We discuss the possibility of interpreting a q-deformed non-interactingsystem as incorporating the effects of interactions among its particles. Thiscan be accomplished, for instance, in an ensemble of $q$-Bosons by means of thevirial expansion of a real gas in powers of

In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007),10367-10382, hep-th/0611160] we have shown how for canonical parametrized fieldtheories, where space-time is placed on the same footing as the other fields inthe theory, the representation of

We classify N=2 superconformal DeWitt super-Riemann surfaces with genus-zerobody modulo N=2 superconformal equivalence. In particular, we prove that thereis a countably infinite family of N=2 superconformal equivalence classes of N=2superconformal super-Riemann surfaces with genus-zero compact body. Furthermorewe show that there

We construct here the parametric representation of a translation-invariantrenormalizable scalar model on the noncommutative Moyal space of even dimension$D$. This representation of the Feynman amplitudes is based on some integralform of the noncommutative propagator. All types of graphs (planar andnon-planar)

We consider a superintegrable Hamiltonian system in a two-dimensional spacewith a scalar potential that allows one quadratic and one cubic integral ofmotion. We construct the most general cubic algebra and we present specificrealizations. We use them to calculate the energy

We prove versions of super spin-charge separation for all three of thesymmetry groups SU(N), Sp(2N), and SO(N) of disordered Dirac fermions in 2+1dimensions, which involve the supercurrent-algebras gl (1|1)_{N},osp(2|2)_{-2N}, and osp(2|2)_N respectively. For certain restricted classes ofdisordered potentials, the latter

A vertex 2-coloring of a graph is said to be perfect with parameters$(a_{ij})_{i,j=1}^k$ if for every $i,j\in\{1,...,k\}$ every vertex of color $i$is adjacent with exactly $a_{ij}$ vertices of color $j$. We consider theperfect 2-colorings of the distance-2 graph of the

We study final group topologies and their relations to compactnessproperties. In particular, we are interested in situations where a colimit ordirect limit is locally compact, a k_\omega-space, or locally k_\omega. As afirst application, we show that unitary forms of complex

We show that certain free energy functionals that are not convex with respectto the usual convex structure on their domain of definition, are strictlyconvex in the sense of displacement convexity under a natural change ofvariables. We use this to show

The aim of this paper is to study the $q$-Schr\"{o}dinger operator $$ L=q(x)-\Delta_q, $$ where $q(x)$ is a given function of $x$ defined over$\mathbb{R}_{q}^{+}=\{q^n,\quad n\in\mathbb Z\}$ and $\Delta_q$ is the$q$-Laplace operator $$ $$

Lower bounds estimates are proved for the first eigenvalue for the DirichletLaplacian on arbitrary triangles using various symmetrization techniques. Theseresults can viewed as a generalization of P\'olya's isoperimetric bounds. It isalso shown that amongst triangles, the equilateral triangle minimizes thespectral

The framework of group classification is analyzed, substantially extended andenhanced based on the new notions of conditional equivalence group andnormalized class of differential equations. Effective new techniques related togroup classification of differential equations are proposed. Using these, weexhaustively describe admissible

In our previous paper [12] (Rev. Math. Phys. 16, 383-420 (2004)), a generalframework was outlined to treat the approximate solutions of semilinearevolution equations; more precisely, a scheme was presented to infer from anapproximate solution the existence (local or global in

We study subrings in the Chow ring $\CH^*(A)_{{\Bbb Q}}$ of an abelianvariety $A$, stable under the Fourier transform with respect to an arbitrarypolarization. We prove that by taking Pontryagin products of classes ofdimension $\leq 1$ one gets such a subring.

The transport capacity of a dense ad hoc network with n nodes scales like\sqrt(n). We show that the transport capacity divided by \sqrt(n) approaches anon-random limit with probability one when the nodes are i.i.d. distributed onthe unit square. We prove