## [ Mythology & Folklore ] Open Question: Why did Trump spend 290 of his 547 days in office, either playing golf or at his private clubs and properties? That's more than half?

Do you think maybe it's because he works 10 times as hard as other presidents, so he needs 10x the holidays?

Should not my tax money be used for something useful? Like a nurse with special needs?

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## Prove that two different pairs of natural numbers do not exist with these properties

The problem is to prove the nonexistence or to show that there are two different pairs (up to the permutation) of natural numbers $$(a, b)$$ and $$(c, d)$$ s.t. $$lcm (a, b) = lcm (c, d)$$
$$gcd (a, b) = gcd (c, d)$$ and
$$frac {a + b} {2} = frac {c + d} {2}$$

It is easy to show that if LCM and GCD are the same, two pairs have the same product and the same sum AND the same GCD. I have the intuition that it is impossible to exist two different pairs under these conditions, but it is unclear how to prove it exactly.

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## c ++ classes with different properties – right approach?

Let's say I have lessons `NumericalDataSet` with the property `data` of the type `std::vector>` and `LabeledDataSet` with the property `data` of the type `std::vector>>`, All other methods and properties are the same. What is the right approach to deal with this?

Should I make an abstract class `DataSet` to inherit with the two or is it better to use a heterogeneous container like boost :: any?

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## discrete mathematics – properties of relationship evidence

I practice some characteristics of relationships and I can not seem to figure out a specific question. It follows

``````Consider the relation R on Z+(positive integers) as: For all m,n belonging to Z+, mRn means m|n.
Is R reflexsive, symmetric or transitive?
Provide a complete proof or counterexample for each property.
You may only use the definition of divides
``````

The definition of divisions according to my special textbook is as follows.

``````let n,d ∈ ℤ+ and d≠0.
n is divisible by d if and only if ∃ k ∈ ℤ such that n = dk
``````

How would I go about doing that? Every help is appreciated. Many thanks

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## fa.functional analysis – Basic properties of expectation in non-separable Banach spaces

$$def E { hskip.15ex mathsf {E} hskip.10ex}$$
To let $$B$$ be a (perhaps inseparable) Banach room equipped with the Borel $$sigma$$-Algebra $$mathscr {B} (B)$$, To let $$R: B to mathbb {R}$$ Let be a limited linear operator.

To let $$( Omega, mathcal {F}, P)$$ be a probability space. To let $$F$$ be a $$mathscr {B} (B) | mathcal {F}$$measurable assignment $$Omega to B$$, Suppose that $$E | F | < infty$$,

Question: Is it true without further assumptions that $$E F$$ is well defined, belongs to $$B$$ and
$$E RF = R E F?$$

Note: As a rule (eg in the Ledoux-Talagrand book) the separability of room B is additionally imposed. I wonder if the statement is true without this assumption. What happens, for example, if $$B$$ is only a space of limited measurable functions?

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## Proof of Gaussian integral properties

Hello, I work with a model of Gaussian demand. The following should be an easily derived property, but I could not reproduce it myself.
Why is $$f (x)> xF (x)$$ to the
$$F (x) = int_ {x} ^ { infty} dfrac {1} { sqrt {2 pi}} e ^ {- frac {1} {2} t ^ 2} dt$$

Thanks for your help

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## smt-solver – program synthesis based on functional properties

I am fairly new to program synthesis and the use of SMT solvers for this purpose. Given a function GI want to generate all functions f and H such that:

f. g = h. f

Are there any tools and techniques for program synthesis that allow me to search the program area for these functions?

I assume that the search space for general programming languages ​​like Haskell will be extremely large. How should one proceed to curtail the search space: would one have to drastically reduce the search space by defining a small language and performing the search through that language? It would seem that the type constraints of the above equation would also help cropping the search space. Any observations or references to tools, papers or presentations are welcome.

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## mesh – solving a wave equation with finite elements, if the material properties in a range vary continuously

I solve the one-dimensional wave equation over regions in which the volume modulus (and thus the wave velocity) varies continuously over a region. The current version seems to assume that the material properties are constant over a FEM element. Some references suggest that isoparametric elements can help model regions in which the material properties vary continuously. Can you suggest how to model regions where the material properties vary continuously?

In the wave equation code I use, Kappa and Rho can vary over an element. The code is as follows:

``````eqn = 1/(Kappa)(x) D(u(t, x), {t, 2}) +
Div(-(Rho)(x)*Grad(u(t, x), {x}), {x}) ==
1/(Kappa)(x)*10*Exp(-50 (x^2))*Sin(2 (Pi) f t) +
NeumannValue(0, x == 0) + NeumannValue(-Derivative(1, 0)(u)(t, x), x ==
xMax);
ic = {u(0,x) == 0, Derivative(1, 0)(u)(0, x) == 0};
``````

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## Properties – Created columns do not appear in the page detail form of the Web page in SharePoint Online?

I need to add properties for date and time types and change them using the site's page details form.

If I add properties to the page library, it will not appear in the form of page details of the web page in the properties list.

It has been working since yesterday.

Do you have any idea?

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