scholarly journals On related vector fields of capillary surfaces

1981 ◽  
Vol 4 (3) ◽  
pp. 473-484
Author(s):  
Afet K. Özok
Keyword(s):  
Vector Fields ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Conformal Killing ◽  
Capillary Surfaces ◽  
Killing Vectors ◽  
Conformal Killing Vectors ◽  
Necessary And Sufficient ◽  
Dimensional Domain

In this paper, some necessary and sufficient conditions are given for the related vector fields of capillary surfaces to be Killing, conformal Killing, and homothetic conformal Killing vectors in then-dimensional domainΩ, and a construction of capillary surfaces is also given by means of the related vector fields.

ON FLOW BARRIERS AND SWITCHABILITY IN DISCONTINUOUS DYNAMICAL SYSTEMS

2011 ◽  
Vol 21 (01) ◽  
pp. 1-76 ◽  
Author(s):  
ALBERT C. J. LUO
Keyword(s):  
Dynamical Systems ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Friction Model ◽  
Necessary And Sufficient Conditions ◽  
Separation Boundary ◽  
Boundary Flow ◽  
Pass Through ◽  
Necessary And Sufficient ◽  
And Control

In this paper, the theory of flow barriers in discontinuous dynamical systems is systematically presented as a new theory for the first time, which helps one rethink the existing theories of stability and control in dynamical systems. The concept of flow barriers in discontinuous dynamical systems is introduced, and the passability of a flow to the separation boundary with flow barriers is presented. Because the flow barriers exist on the separation boundary, the switchability of a flow to such a separation boundary is changed accordingly. The coming and leaving flow barriers in passable flows are discussed first, and the necessary and sufficient conditions for a flow to pass through the boundary with flow barrier are developed. Flow barriers for sink and source flows are also discussed. Once the sink flow is formed, the boundary flow will exist. When the boundary flow disappears from the boundary, the boundary flow barrier on the boundary may exist, which is independent of vector fields in the corresponding domains. Thus, the necessary and sufficient conditions for formations and vanishing of the boundary flow are developed. A periodically forced friction model is presented as an example for a better understanding of flow barrier existence in physical problems. The flow barrier theory presented in this paper may provide a theoretic base to further develop control theory and stability.

SPACE–TIMES WITH A TWO-DIMENSIONAL GROUP OF CONFORMAL MOTIONS

1996 ◽  
Vol 11 (05) ◽  
pp. 845-861 ◽  
Author(s):  
CHARALAMPOS KOLASSIS ◽  
GARRY LUDWIG
Keyword(s):  
Simple Proof ◽  
Sufficient Conditions ◽  
Conformal Killing ◽  
Two Dimensional ◽  
Spin Coefficient ◽  
Dimensional Group ◽  
Star Operation ◽  
Conformal Killing Vectors ◽  
Necessary And Sufficient ◽  
Coefficient Formalism

The necessary and sufficient conditions for a space–time to admit a two-dimensional group of conformal motions (and, in particular, of homothetic motions) acting on nonnull orbits are found in the compacted spin-coefficient formalism. Although the discussion is restricted to the case of spacelike orbits, similar results are readily obtained for timelike orbits via the (modified) Sachs star operation. A number of theorems are obtained dealing with such topics as the Gaussian curvature of the group orbits, orthogonal transitivity, and hypersurface orthogonality of the conformal Killing vectors. A simple proof is presented of a generalization of a theorem due to Papapetrou.

scholarly journals Magnetic vector fields: New examples

2018 ◽  
Vol 103 (117) ◽  
pp. 91-102
Author(s):  
Jun-Ichi Inoguchi ◽  
Marian Munteanu
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Magnetic Vector ◽  
Necessary And Sufficient

In a previous paper, we introduced the notion of magnetic vector fields. More precisely, we consider a vector field ? as a map from a Riemannian manifold into its tangent bundle endowed with the usual almost K?hlerian structure and we find necessary and sufficient conditions for ? to be a magnetic map with respect to ? itself and the K?hler 2-form. In this paper we give new examples of magnetic vector fields.

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> 0 for eachj> 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.

ON A PERFECT FLUID K¨ AHLER SPACETIME

2016 ◽  
Vol 12 (3) ◽  
pp. 4350-4355
Author(s):  
VIBHA SRIVASTAVA ◽  
P. N. PANDEY
Keyword(s):  
Field Equation ◽  
Perfect Fluid ◽  
Sectional Curvature ◽  
Einstein Field Equation ◽  
Cosmological Term ◽  
Conformal Killing ◽  
Killing Vectors ◽  
Projectively Flat ◽  
Conformal Killing Vectors

The object of the present paper is to study a perfect fluid K¨ahlerspacetime. A perfect fluid K¨ahler spacetime satisfying the Einstein field equation with a cosmological term has been studied and the existence of killingand conformal killing vectors have been discussed. Certain results related to sectional curvature for pseudo projectively flat perfect fluid K¨ahler spacetime have been obtained. Dust model for perfect fluid K¨ahler spacetime has also been studied.

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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