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Is it common to omit a preposition (in / on / of) before “the month (year / week /day) when they are used adjectively and adverbially?

There was the following sentence in New York Times (April 12) article titled, ‘Lone Wolf’ Theory Gains Ground in Texas Deaths” “The Kaufman County district attorney’s office is small com

english-language

Can every recursively enumerable language be defined with regular expression?

Can every recursively enumerable language be defined with regular expression? I came across this question, when studying for my test: Prove that for any finite language $L$, there is a Turing mach...

computer-science

Is there any source for raw data of SNP genotype frequency?

On sites like SNPedia, some pages contain the frequency of the SNP in question in different populations, based on published research. I'm trying to write a script that takes 23andme data and compa

biology

How many strings are close to a given set of strings?

This question has been prompted by Efficient data structures for building a fast spell checker. Given two strings $u,v$, we say they are $k$-close if their Damerau–Levenshtein distance¹ is sma

computer-science

Example of existence proof in dependent typing?

I understand that $\Pi$ types are generalizations of functions and can be interpreted similar to $\forall$ in logic. I also know that $\Sigma$ types are generalizations of tuples and can be interpr...

computer-science

Under what conditions do dendritic spines form?

I'm looking for resources or any information about the formation of dendritic spines and synaptogenesis, especially in relation to how new connections are formed on a daily basis. Does the electr

biology

Why is the resting membrane potential of cardiomyocyte more stable than that of Pacemaker in Phase 4?

There must be some channels that keeps this very stable. It seems to be that the resting membrane potential of pacemaker cells is steadily increasing until the threshold voltage. I think the same m...

biology

I had a homework question that I could not figure out. It states: A woman has cystic fibrosis in her family and did not want to have a child that suffered from the disease. She and her spous...

biology

Is the total mass of the universe constant in time?

Is the total mass of the universe constant in time?

physics

Index of a maximal subgroup in a finite group

My question is very simple and maybe trivial. Here it is. Is the index of a maximal subgroup in a finite group always a prime number? Thanks in advance.

mathematics

When happens when pollen grains land on the a part other than the stigma of a flower of the same species?

When happens when pollen grains land on the a part other than the stigma of a flower of the same species? Would the pollen be transported to the stigma or would it just sit where it landed and noth...

biology

Proving the AM-GM Inequality with Lagrange Multipliers

Exercise: Let $x_1,x_2,...,x_n$ be real positive numbers. Prove the arithmetic-geometric mean inequality, $(x_1x_2...x_n)^{1/n}\le (x_1+x_2+...+x_n)/n$. Hint: Consider the function

mathematics

LHC data and mathematics of QFT

I'm reading Frederic's Paugam Towards the Mathematics of Quantum Field Theory, an advanced theoretical physics book. I would like to know how I could apply the theories in this book. For exa

physics

Magnetic field of a static disk magnet

I have a magnetic disk (Radius R, height h) that creates magnetic field lines (axisymmetrical). I simulated the field lines, exported the data and am now trying to fit a function into the data to h...

physics

Tensorial version of Hooke's law

It is well known that $${\boldsymbol F} = k {\boldsymbol x}$$ for isotropic media. Also, according to Wikipedia $$F_k = k_{jk} x_j$$ for some elastic tensor $k_{jk}$. I'm a bit confused as to h

physics

How to bring singular and plural conditions under a single sentence?

I am doing a sentence like the below. "He may undergo a scan,(or scans). The resulting image/images will be examined by the doctor." I am thinking of this one. "He may undergo a grou

english-language

magma computer algebra system local and global variables syntax

function Max(x) max := 0; L := []; for i := 1 to x do P2&lt;x,y,z&gt; := ProjectiveSpace(Rationals(),2); C_i := Curve(P2, x^3+y^3-i*z^3); E_i, C_itoE_i :=

mathematics

Can ECpqANpq get proved in intuitionistic logic?

I use Lukasiewicz/Polish notation. Given intuitionistic logic with the optional axioms for equivalence and negation given in the Wikipedia, can ECpqANpq or in other notation

mathematics

Distribution of number of unique elements

I've been stuck on the following problem for a few days and would really appreciate some help. This isn't homework. The context of this problem is that $m$ and $n$ may be extremely large but t

mathematics

Solubility, pressure and Henry's law

Im trying to do my chem homework and I'm stumped. Determine the solubility of $\ce{N2}$ in water exposed to air at 25°C, if the atmospheric pressure is 1.2 atm, assume that the mole fr

chemistry

Did these scientists actually detect dark matter?

I came across an article in The Guardian (definitely not the best source for science, but that's why I'm asking this question) that said that a team of scientists may have detected dark matter

physics

Solving quadratic equations in the field $F_5$

Let $y = x^2 + 2x + 2 = 0$. Solve the equation in the field $F_5$. So I used the common $b^2 - 4ac$ formula and got that $x$ is either $-1/2$ or $-3/2$ but I'm not sure if this is in the field...

mathematics

Does the category of directed systems have enough injectives?

Let $\mathscr{C}$ be an abelian category with enough injectives. Let $\mathscr{C}_A$ denote the abelian category of directed systems of objects of $\mathscr{C}$ indexed by $A$. Does $\mathscr{C}_A$

mathematics

If I define $I.J=\{ij : i \in I$ & $j \in J \}$. Then prove that it is not necessrily an ideal, where $I,J$ are ideals in a ring $R$.

If I define $I.J=\{ij : i \in I$ &amp; $j \in J \}$. Then prove that it is not necessrily an ideal, where $I,J$ are ideals in a ring $R$. I have found one counter example in $R[x,y,z]$ for

mathematics

On a decomposition of a conditional distribution

I am trying to make some sense out of equation (7) in the recent paper of Peter van Leeuwen: "Representation errors and retrievals in linear and nonlinear data assimilation"

mathematics