January 1995 arXiv papers — page 10

Quo-Shin Chi, Lorenz J Schwachhöfer

Bryant \cite{Br} proved the existence of torsion free connections with exotic holonomy, i.e. with holonomy that does not occur on the classical list of Berger \cite{Ber}. These connections occur on moduli spaces $\Y$ of rational contact curves in a contact threefold $\W$. Therefore, they are naturally contained in the moduli space $\Z$ of all rational curves

Baowen Li, Marko Robnik

We study the statistical properties of the high-lying chaotic eigenstates (200,000 and above) which are deep in the semiclassical regime. The system we are analyzing is the billiard system inside the region defined by the quadratic (complex) conformal map of the unit disk as introduced by Robnik (1983). We are using Heller's method of plane wave decompos

Thomas Traexler, Wolfram Just, Herwig Sauermann

Spatially homogeneous solutions of the Landau--Lifshitz--Gilbert equation are analysed. The conservative as well as the dissipative case is considered explicitly. For the linearly polarized driven Hamiltonian system we apply canonical perturbation theory to uncover the main resonances as well as the global phase space structure. In the case of circularly pol

Per Dahlqvist

We compute the Lyapunov exponent, generalized Lyapunov exponents and the diffusion constant for a Lorentz gas on a square lattice, thus having infinite horizon. Approximate zeta functions, written in terms of probabilities rather than periodic orbits, a re used in order to avoid the convergence problems of cycle expansions. The emphasis is on the relation be

Peter L. Biermann, T. K. Gaisser, Todor Stanev

Motivated by recent measurements of the major components of the cosmic radiation around 10 TeV/nucleon and above, we discuss the phenomenology of a model in which there are two distinct kinds of cosmic ray accelerators in the galaxy. Comparison of the spectra of hydrogen and helium up to 100 TeV per nucleon suggests that these two elements do not have the sa

Kiwoon Choi, Jihn E. Kim, Gye T. Park

We argue that the hidden sector potential energy is generically of order the intermediate scale although the true cosmological constant does vanish. This would significantly change the predicted values of soft parameters for a variety of supergravity models including those derived from string theory. We stress that this point is particularly relevant for sup

M. Shifman, N. G. Uraltsev

We comment on two recent calculations of the second order perturbative corrections in the heavy flavor semileptonic transitions within the Brodsky-Lepage-Mackenzie approach. It is pointed out that the results do not show significant enhancement either in the inclusive $b\rightarrow c$ decays or in the exclusive amplitudes at zero recoil provided that the exp

M. Finkelberg, V. Schechtman

This paper is a sequel to "Localization of $\frak{u}$-modules. I", hep-th/9411050. We are starting here the geometric study of the tensor category $\cal{C}$ associated with a quantum group (corresponding to a Cartan matrix of finite type) at a root of unity. The main results establish isomorphisms between homogeneous components of irreducible objects

Daniel C. Galehouse

Studies of geometrical theories suggest that fundmental problems of quantization arise from the disparate usage of displacement operators. These may be the source of a concealed inconsistency in the accepted formalism of quantum physics. General relativity and related theories cannot be quantized by the classical procedure. It is necessary to avoid the const

Andreas Juhl

The Ruelle zeta-function of the geodesic flow on the sphere bundle $S(X)$ of an even-dimensional compact locally symmetric space $X$ of rank $1$ is a meromorphic function in the complex plane that satisfies a functional equation relating its values in $s$ and $-s$. The multiplicity of its singularity in the central critical point $s = 0$ only depends on the

Felix Lazebnik, Vasiliy A. Ustimenko, Andrew J. Woldar

Let $k\ge 1$ be an odd integer, $t=\lfloor {{k+2}\over 4}\rfloor$, and $q$ be a prime power. We construct a bipartite, $q$-regular, edge-transitive graph $C\!D(k,q)$ of order $v \le 2q^{k-t+1}$ and girth $g \ge k+5$. If $e$ is the the number of edges of $C\!D(k,q)$, then $e =Ω(v^{1+ {1\over {k-t+1}}})$. These graphs provide the best known asymptotic lower bo

Konstantin Mischaikow, Marian Mrozek

A new technique for obtaining rigorous results concerning the global dynamics of nonlinear systems is described. The technique combines abstract existence results based on the Conley index theory with computer- assisted computations. As an application of these methods it is proven that for an explicit parameter value the Lorenz equations exhibit chaotic dyna

Paul H. Edelman, Victor Reiner

We produce a one-parameter family of hyperplane arrangements that are counterexamples to the conjecture of Saito that the complexified complement of a free arrangement is $K(π,1)$. These arrangements are the restriction of a one-parameter family of arrangements that arose in the study of tilings of certain centrally symmetric octagons. This other family is d

Liming Ge

We prove a basic result about tensor products of a $\text{II}_1$ factor with a finite von Neumann algebra and use it to answer, affirmatively, a question asked by S. Popa about maximal injective factors.

Eugene Gutkin, Nicolai Haydn

We obtain geometric upper bounds on the topological entropy of generalized polygon exchange transformations. As an application of our results, we show that billiards in polygons and rational polytopes have zero topological entropy.

Yaakov Ben Natan, Yoav Benyamini, Håkan Hedenmalm, Yitzhak Weit

Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal $I$ in $\loneg$, the space of radial integrable functions on $G=SU(1,1)$, so that $I=\loneg$ or $I=\lonez$---the ideal of $\loneg$ functions whose integral is zero. This is then used to prove a generalization of Furstenberg's theorem which ch

Peter Borwein, Tamás Erdélyi

Two relatively long-standing conjectures concerning Müntz polynomials are resolved. The central tool is a bounded Remez type inequality for non-dense Müntz spaces.

Alan Edelman, Eric Kostlan

We provide an elementary geometric derivation of the Kac integral formula for the expected number of real zeros of a random polynomial with independent standard normally distributed coefficients. We show that the expected number of real zeros is simply the length of the moment curve $(1,t,\ldots,t^n)$ projected onto the surface of the unit sphere, divided by

Solomon Friedberg, Hervé Jacquet

The authors establish the fundamental lemma for a relative trace formula. This trace formula compares generic automorphic representations of GSp$(4)$ with automorphic representations of GL$(4)$ which are distinguished with respect to a character of the Shalika subgroup, the subgroup of matrices of $2\times 2$ block form $$ \pmatrix g&0\\0&g\endpmatrix \pmatr

A. A. Deriglazov

The Hamiltonization of local symmetries of the form $δq^A = \ea{R_a}^A(q,\dot q)$ or $δq^A = \dot\ea{R_a}^A (q,\dot q)$ for arbitrary Lagrangean model $L(q^A,\dot q^A)$ is considered. We show as the initial symmetries are transformed in the transition from $L$ to first order action, and then to the Hamiltonian action $S_H=\int{\rm d}τ(p_A\dot q^A-H_0-v^αΦ_α)

M. G. -H. Mostafa, C. Y. wong

The boundary of a boson system plays an important role in determining the momentum distribution of the bosons. For a boson system with a cylindrical boundary, the momentum distribution is enhanced at high transverse momenta but suppressed at low transverse momenta, relative to a Bose-Einstein distribution. The boundary effects on systems of massless gluons a

P. Cichosz

Temporal difference (TD) methods constitute a class of methods for learning predictions in multi-step prediction problems, parameterized by a recency factor lambda. Currently the most important application of these methods is to temporal credit assignment in reinforcement learning. Well known reinforcement learning algorithms, such as AHC or Q-learning, may

S. Hanks, D. S. Weld

The paradigms of transformational planning, case-based planning, and plan debugging all involve a process known as plan adaptation - modifying or repairing an old plan so it solves a new problem. In this paper we provide a domain-independent algorithm for plan adaptation, demonstrate that it is sound, complete, and systematic, and compare it to other adaptat

T. G. Dietterich, G. Bakiri

Multiclass learning problems involve finding a definition for an unknown function f(x) whose range is a discrete set containing k &gt 2 values (i.e., k ``classes''). The definition is acquired by studying collections of training examples of the form [x_i, f (x_i)]. Existing approaches to multiclass learning problems include direct application of mult