Gabor analysis over finite Abelian groups

The topic of this paper are (multi-window) Gabor frames for signals over finite Abelian groups, generated by an arbitrary lattice within the finite time-frequency plane. Our generic approach covers simultaneously multi-dimensional signals as well as non-separable lattices. The main results reduce to well-known fundamental facts about Gabor expansions of finite signals for the case of product lattices, as they have been given by Qiu, Wexler-Raz or Tolimieri-Orr, Bastiaans and Van-Leest, among others. In our presentation a central role is given to spreading function of linear operators between finite-dimensional Hilbert spaces. Another relevant tool is a symplectic version of Poisson's summation formula over the finite time-frequency plane. It provides the Fundamental Identity of Gabor Analysis.In addition we highlight projective representations of the time-frequency plane and its subgroups and explain the natural connection to twisted group algebras. In the finite-dimensional setting these twisted group algebras are just matrix algebras and their structure provides the algebraic framework for the study of the deeper properties of finite-dimensional Gabor frames.Comment: Revised version: two new sections added, many typos fixe

Pomoc zagraniczna dla Polski w zakresie kształcenia zawodowego

Based on experiences from carrying out foreign assistance programmes in support of the reform of vocational education in Poland, the author of the article describes various forms of this assistance and estimates their scale. His approach gives an insight into the possible impact of foreign assistance on reform of the educational system. Based on the nature of foreign assistance, the assumptions concerning how it is to be used and the real results achieved, in his conclusions the author sets forth the conditions of success of these programmes. He indicates the need for partnership in this process as well as the need to treat foreign assistance as part of a wider plan of actions to reform the educational system, in his opinion, success in the latter field will be of decisive importance for assessment of the effectiveness of similar programmes in the future.Opierając się na doświadczeniach z realizacji programów pomocy zagranicznej, ukierunkowanej na wspieranie reformy systemu kształcenia zawodowego w Polsce, autor przedstawia różne formy tej pomocy oraz dokonuje szacunku jej skali. Prezentowane podejście daje pogląd na możliwości wpływu pomocy zagranicznej na proces reformy systemu edukacyjnego. Na podstawie charakteru pomocy zagranicznej, założeń dotyczących sposobów jej wykorzystania i osiąganych realnych efektów, autor formułuje we wnioskach warunki powodzenia realizacji omawianych programów. Wskazuje m.in. na konieczność partnerstwa w tym procesie, a także na potrzebę traktowania pomocy zagranicznej jako elementu szerszego planu przedsięwzięć związanych z reformą systemu edukacji. Powodzenie w tej ostatniej dziedzinie będzie miało - zdaniem autora - decydujące znaczenie dla oceny efektywności realizacji podobnych programów w przyszłości

Minimization of entropy functionals

Entropy functionals (i.e. convex integral functionals) and extensions of these functionals are minimized on convex sets. This paper is aimed at reducing as much as possible the assumptions on the constraint set. Dual equalities and characterizations of the minimizers are obtained with weak constraint qualifications

Blood-feeding in the young adult filarial worms litomosoides sigmodontis

In this study with the filarial model Litomosoides sigmodontis, we demonstrate that the worms ingest host red blood cells at a precise moment of their life-cycle, immediately after the fourth moult. The red blood cells (RBC) were identified microscopically in live worms immobilized in PBS at 4 degrees C, and their density assessed. Two hosts were used: Mongolian gerbils, where microfilaraemia is high, and susceptible BALB/c mice with lower microfilaraemia. Gerbils were studied at 12 time-points, between day 9 post-inoculation (the worms were young 4th stage larvae) and day 330 p.i. (worms were old adults). Only the very young adult filarial worms had red blood cells in their gut. Haematophagy was observed between days 25 and 56 p.i. and peaked between day 28 and day 30 p.i. in female worms. In males, haematophagy was less frequent and intense. Similar kinetics of haematophagy were found in BALB/c mice, but frequency and intensity tended to be lower. Haematophagy seems useful to optimize adult maturation. These observations suggest that haematophagy is an important step in the life-cycle of L. sigmodontis. This hitherto undescribed phenomenon might be characteristic of other filarial species including human parasites

On powers associated with Sierpiński numbers, Riesel numbers and Polignac\u27s conjecture

We address conjectures of P. Erdős and conjectures of Y.-G. Chen concerning the numbers in the title. We obtain a variety of related results, including a new smallest positive integer that is simultaneously a Sierpiński number and a Riesel number and a proof that for every positive integer r, there is an integer k such that the numbers k,k2, k3,...,kr are simultaneously Sierpiński numbers

Robust and efficient estimation of the shape parameter of alpha-stable distributions

In this paper we consider robust and efficient estimators of the shape parameter of symmetric alpha-stable distributions obtained by using the Minimum Density Power Divergence method introduced in Basu, Harris, Hjort and Jones (1998). We established their high asymptotic efficiency and verified these results in simulations. The functionals corresponding to the estimators have bounded influence functions and simulations confirm their robustness when the sample distribution is in a vicinity of the model distribution. The simulations also show that the Minimum Density Power Divergence Estimators (MDPDEs) of the shape parameter of alpha-stable distributions have superior performance over other existing estimators. The high efficiency combined with robustness of the MDPDEs in estimating the shape parameter of alpha-stable distributions make them an attractive alternative to the preceding estimation procedures considered in the literature