Nonsymmetric Askey-Wilson polynomials as vector-valued polynomials

Nonsymmetric Askey-Wilson polynomials are usually written as Laurent polynomials. We write them equivalently as 2-vector-valued symmetric Laurent polynomials. Then the Dunkl-Cherednik operator of which they are eigenfunctions, is represented as a 2x2 matrix-valued operator. As a new result made possible by this approach we obtain positive definiteness of the inner product in the orthogonality relations, under certain constraints on the parameters. A limit transition to nonsymmetric little q-Jacobi polynomials also becomes possible in this way. Nonsymmetric Jacobi polynomials are considered as limits both of the Askey-Wilson and of the little q-Jacobi case.Comment: 16 pages. Dedicated to Paul Butzer on the occasion of his 80th birthday. v4: minor correction in (4.14

Primary cervical malignant teratoma with a rib metastasis in an adult: Five-year survival after surgery and chemotherapy: A case report with a review of the literature

We report a case of a man presenting with a cervical malignant teratoma and a chondrosarcomatous rib metastasis. He was alive and free of recurrence five years and 10 months (= 70 months) after resection of the primary mass, followed by chemotherapy and subsequent resection of the rib tumor. This is the 35th patient reported in the literature and the first description in which an ‘adjuvant' or primary chemotherapy was used. Previous patients with a cervical malignant teratoma, reported after lethal outcome, had survivals of one to 22 months (median nine months). In all patients with a preoperative clinical impression of an aggressive, differentiated or undifferentiated malignancy, the definite diagnosis of teratoma could only be made histologically. By analogy to germ cell tumors, the prognosis of malignant teratoma might be improved if complete excision is combined with new, adjuvant chemotherapy protocols for germ cell tumors. Lessons learned from this case are placed in the context of germ cell tumors in general and of non-gonadal malignant teratomas in particula

The discretised harmonic oscillator: Mathieu functions and a new class of generalised Hermite polynomials

We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansatz defines a new class of generalised Hermite polynomials which are explicit functions of the coupling parameter and tend to ordinary Hermite polynomials in the limit of vanishing coupling constant. The polynomials become orthogonal as parts of the eigenvectors of a Hermitian matrix and, consequently, the exponential part of the solution can not be excluded. We have conjectured the general structure of the solution, both with respect to the quantum number and the order of the expansion. An explicit proof is given for the three leading orders of the asymptotical solution and we sketch a proof for the asymptotical convergence of eigenvectors with respect to norm. From a more practical point of view, we can estimate the required effort for improving the known solution and the accuracy of the eigenvectors. The applied method can be generalised in order to accommodate several variables.Comment: 18 pages, ReVTeX, the final version with rather general expression

IDENTIFICATION OF CRITICAL POINTS IN MONITORING THE ORIGIN OF BEEF

Javnost sve više traži transparentnost u proizvodnji hrane. Osim dobro opisanih i dokumentiranih metoda proizvodnje, pouzdano identificiranje podrijetla hrane od životinja na svakom stupnju proizvodnje postaje sve važnije. Stoga ja ovaj parametar središnja točka u provođenju sustava menadžmenta procesa orijentiranog na kakvoću u proizvodnji životinja. Ovo je osobito točno za proizvodnju govedine zbog moguće veze izmedu BSE i Creutzfeld – Jacob sindroma. DNA analiza životinja i hrane od njih proizvedene pruža potencijalno najvišu razinu pouzdanosti u traganju za podrijetlom. Zaključci : Pouzdano traganje za podrijetlom govedine može se provesti na osnovi DNA analiza. - ldentificirane su kritične točke za uzimanje uzoraka tkiva na različitim stupnjevima klanja i prerade. Nakon toga postupak uzimanja uzoraka se poboljšao. - Prosječno 4% polovica dobilo je pogrešne naljepnice u postupku klanja u našem istraživanju. To upućuje na potrebu poboljšanja sustava menadžmenta kakvoće u klaonicama. - Troškovi primijenjenog sustava praćenja za sada su previsoki za široku primjenu u praksi.The public increasingly demands transparency in the production of foodstuff. Beside well characterized and documented production methods the reliable identification of the origin of animal derived food at any point of the production process becomes more important. Therefore, this parameter is a central point in the implementation of process - oriented quality management systems in animal production. This is especially true for beef production due to the potential relationship between BSE and Creutzfeld -Jacob- Syndrome. The DNA analysis of the animals and foodstuff produced of them provides potentially the highest level of reliability for the tracing of origin

On Hirschman and log-Sobolev inequalities in mu-deformed Segal-Bargmann analysis

We consider a deformation of Segal-Bargmann space and its transform. We study L^p properties of this transform and obtain entropy-entropy inequalities (Hirschman) and entropy-energy inequalities (log-Sobolev) that generalize the corresponding known results in the undeformed theory.Comment: 42 pages, 3 figure

On Poincare and logarithmic Sobolev inequalities for a class of singular Gibbs measures

This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular pair interaction. The functional inequalities come from convexity. We prove and characterize optimality in the case of quadratic confinement via a factorization of the measure. This optimality phenomenon holds for all beta Hermite ensembles including the Gaussian unitary ensemble, a famous exactly solvable model of random matrix theory. We further explore exact solvability by reviewing the relation to Dyson-Ornstein-Uhlenbeck diffusion dynamics admitting the Hermite-Lassalle orthogonal polynomials as a complete set of eigenfunctions. We also discuss the consequence of the log-Sobolev inequality in terms of concentration of measure for Lipschitz functions such as maxima and linear statistics.Comment: Minor improvements. To appear in Geometric Aspects of Functional Analysis -- Israel Seminar (GAFA) 2017-2019", Lecture Notes in Mathematics 225

РОЗРОБКА РЕГІОНАЛЬНОГО ПРОГНОЗУ ЕКОЛОГО-ЕКОНОМІЧНИХ РИЗИКІВ ПРИ ЗАКРИТТІ ШАХТ ЗАХІДНОГО ДОНБАСУ (звіт по темі ГП-412) (заключний)

Рукопис закінчено 5 грудня 2010 р. Результати роботи розглянуто науково-технічною радою, протокол № 4 від 09.12.2010 р.РЕФЕРАТ Звіт про НДР: 98 c, 27 рис., 9 табл., 29 джерело, 3 додатки. Об’єкт дослідження – процес аналізу та прогнозування еколого-економічних ризиків, які викликані гірничовидобувними роботами. Мета проекту – розробка методики регіонального прогнозу еколого-економічних ризиків, можливість виникнення яких зумовлена техногенним впливом вугільних шахт, що функціонують або закриваються. Мета етапу – апробація розробленої методики регіонального прогнозу еколого-економічних ризиків з урахуванням взаємного впливу шахтних ком-плексів Західного Донбасу, що працюють та закриваються. На основі результатів проведення експериментального моделювання еколого-економічного ризику для шахт родовища Західного Донбасу та аналізу розроблених моделей еколого-економічних ризиків отримано якісні й кількісні показники, які дали можливість розробити набор керуючих заходів для мінімізації наслідків функціонування або закриття шахтних комплексів