## First order method of characteristics

$$cos(y)frac{partial u}{partial x} + x frac{partial u}{partial y} = frac{x}{u}$$

And can’t seem to get past the characteristics, namely:

$$frac{dx}{cos(y)} = frac{dy}{x}$$

and

$$frac{du}{x/u} = frac{dx}{cos(y)}.$$

How might I proceed here?

## algorithms – Characteristics of max-heaps

I have just reached the priority queue section where the book I am currently reading about algorithms talked about max-heaps and min-heaps. As a part of its structure, the book would ask the reader a question about the content of each chapter. In this chapter, the book asked the reader to agree or disagree with the following statement, and asked the reader the following question (included below).

Statement: “Joe made a claim that the minimum element of a max-heap which is binary must be one of its leaf nodes”.

Question: “Which of the following statements did you have to assume to hold true in order to make a decisively decide whether the statement above is true/false?”
(1) All nodes in the max-heap should be distinct/unique.
(2) There is only one maximum among the nodes

After some thought, I have agreed with this statement since I know that based on the properties of a max-heap every parent node should be greater than or equal to its children. In order to decide, I had to suppose that (1) is true. Would assuming that (2) is true would also be helpful, or even more appropriate than supposing that (1) is true to come up with a decisive choice?

## set theory – A sequence of cardinal characteristics constructed with hypergraph coloring

Let $$(omega)^omega$$ denote the collection of infinite subsets of $$omega$$.

A hypergraph $$H=(V,E)$$ consists of a set $$V$$ and a collection of subsets $$E subseteq {cal P}(V)$$. A coloring is a map $$c: Vto kappa$$, where $$kappa neq emptyset$$ is a cardinal, such that for every $$ein E$$ with $$|e|geq 2$$ the restriction $$c|_e$$ is non-constant. We denote the minimal cardinal $$kappa$$ such that there is a coloring $$c: Vto kappa$$ by $$chi(H)$$ and call it the chromatic number of $$H$$

If $$Asubseteq (omega)^omega$$ is finite or countable, then the chromatic number of $$(omega, A)$$ equals $$2$$. This motivates the following cardinals: for any integer $$ngeq 2$$ let $${frak k}_n$$ be the minimum cardinality of a set $$Asubseteq (omega)^omega$$ such that $$chi(omega, A) > n$$.

Is it consistent in $${sf ZFC}$$ that $${frak k}_n < {frak k}_{n+1} < 2^{aleph_0}$$
for all integers $$ngeq 2$$?

## nt.number theory – Siegel’s formula for generalized theta series with characteristics?

Thanks for contributing an answer to MathOverflow!

But avoid

• Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.

## real analysis – To find zero set of an convolution of two characteristics function

For $$E=(0,1)setminus mathbb{Q}, ~l>0$$ and consider the function
$$chi_{(-l,l)}*chi_E(x)=int_{-l}^{l}chi_E(x-t)dt.$$
What is the zero set of the above function (in terms of $$l$$ may be)?

Notations: $$mathbb{Q}$$ is the set of rationals. $$chi_E$$ is the characteristic function of $$E.$$

Many small businesses don’t get success they want from advertising due to availability of very little resources. The results are simply flat due to lack of good ideas for improvements. Whether the ads are put in a local newspaper or are printed in the famous periodical or posted on a website, the money invested should gain the desired outcome. There are some common mistakes small businesses and professional service providers do when designing and posting the advertisement, which leads to the failure of the advertisement.

Bigger is better is believed in by many. That’s exactly what some of the small firms think when they want to advertise their product. They think bigger and select a medium where they need to invest a lot of money, but do not reach the targeted market. Like if a company specializes in designing diet plans and want to help out people who had disappointing results from their individual diet plans, and the company chooses to advertise a full page in the local paper instead of running advertisement in a health magazine, obviously not many of the dieters will notice the advertisement and the advertisement doesn’t get the desired attention.

So the point is to come up with the best campaign, which will increase the probability of the ad getting viewed and the right customers trying to buy the product or sign up for the service. Studies and research can be carried out on the market and targeted audience can be narrowed down. Once getting the list of newspapers, magazines and magazines meant for the customers in mind, find out how many readers they have and the cost they ask for posting the ad. Special deals are offered by them from time to time and can only be found by watchful eye.

It is estimated that everyday people are subjected to around three thousand commercials. That is a huge number and if someone desires to be noticed, he should certainly be different. Not only the services and product sold should be unique in the market, so should be the advertisement. For example, if a business selling mattresses says, “We sell mattresses”, it will not make a statement and will be passed off as any other mattress advertisement. But if they say, “Our mattresses are of the finest quality”, it will make the advertisement stand out in the crowd. Other catch lines are “Are you suffering from back pain? Probably you must try our mattresses “, are more specific and will catch the fancy of the people who are suffering from back pains since a long time. The advertisement should also focus on the uniqueness of the product and how it is better compared to the competitors’ product.

Focusing on the problems of the customers and giving a solution for them, is what a customer demands. A customer does not buy a product; he buys benefits in the form of a product. The real value of the product should be realized and a clear picture of it should be presented to the customer so he will be able to relate with the product. If the advertisement doesn’t specify the solution it can provide, the customers will never know of it. So focusing on the customers problem is what some ads miss.

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## prime numbers – Known table of $GF(p)$ and characteristics

Is there a list of Galois Fields, $$GF(p)$$ and its known multiplicative generator(s), $$g$$?
I know the general case of finding the generators may take long especially for large $$p$$, but was wondering if there was OEIS entry or other resource? I am specifically looking for primes of the order of 512 bits or greater. Larger the better.

## Activate 'Reports on demographic characteristics and interests' does not exist

Hi, I have several different websites in my Google Analytics. On all – except one – I was able to activate 'Reports on demographic characteristics and interests' in the property settings (to get the information about age and gender). On one page this area is not even displayed. 'Property hit volume' is directly followed by 'In-Page-Analysis' (see screenshot). Does anyone have any idea what might be causing it?
Thanks for help.
Markus, from Austria

## What are the best characteristics of binary HYIP script? – MLM & Network Marketing

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## What characteristics should I know before buying a Drone?

hey dudes,
I decided to buy a Drone. Found rckane.cz shop, they offer a great number of Drones.
What characteristics should I know before buying a Drone? Any recommendations on a certain model?

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