Testing goodness of fit for the distribution of errors in multivariate linear models

In this paper, to test goodness of fit to any fixed distribution of errors in multivariate linear models, we consider a weighted integral of the squared modulus of the difference between the empirical characteristic function of the residuals and the characteristic function under the null hypothesis. We study the limiting behaviour of this test statistic under the null hypothesis and under alternatives. In the asymptotics, the rank of the design matrix is allowed to grow with the sample size.     

<Emphasis FontCategory="NonProportional">L</Emphasis>-Matrices and solvability of linear complementarity problems by a linear program-Matrices and solvability of linear complementarity problems by a linear program

The classes ofL ₁-matrices,L ₂-matrices,L ₃-matrices andW-matrices are introduced to study solvability of a linear complementarity problem via solving a linear program. Three sufficient conditions are presented to guarantee that a linear complementarity problem is solvable via a linear program. The new sufficient conditions are weaker than the ones introduced by Mangasarian. This fact is also illustrated by an example. Partially supported by NSFC. This author is also with College of Business Administration of Human University as a Lotus chair professor.     

Time-domain simulations of sound propagation through screen-induced turbulence

A flow model in combination with a statistical-dynamical turbulence generator and a linearised Euler time-domain model for sound waves were used to simulate the effect of screen-induced turbulence on the noise level in the acoustical shadow of a screen in wind. Instead of simulating a great number of different frozen turbulence realisations, the concept of transient turbulence was successfully tested and applied. This concept is adequate to the time-domain model and reduces the computational demands. Several two-dimensional simulations allowed to isolate the individual effects of wind and screen on the propagation of 500 Hz sound waves over a 4-m high noise barrier. At a distance of 250 m from the source (240 m behind the screen) the sheltering effect of the screen and the refraction effect of the wind are in the order of 6 and 4 dB, respectively. The screen-induced turbulence leads to fluctuations in the noise level with a standard deviation of 1.2 dB and a maximum amplitude of 3 dB. However, the time averaged effect turned out to be in the order of merely 0.2 dB. The effect of the screen-induced turbulence on the average noise level behind the screen is therefore negligible.     

向量优化问题广义有效点的一个存在性定理

利用集值映射不动点定理及最优化问题与变分不等式的关系给出线性G^↑ateaux可微的锥凸映射的广义有效点的一个存在性定理。     

Separating the solution sets of analytical and polynomial systems

A linear inequality system with infinitely many constraints is polynomial (analytical) if its index set is a compact interval of the real line and all its coefficients are polynomial (analytical, respectively) functions of the index on this interval. This paper provides an example of analytical system whose solution set cannot be the solution set of any polynomial system. Research supported by DGES of Spain and FEDER of UE, Grant BFM2002-04114-C02-01. Research supported by CONACyT of Mexico, Grant 130036. Research partially supported by CONACyT of Mexico, Grant 44003.     

A class of polynomial variable metric algorithms for linear optimization

In the paper, the behaviour of interior point algorithms is analyzed by using a variable metric method approach. A class of polynomial variable metric algorithms is given achieving O ((n/β)L) iterations for solving a canonical form linear optimization problem with respect to a wide class of Riemannian metrics, wheren is the number of dimensions and β a fixed value. It is shown that the vector fields of several interior point algorithms for linear optimization is the negative Riemannian gradient vector field of a linear a potential or a logarithmic barrier function for suitable Riemannian metrics. Research Partially supported by the Hungarian National Research Foundation, Grant Nos. OTKA-T016413 and OTKA-2116.     

THE SCHWARZIAN DERIVATIVE IN SEVERAL COMPLEX VARIABLES(II)

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具有离散参数齐次随机场的线性预测(V)

本文提出并研究下列四类线性预测问题：2（n0），6（n0），5（NO，n0）及3（N0，n0）．不仅求出了它们的预测误差，而且也求出了它们的预测值．因而不仅推广了而且也改进了[2－5]中的结果．本文还给出了场｛X（m，n）｝的一个新形式的表示式．     

某些级数的无理性

本文证明了某些与二阶线性递推数列有关的无穷级数的和的无理性．特别，推广了某些与Ｆｉｂｏｎａｃｃｉ和Ｌｕｃａｓ数列有关的无理性结果     

The unsatisfiability threshold revisited

The problem of determining the unsatisfiability threshold for random 3-SAT formulas consists in determining the clause to variable ratio that marks the experimentally observed abrupt change from almost surely satisfiable formulas to almost surely unsatisfiable. Up to now, there have been rigorously established increasingly better lower and upper bounds to the actual threshold value. In this paper, we consider the problem of bounding the threshold value from above using methods that, we believe, are of interest on their own right. More specifically, we show how the method of local maximum satisfying truth assignments can be combined with results for the occupancy problem in schemes of random allocation of balls into bins in order to achieve an upper bound for the unsatisfiability threshold less than 4.571. In order to obtain this value, we establish a bound on the q-binomial coefficients (a generalization of the binomial coefficients). No such bound was previously known, despite the extensive literature on q-binomial coefficients. Finally, to prove our result we had to establish certain relations among the conditional probabilities of an event in various probabilistic models for random formulas. It turned out that these relations were considerably harder to prove than the corresponding ones for unconditional probabilities, which were previously known.