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Abstract

A definition of a generalized quotient topology is given and some characterizations of this concept, up to generalized homeomorphisms, are furnished. For the first approach, we exhibit a monotonic map spanning that generalized quotient topology. We also prove that the notions of generalized normality and generalized compactness are preserved by those quotient structures.

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Abstract

Let {X,X n; n≧1} be a sequence of B-valued i.i.d. random variables. Denote if ∥X m∥ is the r-th maximum of {∥X k∥; kn}, and let be the trimmed sums, where . Given a sequence of positive constants {h(n), n≧1}, which is monotonically approaching infinity and not asymptotically equivalent to loglogn, a limit result for is derived.

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Abstract  

We show that the classical monotonicity conditions can be moderated in four theorems of P. Chandra.

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Abstract

Let fL 2π be a real-valued even function with its Fourier series , and let S n(f,x) be the nth partial sum of the Fourier series, n≧1. The classical result says that if the nonnegative sequence {a n} is decreasing and , then if and only if . Later, the monotonicity condition set on {a n} is essentially generalized to MVBV (Mean Value Bounded Variation) condition. Very recently, Kórus further generalized the condition in the classical result to the so-called GM7 condition in real space. In this paper, we give a complete generalization to the complex space.

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. Appl. 354 213 – 219 10.1016/j.jmaa.2008.12.054 . [3] Zhou , S. P. , Zhou , P. and Yu , D. S. , Ultimate generalization to monotonicity for

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, S. P. , Zhou , P. and Yu , D. S. , Ultimate generalization for monotonicity for uniform convergence of trigonometric series , arXiv: math.CA/0611805 v1 November 27, 2006 , preprint; Science China , 53 ( 2010 ), 1853 – 1862

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This paper is devoted to study the following Schrödinger-Poisson system {Δu+(λa(x)+b(x))u+K(x)ϕu=f(u),x3,Δϕ=4πK(x)u2,x3, where λ is a positive parameter, aC(R3,R+) has a bounded potential well Ω = a −1(0), bC(R3, R) is allowed to be sign-changing, KC(R3, R+) and fC(R, R). Without the monotonicity of f(t)=/|t|3 and the Ambrosetti-Rabinowitz type condition, we establish the existence and exponential decay of positive multi-bump solutions of the above system for λΛ¯, and obtain the concentration of a family of solutions as λ →+∞, where Λ¯>0 is determined by terms of a, b, K and f. Our results improve and generalize the ones obtained by C. O. Alves, M. B. Yang [3] and X. Zhang, S. W. Ma [38].

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Abstract  

We investigate the relations between decreasing sequences of sets and the insertion of semi-continuous functions, and give some characterizations of countably metacompact spaces, countably paracompact spaces, monotonically countably paracompact spaces (MCP), monotonically countably metacompact spaces (MCM), perfectly normal spaces and stratifiable spaces.

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. Monoton matrices and finding cliques in a graph . Annales Univ. Sci. Budapest., Sect. Computatorica 41 ( 2013 ), 307 – 322 . [8] Weisstein , E. W . Monotonic matrix . in MathWorld–A Wolfram Web Resource .

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Abstract  

Relations between I-approximate Dini derivatives and monotonicity are presented. Next, some generalizations of the Denjoy–Young–Saks Theorem for I-approximate Dini derivatives of an arbitrary real function are proved.

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