Anomalous scaling in the model of turbulent advection of a vector field

We consider the model of turbulent advection of a passive vector field ϕ by a two-dimensional random velocity field uncorrelated in time and having Gaussian statistics with a powerlike correlator. The renormalization group and operator product expansion methods show that the asymptotic form of the structure functions of the ϕ field in the inertial range is determined by the fluctuations of the energy dissipation rate. The dependence of the asymptotic form on the external turbulence scale is essential and has a powerlike form (anomalous scaling). The corresponding exponents are determined by the spectrum of the anomalous dimension matrices of operator families consisting of gradients of ϕ. We find a basis constructed from powers of the dissipation and enstrophy operators in which these matrices have a triangular form in all orders of the perturbation theory. In the two-loop approximation, we evaluate the anomalous-scaling exponents for the structure functions of an arbitrary order. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 467–487, March, 2006.     

Renormalization Group Analysis of Models of Advection of a Vector Admixture and a Tracer Field by a Compressible Turbulent Flow

Theoretical and Mathematical Physics - Using a quantum field theory renormalization group, we consider models of advection of a vector field and a tracer field by a compressible turbulent flow....     

On Causal Invertibility with Respect to a Cone of Integral-Difference Operators in Vector Function Spaces

Let \(\mathbb{S}\) be a cone in ? ⁿ . A bounded linear operator T: L _p (? ⁿ ) → L _p (? ⁿ ) is said to be causal with respect to \(\mathbb{S}\) if the implication x(s) = 0 (s ε W ? \(\mathbb{S}\)) ? (Tx) (s) = 0 (s ε W ? \(\mathbb{S}\)) is valid for any x ε L _p (? ⁿ ) and any open subset W\(\subseteq\) ? ⁿ . The set of all causal operators is a Banach algebra. We describe the spectrum of the operator

$(Tx)(t) = \sum\limits_{n = 1}^\infty {a_n x(t - t_n )} + \int {\mathbb{S}g(s)x(t - s)ds,} \quad t \in \mathbb{R}^n ,$

in this algebra. Here x ranges in a Banach space \(\mathbb{E}\), the a _n are bounded linear operators in \(\mathbb{E}\), and the function g ranges in the set of bounded operators in \(\mathbb{E}\).

     

上三角算子矩阵的本征函数展开法在应力形式的二维弹性问题中的应用

深入研究了求解基于应力形式的二维弹性问题的本征函数展开法．根据已有的研究结果,将基于应力形式的二维弹性问题的基本偏微分方程组等价地转化为上三角微分系统,并导出了相应的上三角算子矩阵．通过深入研究,分别获得了该算子矩阵的两个对角块算子更为简洁的正交本征函数系,并证明了它们在相应空间中的完备性,进而应用本征函数展开法给出了该二维弹性问题的更为简洁实用的一般解．此外,对该二维弹性问题,还指出了什么样的边界条件可以应用此方法求解．最后应用具体的算例验证了所得结论的合理性．     

幂律速度运动表面上磁流体在驻点附近的滑移流动

从理论上研究了具有非线性延伸表面的磁流体在滑移流区的动量传输问题.通过Lie群变换把控制方程组转化为常微分方程组,利用同伦分析方法求得了问题的近似解析解.获得的级数解与文献中的数值解吻合得较好.另外,利用级数解分析滑移参数、磁场强度、速度比率参数、吸入喷注参数和幂律指数对流动的影响.结果显示这些参数对壁剪切力和边界层内流场有较大的影响.     

The Spectral Measure of Certain Elements of the Complex Group Ring of a Wreath Product

We use elementary methods to compute the L ²-dimension of the eigenspaces of the Markov operator on the lamplighter group and of generalizations of this operator on other groups. In particular, we give a transparent explanation of the spectral measure of the Markov operator on the lamplighter group found by Grigorchuk and Zuk, and later used by them, together with Linnell and Schick, to produce a counterexample to a strong version of the Atiyah conjecture about the range of L ²-Betti numbers. We use our results to construct manifolds with certain L ²-Betti numbers (given as convergent infinite sums of rational numbers) which are not obviously rational, but we have been unable to determine whether any of them are irrational.     

Discrete Spectrum of the Schrodinger Operator Perturbed by a Narrowly Supported Potential

We study asymptotic properties of the discrete spectrum of the Schrodinger operator perturbed by a narrowly supported potential. The first terms of the asymptotic expansions in the small parameter equal to the width of the support of the potential are constructed for the eigenvalues and the corresponding eigenfunctions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 3, pp. 372–384, December, 2005.     

Certain inequality properties of multivalent analytic functions involving the Dziok-Srivastava operator

The object of the present paper is to derive certain inequality properties of multivalent analytic functions involving the Dziok-Srivastava operator.     

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.     

Subordination properties for a certain class of analytic functions defined by the Salagean operator

In this paper we derive several subordination results for a certain class of analytic functions defined by the Salagean operator.     

Generalization of certain subclasses of multivalent functions with negative coefficients defined by using a differential operator

Making use of a differential operator, we introduce and study a certain class SC_n(j,p,q,α,λ) of p-valently analytic functions with negative coefficients. In this paper, we obtain numerous sharp results including (for example ) coefficient estimates, distortion theorem, radii of close-to convexity, starlikeness and convexity and modified Hadamard products of functions belonging to the class SC_n(j,p,q,α,λ). Finally, several applications investigate an integral operator, and certain fractional calculus operators are also considered.     

On density of transitive operator algebras

In this paper we study the transitive algebra question by considering the invariant subspace problem relative to von Neumann algebras. We prove that the algebra (not necessarily ∗) generated by a pair of sums of two unitary generators of L(F_∞) and its commutant is strong-operator dense in B(H). The relations between the transitive algebra question and the invariant subspace problem relative to some von Neumann algebras are discussed.     

Improving cyclone performance by proper selection of the exit pipe

Cyclone performance is determined by pressure drop and collection efficiency. This study aims to optimize the dimensions of the exit pipe to improve cyclone performance. A numerical technique was used which is based on an Eulerian–Lagrangian approach. The behavior of the cyclone was studied by solving the three-dimensional, incompressible turbulent flow governing equations. The turbulent flow was modeled by using Reynolds Stress Model. Particle trajectories were obtained by solving the particle equation of motion. The collection efficiency was obtained by releasing a specified number of particles at the inlet of the cyclone and by counting the collected particles. The model was verified by comparing the numerical results to published experimental measurements. It was found through this study that increasing exit pipe diameter decreases the pressure drop through the cyclone and affects also the collection efficiency while exit pipe length does not affect cyclone performance significantly. It was concluded that the performance of the standard cyclone can be improved by prober selection for the diameter of the exit pipe. The data obtained through this study was represented in performance maps. These maps allowed the selection of the exit pipe diameter to obtain the maximum collection efficiency while avoiding excessive pressure drop.     

由Srivastava-Khairnar-More算子定义的$p$叶函数类的包含关系

In the present paper, we use the methods of differential subordination and convo- lution to investigate some inclusion properties for certain classes of p-valent analytic functions in the open unit disk, which are associated with the Srivastava-Khairnar-More operator. The results presented here include several previous known results as their special cases.     

An inverse problem for computing a leading coefficient in the Sturm-Liouville operator by using the boundary data

We consider an inverse problem for identifying a leading coefficient α(x) in −(α(x)y′(x))′ + q(x)y(x) = H(x), which is known as an inverse coefficient problem for the Sturm-Liouville operator. We transform y(x) to u(x, t) =  (1 + t)y(x) and derive a parabolic type PDE in a fictitious time domain of t. Then we develop a Lie-group adaptive method (LGAM) to find the coefficient function α(x). When α(x) is a continuous function of x, we can identify it very well, by giving boundary data of y, y′ and α. The efficiency of LGAM is confirmed by comparing the numerical results with exact solutions. Although the data used in the identification are limited, we can provide a rather accurate solution of α(x).     

On a class of analytic functions related to conic domains and associated with Carlson-Shaffer operator

Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigat inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.     

Classes of analytic functions associated with the Choi-Saigo-Srivastava operator

We investigate several properties of the linear Choi-Saigo-Srivastava operator and associated classes of analytic functions which were introduced and studied by J.H. Choi, M. Saigo and H.M. Srivastava [J.H. Choi, M. Saigo, H.M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276 (2002) 432-445]. Several theorems are an extension of earlier results of the above paper.     

Some analytical and numerical investigation of a family of fractional-order Helmholtz equations in two space dimensions

In this article, we aim at solving a family of two-dimensional fractional-order Helmholtz equations by using the Laplace-Adomian Decomposition Method (LADM). The fractional-order derivatives, which we use in this investigation, follows the Liouville-Caputo definition. Our results based upon the LADM are obtained in series form that helps us in analyzing the analytical solutions of the fractional-order Helmholtz equations considered here. For illustration and verification of the analytical procedure using the LADM, several numerical examples and graphical representations are presented for the analytical solution of the fractional-order Helmholtz equations. The mathematical analytic procedure, which we have used here, has shown that the LADM is a fairly accurate and computable method for the solution of problems involving fractional-order Helmholtz equations in two dimensions. In an analogous manner, one can apply the LADM for finding the analytical solution of other classes of fractional-order partial differential equations.     

Actor of a Precrossed Module

Applying the equivalence of the category of precrossed modules with the category of groups with two additional unary operations satisfying the corresponding conditions, the construction of an actor is given in terms of Whitehead group of generalized regular derivations, defined in the article, and the automorphism group of a precrossed module. The analogous approach to this problem in the case of crossed modules leads to the well-known construction given in the works of Lue and Norrie.