Revisiting total, matric, and osmotic suction in partially saturated geomaterials

An accurate quantification of negative pore pressure (commonly referred to as ??suction??) in the pore network is necessary for modeling the mechanical response of unsaturated geomaterials. Traditional definitions and formulations of total, matric, and osmotic suction suggest incorrect pore fluid pressures under certain conditions. In this paper, the notion of suction is revisited by deriving an expression for pore fluid pressure in a simple osmotic, capillary tube using the framework of mixture theory in conjunction with the fundamental laws of thermodynamics. Based on the derived expression for the tube, expressions are derived for total, matric, and osmotic suction for partially saturated geomaterials. Particular attention is given to osmotic suction since confusion regarding its mechanisms has apparently contributed to its misapplication in geomechanics. The new expressions derived herein adequately explain behavior that is incorrectly explained by the traditional formulations and unifies two approaches to modeling osmotic suction previously considered to be in contradiction.     

Explicit Expressions for Timelike and Spacelike Observables of Quantum Chromodynamics in Analytic Perturbation Theory

We study the possibility of expressing the invariant QCD coupling function (i.e., the effective coupling constant) in an explicit analytic form in two- and three-loop approximations as well as in the case of the Padé-transformed -function. Both the timelike and spacelike domains are investigated. Technical aspects of the Shirkov–Solovtsov analytic perturbation theory are considered. Explicit expressions for the two- and three-loop effective coupling functions in the timelike domain are obtained. In the last case, we apply a new method of expanding functions represented in an arbitrary loop order of perturbation theory in powers of the two-loop function. The comparison with numerical data in the infrared region shows that the obtained explicit expressions for the three-loop functions agree fully with the exact numerical results.     

A Series Solution of the Unsteady Von Kármán Swirling Viscous Flows

A new analytic technique is applied to solve the unsteady viscous flow due to an infinite rotating disk, governed by a set of two fully coupled nonlinear partial differential equations deduced directly from the exact Navier-Stokes equations. The system of coupled nonlinear partial differential equations is replaced by a sequence of uncoupled systems of linear ordinary differential equations. Different from all other previous analytic results, our series solution is accurate and valid for all time in the whole spatial region. Accurate expressions for skin friction coefficients are given, which are valid for all time. Such kind of series solutions have not been reported, to the best of our knowledge.      

Certain subclasses of p-valently analytic functions involving a generalized fractional differintegral operator

By making use of the principle of subordination between analytic functions and the generalized fractional differintegral operator, we introduce and investigate some new subclasses of p-valently analytic functions in the open unit disk. Such results as inclusion relationships, integral-preserving properties, convolution properties, subordination and superordination properties, and sandwich theorems for these classes are derived.     

Singular value expansion for the Green function of Helmholtz operator

We consider the integral operator defined on a circular disk, and with kernel the Green function of the Helmholtz operator. We present an analytic framework for the explicit computation of the singular system of this kernel. In particular, the main formulas of this framework are given by a characteristic equation for the singular values and explicit expressions for the corresponding singular functions. We provide also a property of the singular values, that gives an important information for the numerical evaluation of the singular system. Finally, we present a simple numerical experiment, where the singular system computed by a simple implementation of these analytic formulas is compared with the singular system obtained by a discretization of the Green function of the Helmholtz operator.     

Certain family of integral operators preserving subordination and superordination

We obtain subordination, superordination and sandwich-preserving new theorems for certain integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also derived, and the results generalize some recently ones.     

CERTAIN FAMILY OF INTEGRAL OPERATORS PRESERVING SUBORDINATION AND SUPERORDINATION

We obtain subordination, superordination and sandwich-preserving new theorems for certain integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also derived, and the results generalize some recently ones.     

On Cowen–Pommerenke inequalities

C. Cowen and C. Pommerenke established inequalities for the derivatives of analytic self-mappings of the open unit disk at their fixed points. In this article, we show that these inequalities can be derived from Schwarz–Pick inequalities     

On the properties of a certain subclass of close-to-convex functions

In the present paper, we introduce an interesting subclass Kps (h)of analytic functions in the open unit disk U. For functions belonging to theclass Kps (h), basic properties such as the coefficient bounds, the distortionand growth theorems are derived. The results presented here would provideextensions of those given by Q.-H. Xu et al. [2].     

The Coupling of Finite Element Method and Boundary Element Method for Two-Dimensional Helmholtz Equation in an Exterior Domain

This paper presents a new coupling of the finite element method and the boundary element method to solve the two-dimensional exterior Helmholtz problems by using the asymptotic radiation conditions in [1], in which the coupling relations are the same as C. Johnson and J. C. Nedelec's. The error estimates are derived and results of numerical calculation in comparison with analytic solution verify the theoretical estimates.     

Weighted Harmonic Means

The purpose of this study is to develop a conception of the differential subordination involving harmonic means of the expressions \(\psi (p(z), zp'(z);z)\), where p is an analytic function in the unit disk, such that \(p(0)=1, p(z)\not \equiv 1\). Here, we discuss convex weighted harmonic means and we find some applications in the theory of analytic functions.     

Stresses in an elastic plate lying over a base due to strip-loading

The closed-form analytic expressions for the stresses at any point of an elastic plate coupling in different ways to a base as a result of a two-dimensional shear strip-loading are obtained. The contact between the horizontal layer and the base is either smooth-rigid or rough-rigid or welded. The variations of the shear stresses with the horizontal distance have been studied numerically. It is found that the effect of different boundary conditions on the stress field is significant and the stresses for an elastic layer lying over an elastic half-space differ considerably from those of an entire homogeneous elastic half-space.     

On the Reciprocity Principle in the Scattering of Plane Electromagnetic Waves by a Conic Scatterer

Let a plane electromagnetic wave be scattered by a perfectly conducting cone. The diffraction process creates a spherical wave scattered by the vertex of the cone. The diffraction coefficients of this wave, whose analytic expressions are derived in the present paper, possess some symmetry properties. Bibliography: 2 titles.     

Data-Recursive Smoother Formulae for Partially Observed Discrete-Time Markov Chains

Abstract

We address a dynamic portfolio optimization problem where the expected utility from terminal wealth has to be maximized. The special feature of this paper is an additional constraint on the portfolio strategy modeling bounded shortfall risks, which are measured by value at risk or expected loss. Using a continuous-time model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Finally, some numerical results are presented.     

Approximation of Cauchy-Type Integrals

We investigate approximations of analytic functions determined by Cauchy-type integrals in Jordan domains of the complex plane. We develop, modify, and complete (in a certain sense) our earlier results. Special attention is given to the investigation of approximation of functions analytic in a disk by Taylor sums. In particular, we obtain asymptotic equalities for upper bounds of the deviations of Taylor sums on the classes of -integrals of functions analytic in the unit disk and continuous in its closure. These equalities are a generalization of the known Stechkin's results on the approximation of functions analytic in the unit disk and having bounded rth derivatives (here, r is a natural number).On the basis of the results obtained for a disk, we establish pointwise estimates for the deviations of partial Faber sums on the classes of -integrals of functions analytic in domains with rectifiable Jordan boundaries. We show that, for a closed domain, these estimates are exact in order and exact in the sense of constants with leading terms if and only if this domain is a Faber domain.     

Rudin orthogonality problem on the Bergman space

In this paper, we study the Rudin orthogonality problem on the Bergman space, which is to characterize those functions bounded analytic on the unit disk whose powers form an orthogonal set in the Bergman space of the unit disk. We completely solve the problem if those functions are univalent in the unit disk or analytic in a neighborhood of the closed unit disk. As a consequence, it is shown that an analytic multiplication operator on the Bergman space is unitarily equivalent to a weighted unilateral shift of finite multiplicity n if and only if its symbol is a constant multiple of the n-th power of a Möbius transform, which was obtained via the Hardy space theory of the bidisk in Sun et al. (2008) [10].     

激光脉冲放大器增益通量耦合系统解

研究了一个激光脉冲放大器增益通量系统解的问题.首先讨论了较一般的系统, 然后引入一个同伦映射.再利用映射的性质, 引进一个人工参数, 将求解非线性问题转化为求解一系列线性问题.再逐次地求出对应的线性问题的解, 最后得到了原模型解的近似展开式.可以看出, 同伦映射方法是一个解析的方法.它是通过函数的解析运算并用初等函数来表达近似解,其不同于用离散数值运算的数值计算方法.因此通过同伦映射解, 还可以对它继续进行解析运算, 从而可以进行微分和积分等运算来得到与激光脉冲放大器增益通量相关的其他物理量的性态.     

Effects of slip on the non-linear flows of a third grade fluid

The present analysis considers the non-linear problems of steady flow of a third grade fluid between the concentric cylinders. A complete analysis of mathematical modeling is made when no-slip condition is no longer valid. Exact analytic solutions of the following two non-linear problems are derived: (i) when inner cylinder moves and outer cylinder remains stationary and (ii) for inner cylinder at rest and outer cylinder in motion. Graphical results are presented to illustrate the analytic solutions. The corresponding results of no-slip condition are deduced as the limiting cases when the slip parameter is equal to zero.     

矩形微通道热沉内单相稳态层流流体的流动与传热分析

采用解析方法分析了矩形微通道热沉内单相稳态层流流体的流动与传热．基于y方向流速和导热不变的假设,建立流体在矩形微通道内流动的流速方程和传热的温度方程,进而推导出Nusselt数和Poiseuille数的理论表达式．通过计算结果可以看出,推导的Nusselt数和Poiseuille数的解析解与其他文献的结果吻合较好,而且当宽高比趋于无穷大时,Nusselt数和Poiseuille数分别趋近于8.235和96,这与其他文献结果完全相同．在Reynolds数相同时,摩擦因数随着宽高比的增加而增加,而在相同宽高比时,摩擦因数随Reynolds数的增加而减小．