Invariant Finite-Difference Schemes for Cylindrical One-Dimensional MHD Flows with Conservation Laws Preservation

On the basis of the recent group classification of the one-dimensional magnetohydrodynamics (MHD) equations in cylindrical geometry, the construction of symmetry-preserving finite-difference schemes with conservation laws is carried out. New schemes are constructed starting from the classical completely conservative Samarsky-Popov schemes. In the case of finite conductivity, schemes are derived that admit all the symmetries and possess all the conservation laws of the original differential model, including previously unknown conservation laws. In the case of a frozen-in magnetic field (when the conductivity is infinite), various schemes are constructed that possess conservation laws, including those preserving entropy along trajectories of motion. The peculiarities of constructing schemes with an extended set of conservation laws for specific forms of entropy and magnetic fluxes are discussed.Comment: 29 pages; some minor fixes and generalizations + Appendix containing an additional numerical schem

New classes of exact solutions of three-dimensional Navier-Stokes equations

New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are obtained. The general physical interpretation and classification of solutions is given.Comment: 11 page

Lie group analysis of a generalized Krichever-Novikov differential-difference equation

The symmetry algebra of the differential--difference equation $$\dot u_n = [P(u_n)u_{n+1}u_{n-1} + Q(u_n)(u_{n+1}+u_{n-1})+ R(u_n)]/(u_{n+1}-u_{n-1}),$$ where $P$, $Q$ and $R$ are arbitrary analytic functions is shown to have the dimension 1 \le \mbox{dim}L \le 5. When $P$, $Q$ and $R$ are specific second order polynomials in $u_n$ (depending on 6 constants) this is the integrable discretization of the Krichever--Novikov equation. We find 3 cases when the arbitrary functions are not polynomials and the symmetry algebra satisfies \mbox{dim}L=2. These cases are shown not to be integrable. The symmetry algebras are used to reduce the equations to purely difference ones. The symmetry group is also used to impose periodicity $u_{n+N}=u_n$ and thus to reduce the differential--difference equation to a system of $N$ coupled ordinary three points difference equations

Experiment for Testing Special Relativity Theory

An experiment aimed at testing special relativity via a comparison of the velocity of a non matter particle (annihilation photon) with the velocity of the matter particle (Compton electron) produced by the second annihilation photon from the decay Na-22(beta^+)Ne-22 is proposed.Comment: 7 pages, 1 figure, Report on the Conference of Nuclear Physics Division of Russian Academy of Science "Physics of Fundamental Interactions", ITEP, Moscow, November 26-30, 200

Method for preserving the viability of a chicken embryo with a shell defect in experiment

The egg has always been and remains an ideal object for conducting various scientific research. An egg is an isolated egg cell outside the mother’s body. Therefore, it is an ideal object for studying embryogenesis and performing various manipulations during embryogenesis and before the birth of a viable organism. The existing methods allow conducting experimental manipulations with the embryo in  situ, inside the egg shells without damaging them. However, the achievement of ideal parameters for closing the defect of the fertilized egg shell in the experiment is the key to  the successful completion of the experiment. Periods of embryogenesis, especially at the last stage, when osteogenesis occurs, require the presence of a sufficient amount of calcium ions in the metabolism of the developing chicken, which are vital for the formation of a full-fledged chicken.The aim: to develop an optimal method for closing the defect and fixing the egg shell after manipulation or during the experiment.Materials and methods. The experiment was carried out on fertile eggs of the breed of chickens – meat breed of broilers Ross-308 (ROSS-308), JSC Poultry Farm “NovoBaryshevskaya” (Koltsovo, Novosibirsk Region, Russian Federation). In the experiment, 120 fertilized eggs were used. Eggs weighing 60–70 g were incubated at a temperature of 37.5–38.0 °C and 50–55 % humidity. Comparative anatomical and physiological parameters were evaluated on the 7th, 14th, 20th day of incubation and on the 1st day of the postnatal period. In the experimental group, the shell defect was covered with a fragment of the egg shell of the donor. Incubation was carried out in an incubator – a household incubator “Nesushka” (Novosibirsk, Russian Federation).Results. The proposed method of fixing and closing the defect of the fertilized egg shell excludes the use of foreign materials that have an adverse effect on the development of the embryo. There were no anatomical and physiological deviations in the chicks of the study group when comparing the indicators with the parameters in the comparison group and the Hamburger – Hamilton classification

A Dipole Vortex Model of Obscuring Tori in Active Galaxy Nuclei

The torus concept as an essential structural component of active galactic nuclei (AGN) is generally accepted. Here, the situation is discussed when the torus "twisting" by the radiation or wind transforms it into a dipole toroidal vortex which in turn can be a source of matter replenishing the accretion disk. Thus emerging instability which can be responsible for quasar radiation flares accompanied by matter outbursts is also discussed. The "Matreshka" scheme for an obscuring vortex torus structure capable of explaining the AGN variability and evolution is proposed. The model parameters estimated numerically for the luminosity close to the Eddington limit agree well with the observations.Comment: 17 pages, 11 figures, version of this paper is published in Astronomy Report

Тулиевый лазер при уротелиальной карциноме мочевого пузыря с распространением на устье мочеточника

Urothelial transitional cell cancer in developed countries is the 4th most common. In terms of frequency, it is outstripped only by prostate, breast, lung, and colorectal cancer. In the vast majority of cases, urothelial carcinoma develops in the bladder. It accounts for 90—95 % of all cases of transitional cell cancer of the urinary tract. Much less often, in 5—10 % have to deal with its localization in the upper urinary tract (in the calico-pelvic system or ureter). In 17 % of upper urinary tract cancers, bladder cancer is simultaneously diagnosed. The incidence of urothelial transitional cell cancer has increased over the past few decades as a result of improved diagnosis and improved survival of patients with this nosology. The use of modern, high-tech equipment for visualization and direct surgical intervention contributes to such results. The use of laser energy as the main tool for tissue dissection in endoscopic oncourology reveals the undeniable advantages of this method in comparison with the traditional electrosurgery.We present a clinical observation of the diagnosis and surgical treatment of urothelial bladder cancer with invasion of the ureter, performed by en-bloc tulium laser. An operation was performed-transurethral resection of a urothelial bladder tumor with invasion of the ureter, performed by en-bloc tulium laser. Intraoperatively, ureteropieloscopy was performed, and the tumor did not spread to the upper urinary tract beyond the intramural part of the ureter. Thanks to the precision of the action of the tulium laser on the tissue, not resection, but, in fact, dissection of the bladder wall, a high-quality macropreparation was obtained, which made it possible to establish a final diagnosis. Histological conclusion: from the bladder — non-invasive urothelial cancer G2-3; from the mouth of the left ureter — fragments of fibrous tissue lined with urothelium from atypia. 3 months after the operation — no recurrence of urothelial cancer was revealed, which indicates a high quality of the operation.This clinical observation demonstrates the superiority of laser en-bloc dissection compared to the treatment of bladder tumors. Obtaining a macro-product of urothelial transitional cell cancer of the highest quality can contribute to avoiding unjustified radical nephrureterectomies and conducting organ-preserving treatment, for absolute and elective indications. The 1.94 µm Tulium Erbium laser is an effective tool for performing minimally invasive transurethral interventions in non-invasive bladder cancer.Уротелиальный переходно-клеточный рак в развитых странах занимает 4-е место по распространенности. По частоте встречаемости его опережают только рак предстательной железы, молочной железы, легкого и колоректальный рак. В подавляющем большинстве случаев уротелиальная карцинома развивается в мочевом пузыре. На ее долю приходится 90—95 % всех случаев переходно-клеточного рака мочевыводящих путей. Значительно реже (5—10 %) приходиться иметь дело с его локализацией в верхних мочевыводящих путях (в чашечно-лоханочной системе или мочеточнике). В 17 % случаев при раке верхних мочевыводящих путей одновременно диагностируют рак мочевого пузыря. За последние несколько десятилетий частота встречаемости уротелиального переходно-клеточного рака возросла в результате улучшения диагностики и увеличения выживаемости пациентов с данной нозологией. Таким результатам способствует применение современного, высокотехнологичного оборудования для визуализации и непосредственного проведения оперативного вмешательства. Использование лазерной энергии в качестве основного инструмента для диссекции тканей в эндоскопической онкоурологии раскрывает неоспоримые преимущества данного метода по сравнению со ставшей уже традиционной электрохирургией.представляем клиническое наблюдение диагностики и оперативного лечения уротелиального рака мочевого пузыря с инвазией в мочеточник, проведенного en-bloc тулиевым лазером. Пациентке en-bloc тулиевым лазером выполнена трансуретральная резекция уротелиальной опухоли мочевого пузыря с инвазией в мочеточник. Интраоперационно проведена уретеропиелоскопия, выявлено отсутствие распространения опухоли в верхние мочевыводящие пути за пределы интрамурального отдела мочеточника. благодаря прецизионности воздействия тулиевого лазера на ткань, не резекции, а, по сути, диссекции стенки мочевого пузыря получен макропрепарат высокого качества, позволивший установить окончательный диагноз. Гистологическое заключение: из мочевого пузыря — неинвазивный уротелиальный рак G2-3; из устья левого мочеточника — фрагменты фиброзной ткани, выстланные уротелием из атипии. Через 3 мес после вмешательства данных о наличии рецидива уротелиального рака не выявлено, что говорит о высоком качестве проведенной операции.приведенное клиническое наблюдение демонстрирует превосходство лазерной en-bloc диссекции по сравнению с трансуретральной резекцией опухолей мочевого пузыря. Получение макропрепарата уротелиального переходно-клеточный рака наивысшего качества позволяет избегать необоснованных радикальных нефроуретерэктомий и способствует проведению органосохраняющего лечения по абсолютным и элективным показаниям. Тулий-эрбиевый лазер с длиной волны излучения 1,94 мкм — эффективный инструмент для выполнения малоинвазивных трансуретральных вмешательств при неинвазивном раке мочевого пузыря

Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible complex transformations can be used to obtain invertible real transformations that map a system of nonlinear partial differential equations into a system of linear partial differential equation. Explicit invariant criteria are given that provide procedures for writing down the solutions of the linearized equations. A few non-trivial examples are mentioned.Comment: This paper along with its first part ODE-I were combined in a single research paper "Linearizability criteria for systems of two second-order differential equations by complex methods" which has been published in Nonlinear Dynamics. Due to citations of both parts I and II these are not replaced with the above published articl