相关论文: More supplements to a class of logarithmically com…
Associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=f^{(-1)}(F(f(x),f(y)))$ where $F:[0,\infty]^2\rightarrow[0,\infty]$ is an associative function, $f: [0,1]\rightarrow [0,\infty]$ is a monotone function…
In this paper, we obtain coefficient criteria for a normalized harmonic function defined in the unit disk to be close-to-convex and fully starlike, respectively. Using these coefficient conditions, we present different classes of harmonic…
An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.
This note contains some observations on primary matrix functions and different notions of monotonicity with relevance towards constitutive relations in nonlinear elasticity. Focussing on primary matrix functions on the set of symmetric…
Consider a complete asymptotically flat 3-manifold $M$ with non-negative scalar curvature and non-empty minimal boundary $\Sigma$. Fix a number $1 < p < 3$. We derive monotone quantities for $p$-harmonic functions on $M$ which become…
Among all two-dimensional commutative algebras of the second rank a totally of all their biharmonic bases $\{e_1,e_2\}$, satisfying conditions $\left(e_1^2+ e_2^2\right)^{2} = 0$, $e_1^2 + e_2^2 \ne 0$, is found in an explicit form. A set…
We characterize real functions $f$ on an interval $(-\alpha,\alpha)$ for which the entrywise matrix function $[a_{ij}] \mapsto [f(a_{ij})]$ is positive, monotone and convex, respectively, in the positive semidefiniteness order. Fractional…
$c$-cyclical monotonicity is the most important optimality condition for an optimal transport plan. While the proof of necessity is relatively easy, the proof of sufficiency is often more difficult or even elusive. We present here a new…
Threshold phenomena are investigated using a general approach, following Talagrand [Ann. Probab. 22 (1994) 1576--1587] and Friedgut and Kalai [Proc. Amer. Math. Soc. 12 (1999) 1017--1054]. The general upper bound for the threshold width of…
In this article, we characterize completely alternating functions on an abelian semigroup $S$ in terms of completely monotone functions on the product semigroup $S\times \mathbb Z_+$. We also discuss completely alternating sequences induced…
We consider the construction of insurance premiums that are monotonically increasing with respect to a loading parameter. By introducing weight functions that are totally positive of higher order, we derive higher monotonicity properties of…
In this paper, a new proof of the Positive Mass Theorem is established through a newly discovered monotonicity formula, holding along the level sets of the Green's function of an asymptotically flat $3$-manifold. In the same context and for…
Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly…
A monotonicity property of Harnack inequality is proved for positive invariant harmonic functions in the unit ball.
A new uniform asymptotic expansion for the incomplete gamma function $\Gamma(a,z)$ valid for large values of $z$ was given by the author in {\it J. Comput. Appl. Math.} {\bf 148} (2002) 323--339. This expansion contains a complementary…
We provide a sufficient condition for the bounded law of the iterated logarithms for strictly stationary random fields expressable as a functional of i.i.d. random fields when the summation is done on rectangles. The study is done via the…
We study meromorphic functions in a strip almost periodic with respect to the spherical metric. Then we get a complete description of zeros and poles for this class of functions, find a condition for a meromorphic almost periodic function…
A new necessary and sufficient stability test in a tractable number of operations for linear neutral-type delay systems is introduced. It is developed in the Lyapunov-Krasovskii framework via functionals with prescribed derivatives. The…
We prove a lower bound of $\Omega(n^{1/2 - c})$, for all $c>0$, on the query complexity of (two-sided error) non-adaptive algorithms for testing whether an $n$-variable Boolean function is monotone versus constant-far from monotone. This…
Lower and upper bounds $B_a(x)$ on the incomplete gamma function $\Gamma(a,x)$ are given for all real $a$ and all real $x>0$. These bounds $B_a(x)$ are exact in the sense that $B_a(x)\underset{x\downarrow0}\sim\Gamma(a,x)$ and…