequipped.How can I get my hotkeys working?·OTHER ANSWER:I can't seem to set my hotkeys on the PS3. I did it once on accident and can't seem to anymore. I believe you're supposed to press left or right on the D-Pad to set it, but that isn't working for me.I'm getting quite annoyed having to actually go into the favorites to switch from two swords to a bow. Sometimes, when I switch back, I have to go into my inventory to manually equip the other sword as one is left unequipped.How can I get my hotkeys working?
Can't Find Libasound_module_pcm_a52.la and .so When Trying to Fix Surround Sound
Short answer: You do need to compile it as described on the page you linked.I had the same issue on Ubuntu 12.04: The package libasound2-plugins was installed according to Ubuntu's software center and some files belonging to it could be located.However, I gotThus, I compiled it as described on the page linked above, copied itand after that it worked:.• Related QuestionsTraveling within Schengen while waiting for EEA residence card?Legally speaking she's not allowed outside of Norway without the Norwegian residence card; in practice, for any airline but Ryanair, easyJet and WIZZ, you need no ID at all if not checking bags.For Ryanair, easyJet or WIZZ, the old Swedish residence permit will be fine in practice if you print the boarding pass at home and don't check any bags------Add a egaugnaL to a polyglotPrints:Try it online!Next answer must not exceed 2922 bytes.The usual Brain-Flak and Somme fixes.. Now the interesting part is how to distinguish Functoid from the other fungeoids:Functoid ends up taking the same path as Befunge-96 but the behaviour is different when it occurs v^ in a string, thus the "v"@ section terminates Befunge-96 whereas Functoid follows the v------ACL multiple default groups?Try running setfacl -Rdm g:www-data:r-x,g:sambashare:r-x /tmp/temp and setfacl -Rm g:www-data:r-x,g:sambashare:r-x /tmp/temp. Option d sets the defaults, for new files and directories, but does not change existing settings as seen that only root:root has access. -R will be handy to go recursively down existing directories making the required changes.------Does a closed question cancel out that day's valid questions?If you had a question closed on a given day, then that day does not count towards the badge, even if there were other questions on that day that qualified as 'well-received'.As Jon Ericson explains:Days with negatively-scored, closed, or deleted questions are not counted as good asking days even if you do ask a positively-scored question that day------Second order non-linear ode - am I on the right path?$$fracd^2 x dt^2 (a x b) fracdxdt 0$$$$x'' (a x b) x' 0$$$$x'' a xx' bx' 0$$$$x'' frac a 2 (x^2)' bx' 0$$Integrate$$x' frac a 2 x^2 bx K$$$$(xfrac ba)' frac a 2 (x^2 frac 2baxfrac b^2a^2) C$$Substitute $zxfrac ba$$$z' frac a 2 z^2 C$$This last equation is separable------In Episode 9 of Steins;Gate, why did Feris's message affect the past?Her message was sent back in time to her father's phone. The message she sent changed the fact that he had gotten on the plane and died. Without her father in the picture, she sparked the existence of the moe culture in the city. But with her father in the equation, she had never sparked the moeization of the city------If $x3$ is positive, then which one of the following must be positive?Here is a valid deduction for A):Let $x -1$. Then $x3$ is positive, but $x-3$ is negative. So $x-3$ needn't be positive if $x 3$ is positive.Here is a valid deduction for B):Let $x 3$. Then $x3$ is positive, but $x-3 0$. So $(x4)(x-3) 0$ So B needn't be positive if $x 3$ is positive.I'm sure you can do the rest------IIS serving static content gives 503 at randomWe finally solved the issue.It was apparently caused by IIS checking for web.config changes in subdirectories.By setting allowSubDirConfig"false" in our applicationhost.config file, the problem stopped.This is somewhat weird though, as we haven't got any more than 1 web.config file, and it's in the root of the project - still if it works, why complain :-D------Concepts about solving systems of differential equations by eliminationYou have:$x C_1 e^t C_2 te^t$Now plug these into the original equations to find y.$fracdydt C_1 e^t C_2 te^t$$y int c_1 e^t c_2 te^t dt (C_1-C_2) e^t C_2 t e^t$If you have initial conditions, you can now solve for them. If not, you are done.------Finding adjoint of operatorHint You need to show that$$int phimathcalLpsi dx int phimathcalL^starpsi dx$$By definition$$int phimathcalL^starpsi dx int psimathcalLphi dx$$Therefore, to show that $mathcal L$ is selfadjoint you need to show that$$int phimathcalLpsi deta int psimathcalLphi deta$$------A Set of Linear Equations Equal to ZeroAre you sure that $vM0$ has infinitely many solutions for $v$?The question asked is more of a matlab question than a math question: you need to find the function that returns the space of all solutions (i.e. the left nullspace of $M$), not just one.Or, you could ask matlab to solve the equation you're really trying to solve:.------Bounds for Khukhro-Makarenko theoremsThe Second, Third, and many others "Khukhro--Makarenko theorems" were provedhere, see alsoarXiv (so, they are rather"Klyachko--Milentyeva theorems").The bound is always the same:$$log_2|G:N|leqslant f^d(w)-1(log_2(|G:H|!)).$$(In your question, there are several misprints in the estimates.)These facts are special cases of The Large-Subgroup Theorem from the paper cited above.------Use Media Keys for Soundcloud, YouTube, etc.. in Firefox?Yes it is possible! For this download Media Keys from addons.mozilla.org.This tool adds a media key event listener to Firefox and makes it possible touse:on every supported music/video site.For some reason the media keys are only working if Firefox is the active window(occured on Windows 10). Also add-on currently does not workwith Firefox 57.------How do I stop Windows 10 from updating my graphics driver?This seems to be hidden in a very strange place.Open up explorer and go to Control PanelAll Control Panel ItemsSystemGo to "advanced system settings" and the hardware tab. There is a the new (to me) Device Installation Settings button that lets you turn it off.This will turn off all hardware updates and such, rather than the GPU------Proof of test of collinearity and coplanaritySince $xyz 0$ at least one of $x, y$ is not zero and : $$xmathbf a ymathbf b zmathbf c 0 Leftrightarrow x(mathbf a - mathbf c) y(mathbf b - mathbf c) 0.$$ Two dependent vectors lie on a single line through the origin. This works the other way around as well.Extend 1. to cover the coplanar case------How To Include Additional Software In preseed.cfg For Ubuntu Server 13.10You haven't pasted the exact error, but one place to start looking is that the packages "juju" and "openstack" do not exist. For juju the package name you want is juju-core.OpenStack isn't one package, it's an entire set of services so that also won't work. I would debug by removing those two entries and then see if the preseed works------Can I save Roggvir?You can try and save him without getting the 1000 Gold Bounty on your head. To do so, you have to transform into Werewolf-Form, then shout so that everybody runs away scared.. If you manage not to be seen when go into Werewolf-Form or turn back to normal, no bounty will be on your head and you saved a life that day. :).------Value of the origin.You'll need to use the right area element for those coordinates: $dSsin theta , dtheta , dphi$, not just $dtheta , dphi$. (Possibly with $phi$ and $theta$ exchanged, depending on which convention you're using.)You can tell that something is wrong with your integral since it wouldn't give the average value $1$ if you put $u(1,phi,theta)1$ into it.------Find a real matrix $B$ such that $B^3 A$How in the world would the product of three real matrices turn out to have non-real entries? Something must have gone wrong. Try rewriting $sqrt3-8-2,$ and see if that makes a difference. It may be that your calculator chose one of the two non-real cube roots of $-8,$ instead, or perhaps you accidentally entered some even root of $-8$.------Telnet won't work on Windows 8.1You need to install additional components into Windows:Settings > Control PanelGo to the Programs category.In Programs and Features, choose "Turn Windows features on or off".A dialog box appears with a list of programs and a check-box next to each one. Scroll down the list to find "Telnet Client" and tick the box.Then click OK to apply the changes------Solving a partial differential equation helpFix $y$ and name $f(x)u(x,y)$. Then $f$ satisfies the ODE:$$f''yf'0$$The general solution for this ODE is$$f(x)abe^-y,x$$where $a$ and $b$ are constants.Therefore the general form for $u(x,y)$ is$$u(x,y)a(y)b(y)e^-y,x$$where $a$ and $b$ are arbitrary functions.------Quotient of the ring of integers of a quadratic field by the ideal generated by a split integer prime.If $alphaneqbeta$, then $x-alpha$ and $x-beta$ are comaximal in $mathbb F_px$ (that is $(x-alpha)(x-beta)(1)$. So Chinese Remainder Theorem implies $fracmathbb F_px(x-alpha)(x-beta)congfracmathbb F_px(x-alpha)timesfracmathbb F_px(x-beta)congmathbb F_ptimesmathbb F_p$.------HPE Gen10 Proliant 17.10 to 18.04 - GUI does not start - AMD Opteron X3216I have solved this issue. Even though the proliant gen10 has a VGA port, it also has two HPE D-Ports.I bought a D-Port to HDMI adapter and plugged it in - success. X was working fine.So for some odd reason, 17.10 picks up the VGA and defaults to it, but 16.04 and 18.04 ignore the VGA completely. Hope this helps someone else.------Combining all combinations of data from three columns in excelUntested, I do not have Excel available (using LibreOffice at home, this won't work in LibreOffice). IF IT WORKS ;-) it should/does:Assumes "ad" is in cell A1 and the rest just beside it.Fill in D1 and down with combined results as long as the 'current' cell isn't an empty cell in each of A, B, and C columns.------How to find the number of roots using Rouche theorem?First, we factor by $z1$ to get $f(z)(z1)(z^9-z^8z^7dots-z^2z9)$. Let $F(z):z^9-z^8z^7dots-z^2z9$ and $G(z)9$. Then for $F$ of modulus strictly smaller than $1$, $|F(z)-G(z)|leqslant 9|z| lt |G(z)|$. thus for each positive $delta$, we can find the number of zeros of $f$ on $B(0,1-delta)$------Attack Signatures books closedSo you should be able to recognize different exploits, or different attacks because those aren't the same. You can use wireshark to capture packets and analyses them. For attacks you should look for countermeasures. But for attack I mean D/DoS, arbitrary code execution etc. and for exploits I mean MS08-067 for example. If yo need anything else ask here------Find the slope at $theta pi/3$the graph of polar equation $r 2 cos theta$ is a circle centered at $(1,0)$ of unit radius. the point $theta pi/3$ corresponds to $P (1/2, sqrt 3/2)$ in cartesian. so the $(0,0), (1,0)$ and $P$ is an equilateral triangle. so the radius makes an angle $2pi/3$ so the tangent makes $pi/6$ with the positive $x$-axis. so the slope of the tangent is $tan(pi/3) sqrt 3/3.$------Show that a function can not be harmonicLet $Kz in mathbb C:|z| le 1$. Suppose that $u$ is harmonic. Then $max u(K) max u( partial K) max cos t : t in 0,2 pi1$and, since $u(0)1$, the function $u$ has a maximum in $K^o$. By the Maximum - principle, $u$ is constant on $K$, but this is a contradiction to $ u(e^itheta)cos(theta)$------On an Apple 12W USB Charger, how are the D and D- lines configured?After taking some measurements, a 2.4A charger from apple applies approximately 2.68VDC to both D and D-. Most usb chargers advertise compatibility/charge capability with a simple resistive voltage divider on the data lines. Just calculate the required divider to provide that voltage from Vbus, I would take your own measurements though... And be aware of potential damage to the consumer------Paste at cursor instead of belowLike husB commented you have to use a characterwise motion.Note that D deletes from the current cursor position to the end of the line and doesn't delete the line itself.You could overwrite what dd does but I would recommend you map your expected behaviour to a new command, d in the following mapping:The command does the following:------Compare 1 column with 3 others and extract values from col1 that do not appear in other colsYou should really add any formulas that are close but here is one answer put it in E2 and copy all the way down as many rows as are in A.Then just filter the table using this new column.If you use an actual range ($B$2:$D$5) it will run faster then using the whole columns like I did above.
Problem on Apparent Height of Postage Stamp Underneath Paperweight
I believe you made a mistake at $tan angle NGI fracINd Rightarrow IN d tan 60$. It should be $angle NGI 30$ and not $angle NGI 60$.If you use $angle NGI 30$, you get $d - 1.5 fracd tan 30tan(arcsinfrac 3sin 302)approx 0.5 d $ and $dapprox 3.1 cm$.• Related QuestionsI have done that before vs I have done thatAll of these are correct. They can replace each other easily, and in the same conversation. If you want to stress that fact that you only did something once then throw 'once' in there."Yes, I have done that once before." or "Yes, I've lived there once before."------Creating a new cipher! closedIssues:So, this scheme has some pretty major weaknesses. I would say it's fatally flawed, and is easily breakable. There might be some really, really specific letter->number mappings that make the simple attacks not work right, but I strongly suspect that even those are easy to break.------Assuming that $gcd(a,b)1$, show that $gcd(ab,a^2b^2)1$ or $2$.Let $p$ be a prime divisor of $d$. If $p mid a$ then as it divides $ab$ we have that it divides $ab-ab$. But this means that $p1$, as $gcd(a,b) 1$Now similarly we can consider the cases $p mid b$ or $p mid 2$------Differential Equation involving Polynomial DiscriminantsI would suggest computing $f(xc) -f(x) 0$ as a Taylor series, so that the first coefficient, linear in $c$ will contain only first derivatives, and vanish. You might want to use the definition of the discriminant in terms of roots, or otherwise, also. Hope it helps------can vs be able to in presentLong hours and unsociable shifts are not able to act on their own in taking their toll on health, relationships and family life.They require a person subject to health, relationships and family life. Therefore the most logical answer is C. A and D are non-relevant or opinionated------Prove that $U-f(U)$ is an open set.Set $$overlineUx|d(x,x_0)leq1.$$Then $overlineU$ is closed in $X$ and hence compact. Since $f$ is continuous, $f(overlineU)$ is again compact, and in particular closed. By assumption we have$$Usetminus f(U)Usetminus f(overlineU),$$and we're done.------Interfacing microSD with LPC1769 BoardCheck - it's a software stack for LPC1343, but is has a nice FAT / SD card library that is abstract enough, you shuld be able to copy and use it quite easily, all you have to do is to rewrite SPI calls------How to properly simplify and trig substitute this integral?If $x 5sintheta$ then $dx 5costheta, dtheta.$ That was neglected.You also replaced $sqrt25 - (5sintheta)^2$ with $5 - 5sintheta.$ That is also not correct. Notice that, for example,$$sqrt5^2 - 3^3 sqrt25-9 sqrt16 4 ne 5-3, text so sqrt5^2-3^2 text differs from 5-3.$$------Product of Divisors of some $n$ proofLet the set of divisors of $n$ be $s(n)x_1,...,x_d(n).$ Then $$s(n)n/x_1,...,n/x_d(n).$$ $$text Thereforequad prod_xin s(n)xprod_xin s(n)n/xn^d(n)/prod_xin s(n)x.$$------Does reply use the same path from which the ping has been sent?The ping echo request and its reply follow the current routes on the hosts and routers they cross. So, it's definitely possible that each follows a different route - depending on what exactly you're trying to achieve, using asymmetric routing may be seen as bad practice by some------Choosing between two programmers: experience vs. passion closedI would say it depends on the rest of the team:if you have a lot of experienced programmers already, then pick the passionateif, on the other hand, you have only one or two experienced programmers plus many students/cheap-labor-with-little-experience-but-that-don't-cost-much, then the experienced one will be more useful------Effective Mass structure outside first band minimumThe term as you describe it is the effective mass of a carrier in that band and at that k-point. A constant effective mass resulting in a parabolic dispersion is just an approximation. If it's a good or good enough approximation depends on what you need to do.------Invertibility of Time-Dependent Fourier TransformI have the 2nd edition, and there the case $m0$ is considered, so the equation reads (Eq. $(10.21)$ on p. 716)$$xn frac12pi w0int_0^2pi Xn, lambda)dlambda$$(which of course assumes $w0neq 0$). This makes sense because $e^jlambda m$ equals $1$ for $m0$.------Let (X, d) be a metric space and let A be a subset of X. Prove that A is closed if and only if Fr(A) $subseteq$ A.Suppose that $Fr(A) subseteq A$ and let $(a_n)$ be a convergent sequence in $A$ with limit $a$. We have to show that $a in A$.Case 1: $a in A$. Then we are done.Case 2: $a notin A$. Then $a in Fr(A)$. Hence $a in A$.------Are there long arithmetic progressions non-coprime with the given number?Well take$$qkdnq(d-1)nkdn(d-1)ndnkdd(kn)$$Note $n notmid kd$,I guess this is the solution you could try replacing those numbers and checking if it adds up(I currently got no time to do so)------How to mount a windows administrative share on linux via SMBI would add a line for that purpose to /etc/fstab file:After saving changes to this file, mount the file system by means of the command mount -a.In this case the option rw allows the directory to be read-write, otherwise it should have the option ro------Polar coordinates in simple integralIt's just a matter of simply checking that we get the desired result:$$intint_D dx,dystackrel?int_0^1int_0^2pir,dtheta,dr2piint_0^1r,drpi$$The reason why we get the correct result was already stated by Cocopuffs in his comment above------Keyboard shortcut to location bar without selecting all textThere is no shortcut for this yet if I know correctly but you can do it by using AutoHotKey script very easily. First download the AHK for Windows and install it then run the following script.Here CtrlM will focus to the address bar without selecting url.------UML Sequence Diagram with PGF and Tikz produces No shape named inst1 is knownI think you're using a somewhat old version from pgf-umlsd.sty which does not support empty diagrams. Version 0.6 should fix this (and does that in my case) and TeX Live 2011 uses 0.5 as far as I could see.You could download it from: google.com/p/pgf-umlsd.------Using Rsync to backup to an external driveIt really depends on whether you're running databases or not. Rsync will grab a snapshot of every file, and ignore any intervening writes. If you want to back up a database, you should look at setting up an ignore filter and running DB dump tools before the rsync.------conitional probability-probability this given this$$Pleft(Dmid Fright)Pleft(Fmid Dright)timesfracPleft(Dright)Pleft(Fright)$$ and:$$Pleft(Fright)Pleft(Fmid Dright)Pleft(Dright)dotsPleft(Fmid Svcright)Pleft(Svcright)$$------How to interpret this output from MegaCli? duplicateYour answer appears to start at page 13 of this SNIA specification "Mirrored array"Secondary-3 "Spanned 0x03 A combination of stripping and concatenations involving Basic VDs of different sizes."RAID Level Qualifier-0 "Mirroring across two extents"------A small doubt on calculationYou get two equations in two unknowns $a,d$; solve them to find $d$. Since we only want to find $d$, we can equate the coefficient of $a$ by multiplying the first equation by $q$, the second by $p$, and subtracting to get a linear equation for $d$------derivative of limited summationHINT You can do termwise differentiation which is valid within the annulus of convergence or if you do not want a sum as an answer you can for example use the factorization $$(1xcdots x^n)(x-1) x^n1-1$$ followed by differentiating the function this gives you------Is this gradient an isomorphism on its range?Summarizing the hints by @5pm, we can state:Since the norm in $H^1(Omega)/mathbbR$ is equivalent to the $L^2$-norm of the gradient, one has that the $nabla$ as defined above is bounded from below. Thus, $nabla$ is injective and, as it is linear, also closed.------Format Date (25 Jul) using Javascript Object ModelIf the format does not vary from what you presented, you could use split, and access the desired elements in array notation.You lose any date properties by doing this, so if the other elements of the date object are important you're probably better off with moment.js------Strange 'My Documents' Folder behavior after aborted upgrade to Windows VistaFrom my understanding, when Windows is looking for a user's folder, it goes under 'Document and Settings' and then looks for the logged in computer user's directory. It seems that your installation of Windows is looking directly at the folder rather than thinking it's under 'Document and Settings'------Appium: Same code is working Sometimes and failing SometimesAgree - wait should be introduce before any action. Best practices will be to use implicit wait Each time it wont happen that element will be ClickableI'll suggest to use "ExpectedConditions.visibility" instead of "ExpectedConditions.elementToBeClickable"This solution will work for each and every scenario irrespective of action------Complex integration - How to calculate this one?Draw a multi-keyhole contour $Gamma$ around each of the zeroes of $f$ so that $Gamma$ circles $D(0,1)$ once. $f'(z)g(z)/f(z)$ is holomorphic inside $Gamma$, so the integral is zero. Then calculate the residue of $f' g/f$ at each of the zeroes of $f$.------Converting polar equation into cartesian equation to obtain derivativesVery broad hint:$$x r costheta Rightarrow fracdxd theta frac partial xpartial r fracdrdtheta frac partial xpartial thetacostheta (2 sintheta) -r sintheta2costheta sintheta - (1-2 costheta) sintheta$$Do the same for $y$.------Help with the proof of Max Noether's Residue Theorem from Fulton's bookThe equality holds because the divisors are defined in terms of the local rings of the curve $C$. Since $F$ is the form defining $C$, its residue is zero in the coordinate ring and the local rings of the curve. Hence,$$textdiv(F'F G'H') textdiv(G'H')$$------Problem with 2nd degree in minor scaleLiteral transposition from major to minor doesn't work very well. You have discovered one of the reasons.You seem to think minor' just means 'natural minor'. There's the Harmonic and Melodic minor scales as well. Those non-flattened 6ths and 7ths are very useful options when attempting functional harmony------Remote Power On and IPMI Poweredge 2950If you're running vSphere 5 then this will probably help. Installing DOMSA using VUM (VMware Update Manager) is by far the easiest, but if you don't have VUM then one of the other methods should work. pdf.------Given sequence of harmonic functions converges uniformly on compact subsetsConsider first the case of a disk $B$ containing $z_0$. Then $u_n textRe(f_n)$ where $f_n$ is analytic on $B$. By Montel's theorem the $f_n$ form a normal family. What can you say about the limit of a subsequence that converges on $B$?------Inequality related to spectral radiusOne has$$r_a(A)leq left(left|sum_fin mathbfF(n,d) mathbfA_f^*mathbfA_fright|^frac12n right),$$for all $nin mathbbN^*$.If $n1$, then$$r_a(A)leq left|displaystylesum_k1^dA_k^* A_k right|^1/2||A||.$$------Fermat's Little Theorem: Proving an integer exists which satisfies the following criteria mod $5$ duplicate$mnotequiv0bmod5$, since otherwise $dequiv0bmod5$, contradicting the given facts. Hence, since $5$ is a prime number, $m$ has an inverse modulo $5$ let $n$ be this inverse. Multiplying $am^3bm^2cmdequiv0bmod5$ by $n^3$, we can easily verify that $n$ satisfies the final congruence.------PHP phantom cron jobDebian's cron, like many other modern variants, read jobs in files under directories called /etc/cron.d, /etc/cron.hourly, etc., in addition to the traditional /etc/crontab. In particular, the job you see comes from /etc/cron.d/php5 which is installed by the php5-common package------Proving that a unit disc is open in $mathbfR^2$.Yes, it is correct. And, since you always have $R_(a,b)subset D$, then$$Dbigcup_(a,b)in Dbigl(a,b)bigrsubsetbigcup_(a,b)in DR_(a,b)subset D$$and therefore $bigcup_(a,b)in DR_(a,b)D$ indeed------Invariant Subspaces of a representationYour own characterization for an invariant subspace is more correct than the one you quoted. Such a projection $P$ only exists if there is another invariant subspace $W'$ which is complementary to $W$ (where $W' ker P$).In characteristic zero for finite groups, such a $W'$ always exists.------Do I need a comma before particularly?This sentence had raised a question in my mind. Vitamin D has what property against metabolic, neoplastic and immune disorders..... I think it is better to be specific and clear. May be this sentence can be better rephrased as "Vitamin D has prophylactic/preventive/therapeuti effect against metabolic......"
42 Books That Will Make You A Better Person (Each Described In 1 Sentence)
42 Books That Will Make You A Better Person (Each Described In 1 Sentence)
If you read a lot, it can be easy for all the books to blur together. Especially as the years pass, it can be difficult to even remember what books youve read are even about.This is where one sentence book summaries come in. Though one should hope to get a lot from every book they read (and if they dont, what exactly was the point of reading it?) at the very least, a reader ought to walk away with at least one clear insight. Sometimes that insight is the thesis of the book itself, sometimes its a minor detail that made an impact.Below, are some one sentence descriptions of some of the best books ever written and a few of my personal favorites. Candide by Voltaire: Il faut cultiver notre jardin. We must tend our own gardenMans Search for Meaning by Viktor E. Frankl: Even in the depths of the Holocaust even in three concentration camps and the loss of his entire family Viktor Frankl finds meaning and purpose. The Autobiography of Malcolm X by Alex Haley and Malcolm X: Man goes into prison as a criminal, comes out as an uncompromising Civil Rights leader, dies a more open hearted and compassionate person.Essays by Montaigne: There is plenty to study and see simply by looking inwards maybe even an alarming amount.Boyd: The Fighter Pilot Who Changed the Art of War by Robert Coram: To Be or To Do?The Power Broker by Robert A. Caro: There are many forms of power and influence, and not all of them are flashy or even visible but it always has the same effect over time: it corrupts and changes you.Meditations by Marcus Aurelius: Even the most powerful man on earth writes notes to himself about how to be a better person oh and he begins those notes with a series of thank yous to people who have helped him.The Power of No by James Altucher: Your life is defined by how good you get at saying no to the things you need to say no to. Totto-Chan: The Little Girl at the Window by Tetsuko Kuroyanagi: The joy and good nature of children is a precious thing no proper education should involve spoiling it.Mistakes Were Made (But Not by Me) by Carol Tavris and Elliot Aronson: Cognitive Dissonance is one of the most powerful and delusionary forces in the world.Civil War Stories by Ambrose Bierce: War is not glamorous or simply tragic, but rather stupid, ironic, inexplicable, confusing, contradictory and horrifying though this will never stop people from loving it. The War of Art by Steven Pressfield: Beware The ResistanceThe Black Swan by Nassim Taleb: The things youre worried about happening are not the things you should be worried about happening.Fragments by Herclitus: You cant step in the same river twice and this is a good metaphor for life.Enders Game by Orson Scott Card: No one is coming to save usits all on you. 48 Laws of Power by Robert Greene: All the collected but never spoken amoral strategies for getting, keeping, wielding and protecting against power.Philosophy As a Way of Life by Pierre Hadot: If you think ancient philosophy was the academic pursuit of arcane knowledge, youre totally missing the point.The Memoirs of Ulysses S Grant by Ulysses S Grant: Just the idea that this man wrote this beautiful and incisive history of life and timesas he was painfully dying of cancer, trying to leave something to define his legacy and support his family after he was gone. Rules for Radicals by Saul Alinsky: Power is not what you have, its what the enemy thinks you have and what it fears you might do with it.The Book of Five Rings by Musashi: Observing and perceiving are very different things and perception (since it has opinion in it) is always weaker than observation.The Prince by Machiavelli: Fate must be wrestled with and thrown down if you want to get what you want out of life. The Great Gatsby by F. Scott Fitzgerald: Young man falls in love with a careless woman he cannot have and becomes rich and powerful trying to get her back while another young man watches in admiration and horror.What Makes Sammy Run? by Budd Schulberg: The chasing of the American Dream by a ruthless hustler whose punishment is getting everything he ever wanted.Fight Club by Chuck Palahniuk: A guy is so unhappy with modern life that he invents an alter ego to destroy that life and himself. Endurance by Ernest Shackleton: Fortitudine vincimus (by endurance we conquer).The Score Takes Care of Itself by Bill Walsh: Handle the little things well and the score will take care of itself.Essentialism by Greg McKeown and The One Thing by Jay Papasan and Gary Keller: Cut out the crap, focus on the truly important thing (or couple things). How Adam Smith Can Change Your Life by Russ Roberts // The Theory of Moral Sentiments by Adam Smith: First that Adam Smith wasnt some ruthless capitalist but and a thoughtful thinker and second, try to judge your own behavior and moral behavior using what he called the indifferent spectatorEleanor Roosevelt I & II by Blanche Wiesen Cook: God, what a tolerant lady of a real awful mother/father and a selfish, hurtful husband but she could focus on the good in people and thats what made her so effective.On the Shortness of Life by Seneca: People only think life is short because they waste so damn much of it focused on things they cant control and fears about things they refuse to question.Blue Ocean Strategy by W. Chan Kim and Rene Mauborgne: Dont compete where everyone else is competingthat is strategic death. The 4-Hour Workweek by Tim Ferriss: Its not about working four hours a week, its about not doing more than four hours of work you dont like or dont actually need to do per week.The Truth by Neil Strauss: If you want to have successful relationships, fix yourself and your childhood issues the rest will follow, quickly and more easily than you think.Titan: The Life of John D. Rockefeller, Sr. by Ron Chernow: Discipline and rational thought is what allows one to take advantage of opportunities and crisesand also prevent wealth from changing ones life. Lincolns Melancholy by Joshua Wolf Shenk: Lincolns wisdom and perspective came from a dark place in his own lifeif we can transform our own suffering the same way, we will be great.Sherman: Soldier, Realist, American by B.H. Liddell Hart: Poise not pose.The Strategy Paradox by Michael Raynor: Successfully executing a strategy requires complete committmentwhich also substantially increases your odds of failure.Shadow Divers by Robert Kurson: If an undertaking was easy, someone else already would have done it. Tiny Beautiful Things by Cheryl Strayed: Be ten times more magnanimous than you think yourself capable of being.A New Pair of Glasses by Chuck C: Rule 62 of Alcoholics Anonymous: Dont take yourself too damn seriously.The Apprenticeship of Duddy Kravitz by Mordecai Richler: If you dont have values, the hustler will lose everything in the end. Blood Meridian by Cormac McCarthy // The Sea Wolf by Jack London: Never forget how dark and disturbed human beings can beit lurks beneath the surface.Like to Read?Ive created a list of 15 books youve never heard of that will alter your worldview and help you excel at your career.Get the secret book list here!This originally appeared on Thought Catalog.
When a rewrite isnt: rebuilding Slack on the desktop
When a rewrite isnt: rebuilding Slack on the desktop
by Mark Christian and Johnny RodgersA new version of Slack is rolling out for our desktop customers, built from the ground up to be faster, more efficient, and easier to work on.Conventional wisdom holds that you should never rewrite your code from scratch, and thats good advice. Time spent rewriting something that already works is time that wont be spent making our customers working lives simpler, more pleasant, and more productive. And running code knows things: hard-won knowledge gained through billions of hours of cumulative usage and tens of thousands of bug fixes.Still, software codebases have life spans. The desktop version of Slack is our oldest client, growing out of a period of rapid development and experimentation during the earliest moments of our company. During this period, we were optimizing for product-market fit and in a constant sprint to keep up with our customers as their use and expectations of the product grew.Today, after more than half a decade of hyper-growth, Slack is used by millions of people with larger companies working with more data than we ever could have imagined when we first started. Somewhat predictably, a few internal cracks were starting to show in the desktop clients foundation. Additionally, the technology landscape had shifted away from the tools we chose in late 2012 (jQuery, Signals, and direct DOM manipulation) and toward a paradigm of composable interfaces and clean application abstractions. Despite our best efforts to keep things snappy, it became clear that some fundamental changes would be required to evolve the desktop app and prepare it for the next wave of product development.The architecture of the existing desktop app had a number of shortcomings:Manual DOM updates. Slacks original UI was built using HTML templates that needed to be manually rebuilt whenever the underlying data changed, making it a pain to keep the data model and user interface in sync. We wanted to adopt React, a popular JavaScript framework that made this sort of thing more automatic and less prone to potential errors.Eager data loading. The data model was complete, meaning that each user session started by downloading everything relevant to the user. While great in theory, in practice this was prohibitively expensive for large workspaces and meant that we had to do a lot of work to keep data models up-to-date over the course of a users session.Multiple processes for multiple workspaces. When signed into multiple workspaces, each of those workspaces was in fact running a stand-alone copy of the web client inside a separate Electron process, which meant that Slack used more memory than users expected. The first two problems were the sort of things that we could incrementally improve over time, but getting multiple workspaces to run within a single Electron process meant changing a fundamental assumption of the original design that there is only ever a single workspace running at a time. Although we made some incremental improvements for folks with lots of idle workspaces, truly solving the multiple process problem meant rewriting Slacks desktop client from scratch.Bit by bitThe Ship of Theseus is a thought experiment that considers whether an object that has had each of its pieces replaced one-by-one over time is still the same object when all is said and done. If every piece of wood in a ship has been replaced, is it the same ship? If every piece of JavaScript in an app has been replaced, is it the same app? We sure hoped so, because this seemed like the best course of action.Our plan was to:keep the existing codebase;create a modern section of the codebase that would be future-proof and work the way we wanted it to;modernize the implementation of Slack bit by bit, replacing existing code with modern code incrementally;define rules that would enforce a strict interface between existing and modern code so it would be easy to understand their relationship;and continually ship all of the above with the existing app, replacing older modules with modern implementations that suited our new architecture.The final step and the most important one for our purposes was to create a modern-only version of Slack that would start out incomplete but gradually work its way toward feature completeness as modules and interfaces were modernized. Weve been using this modern-only version of the app internally for much of the last year, and it is now rolling out to customers.Modern timesThe first order of business was to create the modern codebase. Although this was just a new subdirectory in our codebase, it had three important rules enforced by convention and tooling, each of which was intended to address one of our existing apps shortcomings:All UI components had to be built with ReactAll data access had to assume a lazily loaded and incomplete data modelAll code had to be multi-workspace awareThe first two rules, while time-consuming to fulfill, were relatively straightforward. However, moving to a multi-workspace architecture was quite the undertaking. We couldnt expect every function call to pass along a workspace ID, and we couldnt just set a global variable saying which workspace was currently visible since plenty of things continue to happen behind the scenes regardless of which workspace the user is currently looking at.The key to our approach ended up being Redux, which we were already using to manage our data model. With a bit of consideration and the help of the redux-thunk library, we were able to model virtually everything as actions or queries on a Redux store, allowing Redux to provide a convenient abstraction layer around the concept of individual workspaces. Each workspace would get its own Redux store with everything living within it the workspaces data, information about the clients connectivity status, the WebSocket we use for real-time updates you name it. This abstraction created a conceptual container around each workspace without having to house that container in its own Electron process, which was what the legacy client did. With this realization, we had our new architecture in place:A legacy of interoperabilityAt this point we had a plan and an architecture we thought would work, and we were ready to work our way through the existing codebase, modernizing everything until we were left with a brand new Slack. There was just one last problem to solve.We couldnt just start replacing old code with new code willy-nilly; without some type of structure to keep the old and new code separate, theyd end up getting hopelessly tangled together and wed never have our modern codebase. To solve this problem, we introduced a few rules and functions in a concept called legacy-interop:old code cannot directly import new code: only new code that has been exported for use by the old code is availablenew code cannot directly import old code: only old code that has been adapted for use by modern code is available.Exporting new code to the old code was simple. Our original codebase did not use JavaScript modules or imports. Instead, it kept everything on a top-level global variable called TS. The process of exporting new code just meant calling a helper function that made the new code available in a special TS.interop part of that global namespace. For example, TS.interop.i18n.t() would call into our modern, multi-workspace aware string localization function. Since the TS. interop namespace was only used from our legacy codebase, which only loaded a single workspace at a time, we could do a simple look-up to determine the workspace ID behind the scenes without requiring the legacy code to worry about it.Adapting old code for new code was less trivial. Both the new code and the old code would be loaded when we were running the classic version of Slack, but the modern version would only include the new code. We needed to find a way to make it possible to conditionally tap into old code without causing errors in the new code, and we wanted the process to be as transparent to developers as possible.Our solution was called adaptFunctionWithFallback, which took a functions path on our legacy TS object to run, as well as a function to use instead if we were running in the modern-only codebase. This function defaulted to a no-op, which meant that if the underlying legacy code wasnt present, modern code that tried to call it would have no effect and produce no errors. With both of these mechanisms in place, we were able to kick off our modernization effort in earnest. Legacy code could access new code as it got modernized, and new code could access old code until it got modernized. As youd expect, over time there were fewer and fewer usages of old code adapted for use from the modern codebase, trending toward zero as we got ready for release. Putting it all togetherThis new version of Slack has been a long time coming, and it features the contributions of dozens of people who have been working through the last two years to roll it out seamlessly to customers. The key to its success is the incremental release strategy that we adopted early on in the project: as code was modernized and features were rebuilt, we released them to our customers. The first modern piece of the Slack app was our emoji picker, which we released more than two years ago followed thereafter by the channel sidebar, message pane, and dozens of other features. Had we waited until the entirety of Slack was rewritten before releasing it, our users would have had a worse day-to-day experience with emoji, messages, channel lists, search, and countless other features before we could release a big bang replacement. Releasing incrementally allowed us to deliver real value to our customers as soon as possible, helped us stay focused on continuous improvement, and de-risked the release of the new client by minimizing how much completely new code was being used by our customers for the first time.Conventional wisdom states that rewrites are best avoided, but sometimes the benefits are too great to ignore. One of our primary metrics has been memory usage, and the new version of Slack delivers:These results have validated all of the work that weve put into this new version of Slack, and we look forward to continuing to iterate and make it even better as time goes on.When guided by strategic planning, tempered by judicious releases, and buoyed by talented contributors, incremental rewrites are a great way to right the wrongs of the past, build yourself a brand new ship, and make your users working lives simpler, more pleasant, and more productive.Stay tunedWe are eager to share more about what weve learned during this process. In the coming weeks well be writing more at about:Service Workers, our quest for faster boot times and offline supportSlack Kit, our UI component libraryAccessibility, baked in rather than bolted onGantry, our app launching frameworkand rolling out a new client architecture at scale
Let's Talk About the Application of Thermal Conductive Silica Gel in LED Lighting Industry
Thermal conductive silica gel sheet is a widely used thermal conductive interface material. It is in the form of sheet, high pressure shrinkage, high reliability, high temperature resistance, excellent thermal conductivity and insulation, with viscosity on the surface, simple and convenient construction. It can be die-cut and punched according to the size and shape of heating devices.Heat conductive silica gel sheet is a kind of heat conductive medium material made by calendering with silica gel as the base material and adding various auxiliary materials such as metal oxides. It is usually called heat conductive gasket, heat conductive silica gel gasket, heat conductive silicon film, soft heat conductive gasket, heat conductive silica gel pad, etc. it is specially produced for the design scheme of using the gap to transfer heat and can fill the gap, It not only completes the heat transfer between the heating part and the heat dissipation part, but also plays the roles of insulation, shock absorption and sealing. It can meet the design requirements of miniaturization and ultra-thin equipment. It is a good heat conduction filling material with manufacturability and usability, and has a wide range of thickness and Application.Led thermal conductive silicon film is mainly used between aluminum substrate and heat sink, between aluminum substrate and shell, etc. Today, we mainly introduce the successful application of thermal conductive silica gel sheet in LED industry: there are many kinds of LED lamps. For indoor LED lamps, thermal conductive silica gel sheet with relatively low thermal conductivity is generally used, which can reduce the cost of the product and meet the needs of the product itself. For some outdoor high-power LED lamps, such as street lamps, the power is much higher than other indoor lamps, In order to better heat dissipation of lamps and improve the service life of lamps, thermal conductive silica gel sheets with relatively high thermal conductivity are generally used.The inherent viscosity of the heat-conducting silica gel sheet facilitates the construction. If the customer needs the heat-conducting silica gel sheet to have strong viscosity to replace the screw fixation, he can also choose to give one-sided or double-sided adhesive backing to the heat-conducting silica gel sheet. If the heat-conducting silica gel sheet needs to lock the screw, please remember to choose the heat-conducting silica gel sheet containing glass fiber cloth, which has the properties of anti puncture and anti tear. In short, the heat conductive silica gel sheet can be customized according to customer requirements to meet customer needs. It can be die-cut and punched according to the size and shape of heating devices.
7 Tips to Help You Sell Your Farm Fresh Eggs for More Money
The continuing trend of raising backyard chickens has had an unintended negative effect on those selling their extra eggs. Due to a steady supply of fresh eggs from backyard flocks and small local farms at markets, roadside stands and feed stores, egg prices are being kept artificially low. But there are some things you can do to help you sell your fresh eggs for a bit more money. When you begin to calculate your expenses - including egg cartons, labels, business cards, feed, supplements, supplies, the chickens themselves, plus their coop and run, not to mention a little something for your time, and gas to get to the market - it's often hard to sell a dozen eggs for a high enough price to simply break even. Many times, local eggs are sold for about the same price as store-bought eggs, despite being fresher and more nutritious AND laid by happy hens. And when you sell your eggs, you are not only competing against the low grocery-store prices, but also against other local sellers. Studies have shown that buyers will more likely make a purchase when you engage more than one of their senses. So by enticing potential shoppers' sense of touch, sight, sound and possibly even taste, you have a better chance at making that sale. Here are some tips to engage the senses, get your eggs to stand out from the crowd and possibly even fetch a premium price. If you are selling at a farmers' market or fair, crack an egg into a bowl to show potential buyers how great your eggs look. Eggs from chickens that eat a lot of herbs, grass and weeds will naturally have more vibrant yolks and look fresher than store-bought eggs from caged chickens. But you can bump up the wow factor of your chickens' egg yolks even more by feeding foods high in xanthophyll, a carotenoid with a naturally orange pigment. Some foods rich in xanthophyll include basil, carrots, corn, marigolds, parsley, pumpkin, red cabbage and the leaves of most green plants. Adding a pop of color to your cartons can entice buyers to your table. Raise some chickens that lay blue, green or cream-colored eggs to create some eye candy in your cartons! Chicken eggs can be a dime a dozen because of the large supply available, but there are other types of poultry that lay eggs. Duck eggs are larger than chicken eggs and thought to be to be better for baking due to their higher fat content. Tiny quail eggs are considered a delicacy and are often pickled or used by five-star chefs to top burgers or salads due to their smaller size and relative rarity. There might also be a market for turkey and goose eggs in your area - and you will likely be able to set your own price. Studies show that someone is more likely to purchase an item if they have touched or held it. Consider putting out a basket of eggs on your table and handing an egg to anyone who stops at your table. Give out free samples - let people take home an egg to try it for themselves. Hopefully, that will compel them to come back the next week to buy - if they do not buy a dozen eggs on the spot. Make your packaging unique. Instead of simply packaging your eggs in cartons and stacking them on the table, why not tie a pretty ribbon or some baker's twine around the carton and attach a wildflower or sprig of herbs? Maybe even tuck a simple egg recipe in. Or fill large baskets or metal pails with eggs and let your buyers hand select a dozen to put in their carton. And do not forget to pass out business cards. Sending each customer away with your contact information is a must to make it easy for them to locate you when they are ready to reorder. Studies have shown that chickens raised on pasture produce more nutritious eggs than chickens that never see the light of day or step foot on grass. Pasture-raised chickens have access to a more diverse diet, including a variety of forages and insects, which can lead to increased levels of vitamins A and E and omega-3 fatty acids. Other studies have shown that chickens raised on grass lay eggs that are lower in cholesterol than those raised on a commercial feed-only diet. Share this information with your potential customers by printing out a nutritional comparison on cards or handouts that they can take home with them - and be sure the handout has your contact information on it too! If possible, play a recording of chickens softly clucking with an occasional rooster crowing at your booth. The sound of happy chickens in the background will work to engage yet another sense and hopefully give your buyers the urge to bring home some farm fresh eggs! And back to sight for a minute, photographs of your chickens or a large poster showing them happily roaming a field can help reinforce the positive image of your farm and your eggs - you are putting faces and even names to the producers! Using a little creativity will give you a leg up on your competition and hopefully fetch higher prices for your delicious, fresh eggs! Also check your state Department of Agriculture's egg laws or cottage-food regulations, so you are aware of egg grading, handling and storing requirements, rules about the reuse of cartons and carton labeling regulations - including the use of such terms as organic, free-range and pasture-raised. Your local extension service should be able to point you in the right direction to get that information or you can find it online. Egg laws vary state by state.Where do they sell jacuzzi?Jacuzzis R us Sells pretty good ones ay low prices Or craigslist Has one for free in LA Go quick
ไม่มีข้อมูล