Forcing with Proper Classes

ＦｏｒｃｉｎｇｗｉｔｈＰｒｏｐｅｒＣｌａｓｓｅｓＬｉＮａ（ＤｅｐａｒｔｍｅｎｔｏｆＰｏｌｉｔｉｃｓ，ＨｅｎａｎＵｎｉｖｅｒｓｄｙ，Ｋａｉｆｅｎｇ，４７５００１）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒ，ｕｓｉｎｇｔｈｅｍｏｄｅｌＲΔ（Ｂ）－ａｇｅｎｅｒａ...     

Stability of Linear Integrodifferential Systems with Time-varied Confficients with Large Scale

51.IntroductionConsideralinearintegrodifferentialsystemswithtime-variedconfficientswherex6R",A(t)isanXnrealmatrixfunctioncontinuousforoO.ManyscholarshavecontributedtheirpaPers[1-4]todiscussstabilityofzerosolutionofsystem(1.l).Inthispaper,weassumethatsystem(1.1)canbedecomPOsedintotheform=n,A,j(t)isaniXnjrealmatrixfunctioncontinuousforo相似文献   

On wheel–rail contact problem with material properties varying with depth

Numerous laboratory experiments indicate that the use of a layer or a coating material attached to the conventional steel body reduce the magnitude of contact stress. Therefore in this paper we solve numerically the wheel–rail contact problem with friction and wear assuming the existence of a small elastic layer on the rail surface. Material properties of this layer are changing with its depth. The friction between the bodies is governed by Coulomb law. In contact zone Archard's law of wear is assumed. We take special features of this rolling contact problem and use so-called quasistatic approach to solve this contact problem. Finite element method is used as a discretization method. The numerical results including the distribution of normal stress along the contact boundary are provided and discussed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Counting and Probably with Overlap

LastfallatCentralMiddleSchool,43boysand 5 4girlsplayedonasoccerteam .Sincethereisnooverlapbetweenboysandgirls,itiseasytofindhowmanystudentsplayedsoccer .UsethePutting TogetherModelforAdditiontoget 43 + 5 4=97.Youcandrawapicture ,calledaVenndiagram ,toillus tratethissituation ,Separatecirclesrepresentquantitieswithnooverlap .CountingWhenThereIsOverlapSituationswithoverlaparemorecomplicated .Example3 7girlsfromCentralMiddleSchoolplayedbasketballinthewinter .If 9girlsplayedbothsoccerandba…     

Collocation with WEB–Splines

We describe a collocation method with weighted extended B–splines (WEB–splines) for arbitrary bounded multidimensional domains, considering Poisson’s equation as a typical model problem. By slightly modifying the B–spline classification for the WEB–basis, the centers of the supports of inner B–splines can be used as collocation points. This resolves the mismatch between the number of basis functions and interpolation conditions, already present in classical univariate schemes, in a simple fashion. Collocation with WEB–splines is particularly easy to implement when the domain boundary can be represented as zero set of a weight function; sample programs are provided on the website http://www.web-spline.de. In contrast to standard finite element methods, no mesh generation and numerical integration is required, regardless of the geometric shape of the domain. As a consequence, the system equations can be compiled very efficiently. Moreover, numerical tests confirm that increasing the B–spline degree yields highly accurate approximations already on relatively coarse grids. Compared with Ritz-Galerkin methods, the observed convergence rates are decreased by 1 or 2 when using splines of odd or even order, respectively. This drawback, however, is outweighed by a substantially smaller bandwidth of collocation matrices.     

Graphlike Manifolds with Contraction 

Ｇｒａｐｈｌｉｋｅ　Ｍａｎｉｆｏｌｄｓ　ｗｉｔｈ　Ｃｏｎｔｒａｃｔｉｏｎ　ＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓｗｉｔｈＣｏｎｔｒａｃｔｉｏｎＬｉｕＸｉａｏｚｈｅｎ（ＨｅｎａｎＩｎｓｔｉｔｕｔｅｏｆＦｉｎａｎｃｅａｎｄＥｃｏｎｏｍｉｃｓ，Ｚｈｅｎｇｚ...     

Littlewood-Paley operators with variable kernels

In this paper we study a certain directional Hilbert transform and the bound-edness on some mixed norm spaces. As one of applications, we prove the Lp-boundedness of the Littlewood-Paley operators with variable kernels. Our results are extensions of some known theorems.     

Graphlike Manifolds with Contraction 

ＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓｗｉｔｈＣｏｎｔｒａｃｔｉｏｎ ＬｉｕＸｉａｏｚｈｅｎ（刘晓真）Ｇｒａｐｈｌｉｋｅ　Ｍａｎｉｆｏｌｄｓ　ｗｉｔｈ　Ｃｏｎｔｒａｃｔｉｏｎ ￥ＬｉｕＸｉａｏｚｈｅｎ（ＨｅｎａｎＩｎｓｔｉｔｕｔｅｏｆＦｉｎａｎｃｅａｎ...     

π-Formulas with free parameters

In terms of the hypergeometric method, we establish ten general $\pi$-formulas with free parameters which include several known results as special cases.     

Meromorphic Functions with Two Deficient Values

ＭｅｒｏｍｏｒｐｈｉｃＦｕｎｃｔｉｏｎｓｗｉｔｈＴｗｏＤｅｆｉｃｉｅｎｔＶａｌｕｅｓＸｕＷａｎｓｏｎｇ（徐万松）（ＣｏｌｌｅｇｅｏｆＳｃｉｅｎｃｅｓ，ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙｏｆＡｅｒｏｎａｕｔｉｃｓａａｄＡｓｔｒｏｎａｕｔｉｃｓ，Ｎａｎｊ...     

On Projective Modules with Constant Ranks

On Projective Modules with Constant RanksIn this paper,we investigate module structures of rings over which every finitely generated projective module with constant rank is stably free. As applications,we give characterizations of some related rings.     

Hodge integrals with one λ-class

Hodge integrals over moduli space of stable curves play an important roles in understanding the topological properties of moduli space.ELSV formula connects the Hodge integrals with Hurwitz numbers,and the generating function of Hurwitz numbers satisfies the cut-and-join equation.Therefore,it is natural to consider how to use the cut-and-join equation for Hurwitz numbers to compute Hodge integrals which appear in ELSV formula.In this paper,at first,we will review the method introduced in Goulden et al.’s paper to get the λ g conjecture for Hodge integral.Through some variables transformation,the generating function of Hurwitz number becomes a symmetric polynomial which satisfies a symmetrized cut-and-join equation.By comparing the coefficients of the lowest degree term of both sides in this equation,we can get the λ g conjecture.Then,in a similar way,we obtain our main result in this paper:a recursive formula for Hodge integral of type contains only one λ g 1-class.We also point out that our results are closely related to the degree 0 Virasoro conjecture for a curve.     

Generalized Maupertuis’ principle with applications

We give a rigorous proof of the equivalence of Ma's supercritical potential and the minimal action with respect to an associated Jacobi-Finsler metric. As a consequence, we give an explicit representation of the weak KAM solutions of one-dimensional mechanical systems without the quadratic assumption on the kinetic energy term of the Hamiltonians, and a criterion of the integrability result for such a system of arbitrary degree of freedom by the regularity assumption on Mather's α-function is discussed.     

Testing for additivity with B-splines

Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.     

Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order

Recently, Atangana and Baleanu proposed a derivative with fractional order to answer some outstanding questions that were posed by many researchers within the field of fractional calculus. Their derivative has a non-singular and nonlocal kernel. In this paper, we presented further relationship of their derivatives with some integral transform operators. New results are presented. We applied this derivative to a simple nonlinear system. We show in detail the existence and uniqueness of the system solutions of the fractional system. We obtain a chaotic behavior which was not obtained by local derivative.     

Chen’s Theorem with Small Primes

Let N be a sufficiently large even integer. Let p denote a prime and P2 denote an almost prime with at most two prime factors. In this paper, it is proved that the equation N - p+ P2 (p ≤ AT0.945) is solvable.     

Extended partial geometries with minimal μ

Recently Fisher and Hobart extended the original work of Buekenhout and Hubaut on extended generalized quadrangles with a certain minimal value (minimal ) for the nonempty residue intersections. We show that there is another minimal which is sometimes better than the earlier one, and we extend all this to the case of extended partial geometries. We examine especially the triangular case, and find only a few new possibilities, which we are unable to settle, although some of these look extremely interesting.