On a q-analog of the Wallach-Okounkov formula

We obtain a $q$-analog of the well known Wallach-Okounkov result on a joint spectrum of invariant differential operators with polynomial coefficients on a prehomogeneous vector space of complex $n \times n$-matrices. We are motivated by applications to the problems of harmonic analysis in the quantum matrix ball: our main theorem can be used while proving the Plancherel formula (to be published). This paper is dedicated to our friend and colleague Dmitry Shklyarov who celebrates his 30-th birthday on April 8, 2006.Comment: 10 pages, corrected minor misprint

Ukrainian Courts in Dialogue on International Law

The monograph is a result of the project nr 10-ECRP-028 International Law through the National Prism: the Impact of Judicial Dialogue The research is based on laws being in force on 2nd August 201

Demining of Underground Adits in Ukraine

During World War II the Soviet Union established ammunition depots with over 10,000 metric tons (11,023 U.S. tons) of explosives around the Ukrainian towns of Sevastopol and Kerch. Stored in adits, these explosives threaten the peaceful lives of present-day Ukrainians. In 2002, teams began the task of removing unexploded ordnance, landmines and debris. They encountered many problems while pursuing their goal of eliminating these stockpiles by 2010. Their efforts are described in this article

Cholinergic Mechanisms Regulating Cognitive Function and RNA Metabolism

Acetylcholine (ACh) is one of the main neuromodulators in the mammalian central nervous system (CNS). This chemical messenger has been implicated in the underlying physiology of many distinct cognitive functions. However, the exact role that ACh plays in regulating information processing in the brain is still not fully understood. The vesicular acetylcholine transporter (VAChT) is required for the storage of ACh into synaptic vesicles, and therefore it presents a means to modulate release. Diminished VAChT levels cause a decrease in cholinergic tone, whereas increased VAChT expression has been shown to augment ACh release. Previously published data have shown that elimination of VAChT in the basal forebrain in genetically-modified mice impairs learning and memory. For our studies we have used different mouse lines in which the expression of the VAChT gene is changed, both increased and decreased. We are therefore able to study the consequences of altered cholinergic tone in vivo. Our hypothesis is that changes in cholinergic tone produce specific molecular signatures in target brain areas that underlie alterations in cognitive function. Our studies aimed to elucidate the behavioural and molecular consequences of cholinergic dysfunction. Behavioral testing included classical learning and memory tests as well as sophisticated tasks using novel touch screens chambers to measure attention, learning and memory as well as cognitive flexibility. At the molecular level, the goal was to examine how long-term changes in cholinergic tone impact mechanisms regulating synaptic plasticity and neuronal health. Finally, by aging mouse models of cholinergic dysfunction we were able to elucidate the role that cholinergic tone plays in the classical pathological hallmarks of neurodegenerative disorders. Ultimately, by establishing the molecular signature of increased and decreased cholinergic tone in targeted brain regions (cortex and hippocampus) it may become possible to find novel targets for therapeutic interventions to improve cognitive deficits due to altered cholinergic tone

The Afterwar Ordeals and Achievements of Ukrainian Identity as National Spirit of Ukrainians

Духовні висліди Другої світової війни для українців були і є суперечливими, оскільки війна ствердно вплинула на хід об’єднаня українців в одній імперії, яка продовжила виконання давнього російського задуму перетворення українців на росіян. Опір українських націоналістів політиці асиміляції призвів до появи української держави. The spiritual consequences of World War II were and still are contradictory for Ukrainian people, as the War influenced their unity in one empire, which continued the realization of the longtime Russian project to transform Ukrainians into Russians. The resistance of Ukrainian Nationalists against the police of assimilation led to the emergence of the Ukrainian state

Рід Sambucus L. (Sambucaceae Link.) в Україні: видовий склад, еколого-географічне поширення, біоморфологічні особливості, перспективи культивування

The questions of ecological and geographical distributi on, phylogenesis, introduction and perspectives of cultivation of Sambucus L. species in Ukraine have been presented. The biomorphological characteristic of 3 natural and 9 introduction species and worlds sorts are given. The features of their propagation are analyzed.Висвітлено питання філогенезу, еколого-географічного поширення, інтродукції та перспективи культивування представників роду Sambucus L. в Україні. Наведено біоморфологічну характеристику 3 аборигенних і 9 інтродукованих видів, світовий сортимент, проаналізовано особливості розмноження

Кількісні морфологічні ознаки та мінливість вегетативних і генеративних органів бузини чорної (Sambucus nigra L.) у Лісостепу України

Quantitative morphological signs of vegetative and generative organs of an elderberry (Sambucus nigra L.) forms, selected in natural populations in Ukraine, are investigated. Variability is shown, the range of variations of signs for an estimation of selection value perspective forms is defined.Досліджено кількісні морфологічні ознаки вегетативних і генеративних органів форм бузини чорної (Sambucus nigra L.), відібраних у природних популяціях в Україні. Встановлено мінливість, визначено діапазон варіювання ознак для оцінки селекційної значущості перспективних форм

Harmonic Analysis on Quantum Complex Hyperbolic Spaces

In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami operator and its radial part. The latter appear to be second order $q$-difference operator, whose eigenfunctions are related to the Al-Salam-Chihara polynomials. We prove a Plancherel type theorem for it

Історія інтродукції видів роду Sambucus L. в Україні

On the basis of literature data the history of introduction of species of Sambucus L. in Ukraine is presented. Data about the structure of Sambucus species collections in botanical gardens of Ukraine are cited.На основі літературних джерел висвітлено історію інтродукції видів роду Sambucus L. в Україні. Наведено дані про склад колекцій видів роду Sambucus у ботанічних садах України