Elastic line deformed on a pseudo-hypersurface by an external field in pseudo-Euclidean spaces

We derive intrinsic formulation for elastic line deformed on a pseudo-hypersurface by an external field in the pseudo-Euclidean spaces E_v~n.This formulation determines elastic line deformed on a pseudo-hypersurface.     

Ring structures on groups of arithmetic functions

Using the theory of Witt vectors, we define ring structures on several well-known groups of arithmetic functions, which in another guise are formal Dirichlet series. The set of multiplicative arithmetic functions over a commutative ring R is shown to have a unique functorial ring structure for which the operation of addition is Dirichlet convolution and the operation of multiplication restricted to the completely multiplicative functions coincides with point-wise multiplication. The group of additive arithmetic functions over R also has a functorial ring structure. In analogy with the ghost homomorphism of Witt vectors, there is a functorial ring homomorphism from the ring of multiplicative functions to the ring of additive functions that is an isomorphism if R is a Q-algebra. The group of rational arithmetic functions, that is, the group generated by the completely multiplicative functions, forms a subring of the ring of multiplicative functions. The latter ring has the structure of a Bin(R)-algebra, where Bin(R) is the universal binomial ring equipped with a ring homomorphism to R. We use this algebra structure to study the order of a rational arithmetic function, as well the powersfα for α∈Bin(R) of a multiplicative arithmetic function f. For example, we prove new results about the powers of a given multiplicative arithmetic function that are rational. Finally, we apply our theory to the study of the zeta function of a scheme of finite type over Z.     

Numerical simulation of the rheological properties of granular composites by using a structural approach

Composites with an elastomeric matrix containing rigid particles of diameter 10–1000 μm are studied. One of possible mechanisms of the rheological behavior of such filled systems, related to the origination and growth of vacuoles near the rigid inclusions in a viscous matrix, is considered. For simulating the mechanism of formation of rheological properties of the filled elastomers, we use a structural cell in the form of an elastomeric cylinder, whose height and diameter are equal in magnitude, with a rigid spherical inclusion at its center. Deformation of the cells is examined with the observance of boundary conditions providing the preservation of their close packing. The inclusion is assumed to be rigid, and the matrix properties are described by equations of the linear hereditary viscoelasticity theory. The formation of vacuoles is described by using the approach suggesting that an initial debonding begins to propagate when the energy accumulated in the extended matrix reaches a value sufficient to create a new interface. The heterogeneity of the composite is simulated by taking into account the variability of the local filler concentration. Creep curves obtained for composite cells with different content of the solid phase are presented. Comparisons between the numerical and experimental results show a satisfactory agreement. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 895–906, November–December, 2008.     

An inhomogeneous wave equation and non-linear Diophantine approximation

A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution is studied. Both the Lebesgue and Hausdorff measures of this set are obtained.     

水／离子液体两相体系中出芽短梗霉催化4-氯-乙酰乙酸乙酯不对称还原合成（S）-4-氯-3-羟基-丁酸乙酯

考察了水/离子液体两相体系中出芽短梗霉(Aureobasidium pullulansCGMCC1244)催化4-氯乙酰乙酸乙酯(COBE)不对称还原生成光学活性(S)-4-氯-3-羟基丁酸乙酯((S)-CHBE)的性能,并对反应条件如摇床转速、相体积比、温度、初始底物浓度和pH值等进行了优化.结果表明,在水/1-丁基-3-甲基咪唑六氟磷酸盐体系中,出芽短梗霉催化COBE不对称还原生成(S)-CHBE,在30℃,pH6·6,摇床转速180r/min和不对称反应8h条件下,反应物的转化率、产物ee值和浓度分别达到95·6%,98·5%和47·1g/L.在控制pH值为6·6的情况下,通过分添加底物可有效提高产物(S)-CHBE浓度至75·1g/L.     

Chromatic Uniqueness of a Family of K_4-Homeomorphs

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ａｌｌｇｒａｐｈｓｃｏｎｓｉｄｅｒｅｄｉｎｔｈｉｓｐａｐｅｒａｒｅｆｉｎｉｔｅ,ｕｎｄｉｒｅｃｔｅｄ ,ｕｎｌｏｏｐｅｄａｎｄｓｉｍｐｌｅｇｒａｐｈｓ.ＷｅｄｅｎｏｔｅｔｈｅｃｈｒｏｍａｔｉｃｐｏｌｙｎｏｍｉａｌｏｆａｇｒａｐｈＧｂｙＰ(Ｇ ,λ)ｏｒＰ(Ｇ) .ＷｅｓａｙｇｒａｐｈｓＧａｎｄＨｔｏｂｅｃｈｒｏｍａｔｉａｌｌｙｅｑｕｉｖａｌｅｎｔｉｆＰ(Ｇ) =Ｐ(Ｈ) .ＴｈｅｃｈｒｏｍａｔｉｃｕｎｉｑｕｅｎｅｓｓｏｆａｇｒａｐｈＧｉｓｅｓｔａｂｌｉｓｈｅｄｉｆｉｔｃａｎｂｅｄｅｄ…     

A renewal jump-diffusion process with threshold dividend strategy

In this paper, we consider a jump-diffusion risk process with the threshold dividend strategy. Both the distributions of the inter-arrival times and the claims are assumed to be in the class of phase-type distributions. The expected discounted dividend function and the Laplace transform of the ruin time are discussed. Motivated by Asmussen [S. Asmussen, Stationary distributions for fluid flow models with or without Brownian noise, Stochastic Models 11 (1) (1995) 21–49], instead of studying the original process, we study the constructed fluid flow process and their closed-form formulas are obtained in terms of matrix expression. Finally, numerical results are provided to illustrate the computation.     

Hyperfine Field in Ferromagnetic CoPd Alloys

The magnetic hyperfine interaction of ⁶⁰Co in the completely miscible alloy Co _x Pd_1−x was investigated for different values of x by measuring the nuclear orientation of ⁶⁰Co as function of temperature and by nuclear magnetic resonance of the oriented ⁶⁰Co nuclei. A broad resonance signal of Gaussian shape could be observed down to x=60%. The dependence of the mean magnetic hyperfine field on the Co concentration was observed to be linear very similar to that of experimental values of the magnetic moment per atom in the literature. The magnetic hyperfine field and its broad distribution are discussed in a simple model with RKKY interaction. This revised version was published online in September 2006 with corrections to the Cover Date.     

Defining and optimizing algorithms for neighbouring particle identification in SPH fluid simulations

Lagrangian particle methods such as smoothed particle hydrodynamics (SPH) are very demanding in terms of computing time for large domains. Since the numerical integration of the governing equations is only carried out for each particle on a restricted number of neighbouring ones located inside a cut‐off radius r_c, a substantial part of the computational burden depends on the actual search procedure; it is therefore vital that efficient methods are adopted for such a search. The cut‐off radius is indeed much lower than the typical domain's size; hence, the number of neighbouring particles is only a little fraction of the total number. Straightforward determination of which particles are inside the interaction range requires the computation of all pair‐wise distances, a procedure whose computational time would be unpractical or totally impossible for large problems. Two main strategies have been developed in the past in order to reduce the unnecessary computation of distances: the first based on dynamically storing each particle's neighbourhood list (Verlet list) and the second based on a framework of fixed cells. The paper presents the results of a numerical sensitivity study on the efficiency of the two procedures as a function of such parameters as the Verlet size and the cell dimensions. An insight is given into the relative computational burden; a discussion of the relative merits of the different approaches is also given and some suggestions are provided on the computational and data structure of the neighbourhood search part of SPH codes. Copyright © 2008 John Wiley & Sons, Ltd.