We characterize real functions f on an interval (−α, α) for which the entrywise matrix function [aij ] 7→ [f(aij)] is positive, monotone and convex, respectively, in the positive semidefiniteness order. Fractional power functions are exemplified and related weak majorizations are shown. AMS subject classification: 15A45, 15A48

Let A = (aij) be the generic n×n circulant matrix given by aij = xi+j , with subscripts on x interpreted mod n. Define d(n) (resp. p(n)) to be the number of terms in the determinant (resp. permanent) of A. The function p(n) is well-known and has several combinatorial interpretations. The function d(n), on the other hand, has not been studied previously. We show that when n is a prime power, d(n...

(1.2) Let k be an algebraically closed field of arbitrary characteristic. For a ring A, an A-module means a left A-module, unless otherwise specified. However, an ideal of A means a two-sided ideal, not a left ideal. Amod denotes the category of finitely generated A-modules. For a group G, a G-module means a kG-module, where kG is the group algebra of G over k. If V is a finite dimensional vect...

We define a class of formal expansions ∑∞ `=−∞ α`z ` of a rational function with at least one nonzero pole. To distinct formal expansions ∑∞ `=−∞ α`z ` and ∑∞ `=−∞ β`z ` in this class we associate structured arrays A = (aij) ∞ i,j=1 and B = (bij) ∞ i,j=1, defined by aij = ∑k ν=1 aναpνi+qj+τν and bij = ∑k ν=1 aνβpνi+qj+τν , where q ( 6= 0), p1, . . . , pk , and τ1, . . . , τk are integers and a1...

Latar belakang. Artritis idiopatik juvenil (AIJ) sistemik merupakan penyakit inflamasi yang tidak hanya melibatkan sendi tetapi juga keterlibatan dan tipe terberat dari AIJ. Tatalaksana standar diberikan sering memberikan respons klinis optimal sehingga meningkatkan morbiditas mortalitas. Pemberian agen biologis seperti tocilizumab atau anakinra pilihan untuk tatalaksana AIJ sistemik. Tujuan. M...

Quasideterminants of noncommutative matrices introduced in [GR, GR1] have proved to be a powerfull tool in basic problems of noncommutative algebra and geometry (see [GR, GR1-GR4, GKLLRT, GV, EGR, EGR1, ER,KL, KLT, LST, Mo, Mo1, P, RS, RRV, Rsh, Sch]). In general, the quasideterminants of matrix A = (aij) are rational functions in (aij)’s. The minimal number of successive inversions required to...

Complex information extraction (IE) pipelines assembled by plumbing together off-the-shelf operators, specially customized operators, and operators re-used from other text processing pipelines are becoming an integral component of most text processing frameworks. A critical task faced by the IE pipeline user is to run a post-mortem analysis on the output. Due to the diverse nature of extraction...

In this paper, we consider the following type of non-local (pseudo-differential) operators L on Rd: Lu(x) = 1 2 d ∑ i,j=1 ∂ ∂xi ( aij(x) ∂ ∂xj ) + lim ε↓0 ∫ {y∈Rd: |y−x|>ε} (u(y) − u(x))J(x, y)dy, where A(x) = (aij(x))1≤i,j≤d is a measurable d × d matrix-valued function on Rd that is uniformly elliptic and bounded and J is a symmetric measurable non-trivial nonnegative kernel on Rd × Rd satisfy...