In this paper we establish a formula for the average of representation numbers of ternary quadratic forms in a spinor genus over a totally real number field. The significant fact about the formula is the fact that it is given in terms of local qu...
We generalize the Stirling numbers of the first kind $s(a,k)$ to the case where $a$ may be an arbitrary real number. In particular, we study the case in which $a$ is an integer. There, we discover new combinatorial properties held by the classical...
Here presented is a unified approach to Stirling numbers and their generalizations as well as generalized Stirling functions by using generalized factorial functions, $k$-Gamma functions, and generalized divided difference. Previous well-known extens...
We introduce a class of $f(t)$-factorials, or $f(t)$-Pochhammer symbols, that includes many, if not most, well-known factorial and multiple factorial function variants as special cases. We consider the combinatorial properties of the corresponding ge...
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Let $Q(x_1, \cdots,x_n)$ be a real indefinite quadratic form of the type $(r,s)$, $n=r+s$, signature $σ=r-s$ and determinant $D\neq 0$. Let $Γ_{r,n-r}$ denote the infimum of all numbers $Γ$ such that for any real numbers $c_1, c_2 ,\cdots, c_n$ th...
We shall given a new effectively computable upper bound of odd perfect numbers whose Euler factors are powers of fixed exponent, improving our old result in T. Yamada, Colloq. Math. 103 (2005), 303--307....
What is a counting number in Maths? In Mathematics, counting numbers are natural numbers, that are used to count anything.
In math, ‘to count’ or counting can be defined as the act of determining the quantity or the total number of objects in a set or a group. In other words, to count means to say numbers in order while …
We investigate the translational motion of rotating colloidal systems at moderate Reynolds numbers (Re), focusing on particle dimers in snowman-like configurations under three scenarios: (i) two co-rotating spheres driven by an external field, (ii) t...
Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of common prop...
In 1998 Don Zagier introduced the modified Bernoulli numbers $B_{n}^{*}$ and showed that they satisfy amusing variants of some properties of Bernoulli numbers. In particular, he studied the asymptotic behavior of $B_{2n}^{*}$, and also obtained an ex...
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Oct 22, 2008 · I match these to a file to update any card numbers to the account number so that I am only working with account numbers. I created a view linking the table to the account/card database to …
The Nilsson model is a simple microscopic model which has been extensively used over the years for the interpretation of a bulk of experimental results. The single particle orbitals in this model are labeled by quantum numbers which are good in the l...