四元Heisenberg群上次拉普拉斯算子的m幂次的基本解

本文研究了四元Heisenberg群上次拉普拉斯算子的m幂次的基本解,该结论是Heisenberg群上结果的推广.本文利用了四元Heisenberg群上的Fourier变换理论构造了该群上次拉普拉斯算子的m幂次的基本解,并且给出了基本解的积分表示.     

四元Heisenberg群上次拉普拉斯算子的m幂次的基本解

本文研究了四元Heisenberg群上次拉普拉斯算子的m幂次的基本解,该结论是Heisenberg群上结果的推广.本文利用了四元Heisenberg群上的Fourier变换理论构造了该群上次拉普拉斯算子的m幂次的基本解,并且给出了基本解的积分表示.     

A Unified Fixed Point Theory for Countably P -Concentrative Multimaps

New fixed point results and Leray-Schauder alternatives are presented for countably P -concentrative multimaps. The notion of an essential map is also introduced for a wide class of maps.     

Finite speed of propagation and local boundary conditions for wave equations with point interactions

We show that the boundary conditions entering in the definition of the self-adjoint operator describing the Laplacian plus a finite number of point interactions are local if and only if the corresponding wave equation has finite speed of propagation.

     

A Few Exact Solutions for the Model of Equal Spin-Spin Interactions

For the model of equal spin-spin interactions, we obtain exact Heisenberg expressions for the spin operator components and use them to find the relations that hold for spin operators appearing in the thermodynamic mean. We use the obtained exact relations for the means to describe the thermodynamics of the model under consideration. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 3, pp. 411–419, December, 2005.     

A Weierstrass Representation Formula for Minimal Surfaces in ℍ3 and ℍ2 × ℝ

We give a general setting for constructing a Weierstrass representation formula for simply connected minimal surfaces in a Riemannian manifold. Then, we construct examples of minimal surfaces in the three dimensional Heisenberg group and in the product of the hyperbolic plane with the real line. Work partially supported by RAS, INdAM, FAPESP and CNPq     

自由能展开式中点群的不可约表示的基函数

一个群的基函数的选择并非唯一，不同的基函数对应不同的表示矩阵。即使相同的表示矩阵，基函数也可以有不同的选择。在相变的宏观唯象理论中， 自由能展开式可由同一个表示矩阵的基函数来构造，因而给出不可约表示的基函数表就非常有意义。现有文献给出的32点群不可约表示的基函数只写到二次幂，而且有些文献中的同一个不可约表示所选取的不同的基函数却对应不同的表示矩阵，这样在构造群变换不变式时，就会出错。该文将基函数表写至三次幂, 这有助于准确、迅速地写出到六次幂群变换不变的自由能表达式。由新的基函数表发现十八种点群有三次幂的群操作不变式, 高温相属这些点群铁电体, 发生的本征铁电相变为一级相变。     

Aircraft proximity termination conditions for 3D turn centric modes

International airspace design is undergoing significant change that requires formal and rigorous mathematical specifications to assure the safety of flight operations. Aircraft proximity management is one such area. The Point of Closest Approach (PCA) between aircraft flightpaths is the position along a flightpath at which the minima in relative range occurs. To date, PCA has been estimated primarily based on the assumption of a linear extrapolation of the velocity vectors of each aircraft involved, however, this assumption is limiting and aircraft in turning flight must also be considered. A generalised geometric and vector construction for the determination of PCA is presented. A solution based on a characterization of Fermat’s method for stationary points is presented that results in a complex transcendental equation. By casting the equation in a determinant structure a co-linearity condition is revealed between three unique 2D points. A novel aspect is that one of these points is a fixed reference point that lies on either the vector between the aircraft turn centres or on one of its extensions providing a reference to determine the location of the PCA. The analytic method can be readily applied in a laboratory test environment or in an automated guidance context. The rigorous proof enables a higher confidence in achieving dependable operations in a safety critical context and in the adequacy of test strategies when developing algorithms for aircraft avionics.     

Fuzzy度量空间扩张型映象的不动点定理

本文给出Ｆｕｚｚｙ度量空间一些扩张型映象的不动点定理,这些结果发展和改进了普通度量空间中相应的结果。     

Fuzzy度量空间型映象的不动点定理

本文给出Ｆｕｚｚｙ度量空间一些扩张型映象的不动点定理,这些结果发展和改进了普通度量空间中相应的结果。     

Quasirecognizability by the Set of Element Orders for Groups 3 D 4(q), for q Even

It is proved that if G is a finite group with an element order set as in the simple group ³D₄(q), where q is even, then the commutant of G/F(G) is isomorphic to ³D₄(q) and the factor group G/G′ is a cyclic {2, 3}-group. __________ Translated from Algebra i Logika, Vol. 45, No. 1, pp. 3–19, January–February, 2006.     

Parabolic permutation representations of the groups2 F 4(q) and3 D 4(q 3)

In the paper, the ranks, degrees, subdegrees, and double centralizers of permutation representations of the bounded groups² F ₄(q) and³ D ₄(q ³) with respect to parabolic maximal subgroups of nonminimal index are found. Translated fromMatematicheskie Zametki, Vol. 67, No. 1, pp. 69–76, January, 2000.     

Conservation laws for two-phase filtration models

The paper is devoted to investigation of group properties of a one-dimensional model of two-phase filtration in porous medium. Along with the general model, some of its particular cases widely used in oil-field development are discussed. The Buckley–Leverett model is considered in detail as a particular case of the one-dimensional filtration model. This model is constructed under the assumption that filtration is one-dimensional and horizontally directed, the porous medium is homogeneous and incompressible, the filtering fluids are also incompressible. The model of “chromatic fluid” filtration is also investigated. New conservation laws and particular solutions are constructed using symmetries and nonlinear self-adjointness of the system of equations.     

Comparison Principles for Some Fully Nonlinear Sub-Elliptic Equations on the Heisenberg Group

In this paper,we prove a form of the strong comparison principle for a class of fully nonlinear subelliptic operators of the form■H^2,sψ+L(·,ψ,■Hψ)on the Heisenberg group,which include the CR invariant operators.     

Best Constants for Moser-Trudinger Inequalities, Fundamental Solutions and One-Parameter Representation Formulas on Groups of Heisenberg Type

We derive the explicit fundamental solutions for a class of degenerate (or singular) one-parameter subelliptic differential operators on groups of Heisenberg (H) type. This extends the results of Kaplan of the sub-Laplacian on H-type groups, which in turn generalizes Folland's result on the Heisenberg group. As an application, we obtain a one-parameter representation formula for Sobolev functions of compact support on H-type groups. By choosing the parameter equal to the homogeneous dimension Q and using the Moser-Trudinger inequality for the convolutional type operator on stratified groups obtained in [18], we get the following theorem which gives the best constant for the Moser-Trudinger inequality for Sobolev functions in H-type groups. Let ${\Bbb G}We derive the explicit fundamental solutions for a class of degenerate (or singular) one-parameter subelliptic differential operators on groups of Heisenberg (H) type. This extends the results of Kaplan of the sub-Laplacian on H-type groups, which in turn generalizes Folland's result on the Heisenberg group. As an application, we obtain a one-parameter representation formula for Sobolev functions of compact support on H-type groups. By choosing the parameter equal to the homogeneous dimension Q and using the Moser-Trudinger inequality for the convolutional type operator on stratified groups obtained in [18], we get the following theorem which gives the best constant for the Moser-Trudinger inequality for Sobolev functions in H-type groups. Let ? be any group of Heisenberg type whose Lie algebra is g enerated by m left invariant vector fields and with a q-dimensional center. Let and Then, with A _Q as the sharp constant, where ∇_? denotes the subellitpic gradient on ? This continues the research originated in our earlier study of the best constants in Moser-Trudinger inequalities and fundamental solutions for one-parameter subelliptic operators on the Heisenberg group [18]. Received March 15, 2001, Accepted September 21, 2001     

Wiener's lemma for twisted convolution and Gabor frames

We prove non-commutative versions of Wiener's Lemma on absolutely convergent Fourier series (a) for the case of twisted convolution and (b) for rotation algebras. As an application we solve some open problems about Gabor frames, among them the problem of Feichtinger and Janssen that is known in the literature as the ``irrational case'.

     

Nonexistence results for higher order pseudo‐parabolic equations in the Heisenberg group

Sufficient conditions are obtained for the nonexistence of solutions to the nonlinear higher order pseudo‐parabolic equation where is the Kohn‐Laplace operator on the (2N + 1)‐dimensional Heisenberg group , m≥1,p > 1. Then, this result is extended to the case of a 2 × 2‐system of the same type. Our technique of proof is based on judicious choices of the test functions in the weak formulation of the sought solutions. Copyright © 2016 John Wiley & Sons, Ltd.     

The number of symmetric colorings of the dihedral group D3

We compute the number of symmetric r-colorings and the number of equivalence classes of symmetric r-colorings of the dihedral group D₃.     

A novel variational method for 3D viscous flow in flow channel of turbomachines based on differential geometry

ABSTRACT

This paper presents a novel variational method for treating three-dimensional rotational Navier-Stokes equations in flow channel of turbomachines. The proposed method establishes a new semi-geodesic coordinate system on the central surface of blades. From the perspective of differential geometry, the system under concern is split into a set of membrane operator equations on two-dimensional manifolds and bending operator equations along hub circle. The third variable of the new coordinate system is approximated by the central difference scheme. We derive a new formulation of two-dimensional Navier-Stokes equations with three components on the manifolds in the variational sense. The well-posedness of the proposed variational formulation is rigorously justified.