In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative geometry produced by the presence of a magnetic field. We recall how one can obtain this way a single electron model of the integer quantum Hall effect. While in th...

Multi-choice programming solves some optimization problems where multiple information exists for a parameter. The aim of this paper is to select an appropriate parameter from a set of multiple choices, which optimizes the objective function. We consider a linear programming problem where the right hand side parameters are multi-choice in nature. In this paper, the multiple choices of a paramete...

In this work, we use the generalized exponential function in the fractional-order domain to define generalized cosine and sine functions. We then re-visit some important trigonometric identities and generalize them from the narrow integer-order subset to the more general fractional-order domain. It is clearly shown that trigonometric functions and trigonometric identities in the transient-time ...

We present a bit-parallel technique to search a text of length n for a regular expression of m symbols permitting k differences in worst case time O(mn/ logk s), where s is the amount of main memory that can be allocated. The algorithm permits arbitrary integer weights and matches the complexity of the best previous techniques, but it is simpler and faster in practice. In our way, we define a n...

One of the design parameters in closed queueing networks is Np, the number of customers of class p. It has been assumed that Np must be an integer. However, integer choices will usually not achieve the target throughput for each class simultaneously. We use Mean Value Analysis with the Schweitzer-Bard approximation and nonlinear programming to determine the value of Np needed to achieve the pro...

An integral formula for the solutions of Knizhnik-Zamolodchikov (KZ) equation with values in an arbitrary irreducible representation of the symmetric group SN is presented for integer values of the parameter. The corresponding integrals can be computed effectively as certain iterated residues determined by a given Young diagram and give polynomials with integer coefficients. The derivation is b...

The quantization of the continous cat maps on the torus has led to rather pathological quantum objects [6]. The non-generic behaviour of this model has led some to conclude that the Correspondence Principle fails in this case [2]. In this note we introduce the quantum sawtooth models, since this is the natural family to which the cat maps belong. Thus, a simple propagator depending on a paramet...

We discuss an equivalence relation on the set of square binary matrices with the same number of 1’s in each row and each column. Each binary matrix is represented using ordered n-tuples of natural numbers. We give a few starting values of integer sequences related to the discussed problem. The obtained sequences are new and they are not described in the On-Line Encyclopedia of Integer Sequences...

This work studies the typical behavior of random integer-valued Lipschitz functions on expander graphs with sufficiently good expansion. We consider two families of functions: M -Lipschitz functions (functions which change by at most M along edges) and integer-homomorphisms (functions which change by exactly 1 along edges). We prove that such functions typically exhibit very small fluctuations....

3D geometry is one of the most extensively used data in military, engineering, and multimedia communication. In a distributed environment, efficient visual data exchange is desirable for real-time collaboration. Geometry compression is an effective way to distribute high-volume geometry data within limited bandwidth and storage capacity. In this paper, a new time-varying 3D geometry compression...