math updates on arXiv.orgMathematics (math) updates on the arXiv.org e-print archiveThe Quasi-Holonomic Ansatz and Restricted Lattice Walks. (arXiv:0806.4318v1 math.CO)- (Found June 29, 2008 ) The great enumerator Germain Kreweras empirically discovered this intriguing fact, and then needed lots of pagesK, and lots of human ingenuity, to prove it. Other great enumerators, for example, Heinrich NiederhausenN, Ira GesselG1, and Mireille Bousquet-M'elouB, found other ingenious, simpler'' proofs. Yet none of them is as simple as ours! Our proof (with the generous help of our faithful computers) is ugly'' in the traditional sense, since it would be painful for a lowly human to follow all..http://arxiv.org/abs/0806.4318 The doubly periodic Scherk-Costa surfaces. (arXiv:0806.4313v1 math.DG)- (Found June 29, 2008 ) We present a new family of embedded doubly periodic minimal surfaces, of which the symmetry group does not coincide with any other example known before.http://arxiv.org/abs/0806.4313 Deformation of central charges, vertex operator algebras whose Griess algebras are Jordan algebras. (arXiv:0806.4308v1 math.QA)- (Found June 29, 2008 ) If a vertex operator algebra $V=oplus_n=0inftyV_n$ satisfies $dim V_0=1, V_1=0$, then $V_2$ has a commutative (nonassociative) algebra structure called Griess algebra. One of the typical examples of commutative (nonassociative) algebras is a Jordan algebra. For example, the set $Sym_d(C)$ of symmetric matrices of degree $d$ becomes a Jordan algebra. On the other hand, in the theory of vertex operator algebras, central charges influence the properties of vertex operator algebras. In this paper,..http://arxiv.org/abs/0806.4308 Proof of Ira Gessel's Lattice Path Conjecture. (arXiv:0806.4300v1 math.CO)- (Found June 29, 2008 ) We present a computer-aided, yet fully rigorous, proof of Ira Gessel's tantalizingly simply-stated conjecture that the number of ways of walking $2n$ steps in the region $x+y geq 0, y geq 0$ of the square-lattice with unit steps in the east, west, north, and south directions, that start and end at the origin, equals $16nfrac(56)_n(12)_n(53)_n(2)_n$ .http://arxiv.org/abs/0806.4300 A method of quaternion typification of Clifford algebra elements. (arXiv:0806.4299v1 math-ph)- (Found June 29, 2008 ) We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method of analysis of commutators and anticommutators of Clifford algebra elements. This method allows us to find out and prove a number of new properties of Clifford algebras.http://arxiv.org/abs/0806.4299 Two sample constructions of all the Hilbert spaces for a given operator $H$ of an observable. (arXiv:0806.4295v1 math-ph)- (Found June 29, 2008 ) In Quantum Theory an operator $H$ represents an observable provided only that it is self-adjoint in a Hilbert space $cal L_Theta(physical)$ equipped with a metric $Theta$. This means that for a given $H$, equation $Hdagger Theta = Theta H$ specifies a complete menu of all the eligible $Theta=Theta(H)$ needed to determine the inner product. We illustrate the feasibility of the construction of all of these $Theta$s. It is based on the computerized symbolic manipulations followed by an...http://arxiv.org/abs/0806.4295 The Ratio Monotonicity of the Boros-Moll Polynomials. (arXiv:0806.4333v1 math.CO)- (Found June 29, 2008 ) In their study of a quartic integral, Boros and Moll discovered a special class of Jacobi polynomials, which we call the Boros-Moll polynomials. Kauers and Paule proved the conjecture of Moll that these polynomials are log-concave. In this paper, we show that the Boros-Moll polynomials possess the ratio monotone property which implies the log-concavity and the spiral property. We conclude with a conjecture which is stronger than Moll's conjecture on the $infty$-log-concavity.http://arxiv.org/abs/0806.4333 The triangle-free process. (arXiv:0806.4375v1 math.CO)- (Found June 29, 2008 ) Consider the following stochastic graph process. We begin with the empty graph on n vertices and add edges one at a time, where each edge is chosen uniformly at random from the collection of potential edges that do not form triangles when added to the graph. The process terminates at a maximal traingle-free graph. Here we analyze the triangle-free process, determining the likely order of magnitude of the number of edges in the final graph. As a corollary we show that the triangle-free process...http://arxiv.org/abs/0806.4375 On submanifolds with recurrent second fundamental form in spaces of constant curvature. (arXiv:0806.4360v1 math.DG)- (Found June 29, 2008 ) The complete local classification and geometric description of n-dimensional submanifolds F with recurrent nonparallel second fundamental form in the spaces of constant curvature M(c) are obtained in this article.http://arxiv.org/abs/0806.4360 Group classification of a nonlinear sound wave model. (arXiv:0806.4359v1 math.AP)- (Found June 29, 2008 ) Based on a recent classification of subalgebras of the symmetry algebra of the Zabolotskaya-Khokhlov equation, all similarity reductions of this equation into ordinary differential equations are obtained. Large classes of group invariant solutions of the equation are also determined, and some properties of these solutions are discussed.http://arxiv.org/abs/0806.4359 |