Sensitivity Analysis of M-Estimates of Nonlinear Regression Model: Influence of Data Subsets

Asymptotic representations of the difference of M-estimators of the parameters of nonlinear regression model for the full data and for the subsample of data are given for the following three situation: i) fix number of points excluded from data, ii) increasing number, however asymptotically negligible part of data excluded, and finally iii) asymptotically fix portion of data excluded. Asymptotic normality of the difference of estimators (for the two latter cases) is proved.     

Topologically Free Partial Actions and Faithful Representations of Crossed Products

We study the relationship between the topological freeness of partial actions of discrete groups and faithful representations of the corresponding crossed products.     

On the calculation of force constants using isotopic frequencies by parametric method: Application to systems of (3×3) order

A method is proposed for the determination of angle parameters for ONF, ONCl and ONBr, utilising the isotopic frequencies of two isotopically substituted molecules. The force constants, Coriolis coupling constants, inertia defect, mean amplitudes of vibration and rotational distortion constants were also calculated and compared with literature values.     

左删失右截断数据的分位数的固定宽度序贯置信区间估计

基于左截断右删失数据下的乘积限估计构造了分位数固定宽度序贯置信区间及其估计，研究了序贯置信区间估计的渐近性质。作为副产品，获得了分位数估计近邻点的Bahadur表示定理。这个表示定理是推导分位数固定宽度序贯置信区间估计渐近性质的重要基础。同时，在文中，进行了一些计算机模拟试验，证明了左截断右删失数据下分位数估计的序贯方法是效的和精确的。     

Wavelet bases in generalized Besov spaces

In this paper we obtain a wavelet representation in (inhomogeneous) Besov spaces of generalized smoothness via interpolation techniques. As consequence, we show that compactly supported wavelets of Daubechies type provide an unconditional Schauder basis in these spaces when the integrability parameters are finite.     

New Correlation Duality Relations for the Planar Potts Model

We introduce a new method to generate duality relations for correlation functions of the Potts model on a planar graph. The method extends previously known results, by allowing the consideration of the correlation function for arbitrarily placed vertices on the graph. We show that generally it is linear combinations of correlation functions, not the individual correlations, that are related by dualities. The method is illustrated in several non-trivial cases, and the relation to earlier results is explained. A graph-theoretical formulation of our results in terms of rooted dichromatic, or Tutte, polynomials is also given.     

Constant tolerance intersection graphs of subtrees of a tree

A chordal graph is the intersection graph of a family of subtrees of a host tree. In this paper we generalize this. A graph G=(V,E) has an (h,s,t)-representation if there exists a host tree T of maximum degree at most h, and a family of subtrees {S_v}_v∈V of T, all of maximum degree at most s, such that uv∈E if and only if |S_u∩S_v|?t. For given h,s, and t, there exist infinitely many forbidden induced subgraphs for the class of (h,s,t)-graphs. On the other hand, for fixed h?s?3, every graph is an (h,s,t)-graph provided that we take t large enough. Under certain conditions representations of larger graphs can be obtained from those of smaller ones by amalgamation procedures. Other representability and non-representability results are presented as well.     

Electromagnetic Signal Processing and Noncommutative Tomography

A generic electromagnetic signal described by Maxwell equations both in vacuum and media is considered in the tomographic representation. The Ville–Wigner phase-space representation of the electromagnetic field is also discussed. Relations between different representations of the electromagnetic signal are elucidated. The connection of the Fourier analysis of the electromagnetic signal and other mathematical approaches like the Radon transform of the analytic signal is presented. The distinguishing property of the tomogram to coincide with the probability density of a random variable considered in a reference frame in the signal's phase space is pointed out. The entropy of the signal related to the probability density is studied.     

Effective potential, Bohm’s potential plus classical potential, analysis of quantum transmission

The influence of spreading, in wavepacket transmission across a potential barrier has been analyzed, by considering several collisions between a wavepacket and a potential barrier, in which the initial distance between the packet and the barrier—the launching distance, is changed. An effective total potential (Bohm’s quantum potential plus classical potential), has been used, to show that, for suitable classical barrier widths and heights, light masses, as well as mean collision energies, one should expect an increase of the quantum transmission factor as the initial wavepacket—barrier distance is decreased. Numerically converged time-dependent wavepacket propagation calculations confirm that trend, leading to an increase as high as 20% per ?, in thin square and Eckart barrier problems. Possibilities of experimentally measuring this effect are also analyzed.