Singularity Spectrum of Generic ��-H?lder Regular Functions After Time Subordination

A question of Yves Meyer motivated the research concerning “time” subordinations of real functions. Denote by B₁^a{\mathcal {B}}_{1}^{\alpha} the metric space of functions with Lipschitz constant 1 defined on [0,1], equipped with the complete metric defined via the supremum norm. Given a function g ? B₁^ag\in {\mathcal {B}}_{1}^{\alpha} one obtains a time subordination of g simply by considering the composite function Z=g○f, where f∈ℳ:={f:f(0)=0, f(1)=1 and f is a continuous nondecreasing function on [0,1]}. The metric space E^a=M×B₁^a\mathcal {E}^{\alpha}=\mathcal {M}\times {\mathcal {B}}_{1}^{\alpha} equipped with the product supremum metric is a complete metric space. In this paper for all α∈[0,1) multifractal properties of g○f are investigated for a generic (typical) element (f,g)∈ℰ ^α . In particular we determine the generic H?lder singularity spectrum of g○f.     

An Interplay of Multidimensional Variations in Fourier Analysis

We compare the Fourier integral of a function of bounded variation and the corresponding trigonometric series, generated by that function, in the multidimensional case. Several known notions of bounded variation are used and a new one is introduced. The obtained results are applied to integrability of multidimensional trigonometric series.     

Sampling Theorem and Discrete Fourier Transform on?the?Hyperboloid

Using Coherent-State (CS) techniques, we prove a sampling theorem for holomorphic functions on the hyperboloid (or its stereographic projection onto the open unit disk $\mathbb{D}_{1}$ ), seen as a homogeneous space of the pseudo-unitary group SU(1,1). We provide a reconstruction formula for bandlimited functions, through a sinc-type kernel, and a discrete Fourier transform from N samples properly chosen. We also study the case of undersampling of band-unlimited functions and the conditions under which a partial reconstruction from N samples is still possible and the accuracy of the approximation, which tends to be exact in the limit N????.     

Finslerian 3-spinors and the generalized Duffin�CKemmer equation

The main facts of the geometry of Finslerian 3-spinors are formulated. The close connection between Finslerian 3-spinors and vectors of the 9-dimensional linear Finslerian space is established. The isometry group of this space is described. The procedure of dimensional reduction to 4-dimensional quantities is formulated. The generalized Duffin?CKemmer equation for a Finslerian 3-spinor wave function of a free particle in the momentum representation is obtained. From the viewpoint of a 4-dimensional observer, this 9-dimensional equation splits into the standard Dirac and Klein?CGordon equations.     

Quantum Diffusion and Delocalization for Band Matrices with General Distribution

We consider Hermitian and symmetric random band matrices H in d \geqslant 1{d \geqslant 1} dimensions. The matrix elements H _xy , indexed by x,y ? L ì \mathbbZ^d{x,y \in \Lambda \subset \mathbb{Z}^d}, are independent and their variances satisfy s_xy²:=\mathbbE |H_xy|² = W^-d f((x - y)/W){\sigma_{xy}^2:=\mathbb{E} |{H_{xy}}|^2 = W^{-d} f((x - y)/W)} for some probability density f. We assume that the law of each matrix element H _xy is symmetric and exhibits subexponential decay. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales t << W^d/3{t\ll W^{d/3}} . We also show that the localization length of the eigenvectors of H is larger than a factor W^d/6{W^{d/6}} times the band width W. All results are uniform in the size |Λ| of the matrix. This extends our recent result (Erdős and Knowles in Commun. Math. Phys., 2011) to general band matrices. As another consequence of our proof we show that, for a larger class of random matrices satisfying ?_xs_xy²=1{\sum_x\sigma_{xy}^2=1} for all y, the largest eigenvalue of H is bounded with high probability by 2 + M^{-2/3 + e}{2 + M^{-2/3 + \varepsilon}} for any ${\varepsilon > 0}${\varepsilon > 0}, where M : = 1 / (max_x,ys_xy²){M := 1 / (\max_{x,y}\sigma_{xy}^2)} .     

A Class of Dust-Like Self-Similar Solutions of the Massless Einstein�CVlasov System

In this paper the existence of a class of self-similar solutions of the Einstein–Vlasov system is proved. The initial data for these solutions are not smooth, with their particle density being supported in a submanifold of codimension one. They can be thought of as intermediate between smooth solutions of the Einstein–Vlasov system and dust. The motivation for studying them is to obtain insights into possible violation of weak cosmic censorship by solutions of the Einstein–Vlasov system. By assuming a suitable form of the unknowns it is shown that the existence question can be reduced to that of the existence of a certain type of solution of a four-dimensional system of ordinary differential equations depending on two parameters. This solution starts at a particular point P ₀ and converges to a stationary solution P ₁ as the independent variable tends to infinity. The existence proof is based on a shooting argument and involves relating the dynamics of solutions of the four-dimensional system to that of solutions of certain two- and three-dimensional systems obtained from it by limiting processes. The spacetimes constructed do not constitute a counterexample to cosmic censorship since they are not asymptotically flat. They should be seen as the first step on a possible path towards constructing solutions of importance for understanding the issue of the formation of naked singularities in general relativity.     

Unimodularity of zeros of self-inversive polynomials

We generalise a necessary and sufficient condition given by Cohn for all the zeros of a self-inversive polynomial to be on the unit circle. Our theorem implies some sufficient conditions found by Lakatos, Losonczi and Schinzel. We apply our result to the study of a polynomial family closely related to Ramanujan polynomials, recently introduced by Gun, Murty and Rath, and studied by Murty, Smyth and Wang as well as by Lalín and Rogers. We prove that all polynomials in this family have their zeros on the unit circle, a result conjectured by Lalín and Rogers on computational evidence.     

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在对国内外液态锂回路研究综述的基础上,重点介绍了四川大学流动液态锂回路的研究进展。为开展等离子体与流动自由液态锂表面相互作用的研究而设计了该回路,其目标是：(1)获得稳定、均匀的流动自由液态锂表面;(2)研究等离子体辐照下液态锂的蒸发、溅射以及氢、氢同位素和氦在液态锂中的滞留行为;(3)研究等离子体辐照下液态锂与结构材料的相容性。系统包括液态锂循环部分和直线高密度等离子体发生装置。     

聚变堆熔盐冷却偏滤器靶板结构设计与分析

为提高偏滤器的抗中子辐照能力,兼顾高热承载能力和聚变堆经济性的需要,提出了基于熔盐冷却(MSC)的偏滤器靶板结构设计。它采用FLiNaK作为冷却剂,钨镧合金为热沉材料,钨为第一壁材料。通过数值计算评估了靶板的热负荷承载能力,并完成了偏滤器冷却剂回路设计,优化了偏滤器各模块之间的流量分配。此MSC偏滤器靶板设计可以有效去除10~15MW•m^-2热负荷,为适应未来聚变堆偏滤器靶板发展的需要提供了一种设计解决方案。     

Quinolones control in milk and eggs samples by liquid chromatography using a surfactant-mediated mobile phase

Four quinolones (danofloxacin, difloxacin, flumequine and marbofloxacin) were determined in milk and egg samples by a simplified high-performance liquid chromatographic procedure using a micellar mobile phase. No extraction was needed to precipitate the proteins from the matrices since they were solubilised in micelles. The only pretreatment steps required were homogenisation, dilution and filtration before injecting the sample into the chromatographic system. An adequate resolution of the quinolones was achieved by a chemometrics approach where retention was modelled as a first step using the retention factors in only five mobile phases. Afterwards, an optimisation criterion was applied to consider the position and shape of the chromatographic peaks. Analytical separation involved a C18 reversed-phase column, a hybrid micellar mobile phase of 0.05 M sodium dodecyl sulphate, 10% (v/v) butanol and 0.5% (v/v) triethylamine buffered at pH 3 and fluorimetric detection. Quinolones were eluted in less than 15 min without the protein band or other endogenous compounds from the food matrices interfering. The calculated relevant validation parameters, e.g., decision limit (CC(α)), detection capability (CC(β)), repeatability, within-laboratory reproducibility, recoveries and robustness, were acceptable and complied with European Commission Decision 2002/657/EC. Finally, the proposed method was successfully employed in quantifying the four quinolones in spiked egg and milk samples.