Representation of Probabilistic Data by Quantum-Like Hyperbolic Amplitudes

In this paper we study the problem of representation of statistical data of any origin by hyperbolic probabilistic amplitudes (normalized vectors in hyperbolic Hilbert space). It generalizes the conventional QM which is based on complex Hilbert space. We performed extended numerical simulation. Similar to the conventional quantum formalism for Bloch’s sphere, we visualize results of simulation for a special class of statistical data on so called Bloch’s hyperboloid. The notion of hyperbolic qubit is introduced.     

A Representation of Hyperbolic Motions Including the Infinite-Dimensional Case

Let X be a real inner product space of (finite or infinite) dimension ???2, O(X) be its group of all surjective (hence bijective) orthogonal transformations of X, T(X) be the set of all hyperbolic translations of X and M(X, hyp) be the group of all hyperbolic motions of X. The following theorem will be proved in this note. Every ${\mu\in M(X,{\mbox hyp})}$ has a representation ?? = T · ?? with uniquely determined ${T\in T(X)}$ and uniquely determined ${\omega\in O(X)}$ .     

Multiplicative Representation of a Hyperbolic non Distributive Algebra

The multiplicative or polar representation of hyperbolic scator algebra in 1 + n dimensions is introduced. The transformations between additive and multiplicative representations are presented. The addition and product operations are consistently defined in either representation using additive or multiplicative variables. The product is shown to produce a rotation and scaling for equal director components and solely a scaling in the orthogonal components.     

On the Volume Formula for Hyperbolic Tetrahedra

We present a volume formula for arbitrary hyperbolic tetrahedra and give applications for Coxeter tetrahedra. Received November 6, 1997, and in revised form April 29, 1998.     

On a Numerical Algorithm for Solving Boundary-Value Problems for Systems of Hyperbolic Equations of the First Order

In this article, we develop and substantiate a two-step, explicit–implicit numerical algorithm for solving boundary-value problems for systems of partial hyperbolic differential equations of the first order. The algorithm is based on finite-difference schemes with the differences taken against the flow. The approximation error of the solution has order two in the time variable and order one in the spatial variables.     

关于双曲等距变换的表示

本文得到Mbius变换和Clifford矩阵在Iso(H_0~n)中对应元素的具体表达式。     

On the Volumes of Hyperbolic Simplices

Mathematical Notes - We present an explicit formula for calculating the volume of an arbitrary hyperbolic 4-simplex in terms of the coordinates of its vertices; by this formula, the volume can be...     

On the Isometry Groups of Hyperbolic Orbifolds

A generic, geometrically finite, hyperbolic n-orbifold is proved to have a finite group of isometries.     

On the Homogenization of Periodic Hyperbolic Systems

Mathematical Notes -     

On the Cauchy Problem for Hyperbolic Operators with Double Characteristics

We show that for a class of hyperbolic second order operators with double characteristics the Ivrii–Petkov condition is also sufficient for the well-posedness of the Cauchy problem in C ^∞.     

AHP中判断矩阵一致性改进的迭代算法

本文研究了扰动矩阵与判断矩阵的不一致性的关系 ,提出了一种新的改进判断矩阵一致性的迭代算法 .     

On the Decay of Solutions for Some Nonlinear Dissipative Hyperbolic Equations

In this paper we show the decay of solutions to the initial-boundary value problem for somenonlinear hyperbolic equation with a nonlinear dissipative term,by using a difference inequality.     

New Algorithm for the Conical Combination Representation Problem of a Vector

An important problem in constrained optimization is to determine whether or not a vector can be represented as the conical combination (i.e., linear nonnegative combination) of some given vectors. This problem can be transformed into a special linear programming problem (SLP). A new approach, the variable-dimension boundary-point algorithm (VDBPA), based on the projection of a vector into a variable-dimension subspace, is proposed to solve this problem. When a conical combination representation (CCR) of a vector exists, the VDBPA can compute its CCR coefficients; otherwise, the algorithm certificates the nonexistence of such representation. In order to assure convergence, the VDBPA may call the lexicographically ordered method (LOM) for linear programming at the final stage. In fact, the VDBPA terminates often by solving SLP for most instances before calling the LOM. Numerical results indicate that the VDBPA works more efficiently than the LOM for problems that have more variables or inequality constraints. Also, we have found instances of the SLP, when the number of inequality constraints is about twice the number of variables, which are much more difficult to solve than other instances. In addition, the convergence of the VDBPA without calling the LOM is established under certain conditions.     

On Robustness of Orbit Spaces for Partially Hyperbolic Endomorphisms

In this paper, the robustness of the orbit structure is investigated for a partially hyperbolic endomorphism f on a compact manifold M. It is first proved that the dynamical structure of its orbit space(the inverse limit space) M~f of f is topologically quasi-stable under C~0-small perturbations in the following sense: For any covering endomorphism g C~0-close to f, there is a continuous map φ from M~g to Multiply form -∞ to ∞ M such that for any {y_i }_(i∈Z) ∈φ(M~g), y_(i+1) and f(y_i) differ only by a motion along the center direction. It is then proved that f has quasi-shadowing property in the following sense: For any pseudo-orbit {x_i }_(i∈Z),there is a sequence of points {y_i }_(i∈Z) tracing it, in which y_(i+1) is obtained from f(y_i) by a motion along the center direction.     

An Algorithm for a Letter-Based Representation of All-Pairwise Comparisons

All-pairwise comparisons among a set of t treatments or groups are one of the most frequent tasks in applied statistics. Users of statistical software are accustomed to the familiar lines display, in which treatments that do not differ significantly, are connected by a common line or letter. Availability of the lines display is restricted mainly to the balanced analysis of variance setup. This limited availability is at stark variance with the diversity of statistical methods and models, which call for multiple comparisons. This article describes a general method for graphically representing any set of t(t?1)/2 all-pairwise significance statements (p values) for t treatments by a familiar letter display, which is applicable regardless of the underlying data structure or the statistical method used for comparisons. The method reproduces the familiar lines display in case of the balanced analysis of variance. Its broad applicability is demonstrated using data from an international multienvironment wheat yield trial and from a fish catching survey.     

On a Version of the Hyperbolic Annulus Principle

A sufficiently general class of diffeomorphisms of the annulus (the direct product of a ball in \(\mathbb{R}^{k}\), k ≥ 2, by an m-dimensional torus) is studied. The so-called annulus principle, i.e., a set of sufficient conditions under which the diffeomorphisms of the class under study have a mixing hyperbolic attractor, is obtained.     

On Hyperbolic Pencils for the Grad Moment Systems in Nonequilibrium Thermodynamics

In this paper, we derive sufficient conditions for the stability of a solution to the Cauchy problem of systems of moments of nonequilibrium thermodynamics linearized in the neighborhood of the equilibrium state that are very close to the necessary conditions. The stability conditions are presented in the form of a parametric Hermite theorem for polynomial hyperbolic pencils of any order.__________Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 24, pp. 67–94, 2004.     

On the Consistency of a Positive Theory

In positive theories, we have an axiom scheme of comprehension for positive formulas. We study here the “generalized positive” theory GPK_∞⁺. Natural models of this theory are hyperuniverses. The author has shown in [2] that GPK_∞⁺ interprets the Kelley Morse class theory. Here we prove that GPK_∞⁺ + AC_WF (AC_WF being a form of the axiom of choice allowing to choose elements in well-founded sets) and the Kelley-Morse class theory with the axiom of global choice and the axiom “On is ramifiable” are mutually interpretable. This shows that GPK_∞⁺ + AC_WF is a “strong” theory since “On is ramifiable” implies the existence of a proper class of inaccessible cardinals.