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Why your data strategy and loyalty program do belong together
Oct 11, 2018
One of the inherent benefits of loyalty programs is the data and insights marketers can glean about their best customers. Yet, as I talk with clients I often find marketers have the perception that their data strategy and loyalty programs do not belong together, and they are treated as separate marketing entities with unique teams, goals and plans.
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| Metamath Proof Explorer Deduction Form and Natural Deduction |
||
| Mirrors > Home > MPE Home > Deductions |
| Contents of this page |
A Theorem fine is Deduction, For it allows work-reduction: To show "A implies B", Assume A and prove B; Quite often a simpler production. --Stefan Bilaniuk A Problem Course in Mathematical Logic, 2003 [external] |
When being rigorous, it is surprisingly complicated to convert some deduction in the form into some theorem in the form . The deduction says, "if we can prove then we can prove ," which is in some sense weaker than saying " implies ." In particular, there is no axiom of logic that permits us to directly obtain the theorem given the deduction. The conversion of a deduction to a theorem does not even hold in general for quantum propositional calculus, which is a weak subset of classical propositional calculus. It has been shown that adding the Standard Deduction Theorem to quantum propositional calculus turns it into classical propositional calculus!
This is in contrast to going the other way; if we have the theorem, it is easy to recover the deduction using modus ponens ax-mp. An example of this is the derivation of the inference simpli from the theorem simpl.
In traditional logic books, this is often resolved using a metatheorem called the Deduction Theorem (discovered independently by Herbrand and Tarski around 1930). The deduction theorem, aka the standard deduction theorem, provides an algorithm for constructing a proof of a theorem from the proof of its corresponding deduction. See, for example, Margaris, First Order Mathematical Logic, p. 56. To construct a proof for a theorem, the deduction theorem's algorithm looks at each step in the proof of the original deduction and rewrites the step with several steps wherein the hypothesis is eliminated and becomes an antecedent. Ordinary mathematical proofs invoke this algorithm when converting a deduction into a theorem.
However, in practice, no one actually carries out this conversion algorithm in ordinary mathematics. Instead, mathematicians often stop once they believe the conversion algorithm could be done. This sharply contrasts with Metamath's philosophical goal, which is to show all proofs directly from the axiom system in its database, and not skip steps or rely on higher-level metatheorems derived outside of that axiom system.
Metamath is capable of converting a hypothesis into an antecedent. We have found that in many cases only a weakened form of the deduction theorem is necessary, called the weak deduction theorem (dedth and its variants). The weak deduction theorem is often easier to use, when it is necessary to use some version of the deduction theorem in the Metamath Proof Explorer (MPE). Earlier versions of MPE applied the deduction theorem, or a weakened form of it, in a number of situations. For more information about using the deduction theorem and the weak deduction theorem, including more details of why this can be complicated, see the deduction theorem page.
Today, the deduction theorem (including the weak variant of it) is rarely used in MPE when creating new proofs. That is because we have found much easier ways to achieve the same result. The rest of this page explains these easier ways.
In particular, there is a preference for writing assertions in "deduction form" instead of writing a proof that would require use of the deduction theorem. Applying this approach is called "deduction style". An assertion is in deduction form if the conclusion is an implication with a wff variable as the antecedent (usually ), and every MPE hypothesis ($e statement) is either a definition or is also an implication with the same wff variable as the antecedent (usually ). A definition can be for a class variable (this is a class variable followed by "=") or a wff variable (this is a wff variable followed by ); in practice definitions (if used) are for class variables. In practice, a proof in deduction form will also contain many steps that are implications where the antedent is either that wff variable (normally ) or is a conjunction (......) including that wff variable ().
For example, lhop (L'Hopital's rule) is in deduction form, because its conclusion and most of its MPE hypotheses are implications with as the antecent. It has one MPE hypothesis that is not an implication, but that hypothesis is a definition of a class variable - which is also allowed in deduction form. Later, in the section on Definitions in deduction form, we'll explain why definitions are allowed in deduction form.
In deduction form the antecedent (e.g., ) mimics the context handled in the deduction theorem. The deduction form antecedent can also be used to represent the context necessary to support natural deduction systems. For example, if the antecedent is a conjunction, the other terms can represent the temporary assumptions that are sometimes used in natural deduction. Before we discuss how to do natural deduction in MPE, we will first explain what natural deduction is.
Natural deduction (ND) systems, as such, were originally introduced in 1934 by two logicians working independently: Jaśkowski and Gentzen. ND systems are supposed to reconstruct, in a formally proper way, traditional ways of mathematical reasoning (such as conditional proof, indirect proof, and proof by cases). As reconstructions they were naturally influenced by previous work, and many specific ND systems and notations have been developed since their original work.
[Indrzejczak] pages 31-32 suggests that any natural deductive system must satisfy at least these three criteria:
There are many variations in ND systems. [Indrzejczak] page 32 believes that two kinds of variations are especially important:
The most common and recommended approach for applying ND in MPE is to use deduction form and apply the MPE proven assertions that are equivalent to ND rules. For example, MPE's jca is equivalent to ND rule I (and-insertion). See MPE equivalents of typical natural deduction (ND) rules for a list of equivalences. This approach for applying an ND approach within MPE relies on Metamath's wff metavariables in an essential way, and is described in more detail in the presentation "Natural Deductions in the Metamath Proof Language" by Mario Carneiro, 2014.
In this style many steps are an implication, whose antecedent mimics the context () of most ND systems. To add an assumption, simply add it to the implication antecedent (typically using simpr), and use that new antecedent for all later claims in the same scope. If you wish to use an assertion in an ND hypothesis scope that is outside the current ND hypothesis scope, modify the assertion so that the ND hypothesis assumption is added to its antecedent (typically using adantr). Most proof steps will be proved using rules that have hypotheses and results of the form ...
This is most easily understood by looking at some examples. For an annotated example where some traditional ND rules are directly applied in MPE, see ex-natded5.2, ex-natded5.3, ex-natded5.5, ex-natded5.7, ex-natded5.8, ex-natded5.13, ex-natded9.20, and ex-natded9.26.
Only using specific natural deduction rules directly can lead to very long proofs, for exactly the same reason that only using axioms directly in Hilbert-style proofs can lead to long proofs. If the goal is short and clear proofs, then it is better to reuse already-proven proven assertions in deduction form than to start from scratch each time. For example, observe that proof ex-natded5.8 - which is a line-for-line translation of directly using only common ND rules - is much longer than ex-natded5.8-2 (which directly reuses other proven statements) and ex-natded5.2i (which doesn't worry about context). Similarly, ex-natded5.3 is longer than ex-natded5.3-2 and ex-natded5.3i. Here are a few examples of proven assertions that can be useful for proofs in deduction form:
In some cases the metamath.exe "minimize_with" proof command can significantly shorten a proof if the original only uses the equivalent of basic ND inference rules. In practice, the simplest and clearest approach to creating a proof depends on what is to be proved.
Alan Sare has worked on an alternative within MPE, called virtual deduction. Much more information is available at wvd1, and an example is at vk15.4jVD (used to generate vk15.4j). This approach essentially replaces the outermost implication arrow with a different symbol . Alan Sare believes this change makes it easier to visualize proofs, while others disagree. The completeusersproof tool is available which supports this alternative approach.
Frédéric Liné has developed a different metamath-based system to support natural deduction system called natural deduction [retrieved 21-Dec-2016]. He reports that his system was inspired by a slide show, "From Natural Deduction to Sequent Calculus (and back)". Practically this system is equivalent to Mario Carneiro's work.
The actual purpose of the antecedent is to introduce a hypothesis that may not always be satisfiable without some assumptions (and the exact nature of those assumptions is not known inside the theorem, so the generic "" is used). If we are dealing with a true abbreviation, just a short way to write some symbols, then a definition "D = ..." hypothesis will either be satisfied by a similar hypothesis, or by theorem eqid, which will force the substitution of "..." for "D" in the rest of the theorem. Since in any case, the hypothesis can be discharged with no assumptions, the "" is not necessary.
Sometimes, we wish to discharge these hypotheses with something that isn't just an abbreviation. For example, if "J e. ( TopOn ` X )", then X is the base set of the topology J, so X = U. J (toponuni), but since X = U. J is not always true in this situation, we can't prove it without the hypothesis "J e. ( TopOn ` X )". What you have to do here, if you want to use a theorem that has the hypothesis "|- X = U. J" (to prove some statement |- P(X)), is use eqid anyway, producing a proof of P(U. J), then use ( ph -> X = U. J ) and equality theorems to get ( ph -> ( P(X) <-> P(U. J) ) ), then use the proof of |- P(U. J) to yield |- ( ph -> P(X) ). An example of this procedure is the derivation of ishaus2 (which has X = U. J given the context) from ishaus (which assumes X = U. J with no context).
The above procedure is always possible to do, but it is not always convenient since many steps may be needed for the equality proof. In cases where we specifically intend to discharge the assumption with something other than eqid, we sometimes add ph -> to the equalities as well. A common example of this is in structure builder theorems, where we want to use a self-referential expression for the left hand side. For example, we might define a group by
$e |- ( ph -> B = my-base-set ) $e |- ( ph -> .+ = my-group-op(B) ) mygroupval $p |- ( ph -> MyGroup = { <. ( Base ` ndx ) , B >. , <. ( +g ` ndx ) , .+ >. } )
Suppose that my-base-set is a complicated expression, and my-group-op(B) has a lot of references to B, so the fully expanded my-group-op(my-base-set) is really big, and we don't want to use it too many times. In the same context, we then prove:
$e |- ( ph -> B = my-base-set ) $e |- ( ph -> .+ = my-group-op(B) ) mygroupbaslem $p |- ( ph -> ( Base ` MyGroup ) = my-base-set ) mygroupaddlem $p |- ( ph -> ( +g ` MyGroup ) = my-group-op(B) )
and now we can bootstrap the whole thing:
mygroupbas $p |- ( ph -> ( Base ` MyGroup ) = my-base-set ) $= 1::eqid |- ( ph -> my-base-set = my-base-set ) 2::eqid |- ( ph -> my-group-op = my-group-op(my-base-set) ) qed:1,2:mygroupbaslem |- ( ph -> ( Base ` MyGroup ) = my-base-set ) mygroupadd $p |- ( ph -> ( +g ` MyGroup ) = my-base-set ) $= 1::mygroupbas |- ( ph -> ( Base ` MyGroup ) = my-base-set ) 2::eqid |- ( ph -> my-group-op( ( Base ` MyGroup ) ) = my-group-op( ( Base ` MyGroup ) ) ) qed:1,2:mygroupbaslem |- ( ph -> ( +g ` MyGroup ) = my-group-op( ( Base ` MyGroup ) ) )
Note that the contained references of my-group-op are now referencing ( Base ` MyGroup ), which makes this "definition" of a component of MyGroup self-referential. But that was the goal, and we have mygroupbas to expand it as necessary. A more elaborate version of this idea is done in prdsval, with prdsbas, prdsplusg, prdsmulr, etc pulling off components and bootstrapping using the previous theorems.
Finally, there are a few places where X = ... definitions are used by convention, specifically grppropd and other *propd theorems, and isgrpd and other is*d theorems for structures.
As a rule of thumb: Use X = ... abbreviations unless you need to use a non-identity abbreviation for X later.
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Student clubs are that platform which help you to improve yourself to reach height in your career at unique level.They make common student stand out of mob to be differnt student from other
Join clubs to know about your interest other than studies also.
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Motive : Developing Brains of new Things.
Buniyaad- The Dramatics society of kiet Engineering College is formed to attract talents from the institute founded in 2013.
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The students of KIET participate in the Shastra Robot Contest (ABU Robocon) which is an IIT robot competition, where huge number of students form all around country attend.
The students of KIET participate in the Shastra Robot Contest (ABU Robocon) which is an IIT robot competition, where huge number of students form all around country attend.
The students of KIET participate in the Shastra Robot Contest (ABU Robocon) which is an IIT robot competition, where huge number of students form all around country attend.
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Black is a description of a positive balance on a company's financial statements. A company would be said to be "in the black" if it is profitable or, more specifically, if the company produces positive earnings after accounting for all expenses. Conversely, a company with negative earnings would be said to be "in the red."
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Fight Club (1999) * * A movie review by Serdar Yegulalp Copyright 2000 by Serdar Yegulalp
Few movies in 1999 polarized audiences like "Fight Club", which showed Gen-X men beating on each other as a way of attempting to reclaim their masculinity, or something. Three camps seem to have sprung up around the film: hose who love it, those who hate it, and those who find the other two camps wasting their time with a red herring. I'm in the third camp.
"Fight Club", at the very least, opens brilliantly, with an unnamed narrator (Edward Norton) going stir crazy in a homogenized job. The film gets a lot of good mileage out of Norton's disgust with his brand-name existence; I was reminded of Willy Loman ranting, "How can they whip cheese?". In this film, Norton paces through his apartment, obssing over housewares catalogues, while his Ikea-bought furniture all handily display closed-captioned pricetags and manufacturer's descriptions.
Norton is an insomniac, and winds up going to terminal-disease support groups as a coping mechanism. For what, we may ask? For the fact that his life is terminally pallid? How bad can his life be when there are people dying of brain cancer? That's the way he thinks about it, anyway, and for a while it works, until he meets another faker, Marla Singer (Helena Bonham Carter). Marla and the Norton character wind up involved in a tempestuous relationship, which in this movie is a little like saying the Eiffel Tower is tall and pointy.
Things get complicated further by the presence of the handsome and engimatic soap salesman Tyler Durden (Brad Pitt), whom Norton meets on one of his unending business trips. Durden seems to have a knack for telling people what they've always wanted to hear but could never find anyone else to say. This is exactly what Norton thinks he needs, and when he comes back one day to find his apartment blown up, he shacks up with Durden in a house that could only remain standing in the movies and starts plowing through his back copies of "Reader's Digest".
So far the film has been funny and knowing, and made with great skill. Then it takes a left turn that sends everything barrelling over the cliff. Durden, as it turns out, is the mastermind of an underground boxing circle known as Fight Club, where the male disenfranchised can come and feel like gods while beating the tar out of each other. The logic of this will be lost on anyone who has actually been in a fistfight, of course, but the movie is not about logic. "Fight Club" has the peculiar, subterranean arrogance of a precocious writer's first draft, where screwy little details are defended to death over massive plot holes.
Before long Fight Club is running completely out of control, and Durden and Norton are at each other's throats when they're not raiding liposuction clinics for human fat. The parallels with the Nazis are of course not going to be lost on a knowing audience, but by the time we get to such things, they no longer matter.
I suspect "Fight Club" worked better on paper, because what's on film veers between the nauseating and the ridiculous. It's one thing to write about how great it felt to smash your fists into the concrete over and over again, and quite another to actually SEE it. Film has a way of literalizing everything, even things that are designed to be fanciful, and perhaps this story (from a novel by Chuck Palahniuk) just didn't survive the translation intact.
People will say (and have said) that the film is actually "about the nature of violence", but that is approximately as honest as saying that "ID4" was "about" the value of raising funding for SETI.  By the time we get to the "about" part, the movie's already betrayed itself, and smirks at us with its trick third act that doesn't even really explain anything. What's worse, a movie that deals ineptly with a good subject, or one which uses flashy plot mechanisms to tapdance around really dealing with it at all?
The problem isn't with David ("Seven") Fincher's extraordinary direction or the above-average performances by the cast. Let's face it, there are good people at work here: Norton's splendid; Pitt is funny when not being jerked around by the plot; Carter is unexpectedly brassy and scene-stealing. Her weirdo monologues could have been torn out and used as the centerpiece for another, better movie all by themselves.
I wanted to like "Fight Club", or at least appreciate its sardonic flashes of wit, but I could not. It's a cold, crass joke at the expense of its audience; a two-and-a-half-hour red herring that winds up being nothing at all by pretending to be about a lot of things it doesn't really understand.
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[§5-11.5] State fish. The humuhumunukunukuapuaa (Rhinecanthus rectangulus), also known as the rectangular triggerfish, is established and designated as the official fish of the State. [L 2006, c 67, §2]


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CRM-M-46880-2019 (O&M) -1- IN THE HIGH COURT OF PUNJAB AND HARYANA AT CHANDIGARH CRM-M-46880-2019 (O&M) Date of Order: 02.12.2019. Rohit and another ..Petitioners Versus Haryana State Pollution Control Board, Panchkula. ..Respondent
CORAM: HON'BLE MR. JUSTICE ANIL KSHETARPAL Present: Mr. Rakesh Nagpal, Advocate for the petitioners.
Mr.Baldev Raj Mahajan, Advocate General, Haryana. Mr. Pawan Girdhar, Advocate for respondent no.1-HSPCB.
ANIL KSHETARPAL, J(Oral) Petition has been filed under Section 482 of the Code of Criminal Procedure for quashing of a criminal complaint filed by the "Haryana State Pollution Control Board" against the petitioners herein under Section 39 of The Air (Prevention & Control of Pollution), Act, 1981 (hereinafter referred to as 'the Act of 1981') and the order of summoning passed on the same day by the Court thereon.
Allegations against the petitioners are that they have indulged in burning of stubble of wheat crop in violation of directions issued in April, 2016. As per the case of the prosecution a complaint was received on CM window dated 25.04.2016 on which a joint team inspected the land and found that the allegations made in the complaint are correct. The complaint was presented in Court on 16.11.2017. It has been pleaded in the complaint, filed before the learned Judicial Magistrate, that the Committee submitted a 1 of 3 ::: Downloaded on - 08-12-2019 17:54:10 ::: CRM-M-46880-2019 (O&M) -2-
detailed report to the Chairman, Haryana State Pollution Control Board on 18.05.2016 and thereafter process was initiated for getting sanction which was ultimately granted on 12.08.2016.
Learned counsel for the petitioners contends that the complaint as instituted is barred under Section 468 of the Code of Criminal Procedure, 1973. For offence punishable with imprisonment for a period of upto 3 months, the period prescribed is one year for taking cognizance. Even if the period spent for getting sanction, is excluded, still the complaint would be barred.
On the other hand, learned counsel appearing for the Pollution Control Board does not dispute this factual position. However, he submits that under Section 473 Cr.P.C., the Court can extend the period of limitation in certain cases. He, hence, submitted that this court should not exercise jurisdiction at this stage.
With the able assistance of learned counsels for the parties, this Court has gone through the criminal complaint filed, Annexure P-9.
From the reading of the complaint, it is apparent that no reason for extension of time as required under Section 473 Cr.P.C. has been given. Still further, no separate application under Section 473 Cr.P.C. has also been filed.
It is also undisputed that the maximum imprisonment prescribed under the Act of 1981 is 3 months. Hence, the maximum period within which the cognizance could be taken by the Court is one year. Even if the date of filing of the complaint is taken as date of cognizance, still bar as provided under Section 468 Cr.P.C. applies.
Although, learned counsel for the petitioner has pressed various 2 of 3 ::: Downloaded on - 08-12-2019 17:54:10 ::: CRM-M-46880-2019 (O&M) -3-
other points, however, this court is not required to go into the aforesaid issues particularly when the complaint is prove to have been instituted after the prescribed period.
Keeping in view the facts, Complaint No.18 filed under Section 39 read with Section 43 of The Air (Prevention & Control of Pollution), Act, 1981 and the consequential proceedings arising therefrom are ordered to be quashed, however, qua the petitioners only.
Resultantly, with the above-said observations made, the instant petition stands allowed.
December 02, 2019 (ANIL KSHETARPAL)
nt JUDGE
Whether speaking/reasoned : Yes/No
Whether reportable : Yes/No
3 of 3
::: Downloaded on - 08-12-2019 17:54:10 :::


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startsWith() and endsWith() functions in PHP How can I write two functions that would take a string and return if it starts with the specified character/string or ends with it? For example: $str = '|apples}'; echo startsWith($str, '|'); //
Voter Express: Voter Express Lookup Due to COVID-19 and proclamations from the Governor's Office, The May 2, 2020 Uniform Election has been moved to the November 3, 2020 General and Special Election.
Release 3.1.2 · aspnet-contrib/AspNet.Security.OAuth.Providers Added Add ability to specify the prompt parameter for the Discord provider (#367, #415) Thanks @damccull and @lukefulliton! Add a provider for Okta (#403, #442) Thanks @martincostello! Add a provi...
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Hi,
a friend of min runs a small restaurant and asked me to monitor his energy consumption in detail.
The restaurant has an Elster A1140 3phase electricity meters. (Attached you can find a picture of the meter and the distribution board)
What do you think is the easiest / most accurate / cheapest method of monitoring the energy consumption?
Those are the options that I came up with:
1) emonTx Arduino Shield V2 SMT and 3 x CT
- Though the meter is 3phase, there are no 3phase appliances and each phase is used separately. I would connect the CTs to the standart 230V wires that leave the distribution board. However the live and neutral are in insulated together (see attached image). Can you put the CT around both live and neutral to work?
2) Pulse counting from Elster A1140 and photodiode / TSL261R
- The electricity meter emits a pulse for every Wh consumed. However as it is a restaurant it can consume up to 12kW. That would mean ca. 3 pulses per second.
3) Optical communication via IEC 62056-21
- Apparently the protocol that Elster uses is open source. And the optical sensor that fit onto the optical port are expensive.
3) seems expensive, so I will probably chosse between 1) and 2). Question is now which one is more accurate?
Thanks a lot in advance,
Lorenz
Re: Energy metering of small restaurant with / without Elster A1140 meter
Hi
I think the answer will depend on what you are trying to achieve. If you wish to double check the accuracy of the existing meter, then reading its pulses will be a waste of time.
Option 1 will give you the most flexibility. It may be more expensive than 2, but it will give you the ability to graph and log the individual phase currents. Don't forget you have to still add the cost of an Arduino and Raspberry Pi.
I don't know anything about what available for the Elster, but given what I've learnt off this site, my recommendation is bite the bullet and go with 1. There is plenty of help and assistance available if you get stuck.
ONLY ONE wire must pass through the CT. If you have both, the current going to and fro will cancel each other out and you wont read anything.
Regards, Lionel
Re: Energy metering of small restaurant with / without Elster A1140 meter
If you want to measure the total consumption (only - not distinguish between different loads) then by definition the supplier's meter is accurate! Pulse counting or reading the optical port will (only) do automatically what could be done by reading the meter manually.
What do you want to do with the data? You have not mentioned recording or analysing it. You could send the data to emoncms.org web-based of course), or you could run the same software on a Raspberry Pi (or any other web server) locally. The recommended method is to use a RPi for both these options. For emoncms.org, it needs an Internet connection. Normally, the RPi gets its data by radio from your Arduino Shield or an emonTx V3. That means the RPi doesn't have to be next to the meter, but the Arduino or emonTx does, and needs a mains supply to run. The emonTx V3 can get its power from the AC adapter. The Arduino needs a separate 5 V supply as well as the ac adapter, which is in this case only for voltage measurement.
If you go for the emonTx/Shield with CTs, and you're measuring total consumption, you could put the 3 cts either on the incomers (3 browns probably labelled L1, L2, L3) or on the left-most 3 greys going in to the top of the consumer unit.
(BTW, that length of twin&earth is illegal - it should be clipped back! - so that I can't be accidentally caught and damaged.)
Re: Energy metering of small restaurant with / without Elster A1140 meter
Hi Lionel,
thanks a lot for that answer.
I don't want to double check the accuracy of the meter. I would just like to record the consumption profile of the restaurant throughout one week.
For Option 1, my problem is that I do not have any single wires that I could clip the CT around. Unless I use the ones that connect the meter and the distribution box. Do you think the CT (from open energy monitor) would fit around them?
Re: Energy metering of small restaurant with / without Elster A1140 meter
Hi Robert,
thanks for that.
Ideally I would like to track the consumption of individual devices, but as a start it would be enough to create a load profile for one week. And from knowing which devices are running when I can manually determine how much each device is using.
I want to record and plot the data. I will use a 3G dongle to connect to the raspberry pi and then we might run the the data storage and the plotting on Heroku.
Do you think the 3 cts (that openenergy monitor sells) would fit around the 3 greys going to the top of the consumer unit? In the datasheet is says that the max diameter is 15mm.
Thank for the advice with the twin&earth cable. I will let my friend know.
Re: Energy metering of small restaurant with / without Elster A1140 meter
Lorenz, if you want to measure the power consumption on each phase accurately, you will need to monitor the voltage and the current on each one. To monitor the currents, a CT can go around each of the incomers. To monitor the voltages, some means of accessing each of the phases will need to be provided.
I've just developed a 3-phase PCB which could do this for you. It has its own power supply on board and can transmit the resulting power and voltage data by RF. This data could then be received by a standard emonBase unit and the data processed within emonCMS - all of which could become expensive.
As far as I'm aware, there aren't any other Arduino-type platforms which are equipped to measure voltage and current on three phases. For your needs, however, it may be that a simpler approach will suffice which could provide you with a more cost-effective solution.
For monitoring only, my 3-phase PCB could be supplied in a smaller box (approx 190 x 160 mm) as shown here. If you are interested in this option, please send me a PM.
Robin
Re: Energy metering of small restaurant with / without Elster A1140 meter
The YHDC ct will fit on a 25 mm2 meter tail. You need to check the ct data sheet and measure your cables to be certain. You might struggle to get them all on the load side of the meter, but there's no reason why you cannot split them with one or two on the supply side. OK the purists will say you're then measuring the energy consumed by the meter as well, but at around 2 VA I defy anyone to prove it when measuring 100 A.
Robin's 3-phase board will need a low power protected feed of the three phase voltages to work properly (that can be 3 spare 5 A MCB's if available). This will give the most accurate power readings. If you use the emonTx V3 (or a Shield), both can measure only one phase voltage, but you can fudge it in software and by assuming the three phase voltages are identical, get a reasonably good approximation for the three phase powers. You'll need a standard socket for the ac adapter.
Or if you're not really interested in accuracy at this stage, you can measure current only, assume the voltage and estimate apparent power based on that assumption. In which case, your emonTx can be battery-powered for the week and you won't need mains power to it.
However, if you want long-term to measure individual feeds, you need to think of that now and count up how many channels you will need. It may be that you end up with 3 emonTx's, giving you 4 channels per phase (all feeding into the one RPi), and then you'd need 3 sockets, one per phase.
Re: Energy metering of small restaurant with / without Elster A1140 meter
Robin; that genuinely is a great piece of work! Really nice. I'm going to read through a bit more - I haven't been keeping up to date with it lately, but I'm sure you'll be busy shipping units.
Lorenz : There are 2 main ways to kill the costs for the restaurant (i) spend less and (ii) use less. Ask them whether they've critically reviewed their tariff structure and costs for ALL utilities (forgive me if this is obvious, but many people forget this part) and then start off with an emontx installation so you can help the owner to get some quick wins. The Carbon Trust says that "In some kitchens, as little as 40% of the energy consumed is used for the preparation and storage of food"
So, the designs here will help you ask the questions [ e.g. why is our base load 'x' kW?, and why is that chiller 'kicking in' every 'y' minutes?] ; you need to help the restaurant owner answer these q's asap. Don't forget to use the events module to help the restaurant own 'keep' the savings. No point in cutting the demand only to see it go back up next year.
There are lots of actions that can be taken-Feel free to pm me. I've no agenda here but it's useful to talk with people and share what we learn. I have an urgency about reducing waste energy ( just ask my family :-) and running a restaurant isn't easy!
Eamonn


zMerge is the successor to Merge Plugins, and offers a variety of improvements.
zMerge loads plugins when building merges and unloads them immediately afterwards. This means you can build any number of merges covering any number of plugin files as many times as you want without having to restart the program as long as you don't exceed 255 modules in the load order for any individual merge.
zMerge doesn't care about plugin errors or non-contiguous plugins. You no longer need to fix errors in plugins, create a custom Mod Organizer profile, or change your load order prior to creating a merge.
zMerge compacts form IDs when renumbering, so you will never overflow your form ID space from merging too many times. zMerge also has a form ID consistency feature, so adding new plugins to or otherwise updating an existing merge will not break your save games.
zMerge supports MO2 instances out of the box and has integrations for disabling plugins or mods automatically when merges complete successfully.
Added asset handling for INI files and LOD Billboards. The new asset handling system allows new asset handlers to be added cleanly and easily.
In addition, the data tab of the Edit Merge Modal allows users to preview assets detected by zMerge and configure how they will be handled per-merge instead of globally.
Logs are now actively written to disk while the program executes and are more verbose without making the progress log needlessly verbose as well or requiring debug settings.
No more batch script copying and a lower chance of running into file system permission issues.
Merged BSA creation no longer requires integrating with an external application, and is more configurable. BSAs can also be extracted, copied or ignored.
Other planned improvements to zMerge include the following:


|
Line Segment Intersector
1.0
Implementation of Bentley-Ottoman algorithm to find intersection points from a given set of line segments
|
#include <Status.h>
Public Member Functions | |
| void | inorder () |
| void | insert (T) |
| void | remove (T) |
| T * | searchL (T) |
| T * | searchR (T) |
| T * | getRoot () |
Status is a balanced tree, that allows for neighbour search
| T | : template class for which you want to build the status |
| void Status< T >::inorder | ( | ) |
Prints inorder traversal Requires that operator<< for ostream be overloaded for < T > class
| void Status< T >::insert | ( | T | key | ) |
Insert an element into the tree
| element | to insert |
| void Status< T >::remove | ( | T | key | ) |
Removes element from tree Does nothing is element is not present
| T * Status< T >::searchL | ( | T | key | ) |
Searches for element to the left of the param Returns null if no neighbour exists If param doesnt exist, we search for the smallest element greater than it
| Element who's left neighbour we want to search for |
Search the tree for left sibling of node with value key.
| T * Status< T >::searchR | ( | T | key | ) |
Searches for element to the right of the param Returns null if no neighbour exists If param doesnt exist, we search for the smallest element greater than it
| Element who's right neighbour we want to search for |
Search the tree for right sibling of node with value key.


hidden
Defines a after advice
Defines a static after advice
Defines a around advice
Defines a static around advice
Defines a before advice
Defines a static before advice
Defines a getter advice
Defines a setter advice
Defines a static getter advice
Defines a static setter advice
Marks a method explicit as joinpoint shadow Required for annotated methods!
hidden
Generated using TypeDoc
hidden


Hi! I'm Cindy Jin.I am a rising senior in the Bronx High School of Science. I am 17 years old, and I was born on Earth Day. I have several hobbies that I enjoy on my free time.
Find out more about meI am a very timid person when strangers approach me, but as I get to know you better, I am a very lively and friendly person!:D
My favorite subject is math because every concept is logical and there are several ways to get to the same answer. I am always willing to listen and help others in math problems and life problems.
Next: My HobbiesI love to bake all kinds of desserts such as macarons, donuts, and more!
I love playing in the water! I learned how to swim in China.
I love going down steep hills without my feet on the pedals. I learned how to bike instantly without anyone teaching me by looking at the bike.
I have started painting this year. Although I am not good at drawing, I love the fact that you can paint over your mistakes.


Employee {{ employee.id }}
- First Name
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{{ employee.firstName }}
- Last Name
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{{ employee.lastName }}
- Cin
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{{ employee.cin }}
- Phone Number
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- Role
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- Deleted
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- Deleted By
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- Deleted By Name
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{{ !!employee.deletedByName?employee.deletedByName:'-' }}
- Deleted Date
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{{ !!employee.deletedDate?employee.deletedDate:'-' }}
- Created By
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{{ employee.createdBy }}
- Created By Name
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{{ employee.createdByName }}
- Created Date
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{{ employee.createdDate }}


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saveConfigFile(ServersList)
- Method in class com.concordia.dist.asg1.Utilities.
FileStorage
this method saves servers Configurations
saveToFile(String, String)
- Method in class com.concordia.dist.asg1.Utilities.
FileStorage
Save whole string to file.
ServerConfig
- Class in
com.concordia.dist.asg1.Models
Server Configuration Model
ServerConfig()
- Constructor for class com.concordia.dist.asg1.Models.
ServerConfig
serverConfigList
- Variable in class com.concordia.dist.asg1.Models.
ServersList
serverName
- Variable in class com.concordia.dist.asg1.Models.
ServerConfig
ServersList
- Class in
com.concordia.dist.asg1.Models
Server Configuration List Model.
ServersList()
- Constructor for class com.concordia.dist.asg1.Models.
ServersList
ServiceLayerTest
- Class in
com.concordia.dist.asg1.UnitTest
The class
PassengerServiceTest
contains tests for the class
ServiceLayerTest
.
ServiceLayerTest()
- Constructor for class com.concordia.dist.asg1.UnitTest.
ServiceLayerTest
Constructor ServiceLayerTest
setAddress(String)
- Method in class com.concordia.dist.asg1.Models.
Passenger
setBookedBusinessClassSeats(int)
- Method in class com.concordia.dist.asg1.Models.
Flight
setBookedEconomyClassSeats(int)
- Method in class com.concordia.dist.asg1.Models.
Flight
setBookedFirstClassSeats(int)
- Method in class com.concordia.dist.asg1.Models.
Flight
setBookingId(int)
- Method in class com.concordia.dist.asg1.Models.
Passenger
setClass(Enums.Class)
- Method in class com.concordia.dist.asg1.Models.
Passenger
setDate(String)
- Method in class com.concordia.dist.asg1.Models.
Passenger
setDestinaition(Enums.FlightCities)
- Method in class com.concordia.dist.asg1.Models.
Flight
setDestination(Enums.FlightCities)
- Method in class com.concordia.dist.asg1.Models.
Passenger
setFirstName(String)
- Method in class com.concordia.dist.asg1.Models.
Passenger
setFlightDate(String)
- Method in class com.concordia.dist.asg1.Models.
Flight
setFlightID(int)
- Method in class com.concordia.dist.asg1.Models.
Flight
setFlightId(int)
- Method in class com.concordia.dist.asg1.Models.
Passenger
setFlightTime(String)
- Method in class com.concordia.dist.asg1.Models.
Flight
setLastName(String)
- Method in class com.concordia.dist.asg1.Models.
Passenger
setORB(ORB)
- Method in class com.concordia.dist.asg1.Server.
FlightOperationsImplementation
set Orb
setPhone(String)
- Method in class com.concordia.dist.asg1.Models.
Passenger
setSeatsInBusinessClass(int)
- Method in class com.concordia.dist.asg1.Models.
Flight
setSeatsInEconomyClass(int)
- Method in class com.concordia.dist.asg1.Models.
Flight
setSeatsInFirstClass(int)
- Method in class com.concordia.dist.asg1.Models.
Flight
setSource(Enums.FlightCities)
- Method in class com.concordia.dist.asg1.Models.
Flight
shortServerName
- Variable in class com.concordia.dist.asg1.Models.
ServerConfig
shutdown()
- Method in class com.concordia.dist.asg1.Server.
FlightOperationsImplementation
implement shutdown() method
startSerevr(ORB, String[], int, String)
- Static method in class com.concordia.dist.asg1.Server.
MainServer
Binding remote Object to naming service.
startUDPServer()
- Method in class com.concordia.dist.asg1.Server.
FlightOperationsImplementation
Start UDP Server
StaticContent
- Class in
com.concordia.dist.asg1.StaticContent
save all type of Static string, data etc.
StaticContent()
- Constructor for class com.concordia.dist.asg1.StaticContent.
StaticContent
status
- Variable in class com.concordia.dist.asg1.Models.
Response
synchroniztionTest()
- Method in class com.concordia.dist.asg1.UnitTest.
ServiceLayerTest
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#include <uwphysicaldb.h>
Definition at line 61 of file uwphysicaldb.h.
◆ UnderwaterPhysicaldb()
| UnderwaterPhysicaldb::UnderwaterPhysicaldb |
( |
| ) |
|
Constructor of UnderwaterMPhyBpskDb class.
Definition at line 55 of file uwphysicaldb.cpp.
◆ ~UnderwaterPhysicaldb()
| virtual UnderwaterPhysicaldb::~UnderwaterPhysicaldb |
( |
| ) |
|
|
inlinevirtual |
Destructor of UnderwaterMPhyBpskDb class.
Definition at line 73 of file uwphysicaldb.h.
◆ command()
| int UnderwaterPhysicaldb::command |
( |
int |
argc, |
|
|
const char *const * |
argv |
|
) |
| |
|
virtual |
TCL command interpreter.
It implements the following OTcl methods:
- Parameters
-
| argc | Number of arguments in argv. |
| argv | Array of strings which are the command parameters (Note that argv[0] is the name of the object). |
- Returns
- TCL_OK or TCL_ERROR whether the command has been dispatched successfully or not.
Reimplemented from UnderwaterPhysical.
Definition at line 63 of file uwphysicaldb.cpp.
◆ endRx()
| void UnderwaterPhysicaldb::endRx |
( |
Packet * |
p | ) |
|
|
protectedvirtual |
◆ fromKmToMiles()
| const double UnderwaterPhysicaldb::fromKmToMiles |
( |
const double & |
_km | ) |
const |
|
inlineprotected |
Converts from kilometers to miles.
- Parameters
-
| _km | The value to be converted in miles. |
- Returns
- The value converted in miles.
Definition at line 150 of file uwphysicaldb.h.
◆ getNearestNeighbor()
| double UnderwaterPhysicaldb::getNearestNeighbor |
( |
const std::set< double > & |
_set, |
|
|
const double & |
_value |
|
) |
| |
|
protectedvirtual |
Nearest neighbor of a value contained in a set.
- Parameters
-
| Set | that contains the values in which to search. |
| value | to search for. |
- Returns
- Nearest neighbor.
Definition at line 434 of file uwphysicaldb.cpp.
◆ getPERfromSIR()
| double UnderwaterPhysicaldb::getPERfromSIR |
( |
const double & |
_sir, |
|
|
const double & |
_overlap |
|
) |
| |
|
protectedvirtual |
Packet error rate based on Overlap and SIR.
- Parameters
-
- Returns
- PER of the packet retrieved from file.
Definition at line 410 of file uwphysicaldb.cpp.
◆ getPERfromSNR()
| double UnderwaterPhysicaldb::getPERfromSNR |
( |
const double & |
_snr, |
|
|
const int & |
_nbits, |
|
|
const Packet * |
p |
|
) |
| |
|
protectedvirtual |
Packet error rate based on SNR.
- Parameters
-
| SNR. | |
| nbits | length in bit of the packet. |
| p | Packet. |
- Returns
- PER of the packet retrieved from file.
Definition at line 304 of file uwphysicaldb.cpp.
◆ isZero()
| const bool UnderwaterPhysicaldb::isZero |
( |
const double & |
_value | ) |
const |
|
inlineprotected |
Evaluates is the number passed as input is equal to zero.
When C++ works with double and float number you can't compare them with 0. If the absolute value of the number is smaller than eplison that means that the number is equal to zero.
- Parameters
-
| double& | Number to evaluate. |
- Returns
- true if the number passed in input is equal to zero, false otherwise.
- See also
- std::numeric_limits<double>::epsilon()
Definition at line 138 of file uwphysicaldb.h.
◆ recv()
| void UnderwaterPhysicaldb::recv |
( |
Packet * |
p | ) |
|
|
virtual |
recv method.
It is called when a packet is received from the channel
- Parameters
-
| Packet* | Pointer to the packet that are going to be received |
Reimplemented from UnderwaterPhysical.
Definition at line 151 of file uwphysicaldb.cpp.
◆ retrievePerFromFile()
| const double UnderwaterPhysicaldb::retrievePerFromFile |
( |
const std::string & |
_file_name, |
|
|
const double & |
_snr |
|
) |
| const |
|
protectedvirtual |
◆ country
| string UnderwaterPhysicaldb::country |
|
protected |
◆ interf_val
| std::pair<double, double> UnderwaterPhysicaldb::interf_val |
|
protected |
◆ interference_
◆ ipAddr_
| uint8_t UnderwaterPhysicaldb::ipAddr_ |
|
protected |
◆ modulation
| string UnderwaterPhysicaldb::modulation |
|
protected |
◆ osstream
| ostringstream UnderwaterPhysicaldb::osstream |
|
private |
◆ overlap
| std::set<double> UnderwaterPhysicaldb::overlap |
|
protected |
◆ path_
| char* UnderwaterPhysicaldb::path_ |
|
protected |
Name of the trace file writter for the current node.
Definition at line 156 of file uwphysicaldb.h.
◆ range
| std::map<uint8_t, std::set<double> > UnderwaterPhysicaldb::range |
|
protected |
◆ range_nums
| std::map<string, uint8_t> UnderwaterPhysicaldb::range_nums |
|
protected |
Set of the number of ranges for a given pathtype, e.g "AA".
Definition at line 166 of file uwphysicaldb.h.
◆ sir
| std::set<double> UnderwaterPhysicaldb::sir |
|
protected |
◆ snr
| std::set<double> UnderwaterPhysicaldb::snr |
|
protected |
◆ token_separator
| char UnderwaterPhysicaldb::token_separator |
|
protected |
Token used to parse the elements in a line of the database.
Definition at line 175 of file uwphysicaldb.h.
◆ type_of_node
| std::map<uint8_t, string> UnderwaterPhysicaldb::type_of_node |
|
protected |
The documentation for this class was generated from the following files:


Constructor
new Chord()
Properties:
| Name | Type | Description |
|---|---|---|
step |
string | The degree (or step) of the root note of the chord in the scale in roman numerals. Defaults to |
seventh |
boolean |
|
start |
string | The start time of the chord in the sequence, in Tone.js time notation. Defaults to |
duration |
string | The duration of the chord, in Tone.js time notation. Defaults to |
Extends
- Backbone.Model


Rare White Squirrel Caught On Camera In Incredible Photograph
by Emma RosemurgeyAn incredibly rare white squirrel has been pictured in Royal Deeside, Scotland.
According to reports, experts believe the squirrel is actually of the red variety, rather than the grey, due to the hairy tufts that can be visibly seen on the creature’s ears.
The rare picture was taken by conservationists who are working in the area to protect the red squirrel population in the north east of Scotland.
They said they would now be working to discover whether the squirrel was a ‘true albino’ with red eyes.
Conservationist Dr Gwen Maggs told the BBC:
We will set up some remote cameras to try and get some better pictures with a clear view of its eyes.
In any event, this is a rare and exciting discovery.
Alex Stuart, co-ordinator of the North East Scotland Biodiversity Partnership, added:
Partly white animals, like sparrows, crows, blackbirds and even hedgehogs do appear from time to time, but these are not true albinos.
Sightings like this really demonstrate the value of keeping your eyes and ears open – there’s lots of other amazing wildlife to be seen and heard out there as well as white red squirrels.
Meanwhile, a red squirrel was spotted in Aberdeen earlier in the year, which was said to be the first to have been seen so close to the city centre in decades.
The squirrel was spotted by Gina Ganzenmueller, who managed to snap a picture of the rare creature in her back garden, north of Duthie Park, near the River Dee.
She told the BBC:
After years of grey squirrel sightings I’ve finally seen a red squirrel in my back garden.
I was so excited, I couldn’t believe my eyes. I only have a small garden, but Duthie Park is not far away.
Grey squirrels were first introduced to Aberdeen back in the 1970s and they quickly spread through the city and into the surrounding areas.
Ever since, Aberdeenshire’s native red squirrel population has continued to decline due to competition for food and living space.
Dr Gwen Maggs, Saving Scotland’s Red Squirrels Conservation Officer for North East Scotland, said:
The project has been working along the River Dee for 10 years, with help from dedicated volunteers participating in our trap-loan scheme.
As a result of this targeted grey squirrel control red squirrels have gradually returned to North Deeside, with populations establishing through Peterculter, Milltimber, Bieldside and Cults. In 2017 red squirrels arrived at Robert Gordon University.
With healthy populations already in Hazlehead and Seaton Park, we hope that they will soon return to Duthie Park for everyone to enjoy.
Emma Rosemurgey is an NCTJ trained Journalist at UNILAD. She graduated from the University of Central Lancashire in Preston and started her career in regional newspapers before joining the LADbible Group team in 2017.


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fish
- Variable in class com.example.littleync.model.
User
fishButton(View)
- Method in class com.example.littleync.
TravelActivity
Buttton that navigate players to ecopond.
fishCost
- Variable in class com.example.littleync.gameActivities.
ArmoryActivity
fishDisplay
- Variable in class com.example.littleync.gameActivities.
AttributesActivity
fishDisplay
- Variable in class com.example.littleync.gameActivities.
MarketplaceActivity
fishFish()
- Method in class com.example.littleync.model.
User
Called in the Ecopond page at every unit of stamina consumed; increments fish and exp by the current fishing gear level
fishingGearLevel
- Variable in class com.example.littleync.model.
User
fishingGearLevelDisplay
- Variable in class com.example.littleync.gameActivities.
AttributesActivity
fishingGearLevelDisplay
- Variable in class com.example.littleync.gameActivities.
MarketplaceActivity
fishToLevel
- Variable in class com.example.littleync.gameActivities.
ArmoryActivity
fLC
- Static variable in class com.example.littleync.
LoginActivity
ForgotPassword
- Class in
com.example.littleync
Loads the forgot password page, to allow users to reset their password using their known email address.
ForgotPassword()
- Constructor for class com.example.littleync.
ForgotPassword
forgotPasswordInput
- Variable in class com.example.littleync.
ForgotPassword
forgotPasswordScreen(View)
- Method in class com.example.littleync.
LoginActivity
forgotPassword()
fs
- Variable in class com.example.littleync.gameActivities.
AttributesActivity
fs
- Variable in class com.example.littleync.gameActivities.
MarketplaceActivity
fs
- Variable in class com.example.littleync.
SignupActivity
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Home
How does climate change affect people?
Climate Change vs. Humans
Carbon Dioxide
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Powerful Storms
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Electric Battery Technology
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{{createRide?.Trip?.fromAddress?.address?.municipality}}
arrow_forward
{{createRide?.Trip?.layoverAddress?.address?.municipality}}
{{createRide?.Trip?.layoverAddress?.address?.municipality}}
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my name is john gravois. i am 31 and i work for a company based in redlands called esri. esri is a company that is worth a couple billion dollars. we make software for making maps.
the technical term for the place where geography meets technology is GIS or Geographic Information Systems.
i'm not sure how you feel about technology, but a lot of people think geography is boring. is that really true?
what exactly is GIS? what makes it so powerful?
so spatial problem solving has been around a long time, now lets add technology to the picture. now what happens?
whats more fun than cholera? how about lunch?
heres the tl;dr maps and technology are actually awesome learning about science and computers leads to endless job opportunities everyone needs/uses technology, whether they work with maps or not its never too late to start learning.
extra reading/viewing: http://geospatialrevolution.psu.edu/


| Interface | Description |
|---|---|
| JwtManager | |
| LoggedOutUsers |
List of users who logged out but have valid JWT token until they expire
|
| Class | Description |
|---|---|
| AbstractSecurityHandler |
Base class for our security handlers with some shared methods, how to deal with Heathans
|
| BasicHandler |
Handles authentication when mode is “Basic”, so we have encoded: UserName and Password and turn it on our own turf into a JWT Header so it fits into our general approach
|
| ExpiringJwtHandler |
Security handler that handles list of users who logged out despite JWT Token being still valid
|
| KeepUser |
Information about the current user and the permissions the user has in various places
|
| SaltCredentialTool | |
| SingleUserBasicAuthenticationProvider |
Helper class to protect adjacent ports like metrics or admin
|
| TheBarbican |
Module that ensures read & write access to documents is managed by the KeepConfig Configuration has convenience functions to check on forms, aliases and fields TODO: Extract API
|
| Enum | Description |
|---|---|
| DocumentAccess |
What level of document access is required for an existing document based on the Notes ACL
|
| JwtManagerHolder |
Holds the JWT Configuration for the running session of KEEP
|
| LoggedOutUserList |
| Exception | Description |
|---|---|
| JwtManager.JwtNotSetupException |
Manages our handling of JWT elements
|
| Annotation Type | Description |
|---|---|
| AllowOpenAccess |
Annotation to allow open access
|


Trump Steps in to Defend Biden From North Korean Media Branding Ex-Vice President 'Rabid Dog'
The social media crowd met Trump’s tweet with a wave of criticism, and it wasn’t immediately clear whether the president’s message was some kind of attempt to reach out to Kim Jong-un amid the breakdown in denuclearisation talks.
US President Donald Trump has stepped forward to defend his rival, former vice president and Democratic presidential candidate Joe Biden, after the latter got slammed by North Korean media in an apparent response to his criticism of Kim Jong-un.
Earlier, North Korea's official KCNA news agency described Biden as a "rabid dog" that will soon pass away and needs to be put down, adding that he was allegedly exhibiting the "final stage of dementia".
"Mr. Chairman, Joe Biden may be Sleepy and Very Slow, but he is not a rabid dog’," the US president tweeted. "He is actually somewhat better than that, but I am the only one who can get you where you have to be. You should act quickly, get the deal done. See you soon!"
As AFP points out, it wasn’t immediately clear to what extent Trump was “being tongue-in-cheek” in his description of Biden, or whether he was “using his tweet as a way to re-engage with Kim”.
Trump’s message, however, quickly elicited a wave of criticism from social media users who bashed him over his relations with Kim.
Some, however, went on to slam Biden instead.
Earlier, in October, the North Korean delegation led by chief negotiator Kim Myong Gil conducted denuclearisation talks with the US delegation headed by Stephen Biegun in Sweden.
The negotiations, however, fell through, with North Korean diplomats claiming that their US counterparts came to the meeting empty handed.


She was chosen as the spiritual mentor of the group after losing connection with Omicron took over the duties of the leader of Clan
Participant of 12 deadly tournaments. The rapid rise in the home planet allowed Janda obtain master status in the short term.
Being in a new world began to open the ability to use mutations. Thermal, sonic mutations, sucking power of the enemy.
After the Dam fell, most turned to factions, but not this clone. He stuck by his morals and defended his life at all costs. You can still see him running around and killing things. But whatever you do, do not cross his patch.
Undefined.
Undefined.


Lee Li
Front-End Developer
Featured Work
Partera
Project Links
Adchina
Link to project
China Mobile
Link to project


Toggle navigation
Orwell Writer
Export
Save as
Print (Alpha)
Grammar
Welcome to the Orwell Writer. Fullscreen for more. You can type here.
Adjectives
Synonyms
Predecessors
Orwell Writer is a text writing app that was
Youtube
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Github


Use Jasmine to write your unit tests before you begin writing any implementation code.
Plant
function defined.Tree
function defined.increaseHeight
on the prototype of Plant.decreaseHeight
on the prototype of Plant.height
property on Plant.grow
on the prototype of Tree.trim
on the prototype of Tree.trim
method on Tree, the height of the Tree should be reduced by the integer value that is passed as an argument (e.g. PearTree.trim(2)
)trim
method on Tree, the values of the branches
property should be decreased by one.grow
method on Tree, the height of the Tree should be increased by the integer value that is passed as an argument (e.g. PearTree.grow(2)
)Reference: Checkout the setInterval and clearInterval functions in JavaScript
height
.increaseHeight
and decreaseHeight
. Each method should accept an integer value as input.Plant.prototype.increaseHeight = function (growth) { }
increaseHeight
should increase the value of the height
property by the amount passed in as an argument.decreaseHeight
should decrease the value of the height
property by the amount passed in as an argument.branches
.grow
and trim
.grow
method should accept an integer value as input.grow
method should increase the height of the tree.trim
method should accept an integer value as input.Tree.prototype.grow = function (amount) { }
trim
method should decrease the height of the tree.trim
method is called, the number of branches should decrease by one.branch
should increase by one.var PearTree = new Tree();
Pear tree is now 23cm tall and has 2 branches
Oak tree is now 57cm tall and has 4 branches
Every tenth time the trees are grown, invoke the trim
method. Pass one value to the method for the pear tree, and a larger value to the method on the oak tree.


Try out our Premium Member services: Virtual Legal Assistant, Query Alert Service and an ad-free experience. Free for one month and pay only if you like it.
Gujarat High Court Case Information System Print CR.A/2590/2009 1/ 5 ORDER IN THE HIGH COURT OF GUJARAT AT AHMEDABAD CRIMINAL APPEAL No. 2590 of 2009 ========================================================= HARKISHAN R. JOSHI, ASST. LAW OFFICER - Appellant(s) Versus GOVERNMENT OF GUJARAT & 7 - Opponent(s) ========================================================= Appearance : MR KL DAVE for Appellant(s) : 1, MR DC SEJPAL, LD. ADDL. PUBLIC PROSECUTOR for Opponent(s) : 1, None for Opponent(s) : 2 - 8. ========================================================= CORAM : HONOURABLE MR.JUSTICE Z.K.SAIYED Date : 15/02/2010 ORAL ORDER
The appellant had filed this Appeal under Section 374 of the Code of Criminal Procedure, 1973 against the judgment and order of acquittal dated 28th December 2006 passed by the learned 2nd Additional Senior Civil Judge and Judicial Magistrate First Class, Junagadh, in Criminal Case No. 7379 of 1993, whereby the respondents accused have been acquitted from the charges levelled against them.
The brief facts of the prosecution case is that the Respondent No.2-accused is a Firm and Respondent Nos.3 to 7 are the Directors of Respondent No.1 and the Respondent No.8 is a Plant In-charge of the Respondent No.1 Firm. It it also the case of the prosecution that the Respondent No.1 Firm is manufacturing Reactive Dyes using raw materials like H. Acid, Vinyl Sulphone, K. Acid, etc. It is also the case of the prosecution that on 21st May 1993 officials of the appellant had visited the Respondent No.1 and prepared a Report. They had also collected water samples from the Respondent No.1 Firm. It is also the case of the prosecution that on 24th May 1993 they had sent the sample to the Analysis Board for analysis. The appellant had received the Analysis Report on 28th June 1993, which shows that the respondents have committed breach of Section 43, 44 and 47 of the Water Act. It is also the case of the prosecution that every month the respondents manufactured 1 MT Reactive Dyes and generating polluted water. This polluted water is discharged by the respondents without any consent taken from the appellant. Therefore, a complaint was filed by the appellant against the respondents under Sections 24 and 25 of The Water (Prevention and Control of Pollution) Act, 1974 in the Court of learned 2nd Additional Senior Civil Judge and Judicial Magistrate First Class, Junagadh. Pending the trial, original accused no.6 had expired and case against him was abated.
Thereafter, the trial was initiated against the respondents accused in the Court of learned Magistrate. To prove the case against the respondents accused, the prosecution has examined the witnesses and also produced documentary evidence and at the end of the trial, the learned Magistrate has acquitted the respondents accused from the charges levelled against them, vide judgment and order dated 28th December 2006 in Criminal Case No.7379 of 1993.
Being aggrieved by and dissatisfied with the said judgment and order passed by the learned Magistrate, the appellant has filed the present Appeal.
Learned advocate appearing on behalf of the appellant, has contended that the judgment and order of Trial Court is against the provisions of law. The Trial Court has not properly appreciated the facts and evidence led by the prosecution and looking to the provisions of law itself it is clearly established that the prosecution has proved the whole ingredients of offence against the respondents-accused. Learned advocate appearing on behalf of the appellant has also taken this Court through the oral as well as documentary evidence.
I have perused the oral as well as documentary evidence. I have also considered the submissions made by the learned advocate on behalf of the appellant. From the perusal of the judgment of the Trial Court it is established that has not supported the case of prosecution.
Thus, in my opinion, looking to the evidence on record, from the evidence itself it is clearly established that the prosecution has not proved its case beyond reasonable doubt.
At the outset it is required to be noted that the principles which would govern and regulate the hearing of appeal by this Court against an order of acquittal passed by the Trial Court have been very succinctly explained by the Hon'ble Apex Court in catena of decisions. Thus, the powers which this Court may exercise against an order of acquittal are well settled. Thus, in case the Appellate Court agrees with the reasons and the findings given by the lower Court, then the discussion of evidence is not necessary.
I have gone through the judgment and order passed by the Trial Court and have also perused the oral as well as documentary evidence produced before me and also considered the submissions made by the learned advocate for the appellant. On going through the judgment and order passed by the Trial Court and the papers placed before me, I am of the opinion that the Trial Court has not committed any error in not believing the case of the prosecution. I find that the findings recorded by the Trial Court are absolutely just and proper and in recording the said findings no illegality or infirmity has been committed by it. The learned Judge has rightly come to the conclusion that the prosecution has miserably failed to prove the case against the respondent accused.
I am, therefore, in complete agreement with the findings, ultimate conclusion and the resultant order of acquittal recorded by the Court below and hence find no reason to interfere with the same. Hence, the Appeal is hereby dismissed at the admission stage.
In view of above, the Appeal is dismissed. The judgment and order dated 28th December 2006 passed by the learned 2nd Additional Senior Civil Judge and Judicial Magistrate First Class, Junagadh, in Criminal Case No.7379 of 1993 is hereby confirmed. Bail bond, if any, shall stands cancelled.
(Z.
K. Saiyed, J) Anup Top


WITNESS LIST Jurisprudence Committee May 15, 1997-3:15P HB 1317 Registering, but not testifying: For: Herman, Guy (Stat Prob Judges of TX), Austin HB 1553 For: Kelley, Michael (Senator Whitmire), Austin Registering, but not testifying: For: Sommer, John (VALERO), San Antonio On: Selby, Gardner (Comptroller of TX, TPR), Austin HB 1665 For: De La Garza, Luis (Valero Energy Corp.), San Antonio HB 1672 Registering, but not testifying: For: Armstrong, Gaylord (Tx Funeral Directrs Asn), Austin HB 2272 For: Armstrong, Shirley (TX Court Clerk's Assn), Grand Prairie Phariss, Hilda (TX Court Clerks Assn), Bryan On: Henry, Rene (State Comptroller), Austin HB 2488 Registering, but not testifying: For: McKenna, Jan (self), Fort Worth HB 2951 For: Downes, James (Harris Cnty Atty's Ofc), Houston Registering, but not testifying: For: Bush, John (TX Soc. of Psych. Physn), Austin Against: Brady, Denise (The Arc of Texas), Austin Devall, Christine (Mental Health Assn - TX), Austin Herman, Guy (Stat Prob Judges of TX), Austin Mitchell, Beth (Advocacy Inc.), Austin HB 3088 Registering, but not testifying: For: Herman, Guy Judge (Stat Prob Judges of TX), Austin HB 3345 Registering, but not testifying: For: McKenna, Jan (self), Fort Worth


Thank you for purchasing my Template. If you have any questions that are beyond the scope of this help file, please feel free to email via my user page contact form here. Thanks so much!
Created: 31/01/2018 | By: XpeedStudio | Support Desk https://support.xpeedstudio.com/
FundPress - Fundraising Startup HTML5 Responsive Template is built with the Bootstrap 4 framework - that means you have access to all the great features, css & js goodies has to offer. Bootstrap includes a responsive, mobile first fluid grid system that appropriately scales up to 12 columns as the device or viewport size increases.
To learn more about Bootstrap's grid system, please refer to https://v4-alpha.getbootstrap.com/layout/grid/
I'm using one main CSS file (assets/css/styles.css) and sass file available on (assets/sass), in this template which you are free to modify depending on the customization you require. There are also other additional style sheets that I do not recommend changing. Those style sheets reside in the 'css' folder and 'sass' file on 'sass' folder.
The Styles CSS file contains all of the specific stylings for the page. The file is separated into sections using:
/* _component.scss */ 1. Buttons 2. Tab navigation 3. Input group 4. Modal 5. Badge 6. Shape background /* _main.scss */ 1. All style /* _xsStyle.scss */ 1. Default style /* _predefine.scss */ 1. Reset style /* _variable.scss */ 1. All variable list
If you would like to edit a specific section of the site, simply find the appropriate label in the css file, and then scroll down until you find the appropriate style that needs to be edited.
This theme comes with Unlimited color variations. To change the color style from the theme edit the following lines:
... $color-green: #4CC899; $color-navy-blue: #041D57; $color-dark-pink: #F8005E; $color-semi-black: #222222; $color-sky-blue: #3E5A97; $color-dark-ash: #8d97ad; $color-white: #FFFFFF; $color-pelorous: #38C1C2; $color-gray: #f5f5f5; $color-blue: #03194E; $color-black: #000000; $color-brick: #EE393B; $color-brick-light: #FCB6B4; $color-yellow : #FCCA29;
Just change the color code name for example form $color-green: #4CC899;
to #8b1b9a
.
Available assets/sass/_variable.scss
directory
To change the logo edit the following lines:
... ...
The value is the header logo image path from the assets/images/logo_new.png
The value is the footer logo image path from the assets/images/logo_new.png
To add or change a team edit the following lines:
...Popular Campaigns
FundPress has built a platform focused on aiding entrepreneurs, startups, and companies raise capital from anyone.
To add or change a progress element edit the following lines:
...Splash Drone 3 a Fully Waterproof Drone that floats
- $67,000Pledged
- 0% Funded
- 3Days to go
To add or change progress percentage just following lines
find data value and set it
data-value="90"
to example 70
To add or change parallax background image open file eaxmple (filename.html)
change image data-image-src="img/
, find and edit code below:
... ...
To add or change modal element open file eaxmple (filename.html) find and edit code below:
...
To add or change a contact filed edit the following lines:
...
you add your personal image to map window opener just follow example
assets/images/contact/
and rename your images example contact-info-img-1.png
The Contact and Checkout form is based on jQuery. You don't have to know PHP. To change sample email adress, open assets/php/c_config.php
, find and edit code below:
... // put your email address here define('YOUR_EMAIL_ADDRESS', 'email@address.com'); define('YOUR_COMPANY_NAME', 'Enter Your Company Name');
To add or change a blog post content edit the following lines:
...Since FundPress joined Funding in January, we’ve been evolving into something bigger and better.
To add or change a portfolio edit the following lines:
...
you add your personal image to portfolio just go to assets/images/gallery
and rename your image example gallery-1.jpg
Parallax heading is based on jQuery. To add or change a title just following lines.  A Platonic dreamer in a dream world. A masochist with
an idealized ego that denies reality.
To add or change pie chart content edit the following lines:
...
you change or edit pie chart just following instructions find first data-percent="75"
and change to 80
To add or change video content edit the following lines:
...
you add your custom video just following instructions: got to https://www.youtube.com/
copy video url and paste it
To add or change count down timer edit the following lines:
...
you add or change countdown just following instructions: data-countdown="2020/01/01"
and duration set data-countdown="2021/05/01"
To add or change sync slider content edit the following lines:
...
Chnage sync slider preview image and add your own image just following instructions: assets/images/product/product_4.jpg
Chnage sync slider thumb image and add your own image just following instructions: assets/images/product/product_thumb_3.jpg
This theme imports the following Javascript files.
The following Photoshop file are included with the download package place in /PSD/ folder:
fundpress.psd
Once again, thank you so much for purchasing this template. As I said at the beginning, I'd be glad to help you if you have any questions relating to this template. No guarantees, but I'll do my best to assist. If you have a more general question relating to the templates on ThemeForest, you might consider visiting the forums and asking your question in the "Item Discussion" section.
XpeedStudio


{{state === 'error' ? errorMsg : ''}} {{state === 'success' ? 'Success! User Password has been changed!' : ''}}


Implicit Differentiation Questions
Find \({dy\over dx}\) when \(x\) and \(y\) satisfy:
- \(e^{xy} = e^{4y} - e^{5x}\)
- \(\cos(xy)=\sin(x-y)\)
- \(y\tan(x+y) = 4\)
- \(e^{\cos(x)} + e^{\sin(y)} = {1\over
4}\)
- \(e^{xy} + \ln(xy) = \text{cosec}(x) +
4\)
Find \({dy\over dx}\) when \(x\) and \(y\) satisfy:
- \(e^{xy} = e^{4y} - e^{5x}\)
- \(\cos(xy)=\sin(x-y)\)
- \(y\tan(x+y) = 4\)
- \(e^{\cos(x)} + e^{\sin(y)} = {1\over 4}\)
- \(e^{xy} + \ln(xy) = \text{cosec}(x) + 4\)
Solutions We apply the derivative operator \({d\over dx}\) to each equation and rearrange to get \({dy\over dx} = \dots\). The step-by-step solutions for 1. is provided, and the final solutions to the others only being provided.
The left-hand side is equal to \[{d\over dx}e^{xy} = e^{xy}\cdot {d\over dx}(xy) = e^{xy}(y+ x{dy\over dx}) = ye^{xy} + xe^{xy} {dy\over dx}.\] And the right-hand side is equal to \[{d \over dx}(e^{4y} - e^{5x}) = e^{4y}{d\over dx}(4y) - e^{5x}{d\over dx}(5x) = 4e^{4y}{dy\over dx} - 5e^{5x}.\] So we have that: \[ ye^{xy} + xe^{xy}{dy\over dx} = 4e^{4y}{dy\over dx} - 5e^{5x} \] which rearranges to: \[ xe^{xy}{dy\over dx} - 4e^{4y}{dy\over dx} = -ye^{xy} -5 e^{5x}. \] So we have that \[ (xe^{xy} - 4e^{4y}) {dy\over dx} = -ye^{xy} - 5e^{5x} \] and finally so: \[ {dy\over dx} = \frac{-ye^{xy} - 5e^{5x}}{xe^{xy} - 4e^{4y}} = \frac{ye^{xy} + 5e^{5x}}{ 4e^{4y}- xe^{xy}} \]
\[ {dy\over dx} = \frac{\cos(x-y) + y\sin(xy)}{\cos(x-y) - x\sin(xy)} \]
\[ {dy\over dx} =\frac{-y\sec^2(x+y)}{\tan(x+y) +y\sec^2(x+y)} \]
\[{dy\over dx} = \frac{\sin(x)e^{\cos(x)}}{\cos(y)e^{\sin(y)}}\]
\[{dy\over dx} = -1 - \frac{xy \text{cosec}(x)\cot(x)}{xye^{xy} + 1}\]
Find all the points \((x,y)\) on the
graph \((x^2+y^2)^2 = 2x^2 - 2y^2\)
where \(y’ = 0\).
Step 1: Find an expression for \({dy\over dx}\) by taking the \(x\) derivative of the equation: \[\begin{align} {d\over dx} (x^2+y^2)^2 &= {d\over dx}(2x^2- 2y^2) \\ 2(x^2 + y^2) {d\over dx}(x^2+y^2)&=4x - 4y {dy\over dx} \\ 2(x^2 + y^2)(2x +2y{dy\over dx})&=4x - 4y {dy\over dx} \\ 4y(x^2 + y^2){dy\over dx}+ 4y{dy\over dx}&=4x-4x(x^2 + y^2)\\ {dy\over dx}&= {x(1-(x^2 + y^2))\over y(1+(x^2 + y^2))} \end{align}\]
Step 2: Solve \({dy\over dx}=0\). This can occur when \(x = 0\) and \(y\neq 0\), so let’s investigate possible solutions of this type. Substituting this into the equation for the curve, we have that \(y^4 = -2y^2\), which if \(y\neq 0\), leaves \(y^2 =-2\), which has no real solutions. So we are left with the requirement that \(1-(x^2 + y^2)=0\). So we have that the equation of the curve becomes \(1 = 2x^2 - 2y^2\). We can eliminate either \(x\) or \(y\) using the equation \(1 = x^2 + y^2\) - I will choose to eliminate \(x^2\). Then we have that \(x^2 = 1-y^2\). So \[1=2x^2 -2y^2 = 2(1-y^2)-2y^2 = 2-4y^2.\] So we have that \(4y^2 = 1\), which gives us solutions of \(y = \pm {1\over 2}\). Thus we have that \[x^2 = 1-(\pm {1\over 2})^2 = 1-{1\over 4} = {3\over 4}.\] Giving \(x = \pm {\sqrt{3}\over 2}\). So the final solutions are: \[(x,y) = ({\sqrt{3}\over 2},{1\over 2}), \ (-{\sqrt{3}\over 2},{1\over 2}),\ ({\sqrt{3}\over 2},-{1\over 2}),\ (-{\sqrt{3}\over 2},-{1\over 2}) \]
Find the equation of the tangent line to the curve: \(y^2 e^{2x}=3y + x^2\) at the point \((0,3)\)
Find the equation of the tangent line to the curve: \(y^2 e^{2x}=3y + x^2\) at the point \((0,3)\)
- Step 1: Find an expression for \({dy\over dx}\) in terms of \(x\) and \(y\). We do this by taking the \(x\)-derivative of the equation of the curve: \[ \begin{align} {d\over dx}(y^2 e^{2x}) &= {d\over dx}(3y + x^2)\\ 2y{dy\over dx}e^{2x} + 2y^2e^{2x}&=3{dy\over dx} + 2x. \end{align} \] After rearranging we have that \[ \begin{align} (2ye^{2x} - 3){dy\over dx} &= 2x - 2y^2 e^{2x}\\ {dy\over dx}&= \frac{2x - 2y^2 e^{2x}}{(2ye^{2x} - 3)}. \end{align} \] Thus we have that \({dy\over dx}\) at the point \((x,y) = (0,3)\) is equal to \({dy\over dx} = -{18\over 3} = -6\). So the tangent line would have equation \(y = -6x + c\), and intersects the original curve at the point \((0,3)\), thus \(3 = -6\cdot 0 + c \implies c = 3\). Thus the tangent line has equation \(y = -6x +3\).
- Show that \({dy\over dx}\) for the
curve given by \((x+y)(x^2 - xy +
y^2)=1\) is:
\[
{dy\over dx} = - {x^2 \over y^2}
\] whenever \(y\neq 0\)
- Find the equation of the normal when \(x=0\).
- Show that \({dy\over dx}\) for the curve given by \((x+y)(x^2 - xy + y^2)=1\) is:
\[ {dy\over dx} = - {x^2 \over y^2} \] whenever \(y\neq 0\)
- Find the equation of the normal when \(x=0\).
To simplify the calculation we expand the brackets to get that \[ \begin{align} (x+y)(x^2-xy+y^2) &= x^3 - x^2y + xy^2 + yx^2 - xy^2 + y^3 \\ &= x^3 + y^2. \end{align} \] So the equation is just \(x^3 + y^3 = 1\), we then take the \(x\) derivative to give: \[ {d\over dx}(x^3 + y^3) = 3x^2 + 3y^2 {dy\over dx} = 0, \] which rearranges to the answer.
At \(x=0\), we have that \(y^3 = 1\), which has real solution \(y=1\), so the tangent line at \((x,y)=(0,1)\) is given by \(y = 0\cdot x + c\) as \({dy\over dx} = -\frac{0}{1} = 0\) at \((x,y)=(0,1)\). Thus the tangent line is a constant line \(y = 1\). The normal equationIf this is confusing to you, think about the graph \(y=1\) and then construct a perpendicular line that goes through the point \((0,1)\)
is therefore just \(x=0\).
Find the points \((x,y)\) on the graph
\(x^{2/3} + y^{2/3} =8\), where \(y’ = 1\).
Taking the \(x\) derivative of the
equation we have that: \[ {2\over 3}x^{-1/3}
+ {2\over 3}y^{-1 /3}{dy\over dx} = 0.
\] Which rearranges to: \[
{dy\over dx} = - {x^{-1/3}\over y^{-1/3}} = - \frac{y^{1/3}}{x^{1/3}}.
\] This equals \(1\), when \(y^{1 /3} = - x^{1/3}\), and by cubing this
equation we have that \(y = - x\). So
we need to simultaneously satisfy the equations \(x^{2/3} + y^{2/3} =8\) and \(y = -x\). Notice that \((-x)^{2/3} = ((-x)^{1/3})^2 =
((-1)^{1/3}x^{1/3})^2\), assuming we are only interested in the
realThere are also complex numbers which are the cube root
of -1, but we will ignore those
solutions to this equation we have that \((-1)^2 x^{2/3}=x^{2/3}\). So we have that
\(2x^{2/3} = 8\), thus \(x^2= 4^{3} = 64\) and thus \(x=\pm 8\). So the points of the graph are
\((x,y) = (8,-8),\ (-8,8)\).
- The curve C is described by the equation \(3x^2 + 2xy^3 + 16 = 0\). Show that the
normal to C at the point \(x=-4\) is
parallel to the normal to C at \(x=4\).
- Find the distance between the y-intercepts of these two
normals.
- The curve C is described by the equation \(3x^2 + 2xy^3 + 16 = 0\). Show that the normal to C at the point \(x=-4\) is parallel to the normal to C at \(x=4\).
- Find the distance between the y-intercepts of these two normals.
-
When \(x=+ 4\) the equation simplifies to \(y^3= -8\), with \(y=-2\) its solution. And when \(x=-4\), we have that \(y^3 = 8\) and thus \(y=2\).
The normal line to these points are then found by first finding the tangent line. To do this we need an expression for the gradient, \(dy \over dx\), which we get by taking the \(x\)-derivative of the equation: \[\begin{align} 6x + 2y^3 + 6xy{dy\over dx} = 0\\ {dy\over dx} = {-3x -y^3 \over 3xy} \end{align} \]
Thus the gradient at \((x,y) = (4,-2)\) is equal to \[{dy \over dx} = {-12 + 8 \over -24 }=-{4\over 24} = - {1\over 6}.\]
And the gradient at \((x,y) =(-4,2)\) is equal to \[{dy\over dx} = {12 - 8 \over -24} = - {1\over 6}.\] As the tangents have the same gradient, the normal lines at these points will also have the same gradient, as the normal has the negative reciprocal gradient as the tangent, i.e. \(m= 6\) for both normals.
The equations of the normals are \(y = 6x+c\), where \(c\) is the \(y\)-intercept. The normal to the point \((x,y) = (4,-2)\) needs to have \(c = y-6x = -2 - 6\cdot 4 = -26\). The normal to the point \((x,y) = (-4,2)\) needs to have \(c = 2+6\cdot 4 = 26\). So the distance between the \(y\)-intercepts is $52
Find the stationary points and determine their nature* for the curve
with equation \(y^2 = 3x^2 -2xy +
3\)
*are they maxima, minima or indeterminate.
Find the stationary points and determine their nature* for the curve with equation \(y^2 = 3x^2 -2xy + 3\)
*are they maxima, minima or indeterminate.
To find stationary points, we need to find the points where \({dy\over dx}=0\). So we take the \(x\)-derivative of the equation to get: \[ 2y{dy\over dx} = 6x -2y -2x{dy\over dx}. \] Which when rearranged gives: \[ {dy\over dx} = \frac{3x-y}{y+x}. \] This equals zero when \(3x-y=0\) and \(y+x\neq 0\). So when \(y=3x\). We need to then find solutions to \(y=3x\) and \(y^2 = 3x^2-2xy+3\), which we can do by substituting \(y=3x\) in the original equation: \[\begin{align} (3x)^2 &= 3x^2 - 2x(3x) + 3\\ 9x^2&= 3x^3 - 6x^3 +3\\ 12x^2 &= 3\\ x^2 &= {1\over 4}\\ x &= \pm {1\over 2}. \end{align} \] So we have that the stationary points are given by \[ (x,y) = (+{1\over 2}, +{3\over 2}),\ (-\frac{1}{2},-{3\over 2}). \]
To determine whether these stationary points are maximums or miminums (or indeterminates). We need to do the second-derivative test. We need an expression for \({d^2y \over dx^2}\), which we can get by taking the derivative of the expression for \({dy\over dx}\) using the quotient rule: \[\begin{align} {d^2y\over dx^2} &= \frac{(3-{dy\over dx})(y+x) - (3x-y)(1+{dy\over dx})}{(y+x)^2} \\ &= \frac{3y-3x -3x+y - {dy\over dx}(y+x -3x+y)}{(y+x)^2}\\ &= \frac{4y-6x - {dy\over dx}(2y-2x)}{(y+x)^2}. \end{align} \] Note that the points we are interested in have the property that \({dy\over dx}=0\). So we do not need to simplify this any further. For the point \((x,y) = ({1\over 2},{3\over 2})\) we have that: \[\begin{align} {d^2y\over dx^2} &= \frac{ \frac{12}{2}- \frac{6}{2} }{({3\over 2}+{1\over 2})^2} = \frac{6-4}{2^2}\\ &= \frac{2}{4} =\frac{1}{2}> 0. \end{align} \] Meaning that the stationary point at \(({1\over 2},{3\over 2})\) is a minimum. For the point \((x,y) = (-{1\over 2},-{3\over 2})\) we have that: \[\begin{align} {d^2y\over dx^2} = \frac{-6 + 4}{(-2)^2} = \frac{-2}{4} <0. \end{align} \] Making this stationary point a maximum.
Show that \[
{d\over dx}a^{x^{k}} = k a^{x^k} x^{k-1}\ln(a)
\]
Show that \[ {d\over dx}a^{x^{k}} = k a^{x^k} x^{k-1}\ln(a) \]
Rewrite the expression as \(a^{x^k} = (e^{\ln(a)})^{^{x^k}} = e^{\ln(a)x^k}\). Now if we take the derivative we can use the fact that \({d\over dx}e^u = e^u{dx\over du}\).
\[\begin{align} {d\over dx}(a^{x^k}) &= {d\over dx}(e^{\ln(a)x^k}) = e^{\ln(x)x^k} {d\over dx}(\ln(a)x^k) \\ &= e^{\ln(a)x^k}\ln(a) kx^{k-1} \end{align} \] Notice that \(a^{x^k} = e^{\ln(a)x^k}\), so we have the answer.