ﻻ يوجد ملخص باللغة العربية
In this paper, some sufficient conditions for the differentiability of the $n$-variable real-valued function are obtained, which are given based on the differentiability of the $n-1$-variable real-valued function and are weaker than classical conditions.
Two articles published by Information Science discuss the derivatives of interval functions, in the sense of Svetoslav Markov. The authors of these articles tried to characterize for which functions and points such derivatives exist. Unfortunately, t
Let $ xgeq 1 $ be a large number, let $ [x]=x-{x} $ be the largest integer function, and let $ varphi(n)$ be the Euler totient function. The result $ sum_{nleq x}varphi([x/n])=(6/pi^2)xlog x+Oleft ( x(log x)^{2/3}(loglog x)^{1/3}right ) $ was proved
Let $ xgeq 1 $ be a large number, let $ [x]=x-{x} $ be the largest integer function, and let $ sigma(n)$ be the sum of divisors function. This note presents the first proof of the asymptotic formula for the average order $ sum_{pleq x}sigma([x/p])=c_
Let $R = k[w, x_1,..., x_n]/I$ be a graded Gorenstein Artin algebra . Then $I = ann F$ for some $F$ in the divided power algebra $k_{DP}[W, X_1,..., X_n]$. If $RI_2$ is a height one idealgenerated by $n$ quadrics, then $I_2 subset (w)$ after a possib
There is error in (2.1). I am very sorry for inconvenience.