Necessary and sufficient conditions for root clustering of a polytope of polynomials in a simply connected domain

1989 ◽  
Vol 34 (9) ◽  
pp. 986-990 ◽  
Author(s):  
E. Zeheb
Keyword(s):  
Connected Domain ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Simply Connected Domain ◽  
Necessary And Sufficient ◽  
Simply Connected

scholarly journals MOSER–TRUDINGER INEQUALITY ON CONFORMAL DISCS

2010 ◽  
Vol 12 (06) ◽  
pp. 1055-1068 ◽  
Author(s):  
G. MANCINI ◽  
K. SANDEEP
Keyword(s):  
Connected Domain ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Poincaré Metric ◽  
Simply Connected Domain ◽  
Trudinger Inequality ◽  
Necessary And Sufficient ◽  
Simply Connected

We prove that a sharp Moser–Trudinger inequality holds true on a conformal disc if and only if the metric is bounded from above by the Poincaré metric. We also derive necessary and sufficient conditions for the validity of a sharp Moser–Trudinger inequality on a simply connected domain in ℝ2.

scholarly journals Some Conditions on Trans-Sasakian Manifolds to Be Homothetic to Sasakian Manifolds

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1887
Author(s):  
Sharief Deshmukh ◽  
Amira Ishan ◽  
Olga Belova ◽  
Suha B. Al-Shaikh
Keyword(s):  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
3 Dimensional ◽  
Necessary And Sufficient ◽  
Simply Connected

In this paper, we study 3-dimensional compact and connected trans-Sasakian manifolds and find necessary and sufficient conditions under which these manifolds are homothetic to Sasakian manifolds. First, four results in this paper deal with finding necessary and sufficient conditions on a compact and connected trans-Sasakian manifold to be homothetic to a compact and connected Sasakian manifold, and the fifth result deals with finding necessary and sufficient condition on a connected trans-Sasakian manifold to be homothetic to a connected Sasakian manifold. Finally, we find necessary and sufficient conditions on a compact and simply connected trans-Sasakian manifold to be homothetic to a compact and simply connected Einstein Sasakian manifold.

An Inverse Mode Problems for Simply Connected Central Symmetric Spring-Mass Systems

2012 ◽  
Vol 166-169 ◽  
pp. 3399-3402
Author(s):  
Xia Tian ◽  
Chuan Xiao Li
Keyword(s):  
Numerical Methods ◽  
Total Mass ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Positive Mass ◽  
Mass System ◽  
Physical Elements ◽  
Necessary And Sufficient ◽  
Simply Connected

Given the odd /even degree eigenpair and the even degree eigenpair of a simply connected central symmetric spring-mass system respectively. The inverse mode problem of constructing the physical elements of the system from two eigenpairs and the total mass of the system is considered. The necessary and sufficient conditions for constructing of a physical realizable system with positive mass and stiffness elements are established. If these conditions are satisfied, the simply connected central symmetric spring-mass system may be constructed uniquely. The numerical methods and examples are given finally.

scholarly journals Toeplitz operators on Bergman spaces of polygonal domains

2019 ◽  
Vol 62 (4) ◽  
pp. 1115-1136 ◽  
Author(s):  
Paula Mannersalo
Keyword(s):  
Connected Domain ◽  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Sufficient Conditions ◽  
Bergman Projection ◽  
Polygonal Domains ◽  
Simply Connected Domain ◽  
Whitney Decomposition ◽  
Polygonal Boundary ◽  
Simply Connected

AbstractWe study the boundedness of Toeplitz operators with locally integrable symbols on Bergman spaces Ap(Ω), 1 < p < ∞, where Ω ⊂ ℂ is a bounded simply connected domain with polygonal boundary. We give sufficient conditions for the boundedness of generalized Toeplitz operators in terms of ‘averages’ of symbol over certain Cartesian squares. We use the Whitney decomposition of Ω in the proof. We also give examples of bounded Toeplitz operators on Ap(Ω) in the case where polygon Ω has such a large corner that the Bergman projection is unbounded.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Nonlinear boundary-value problems for degenerate differential-algebraic systems

2020 ◽  
Vol 17 (3) ◽  
pp. 313-324
Author(s):  
Sergii Chuiko ◽  
Ol'ga Nesmelova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Algebraic System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Nonlinear ◽  
Differential Algebraic System ◽  
Linear Differential ◽  
Necessary And Sufficient

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.

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