Photorefractive shearing interferometer

A novel method of obtaining shearing interferogram by slightly moving the crystal in a photorefractive interferometer is proposed. This method can measure the phase of an object itself instead of its diffraction field, and it is easy to realize continuously changeable shearing distance in any lateral direction and introduce carrier fringes at the same time. Both the theoretical analysis and experimental verification are given.     

Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments

We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks.     

On quartics with three-divisible sets of cusps

 We study the geometry and codes of quartic surfaces with many cusps. We apply Gr?bner bases to find examples of various configurations of cusps on quartics. Received: 10 May 2002 / Revised version: 11 November 2002 Published online: 3 March 2003 Permanent address: Institute of Mathematics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland. e-mail: rams@mi.uni-erlangen.de, rams@im.uj.edu.pl Research partially supported by the Schwerpunktprogramm ``Global methods in complex geometry' of the Deutsche Forschungsgemeinschaft, and by EAGER. Mathematics Subject Classification (2000): 14J25, 14J17     

Operational characteristics and power scaling of a transverse flow transversely excited CW CO<Subscript>2</Subscript> laser

Transverse flow transversely excited (TFTE) CO₂ lasers are easily scalable to multikilowatt level. The laser power can be scaled up by increasing the volumetric gas flow and discharge volume. It was observed in a TFTE CW CO₂ laser having single row of pins as an anode and tubular cathode that the laser power was not increasing when the discharge volume and the gas volumetric flow were increased by increasing the electrode separation keeping the gas flow velocity constant. The discharge voltage too remained almost constant with the change of electrode separation at the same gas flow velocity. This necessitated revision of the scaling laws for designing this type of high power CO₂ laser. Experimental results of laser performance for different electrode separations are discussed and the modifications in the scaling laws are presented.     

On the Exceptional Zeros of Rankin–Selberg L-Functions

The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,f×g) and L(s, sym²(g)× sym²(g)), where f,g are newforms, holomorphic or of Maass type, on the upper half plane, and sym²(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any LandauSiegel zeros. Such zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound onthe norm of sym²(g).     

The Ideal Retraction Property for Idempotent Semigroups

A semigroup S is said to have the ideal retraction property provided each of its ideals is the image of an idempotent endomorphism of S. The main result of this work is a characterization of those bands which have the idempotent retraction property. All such bands are normal.     

Problems of an additional experiment

In some situations estimates of unknown parameters must be corrected by additional measurements. It is in principle no problem to calculate the corrected estimates, however, it is of more interest to find formulae for correction itself. The formulae enable us to design an additional experiment and to judge its usefulness. The aim of the paper is to find such formulae for several situations. Supported by the grant of the Council of Czech Government MSM 6 198 959 214.     

A note on generalized averaged Gaussian formulas

We have recently proposed a very simple numerical method for constructing the averaged Gaussian quadrature formulas. These formulas exist in many more cases than the real positive Gauss–Kronrod formulas. In this note we try to answer whether the averaged Gaussian formulas are an adequate alternative to the corresponding Gauss–Kronrod quadrature formulas, to estimate the remainder term of a Gaussian rule.     

Mixing characteristics of motionless mixers

Motionless mixers have found a large range of applications, including blending, reaction, dispersion, heat transfer and mass transfer. Understanding the mixing processes that occur in these diverse systems is essential for predicting many aspects of practical importance. The objective of this study is to perform the experimental investigations of mixing characteristics for three different motionless mixers. The red color dye tracer was mixed in the main stream of green hair styling gel, and then the mixing efficiency was quantified by calculating the percentage area concentration of red color at the outlet cross section using a digital image processing technique. In the Sulzer SMX and YHC mixer, a single element mixes the fluid nearly in two dimensions, and three-dimensional mixing is accomplished by the next elements aligned at 90o to their former one. In the Sulzer SMX mixer, the flow appears to be globally well mixed after 5 elements, while in the YHC and YNU mixers, it is necessary to globally well mix more than 1 and 2 elements.     

A tabu search heuristic for solving the CLSP with backlogging and set-up carry-over

In this paper, the multi-item, single-level, capacitated, dynamic lot sizing problem with set-up carry-over and backlogging, abbreviated to CLSP⁺, is considered. The problem is formulated as a mixed integer programming problem. A heuristic method consisting of four elements: (1) a demand shifting rule, (2) lot size determination rules, (3) checking feasibility conditions and (4) set-up carry-over determination, provides us with an initial feasible solution. The resulting feasible solution is improved by adopting the corresponding set-up and set-up carry-over schedule and re-optimizing it by solving a minimum-cost network flow problem. Then the improved solution is used as a starting solution for a tabu search procedure, with the value of moves assessed using the same minimum-cost network problem. Computational results on randomly generated problems show that the algorithm, which is coded in C++, is able to provide optimal solutions or solutions extremely close to optimal. The computational efficiency makes it possible to solve reasonably large problem instances routinely on a personal computer.