Integrable Harmonic Functions on

A class of radial measuresμon ⁿis defined so that integrable harmonic functionsfon ⁿmay be characterized as solutions of convolution equationsf*μ=f. In particular we show thatf*e^{−2*π |x|}) is harmonic if and only ifn<9.     

2 kW, M2 < 10 radially polarized beams from aberration-compensated rod-based Nd:YAG lasers

Radially polarized light in a 2.1 kW, good quality beam was obtained from a Nd:YAG rod-based master oscillator power amplifier. Several techniques were utilized: a pure radially polarized oscillator, efficient pump chambers, external compensation of lower-order aberrations, and higher-order aberration compensation by pairing of pump chambers.     

Computation of functionals over discontinuous sample paths of a stochastic van der pol oscillator

This paper deals with a random van der Pol oscillator. It is assumed that the oscillator is subjected to two different kinds of perturbation. The first kind of perturbation is represented by the standard Wiener process and the second kind by a homogeneous process with independent increments, finite second order moments, mean zero and no continuous sample functions. In order to measure quantitatively the stochastic stability of the oscillator, two functionals are defined over its phase plane sample paths. It is shown that each of these functionals is a solution to a corresponding partial integro-differential equation. A numerical procedure for the solution of these equations, is suggested, and its efficiency and applicability are demonstrated with examples.     

Separation of a finite set in ℝ d by spanned hyperplanes

A question of the following kind will concern us here: what is the minimal numbern, ensuring that any spanning set ofn points in 3-space spans a plane, every open side of which contains at least, say, 1000 points of the set. The answer isn=4001 (see Theorem 2.1 below).This is a part of a Ph.D. thesis, with the same title, supervised by Professor Micha A. Perles in the Hebrew University of Jerusalem     

Limit non-stationary behavior of large closed queueing networks with bottlenecks

In this paper martingales methods are applied for analyzing limit non-stationary behavior of the queue length processes in closed Jackson queueing networks with a single class consisting of a large number of customers, a single infinite server queue, and a fixed number of single server queues with large state independent service rates. It is assumed that one of the single server nodes forms a bottleneck. For the non-bottleneck nodes we show that the queue length distribution at timet converges in generalized sense to the stationary distribution of the M/M/1 queue whose parameters explicitly depend ont. For the bottleneck node a diffusion approximation with reflection is proved in the moderate usage regime while fluid and Gaussian diffusion approximations are established for the heavy usage regime.     

A New Approach to Spinors and Some Representations of the Lorentz Group on Them

We give a geometric realization of space-time spinors and associated representations, using the Jordan triple structure associated with the Cartan factors of type 4, the so-called spin factors. We construct certain representations of the Lorentz group, which at the same time realize bosonic spin-1 and fermionic spin- wave equations of relativistic field theory, showing some unexpected relations between various low-dimensional Lorentz representations. We include a geometrically and physically motivated introduction to Jordan triples and spin factors.     

On convex segments in a triangulation

A segment (=1-cell) of a planar triangulation σ is convex if it is common to two triangles (2-cells) whose union is a convex set. We determine the maximal number of convex segments of a triangulation over all triangulations σ having n boundary vertices and m inner vertices (n3,m0).     

A new computational approach for stochastic fluid models of multiplexers with heterogeneous sources

In this paper we derive an efficient computational procedure for the system in which fluid is produced byN ₁ on-off sources of type 1,N ₂ on-off sources of type 2 and transferred to a buffer which is serviced by a channel of constant capacity. This is a canonical model for multiservice ATM multiplexing, which is hard to analyze and also of wide interest. This paper's approach to the computation of the buffer overflow probability,G(x) = Pr{buffer content >x}, departs from all prior approaches in that it transforms the computation ofG(x) for a particularx into a recursive construction of an interpolating polynomial. For the particular case of two source types the interpolating polynomial is in two variables. Our main result is the derivation of recursive algorithms for computing the overflow probabilityG(x) and various other performance measures using their respective relations to two-dimensional interpolating polynomials. To make the computational procedure efficient we first derive a new system of equations for the coefficients in the spectral expansion formula forG(x) and then use specific properties of the new system for efficient recursive construction of the polynomials. We also develop an approximate method with low complexity and analyze its accuracy by numerical studies. We computeG(x) for different values ofx, the mean buffer content and the coefficient of the dominant exponential term in the spectral expansion ofG(x). The accuracy of the approximations is reasonable when the buffer utilization characterized by G(0) is more than 10^–2.     

Gyrosemidirect Product Structure of Bounded Symmetric Domains

A binary operation ⊕ is defined in any bounded symmetric domain D turning it into a groupoid with relaxed associative and commutative laws, called a gyrogroup. It is shown that the group Aut(D) of all holomorphic automorphisms of D has a gyrosemidirect product structure, a structure that generalizes the semidirect product one. More specifically, the group Aut(D) turns out to be the gyrosemidirect product of the (nongroup) gyrogroup (D, ⊕) and the isotropic group K of D.