Discrete Darboux transformation for discrete polynomials of hypergeometric type

Darboux Transformation, well known in second order differential operator theory, is applied here to the difference equation satisfied by the discrete hypergeometric polynomials(Charlier, Meixner-Krawchuk, Hahn)

Quasi-exactly solvable problems and the dual (q-)Hahn polynomials

A second-order differential (q-difference) eigenvalue equation is constructed whose solutions are generating functions of the dual (q-)Hahn polynomials. The fact is noticed that these generating functions are reduced to the (little q-)Jacobi polynomials, and implications of this for quasi-exactly solvable problems are studied. A connection with the Azbel-Hofstadter problem is indicated.Comment: 15 pages, LaTex; final version, presentation improved, title changed, to appear in J.Math.Phy

Analysis of the influence parameters spine-pelvic balance on the risk of development degeneration and degenerative disease of adjacent segments after lumbar spine rigid fixation

Introduction An increase in the load on adjacent segments causes changes in the parameters of the spinal-pelvic balance and, as a consequence, the development of the so-called biomechanical «stress». Such pressures are a key link in the pathogenesis of degeneration, and in the presence of clinical and neurological manifestations of the latter and adjacent segment degenerative disease (ASD/ASDd).Objective of this study was to assess the effect of the parameters of the spinal pelvic balance on the risk of developing ASD/ASDd after dorsal decompression-stabilizing interventions (DDSI).Material and Methods The study included medical records of patients who underwent DDSI for lumbar spine degenerative diseases. Clinical and instrumental parameters were assessed.Results Based on the inclusion criteria, 98 patients (48 with signs of ASD/ASDd and 50 without) were included in the study. The average postoperative follow-up period for the respondents was 46.6 ± 9.8 months. If PI/ LL parameters were <10 and the ratio of segmental and global lumbar lordosis (LIV-SI/LI-SI) was 50% or more, the incidence of ASD/ASDd was significantly lower in patients who underwent rigid lumbar stabilization surgery.Conclusion The values of PI/LL parameters and the ratio of segmental and global lumbar lordosis are obvious risk factors for the development of ASD/ASDd after rigid lumbar spine DDSI

A survey of Hirota's difference equations

A review of selected topics in Hirota's bilinear difference equation (HBDE) is given. This famous 3-dimensional difference equation is known to provide a canonical integrable discretization for most important types of soliton equations. Similarly to the continuous theory, HBDE is a member of an infinite hierarchy. The central point of our exposition is a discrete version of the zero curvature condition explicitly written in the form of discrete Zakharov-Shabat equations for M-operators realized as difference or pseudo-difference operators. A unified approach to various types of M-operators and zero curvature representations is suggested. Different reductions of HBDE to 2-dimensional equations are considered. Among them discrete counterparts of the KdV, sine-Gordon, Toda chain, relativistic Toda chain and other typical examples are discussed in detail.Comment: LaTeX, 43 pages, LaTeX figures (with emlines2.sty

Factorization method for difference equations of hypergeometric type on nonuniform lattices

We study the factorization of the hypergeometric-type difference equation of Nikiforov and Uvarov on nonuniform lattices. An explicit form of the raising and lowering operators is derived and some relevant examples are given.Comment: 21 page

An SU(2) Analog of the Azbel--Hofstadter Hamiltonian

Motivated by recent findings due to Wiegmann and Zabrodin, Faddeev and Kashaev concerning the appearence of the quantum U_q(sl(2)) symmetry in the problem of a Bloch electron on a two-dimensional magnetic lattice, we introduce a modification of the tight binding Azbel--Hofstadter Hamiltonian that is a specific spin-S Euler top and can be considered as its ``classical'' analog. The eigenvalue problem for the proposed model, in the coherent state representation, is described by the S-gap Lam\'e equation and, thus, is completely solvable. We observe a striking similarity between the shapes of the spectra of the two models for various values of the spin S.Comment: 19 pages, LaTeX, 4 PostScript figures. Relation between Cartan and Cartesian deformation of SU(2) and numerical results added. Final version as will appear in J. Phys. A: Math. Ge

Обоснование конструктивно-технологических параметров модуля мультивентиляторного опрыскивателя

Currently, precision gardening necessitates the use of robotic universal platforms featuring modular multi-fan sprayers, typically equipped with 4-6 fans. As new technologies emerge, the demands placed on spraying ventilation systems are also evolving. (Research purpose) The objective of this research is to establish the design and technological specifications of the multi-fan sprayer module. (Materials and methods) The research is grounded on fundamental equations of energy and mass conservation in the field of applied gas dynamics, specifically the Bernoulli equation and the flow continuity equation. To analyze the pressure distribution within the fan duct and calculate the gas jet, a specific methodology was employed in this research. Additionally, the research utilizes analytical expressions and industry standards to determine universal parameters and dimensions of fans and liquid atomizers. (Results and discussion) Theoretical calculations were performed to determine the main parameters. The results are as follows: the air consumption required to cover a given crown volume is 11.28 cubic meters per second; the air consumption by one fan is 1.88 cubic meters per second; the air flow rate at the fan outlet reaches 17.9 meters per second; pressure generated by the fan is 192.25 pascals; power required to drive one fan is 0.170 kilowatts; the installed power of the fan motor is 0.204 kilowatts; the jet initial section length is 1.53 meters; the axial jet velocity is 13.6 meters per second; the air consumption is 12.84 cubic meters per second; the round jet diameter is 1.58 meters. (Conclusions) The technological scheme of a multi-fan sprayer has been developed and justified. Calculation equations have been proposed to determine the distribution of static, dynamic, and total pressure in different sections of the sprayer fan.  An algorithm for calculating the parameters of the sprayer module has been presented. The numerical values of the parameters for the multi-fan sprayer module have been determined for specific operating conditions.В настоящее время для точного садоводства перспективны роботизированные универсальные платформы, оснащаемые модульными мультивентиляторными опрыскивателями, включающими 4-6 вентиляторов и работающими в точном садоводстве. С появлением новых технологий меняются и требования к вентиляционным системам опрыскивания. (Цель исследования) Обосновать конструктивно-технологические параметры модуля мультивентиляторного опрыскивателя. (Материалы и методы) Провели исследования, опираясь на основные уравнения сохранении энергии и массы в прикладной газовой динамике: уравнение Бернулли, уравнение неразрывности потока. Использовали методику оценки распределения давлений в воздуховоде вентиляторов и аналитические выражения расчета газовой струи, а также стандарты для установления универсальных параметров и размеров вентиляторов и распылителей жидкости. (Результаты и обсуждение) Теоретически рассчитали основные параметры: расход воздуха для покрытия заданного объема кроны – 11,28 метра кубического в секунду; расход воздуха одним вентилятором – 1,88 метра кубического в секунду; скорость потока воздуха при выходе из вентилятора – 17,9 метра в секунду; полное давление, развиваемое вентилятором – 192,25 паскаля; мощность, необходимая для привода одного вентилятора – 0,170 киловатта; установочная мощность двигателя вентилятора – 0,204 киловатта; длину начального участка струи – 1,53 метров; осевую скорость струи – 13,6 метра в секунду, расход воздуха – 12,84 метра кубического в секунду, диаметр круглой струи 1,58 метра. (Выводы) Обосновали технологическую схему мультивентиляторного опрыскивателя. Предложили расчетные уравнения, устанавливающие характер распределения статического, динамического и полного давления в различных сечениях вентилятора опрыскивателя. Представили алгоритм расчета параметров модуля опрыскивателя. Установили для конкретных условий численные значения параметров модуля мультивентиляторного опрыскивателя

Unified description of magic numbers of metal clusters in terms of the 3-dimensional q-deformed harmonic oscillator

Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3)>SOq(3) symmetry are compared to experimental data for atomic clusters of alkali metals (Li, Na, K, Rb, Cs), noble metals (Cu, Ag, Au), divalent metals (Zn, Cd), and trivalent metals (Al, In), as well as to theoretical predictions of jellium models, Woods-Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. In alkali metal clusters and noble metal clusters the 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), while in addition it gives satisfactory results for the magic numbers of clusters of divalent metals and trivalent metals, thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry of systems of several metal clusters. The Taylor expansions of angular momentum dependent potentials approximately producing the same spectrum as the 3-dimensional q-deformed harmonic oscillator are found to be similar to the Taylor expansions of the symmetrized Woods-Saxon and wine-bottle symmetrized Woods-Saxon potentials, which are known to provide successful fits of the Ekardt potentials.Comment: 23 pages including 7 table

ВОЗМОЖНОСТИ ИСПОЛЬЗОВАНИЯ КОМПЬЮТЕРНОЙ ТОМОГРАФИИ ПРИ ИССЛЕДОВАНИИ СКЕЛЕТИРОВАННЫХ ОСТАНКОВ ЧЕЛОВЕКА

Introduction. The investigation is devoted to the possibility of application of computed tomography for forensic examination of skeletal human remains.Aim of study: to evaluate the CT scanning application to skeletons with poor preservation state of bone tissue; to find out the possibility to describe the traumatic lesions on bones; to examine the density of bone tissue.Material and method. The skeletonized remains of General Guden, the participant in the Napoleonic campaign of 1812 were studied by CT scanner «Philips Medical Systems».Results. Antemortem and postmortem traumas are described as well as bone tissue density.Conclusion. Postmortem tomography is the best non-invasive method to study skeletonized human remains in bad preservation state, which allows to define the antemortem and postmortem traumas.Введение. Работа посвящена возможности использования метода компьютерной томографии для проведения судебномедицинской экспертизы скелетированных останков человека.Цель исследования: оценить возможности использования компьютерной томографии при экспертизе скелета человека с плохой сохранностью костной ткани, выявить возможность определения характера травматических повреждений, а также рассмотреть плотность костей различных отделов скелета.Материалы и методы. Объектом исследования стали останки участника Наполеоновской кампании 1812 года генерала Гюдена, обнаруженные в результате раскопок в г. Смоленске в 2019 г. Магнитно-резонансная томография выполнялась на томографе фирмы «Philips Medical Systems» в два этапа.Результаты. Описаны прижизненные и посмертные травмы, определена плотность костной ткани.Заключение. Посмертная томография — это максимально неинвазивный способ изучения  скелетированных останков плохой сохранности при невозможности полной очистки от  грунта, который позволяет определить характер прижизненных и посмертных повреждений костей скелета

Open and Hidden Charm Production in 920 GeV Proton-Nucleus Collisions

The HERA-B collaboration has studied the production of charmonium and open charm states in collisions of 920 GeV protons with wire targets of different materials. The acceptance of the HERA-B spectrometer covers negative values of xF up to xF=-0.3 and a broad range in transverse momentum from 0.0 to 4.8 GeV/c. The studies presented in this paper include J/psi differential distributions and the suppression of J/psi production in nuclear media. Furthermore, production cross sections and cross section ratios for open charm mesons are discussed.Comment: 5 pages, 9 figures, to be published in the proceedings of the 6th International Conference on Hyperons, Charm & Beauty Hadrons (BEACH04), Chicago, IL, June 27 - July 3, 200