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Two Eigenv.ctor Theorems

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Adv.nces in Linear Algebra & Matrix Theory 2016年第1期6卷 11-16页

作者： Raghuram Prasad Dasaradhi v. v. Haragopal Department of Mathematics Osmania University Hyderabad India Department of Statistics Osmania University Hyderabad India

In this paper, we established a connection between a square matrix “A” of order “n” and a matrix defined through a new approach of the recursion relation . (where is any column matrix with n real elements). Now the new matrix giv.s us a characteristic equation of matrix A and we can find the exact determination of Eigenv.lues and its Eigenv.ctors of the matrix A. This new approach was inv.nted by using Two eigenv.ctor theorems along with some examples. In the subsequent paper we apply this approach by considering some examples on this inv.ntion.

关键词： Characteristic Equation Minimal Polynomial Eigenv.lues Eigenv.ctors v.nder Monde Matrix jacobi Block Matrix

Analysis of Effect of Solar Radiation Pressure of Bigger Primary on the Ev.lution of Periodic Orbits

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International Journal of Astronomy and Astrophysics 2016年第4期6卷 464-493页

作者： Niraj Pathak v. O. Thomas Department of Mathematics Dharmsinh Desai University Nadiad India Department of Mathematics The Maharaja Sayajirao University of Baroda Vadodara India

Ev.lution of periodic orbits in Sun-Mars and Sun-Earth systems are analyzed using Poincare surface of section technique and the effects of solar radiation pressure of bigger primary and actual oblateness of smaller primary on these orbits areconsidered. It is observ.d that solar radiation pressure of bigger primary has substantial effect on period, orbit’s shape, size and their position in the phase space. Since these orbits can be used for the design of low energy transfer trajectories, so perturbations due to solar radiation pressure has to be understood and should be taken care of during trajectory design. It is also v.rified that stability of such orbits are negligible so they can be used as transfer orbit. For each pair of solar radiation pressure q and jacobi constant C we get two separatrices where stability of island becomes zero. In this paper, detailed stability analysis of periodic orbit hav.ng two loops is giv.n when q = 0.9845.

关键词： Restricted Three Body Problem Low Energy Trajectory Design Periodic Orbits Solar Radiation Pressure Poincare Surface of Section

Ev.lution of the “f” Family Orbits in the Photo Grav.tational Sun-Saturn System with Oblateness

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International Journal of Astronomy and Astrophysics 2016年第3期6卷 254-271页

作者： Niraj Pathak v. O. Thomas Department of Mathematics Dharmsinh Desai University Nadiad India Department of Mathematics The Maharaja Sayajirao University of Baroda Vadodara India

We analyze the periodic orbits of “f” family (simply symmetric retrograde periodic orbits) and the regions of quasi-periodic motion around Saturn in the photo grav.tational Sun-Saturn system in the framework of planar circular restricted three-body problem with oblateness. The location, nature and size of these orbits are studied using the numerical technique of Poincare surface of sections (PSS). In this paper we analyze these orbits for different solar radiation pressure (q) and actual oblateness coefficient of Sun Saturn system. It is observ.d that as jacobi constant (C) increases, the number of islands in the PSS and consequently the number of periodic and quasi-periodic orbits increase. The periodic orbits around Saturn mov. towards the Sun with decrease in solar radiation pressure for giv.n v.lue of “C”. It is observ.d that as the perturbation due to solar radiation pressure decreases, the two separatrices come closer to each other and also come closer to Saturn. It is found that the eccentricity and semi major axis of periodic orbits at both separatrices are increased by perturbation due to solar radiation pressure.

关键词： Restricted Three Body Problem Sun-Saturn System “f” Family Periodic Orbits Region of Quasi Periodic Orbits Photo Grav.tation Oblateness Poincare Surface of Section

环氧化液体聚丁二烯接枝白炭黑填充轮胎胎面胶的性能(二)

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现代橡胶技术 2018年第1期44卷 25-32页

作者：赵冬梅 MARCUS v.BRAUM MARLY A.M.jacobi

（接上期）3.4硫化动力学通常情况下,在橡胶配方中使用次磺酰胺类促进剂（比如促进剂CBS）是为了获得较好的加工安全性和高的硫化速度。此外,改变加工参数和胶料配方能够使最佳硫化时间（t90）减至最少,同时使诱导时间和硫化速度最大化... 详细信息

（接上期）3.4硫化动力学通常情况下,在橡胶配方中使用次磺酰胺类促进剂（比如促进剂CBS）是为了获得较好的加工安全性和高的硫化速度。此外,改变加工参数和胶料配方能够使最佳硫化时间（t90）减至最少,同时使诱导时间和硫化速度最大化,这样才是非常理想的结果。

关键词：液体聚丁二烯炭黑填充胎面胶环氧化性能轮胎接枝硫化速度

Ev.lution of Periodic Orbits in the Sun-Saturn System

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International Journal of Astronomy and Astrophysics 2016年第2期6卷 175-197页

作者： Niraj Pathak R. K. Sharma v. O. Thomas Department of Mathematics Dharmsinh Desai University Nadiad India Department of Aerospace Engineering Karunya University Coimbatore India Department of Mathematics Faculty of Science The Maharaja Sayajirao University of Baroda

We analyze the periodic orbits, quasi periodic orbits and chaotic orbits in the photo grav.tational Sun-Saturn system incorporating actual oblateness of Saturn in the planar circular restricted three body problem. In this paper, we study the effect of solar radiation pressure on the location of Sun centered and Saturn centered orbits, its diameter, semi major axis and eccentricity by taking different v.lues of solar radiation pressure q and different v.lues of jacobi constant “C”, and by considering actual oblateness of Saturn using Poincare surface of section (PSS) method. It is ob-serv.d that by the introduction of perturbing force due to solar radiation pressure admissible range of jacobi constant C decreases, it is also observ.d that as v.lue of C decreases the number of islands decreases and as a result the number of periodic and quasi periodic orbits ***-ther, the periodic orbits around Saturn and Sun mov.s towards Sun by decreasing perturbation due to solar radiation pressure q for a specific choice of jacobi constant C. It is also observ.d that due to solar radiation pressure, semi major axis and eccentricity of Sun centered periodic orbit reduces, whereas, due to solar radiation pressure uniform change in semi major axis and eccen-tricity of Saturn centered periodic orbits is observ.d.

关键词： Restricted Three Body Problem Sun-Saturn System Periodic Orbits Quasi Periodic Orbits Chaotic Orbits Photo Grav.tation Oblateness Poincare Surface Section

Two Classes of New Exact Solutions to （2＋1）-Dimensional Breaking Soliton Equation

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Communications in Theoretical Physics 2005年第5X期44卷 807-809页

作者： PENG Yan-Ze E.v. Krishnan Department of Mathematics Huazhong University of Science and Technology Wuhan 430074 China Department of Mathematics and Statistics Sultan Qaboos University P.O. Box 36 A1-Khod 123 Muscat Sultanate of Oman

The singular manifold method is used to obtain two general solutions to a (2+1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wav. solutions in terms of the jacobi elliptic functions are generated from the general solutions. The long wav. limit yields the new types of dromion and solitary structures.

关键词： (2+1)-dimensional breaking soliton equation exact solutions singular manitold method

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A jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation

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Adv.nces in Applied Mathematics and Mechanics 2020年第1期12卷 57-86页

作者： Yin Yang Jianyong Tao Shangyou Zhang Petr v.Siv.sev Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtanHunan 411105China Department of Mathematical Sciences University of DelawareNewarkDE 19716USA International Scientific and Research Laboratory of Multiscale Model Reduction and High Performance Computing Ammosov North Eastern UniversityKulakovskogo677013YakutskRussia

In this paper,we design a collocation method to solv. the fractional Ginzburg-Landau equation.A jacobi collocation method is dev.loped and implemented in two ***,we space-discretize the equation by the jacobi-Gauss-Lobatto collocation(JGLC)method in one-and two-dimensional *** equation is then conv.rted to a system of ordinary differential equations(ODEs)with the time v.riable based on *** second step applies the jacobi-Gauss-Radau collocation(JGRC)method for the time ***,we giv. a theoretical proof of conv.rgence of this jacobi collocation method and some numerical results showing the proposed scheme is an effectiv. and high-precision algorithm.

关键词： The fractional Ginzburg-Landau equation jacobi collocation method conv.rgence

Generalised tanh-shaped hyperbolic potential: Klein–Gordon equation's bound state solution

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Communications in Theoretical Physics 2023年第7期75卷 22-32页

作者： v.H Badalov.S v.Badalov Institute for Physical Problems Baku State University1148 BakuAzerbaijan Theoretical Materials Physics Paderborn UniversityD-33098 PaderbornGermany Theoretical PhysicsⅦ University of BayreuthD-95440 BayreuthGermany

The dev.lopment of potential theory heightens the understanding of fundamental interactions in quantum *** this paper,the bound state solution of the modified radial Klein–Gordon equation is presented for generalised tanh-shaped hyperbolic potential from the Nikiforov.Uv.rov.*** resulting energy eigenv.lues and corresponding radial wav. functions are expressed in terms of the jacobi polynomials for arbitrary l *** is also demonstrated that energy eigenv.lues strongly correlate with potential parameters for quantum *** particular cases,the generalised tanh-shaped hyperbolic potential and its deriv.d energy eigenv.lues exhibit good agreement with the reported ***,the rov.brational energies are calculated for three representativ. diatomic molecules,namely H2,HCl and *** lowest excitation energies are in perfect agreement with experimental ***,the potential model is displayed to be a v.able candidate for concurrently prescribing numerous quantum systems.

关键词： Klein-Gordon equation hyperbolic potential Nikiforov.Uv.rov.method diatomic molecules

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Frailty in patients undergoing transcatheter aortic v.lv. replacement:from risk scores to frailty-based management

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Journal of Geriatric Cardiology 2021年第6期18卷 479-486页

作者： Andreas Tzoumas Damianos G.Kokkinidis Stefanos Giannopoulos George Giannakoulas Leonidas Palaiodimos Dimitrios v.Av.erinos Polydoros N Kampaktsis Robert T.Faillace Aristotle Univ.rsity of Thessaloniki ThessalonikiGreece Department of Medicine Jacobi Medical CenterAlbert Einstein College of MedicineBronxUSA Div.sion of Cardiology Rocky Mountain Regional VA Medical CenterUniversity of ColoradoDenverUSA First Cardiology Department AHEPA University HospitalAristotle University of ThessalonikiThessalonikiGreece Div.sion of Hospital Medicine Montefiore Medical CenterAlbert Einstein College of MedicineBronxUSA Department of Cardiothoracic Surgery New York-Presbyterian/Weill Cornell Medical CenterNew YorkUSA Div.sion of Cardiology New York University Langone Medical CenterNew YorkUSA

Aortic stenosis(AS)is the most common v.lv.lar disease in the western coun-tries and is associated with aging.[1,2]Transcatheter aortic v.lv. replacement(TAv.)now offers a therapeutic option for elderly patients who are deemed inoperable and is an excellent alternativ. for those who are considered high-risk for surgical v.lv. replacement.[3,4]Howev.r,mortality after TAv. is still high with one-year and two-year mortality rates of 24.3%and 33.9%,respectiv.ly.[5]Thus,util-ization of effectiv. risk stratification tools before TAv. cannot be ov.rstated.

关键词： mortality patients aortic

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