均值混合正态分布统计量的性质

这篇文章基于基因遗传背景,提出了一类均值混合正态分布,它不同于通常所讨论的方差混合正态分布. 作者研究了这类均值混合正态分布统计量的性质,给出了平移变换群下不变量的稳健性,即它与正态分布下该统计量有相同的性质, 并且讨论了其它统计量的分布.     

Goodness of fit of an assigned set of scores for the analysis of association in a contingency table

The problem of association between two attributes in ap×q contingency table can be looked upon as the problem of relationship between two vector variablesx andy. If there is only one true non-zero canonical correlation betweenx andy, the association between the two attributes is of rank 1 and in this case, one set of scores is adequate to describe the association completely; these scores are nothing but the coefficients in the canonical variates corresponding to the true non-zero canonical correlation. Given a set of hypothetical scoresα ₁,α₁,⋯,α_p for the rows, one is interested in testing their goodness of fit. Tests for this are suggested in this paper. For obtaining these tests, a preliminary result about direction and collinearity factors in discriminant analysis, whenS irrelevant variables are eliminated, is needed. This is derived in part one of this paper. This research was sponsored by the Office of Naval Research, Contract No. N00014-68-A-0515, Project No. NR042-260. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

On the application of some concepts of ring theory to the study of the influence of systems of subgroups of a group

We study groups in which the family L _non-nn(G) of all not nearly normal subgroups has the Krull dimension. A subgroup H of a group G is called nearly normal if H has finite index in its normal closure. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 657–668, May, 2008.     

Best Approximations and Widths of Classes of Convolutions of Periodic Functions of High Smoothness

We consider classes of 2π-periodic functions that are represented in terms of convolutions with fixed kernels Ψ _β ⁻ whose Fourier coefficients tend to zero at exponential rate. We determine exact values of the best approximations of these classes in the uniform and integral metrics. In several cases, we determine the exact values of the Kolmogorov, Bernstein, and linear widths for these classes in the metrics of the spaces C and L. __________ Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 946–971, July, 2005.     

On equivalence of moduli of smoothness of polynomials in ,

It is well known that for functions , 1p∞. For general functions fL_p, it does not hold for 0<p<1, and its inverse is not true for any p in general. It has been shown in the literature, however, that for certain classes of functions the inverse is true, and the terms in the inequalities are all equivalent. Recently, Zhou and Zhou proved the equivalence for polynomials with p=∞. Using a technique by Ditzian, Hristov and Ivanov, we give a simpler proof to their result and extend it to the L_p space for 0<p∞. We then show its analogues for the Ditzian–Totik modulus of smoothness and the weighted Ditzian–Totik modulus of smoothness for polynomials with .     

Coherence of some rings of functions

To say that a commutative ring $\text{R}$ with unit is coherent amounts to saying, in case $\text{R}$ has no divisors of zero, that the intersection of two finitely generated ideals in $\text{R}$ is finitely generated. We prove that the ring H^∞ of bounded analytic functions in the unit disc is coherent, while the disc algebra A is not coherent. For any positive measure μ, L^∞(μ) is coherent.     

Homotopy groups of Hom complexes of graphs

The notion of ×-homotopy from [Anton Dochtermann, Hom complexes and homotopy theory in the category of graphs, European J. Combin., in press] is investigated in the context of the category of pointed graphs. The main result is a long exact sequence that relates the higher homotopy groups of the space Hom_∗(G,H) with the homotopy groups of Hom_∗(G,HI). Here Hom_∗(G,H) is a space which parameterizes pointed graph maps from G to H (a pointed version of the usual Hom complex), and HI is the graph of based paths in H. As a corollary it is shown that πi(Hom_∗(G,H))≅_×[G,ΩiH], where ΩH is the graph of based closed paths in H and _×[G,K] is the set of ×-homotopy classes of pointed graph maps from G to K. This is similar in spirit to the results of [Eric Babson, Hélène Barcelo, Mark de Longueville, Reinhard Laubenbacher, Homotopy theory of graphs, J. Algebraic Combin. 24 (1) (2006) 31-44], where the authors seek a space whose homotopy groups encode a similarly defined homotopy theory for graphs. The categorical connections to those constructions are discussed.     

On dimensions of the groups of biholomorphic automorphisms of real-analytic hypersurfaces

In this paper we study the dependence of the local geometry of real-analytic hypersuffaces in ℂ ⁿ on the dimension of the group of biholomorphic automorphisms of this surface. We also classify the hypersurfaces in terms of this group. We present some examples showing that the classes of the given construction are not empty. We find a new formulation of the Freeman theorem on the so-called straightening of a real-analytic CR-submanifold in ℂ ⁿ with degenerate Levi form of constant rank. Translated fromMatematicheskie Zametki, Vol. 61, No. 3, pp. 349–358, March, 1997. Translated by E. G. Anisova     

Completions of convex families of convex bodies

The paper discusses the existence of a continuous extension of functions that are defined on subsets of ? ⁿ and whose values are convex bodies in ? ⁿ . This problem arose in convex geometry in connection with the notion, recently introduced in algebraic geometry, of convex Newton-Okounkov bodies.     

Further study of growth of fractional-power semigroups

If the resolvent of a closed linear operator A in Banach space is defined and decays suitably in a region asymptotic, in a special sense, to a half-plane, then fractional powers ?(?A)^a generate semigroups, holomorphic in sectors of the complex plane. We show that the growth of such semigroups near the origin, or with angular approach to the edges of their sectors of definition, corresponds to the rate of decay of the resolvent of A and the extent of the resolvent set of A.     

A characterization of p-bases of rings of constants

We obtain two equivalent conditions for m polynomials in n variables to form a p-basis of a ring of constants of some polynomial K-derivation, where K is a unique factorization domain of characteristic p > 0. One of these conditions involves Jacobians while the other some properties of factors. In the case m = n this extends the known theorem of Nousiainen, and we obtain a new formulation of the Jacobian conjecture in positive characteristic.     

Experimental study of young's modulus of glass-plastics

The results of study of Young's modulus of glass-plastics in the 10^–1–10⁵-Hz frequency range are presented. A stepwise variation in the modulus, which governs the relaxation process corresponding to a low-temperature internal-friction peak in the filler, is obtained.Rybinsk Institute of Aircraft Technology. Translated from Mekhanika Polimerov, No. 6, pp. 1089–1091, November–December, 1975.     

Relative Brauer Groups of Function Fields of Curves of Genus One

Abstract

Let Kbe an algebraic function field in one variable over a constant field k. In this paper, we investigate the relative Brauer groups Br(K/k) of Kover kin various cases. When kis a global field, we focus on function fields K = k(C) of genus 1 where Cis the curve of the form y ² = at ⁴ + bwith a, b ∈ k ? {0}, and we describe the Brauer classes in Br(K/k). More precisely, we show that each algebra in Br(K/k) is a quaternion algebra which can be obtained by taking one of a finite number of the x-coordinates of k-rational points on the Jacobian of the curve C. In particular, for the field ? of rational numbers, we determine Br(K/?) precisely in numerous cases and give examples.     

The Number of Geometric Bistellar Neighbors of a Triangulation

The theory of secondary and fiber polytopes implies that regular (also called convex or coherent) triangulations of configurations with n points in R ^d have at least n-d-1 geometric bistellar neighbors. Here we prove that, in fact, all triangulations of n points in R ² have at least n-3 geometric bistellar neighbors. In a similar way, we show that for three-dimensional point configurations, in convex position and with no three points collinear, all triangulations have at least n-4 geometric bistellar flips. In contrast, we exhibit three-dimensional point configurations, with a single interior point, having deficiency on the number of geometric bistellar flips. A lifting technique allows us to obtain a triangulation of a simplicial convex 4-polytope with less than n-5 neighbors. We also construct a family of point configurations in R ³ with arbitrarily large flip deficiency. Received November 25, 1996, and in revised form March 10, 1997.     

Behavior at infinity of solutions of an equation of Osserman-Keller type

We study the behavior at infinity of solutions of equations of the form Δu=u^p, where p>1, in dimensions n?3. In particular we extend results proved by Loewner and Nirenberg in Contribution to Analysis, 1974, pp. 245-272 for the case p=(n+2)/(n−2), n?3, to values of p in the range p>n/(n−2), n?3.     

VC-Dimension of Sets of Permutations

VC-dimension of a set of permutations to be the maximal k such that there exist distinct that appear in A in all possible linear orders, that is, every linear order of is equivalent to the standard order of for at least one permutation . In other words, the VC-dimension of A is the maximal k such that for some the restriction of A to contains all possible linear orders. This is analogous to the VC-dimension of a set of strings. Our main result is that there exists a universal constant C such that any set of permutations with VC-dimension 2 is of size . This is analogous to Sauer's lemma for the case of VC-dimension 2. One corollary of our main result is that any acyclic set of linear orders of is of size , (a set A of linear orders on is called acyclic if no 3 elements appear in A in all 3 orders (i,j,k), (k,i,j) and (j,k,i)). The size of the largest acyclic set of linear orders has interested researchers for many years because it is the largest number of linear orders of n alternatives such that the following is always satisfied: if each one of a set of voters chooses one of these orders as his preference then the majority relation between each two alternatives is transitive. Received August 6, 1998     

Effect of the molecular weight of polystyrene on the viscosity of concentrated solutions

The viscosity of solutions of polystyrene of various molecular weights (from 1.04 · 10² to 3.8 · 10⁵) in a poor solvent (decalin) and a good solvent (ethylbenzene) has been measured at temperatures from 15 to 70°C over a broad range of shear stresses from 10² to 10⁶ dyne/cm². The nature of the solvent has a considerable influence on the critical molecular weight and the absolute value of the viscosities of the solutions over the entire range of molecular weights and on the form of the flow curves of decalin solutions of polystyrene as a function of temperature. The heat of activation of viscous flow increases with increase in molecular weight and shear stress on the interval 20–80°C. The results obtained are explained in terms of the effect of the molecular weight of the polymer, the nature of the solvent, stress and temperature on structure formation in the solution and on the orientation of the macromolecules and structures in the flow process.Ural Gor'kii State University, Sverdlovsk. Translated from Mekhanika Polimerov, No. 5, pp. 920–926, September–October, 1970.     

Critical Pairs of Sequences of a Mixed Frame Potential

The classical frame potential in a finite-dimensional Hilbert space has been introduced by Benedetto and Fickus, who showed that all finite unit-norm tight frames can be characterized as the minimizers of this energy functional. This was the starting point of a series of new results in frame theory, related to finding tight frames with determined lengths. The frame potential has been studied in the traditional setting as well as in the finite-dimensional fusion frame context. In this work we introduce the concept of mixed frame potential, which generalizes the notion of the Benedetto-Fickus frame potential. We study properties of this new potential, and give the structure of its critical pairs of sequences on a suitable restricted domain. For a given sequence {α _m } _{m=1,…, N} in K, where K is ? or ?, we obtain necessary and sufficient conditions in order to have a dual pair of frames {f _m } _{m=1,…, N} , {g _m } _{m=1,…, N} such that ? f _m , g _m  ? = α _m for all m = 1,…, N.     

Sublines of Prime Order Contained in the Set of Internal Points of a Conic

In [2] it was shown that if q ≥ 4n²−8n+2 then there are no subplanes of order q contained in the set of internal points of a conic in PG(2,qⁿ), q odd, n≥ 3. In this article we improve this bound in the case where q is prime to , and prove a stronger theorem by considering sublines instead of subplanes. We also explain how one can apply this result to flocks of a quadratic cone in PG(3,qⁿ), ovoids of Q(4,qⁿ), rank two commutative semifields, and eggs in PG(4n−1,q). AMS Classification:11T06, 05B25, 05E12, 51E15