慢速饮酒血液中酒精含量的数学模型

描述的是在一定时间内慢慢地匀速喝完一定数量酒的问题,并建立了相应的数学模型.同时也建立了快速饮酒的数学模型,以及证明了在各次饮酒后的某时刻酒精含量的可叠加性.     

Fractional extensions of some boundary value problems in oil strata

In the present paper, we solve three boundary value problems related to the temperature field in oil strata — the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional generalization of the incomplete lumped formulation in the radial case. By using the Caputo differintegral operator and the Laplace transform, the solutions are obtained in integral forms where the integrand is expressed in terms of the convolution of some auxiliary functions of Wright function type. A generalization of the Laplace transform convolution theorem, known as Efros’ theorem is widely used.     

Ergodic theory of amenable semigroup actions

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.     

VECTOR-VALUED RANDOM POWER SERIES ON THE UNIT BALL OF C^n

In this article, the authors study the vector-valued random power series on the unit ball of Cn and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between vector-valued random power series and several function spaces are also studied.     

On the Equivalence of Multiparameter Gaussian Processes

Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and Shepp representations. As an application, we study a special type of stochastic equation with linear noise.      

Dependence of calculated electron effective attenuation lengths on transport mean free paths obtained from two atomic potentials

We report changes in electron effective attenuation lengths (EALs) resulting from use of transport mean free paths (TMFPs) obtained from the Dirac–Hartree–Fock (DHF) potential instead of the Thomas–Fermi–Dirac (TFD) potential in an algorithm used in the National Institute of Standards and Technology (NIST) Electron Effective‐Attenuation‐Length Database (SRD 82). TMFPs from the former potential are believed to be more reliable than those obtained from the latter potential. We investigated changes in the EALs for selected photoelectron and Auger‐electron lines in four elemental solids (Si, Cu, Ag, and W), for Si 2p photoelectrons of varying energy in SiO₂, and for photoelectrons excited by Al Kα X rays in four candidate gate‐dielectric materials (HfO₂, ZrO₂, HfSiO₄, and ZrSiO₄). For each material, we computed the change in the average EAL for a range of overlayer‐film thicknesses from zero to a maximum value corresponding to attenuation of the substrate signal to 10% of its original value. This EAL change was a maximum for electrons emitted normally from the surface and decreased monotonically with increasing emission angle. The maximum EAL change varied between ?4.4% and 2.6% for the three groups of materials. We found that the maximum EAL change correlated mainly with the TMFP change. We found that TMFP changes in other solids could generally lead to maximum EAL changes between ?2.6% and 1.9% for electron energies between 500 and 2000 eV. For lower energies, the maximum EAL changes could be larger for some solids. Our revised EALs for Si 2p photoelectrons in SiO₂ excited by Mg and Al Kα X rays agree within 0.5% with values reported by Seah and Spencer from a detailed analysis of SiO₂ film‐thickness measurements by XPS and other techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

The logarithmic norm. History and modern theory

In his 1958 thesis Stability and Error Bounds, Germund Dahlquist introduced the logarithmic norm in order to derive error bounds in initial value problems, using differential inequalities that distinguished between forward and reverse time integration. Originally defined for matrices, the logarithmic norm can be extended to bounded linear operators, but the extensions to nonlinear maps and unbounded operators have required a functional analytic redefinition of the concept.This compact survey is intended as an elementary, but broad and largely self-contained, introduction to the versatile and powerful modern theory. Its wealth of applications range from the stability theory of IVPs and BVPs, to the solvability of algebraic, nonlinear, operator, and functional equations. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65L05     

Fast computation of a rational point of a variety over a finite field

We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety.

     

On error operators related to the arbitrary functions principle

The error on a real quantity Y due to the graduation of the measuring instrument may be asymptotically represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator does not depend on the probability law of Y as soon as this law possesses a continuous density. This feature is related to the “arbitrary functions principle” (Poincaré, Hopf). We give extensions of this property to Rd and to the Wiener space for some approximations of the Brownian motion. This gives new approximations of the Ornstein-Uhlenbeck gradient. These results apply to the discretization of some stochastic differential equations encountered in mechanics.     

含余割核奇异积分修改的反演问题

针对含余害核奇异积分反演问题在指κ＜0时一般无解的情况，本文提出并求解两种修改的反演问题，而后一种修改反演问题的提法与此前类似问题颇不相同，由于运用了推广的留数定理和Bertrand型换序公式使本问题及类似问题解法得以简化。