Let 0 < α < β be two irrational numbers satisfying 1/α+1/β = 1. Then the sequences a′n = bnαc, b′n = bnβc, n ≥ 1, are complementary over Z≥1, thus a′n satisfies: a′n = mex1{ai, bi : 1 ≤ i < n}, n ≥ 1 (mex1(S), the smallest positive integer not in the set S). Suppose that c = β − α is an integer. Then b′n = a′n + cn for all n ≥ 1. We define the following generalization of sequences a′n, b′n: Let...

We determine the class of entire functions for which the Airy kernel (of random matrix theory) is a reproducing kernel. We deduce an Airy sampling series and quadrature formula. Our results are analogues of well known ones for the Bessel kernel. The need for these arises in investigating universality limits for random matrices at the soft edge of the spectrum. 1. Introduction Universality limit...

Sufficient conditions for the solvability of two-point boundary value problems for the system xi = fi(t, x1, x2) (i = 1, 2) are given, where f1 and f2 : [a1, a2]×R → R are continuous functions. 1. Statement of the problems and formulation of the main results Consider the system of ordinary differential equations xi = fi(t, x1, x2) (i = 1, 2) (1.1) with boundary conditions λi1x1(ai) + λi2x2(ai) ...

The aim of this paper is to present a nice series of results, obtained in the papers of Chaitin [2], Solovay [5], Calude et al. [1], Kucera and Slaman [3]. This joint effort led to a full characterization of lower semicomputable random reals, both as those that can be expressed as a “Chaitin Omega” and those that are maximal for Solovay reducibility. The original proofs were somewhat involved; ...

We show that as T→∞, for all t∈[T,2T] outside of a set measure o(T), ∫−logθTlogθT|ζ(1 2+it+ih)|βdh=(logT)fθ(β)+o(1), some explicit exponent fθ(β), where θ>−1 and β>0. This proves an extended version conjecture Fyodorov Keating (Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 372 (2014) 20120503, 32). In particular, it shows that, θ>−1, the moments exhibit phase transition at critical ...

Consider a generic data unit of random size L that needs to be transmitted over a channel of unit capacity. The channel availability dynamics is modeled as an i.i.d. sequence {A,Ai}i>1 that is independent of L. During each period of time that the channel becomes available, say Ai, we attempt to transmit the data unit. If L ≤ Ai, the transmission is considered successful; otherwise, we wait for ...

Abstract Lactoferrin (LF) is known to possess anti-inflammatory activity, although its mechanisms of action are not well-understood. The present study asked whether LF affects the commitment inducible regulatory T cells (Tregs). substantially promoted Foxp3 expression by mouse activated CD4+T cells, and this activity was further enhanced TGF-β1. Interestingly, blocking TGF-β with anti–TGF-β Ab ...

to study the effects of integration of mechanical control with herbicides on yield and yield components of soybean (glycine max) a field experiment was conducted during 2003-2004 at the research farm of agronomy department, agriculture campus of tehran university, karaj. a randomized complete block design (rcbd) of 18 treatments was applied, each treatment being replicated 3 times. treatments i...