1.—On Square-integrable Solutions of Symmetric Systems of Differential Equations of Arbitrary Order.

1976 ◽  
Vol 74 ◽  
pp. 5-40 ◽  
Author(s):  
V. I. Kogan ◽  
F. S. Rofe-Beketov
Keyword(s):  
Arbitrary Order ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Order System ◽  
Symmetric System ◽  
Deficiency Indices ◽  
First Order ◽  
Systems Of Differential Equations ◽  
Matrix Coefficients ◽  
Symmetric Systems

SynopsisThe following results are obtained for symmetric differential expressions of arbitrary order r ≧ 1 with matrix coefficients on the half-line, with a non-negative (and possibly identically degenerate) weight matrix W(t), and with a spectral parameter λ: upper and lower bounds for the deficiency indices N(λ) are found; it is proved that N(λ) is independent of λ for Im λ< 0and for Im λ>0; under very general conditions it is proved that the maximum possible values of the deficiency indices in the half-planesIm λ≷0 can only be attained simultaneously; sufficient conditions for first-order expressions to be quasi-regular are derived; and it isshown that a symmetric system of any order reduces to a canonical, first-order system.Examples are constructed, and the case of the whole line is also touched on.

scholarly journals Synchronization Analysis of Inertial Memristive Neural Networks with Time-Varying Delays

2018 ◽  
Vol 8 (4) ◽  
pp. 269-282 ◽  
Author(s):  
Ruoyu Wei ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Order System ◽  
Time Varying ◽  
Memristive Neural Networks ◽  
Feedback Controllers ◽  
Parameter Mismatch ◽  
First Order ◽  
Variable Transmission ◽  
Response Systems

Abstract This paper investigates the global exponential synchronization and quasi-synchronization of inertial memristive neural networks with time-varying delays. By using a variable transmission, the original second-order system can be transformed into first-order differential system. Then, two types of drive-response systems of inertial memristive neural networks are studied, one is the system with parameter mismatch, the other is the system with matched parameters. By constructing Lyapunov functional and designing feedback controllers, several sufficient conditions are derived respectively for the synchronization of these two types of drive-response systems. Finally, corresponding simulation results are given to show the effectiveness of the proposed method derived in this paper.

Limit-point criteria for systems of differential equations

1980 ◽  
Vol 85 (3-4) ◽  
pp. 233-245 ◽  
Author(s):  
Hilbert Frentzen
Keyword(s):  
Differential Equations ◽  
Limit Point ◽  
Sufficient Conditions ◽  
Second Order ◽  
First Order ◽  
Systems Of Differential Equations ◽  
Sesquilinear Form ◽  
Second Order Systems ◽  
Complex Coefficients ◽  
Second Order Equations

SYNOPSISFor a certain class of first order systems of differential equations several theorems are derived which give sufficient conditions for an appropriate sesquilinear form to be identically zero on suitable spaces of solutions of the system. As a consequence for second order systems limit-point criteria are obtained which include rather general criteria in the case of second order equations. The method used involves sequences of auxiliary functions and is most expedient for the proof of interval limit-point criteria. The theory is also applicable to second order equations with complex coefficients yielding sufficient conditions for the existence of solutions which are not of integrable square.

Calculation of Natural Frequencies and Modes of Steadily Rotating Systems: A Teaching Note

1973 ◽  
Vol 24 (2) ◽  
pp. 139-146 ◽  
Author(s):  
A Simpson
Keyword(s):  
Special Form ◽  
Natural Frequencies ◽  
Order System ◽  
Symmetric System ◽  
System Matrix ◽  
Rotating System ◽  
First Order ◽  
Natural Frequencies And Modes ◽  
Rotating Systems ◽  
Matrix Vector

SummaryThe linear, second-order, ordinary differential equations governing the free-vibration characteristics, in vacuo, of discretised systems executing, at equilibrium, steady rotational motion about a fixed point may be expressed in the well-known matrix-vector form involving real symmetric and skew-symmetric coefficient matrices. Less well known is the fact that the corresponding Hamiltonian first-order system may be cast into a special form involving a skew-symmetric system matrix. In this paper the computational merits of this special form are exploited in the calculation of the natural frequencies and modes of the rotating system.

An Adjustment of Reference Tracking PID Controllers for a First-order System with a Dead Time

2016 ◽  
Vol 136 (5) ◽  
pp. 676-682 ◽  
Author(s):  
Akihiro Ishimura ◽  
Masayoshi Nakamoto ◽  
Takuya Kinoshita ◽  
Toru Yamamoto
Keyword(s):  
Dead Time ◽  
Order System ◽  
Pid Controllers ◽  
Reference Tracking ◽  
First Order

scholarly journals Conceptual Analysis and Empirical Observations of Animal Minds

Philosophia ◽  
2021 ◽  
Author(s):  
Ricardo Parellada
Keyword(s):  
Conceptual Analysis ◽  
Animal Cognition ◽  
Sufficient Conditions ◽  
Second Order ◽  
Alarm Calls ◽  
Vervet Monkeys ◽  
Animal Minds ◽  
First Order

AbstractThe relation between conceptual analysis and empirical observations when ascribing or denying concepts and beliefs to non-human animals is not straightforward. In order to reflect on this relation, I focus on two theoretical proposals (Davidson’s and Allen’s) and one empirical case (vervet monkeys’ alarm calls), the three of which are permanently discussed and considered in the literature on animal cognition. First, I review briefly Davidson’s arguments for denying thought to non-linguistic animals. Second, I review Allen’s criteria for ascribing concepts to creatures capable of correcting their discriminatory powers by taking into account their previous errors. Allen affirms that this is an empirical proposal which offers good reasons, but not necessary or sufficient conditions, for concept attribution. Against Allen, I argue that his important proposal is not an empirical, but a conceptual one. Third, I resort to vervet monkeys to show that Allen’s criteria, and not Davidson’s, are very relevant for ascribing first-order and denying second-order beliefs to this species and thus make sense of the idea of animal cognition.

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

Resolution systems and their applications I

1980 ◽  
Vol 3 (2) ◽  
pp. 235-268
Author(s):  
Ewa Orłowska
Keyword(s):  
Theorem Proving ◽  
Sufficient Conditions ◽  
Predicate Calculus ◽  
Resolution Method ◽  
First Order ◽  
Deductive Systems ◽  
Resolution System ◽  
Resolution Principle ◽  
Necessary And Sufficient ◽  
Classical Predicate

The central method employed today for theorem-proving is the resolution method introduced by J. A. Robinson in 1965 for the classical predicate calculus. Since then many improvements of the resolution method have been made. On the other hand, treatment of automated theorem-proving techniques for non-classical logics has been started, in connection with applications of these logics in computer science. In this paper a generalization of a notion of the resolution principle is introduced and discussed. A certain class of first order logics is considered and deductive systems of these logics with a resolution principle as an inference rule are investigated. The necessary and sufficient conditions for the so-called resolution completeness of such systems are given. A generalized Herbrand property for a logic is defined and its connections with the resolution-completeness are presented. A class of binary resolution systems is investigated and a kind of a normal form for derivations in such systems is given. On the ground of the methods developed the resolution system for the classical predicate calculus is described and the resolution systems for some non-classical logics are outlined. A method of program synthesis based on the resolution system for the classical predicate calculus is presented. A notion of a resolution-interpretability of a logic L in another logic L ′ is introduced. The method of resolution-interpretability consists in establishing a relation between formulas of the logic L and some sets of formulas of the logic L ′ with the intention of using the resolution system for L ′ to prove theorems of L. It is shown how the method of resolution-interpretability can be used to prove decidability of sets of unsatisfiable formulas of a given logic.

On the Boundary Value Problem in A Dihedral Angle for Normally Hyperbolic Systems of First Order

1998 ◽  
Vol 5 (2) ◽  
pp. 121-138
Author(s):  
O. Jokhadze
Keyword(s):  
Partial Differential Equations ◽  
Boundary Value Problem ◽  
Principal Part ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Order System ◽  
First Order ◽  
Dimensional Boundary ◽  
Class Of Functions

Abstract Some structural properties as well as a general three-dimensional boundary value problem for normally hyperbolic systems of partial differential equations of first order are studied. A condition is given which enables one to reduce the system under consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in a certain class of functions if some conditions are fulfilled.

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