Necessary and sufficient conditions for the existence of self-oscillations in a finite-dimensional continuous dynamical system

2008 ◽  
Vol 53 (1) ◽  
pp. 15-18
Author(s):  
O. V. Druzhinina ◽  
A. A. Shestakov
Keyword(s):  
Dynamical System ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Continuous Dynamical System ◽  
Finite Dimensional ◽  
Necessary And Sufficient

scholarly journals Graded modules over simple Lie algebras

2019 ◽  
Vol 53 (supl) ◽  
pp. 45-86
Author(s):  
Yuri Bahturin ◽  
Mikhail Kochetov ◽  
Abdallah Shihadeh
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Arbitrary Dimension ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Simple Lie Algebras ◽  
Simple Modules ◽  
Graded Modules ◽  
Finite Dimensional ◽  
Necessary And Sufficient

The paper is devoted to the study of graded-simple modules and gradings on simple modules over finite-dimensional simple Lie algebras. In general, a connection between these two objects is given by the so-called loop construction. We review the main features of this construction as well as necessary and sufficient conditions under which finite-dimensional simple modules can be graded. Over the Lie algebra sl2(C), we consider specific gradings on simple modules of arbitrary dimension.

Titling pair over split-by-nilpotent extensions

2020 ◽  
pp. 2250019
Author(s):  
Dajun Liu ◽  
Jiaqun Wei
Keyword(s):  
Similar Condition ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Split Extension ◽  
Finite Dimensional ◽  
Necessary And Sufficient ◽  
Finite Dimensional Algebras

Let [Formula: see text], [Formula: see text] be two finite dimensional algebras over a field [Formula: see text], such that [Formula: see text] is a split extension of A by the nilpotent bimodule [Formula: see text]. We mainly give necessary and sufficient conditions for a tilting pair [Formula: see text] such that [Formula: see text] or [Formula: see text] are tilting pairs. Also, we obtain a similar condition such that a Wakamatsu tilting pair [Formula: see text] in [Formula: see text]-mod can be a Wakamatsu tilting pair [Formula: see text] in [Formula: see text]-mod.

scholarly journals POINTED HOPF ALGEBRAS WITH CLASSICAL WEYL GROUPS

2012 ◽  
Vol 23 (06) ◽  
pp. 1250066
Author(s):  
SHOUCHUAN ZHANG ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Hopf Algebras ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weyl Groups ◽  
Drinfeld Modules ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Nichols Algebras ◽  
Necessary And Sufficient

We prove that Nichols algebras of irreducible Yetter–Drinfeld modules over classical Weyl groups A ⋊ 𝕊nsupported by 𝕊nare infinite dimensional, except in three cases. We give necessary and sufficient conditions for Nichols algebras of Yetter–Drinfeld modules over classical Weyl groups A ⋊ 𝕊nsupported by A to be finite dimensional.

scholarly journals Necessary and Sufficient Conditions for Complementary Stochastic Quadratic Operators of Finite-Dimensional Simplex

2017 ◽  
Vol 1 (1) ◽  
pp. 22 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Sherzod Turaev ◽  
Akram Zeki
Keyword(s):  
Dimensional Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finite Dimensional Space ◽  
Quadratic Operator ◽  
Dimensional Simplex ◽  
Quadratic Stochastic Operator ◽  
Finite Dimensional ◽  
Stochastic Operator ◽  
Necessary And Sufficient

We define a complementary stochastic quadratic operator on finite-dimensional space as a new sub-class of quadratic stochastic operator. We give necessary and sufficient conditions for complementary stochastic quadratic operator.  

Sets of Generators of a Commutative and Associative Algebra(1)

1971 ◽  
Vol 14 (3) ◽  
pp. 315-319
Author(s):  
D. Ž. Djoković
Keyword(s):  
Recent Result ◽  
Associative Algebra ◽  
Polynomial Algebra ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Quotient Algebra ◽  
Algebra 1 ◽  
Finite Dimensional ◽  
Necessary And Sufficient ◽  
Special Case

AbstractLet A be a finite dimensional commutative and associative algebra with identity, over a field K. We assume also that A is generated by one element and consequently, isomorphic to a quotient algebra of the polynomial algebra K[X]. If A=K[a] and bi=fi(A), fi(X) ∊ K[X], 1≤i≤r we find necessary and sufficient conditions which should be satisfied by fi(X) in order that A = K[b1, …, br].The result can be stated as a theorem about matrices. As a special case we obtain a recent result of Thompson [4].In fact this last result was established earlier by Mirsky and Rado [3]. I am grateful to the referee for supplying this reference.

scholarly journals ON FINITE DIMENSIONAL REALIZATIONS FOR THE TERM STRUCTURE OF FUTURES PRICES

2006 ◽  
Vol 09 (03) ◽  
pp. 281-314 ◽  
Author(s):  
TOMAS BJÖRK ◽  
MAGNUS BLIX ◽  
CAMILLA LANDÉN
Keyword(s):  
Term Structure ◽  
State Space Model ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Necessary And Sufficient Conditions ◽  
Spot Price ◽  
Futures Prices ◽  
Finite Dimensional ◽  
Futures Price ◽  
Necessary And Sufficient

We consider HJM type models for the term structure of futures prices, where the volatility is allowed to be an arbitrary smooth functional of the present futures price curve. Using a Lie algebraic approach we investigate when the infinite dimensional futures price process can be realized by a finite dimensional Markovian state space model, and we give general necessary and sufficient conditions, in terms of the volatility structure, for the existence of a finite dimensional realization. We study a number of concrete applications including a recently developed model for gas futures. In particular we provide necessary and sufficient conditions for when the induced spot price is a Markov process. In particular we can prove that the only HJM type futures price models with spot price dependent volatility structures which generically possess a spot price realization are the affine ones. These models are thus the only generic spot price models from a futures price term structure point of view.

scholarly journals SKIPPED BLOCKING AND OTHER DECOMPOSITIONS IN BANACH SPACES

2006 ◽  
Vol 17 (02) ◽  
pp. 129-141
Author(s):  
STEVEN F. BELLENOT
Keyword(s):  
Banach Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Separable Space ◽  
Finite Dimensional ◽  
Necessary And Sufficient

Necessary and sufficient conditions are given for when a sequence of finite-dimensional subspaces (Xn) can be blocked to be a skipped blocking decompositon (SBD). These are very similar to known results about blocking of biorthogonal sequences. A separable space X has PCP, if and only if, every norming decomposition (Xn) can be blocked to be a boundedly complete SBD. Every boundedly complete SBD is a JT-decomposition.

COPULA-BASED CHARACTERIZATIONS FOR HIGHER ORDER MARKOV PROCESSES

2009 ◽  
Vol 25 (3) ◽  
pp. 819-846 ◽  
Author(s):  
Rustam Ibragimov
Keyword(s):  
Time Series ◽  
Markov Processes ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Conditional Symmetry ◽  
Finite Dimensional ◽  
Necessary And Sufficient ◽  
Dependence Properties

In this paper, we obtain characterizations of higher order Markov processes in terms of copulas corresponding to their finite-dimensional distributions. The results are applied to establish necessary and sufficient conditions for Markov processes of a given order to exhibitm-dependence,r-independence, or conditional symmetry. The paper also presents a study of applicability and limitations of different copula families in constructing higher order Markov processes with the preceding dependence properties. We further introduce new classes of copulas that allow one to combine Markovness withm-dependence orr-independence in time series.

scholarly journals Deformations and equitopological deformations of strongly pseudoconvex manifolds

1981 ◽  
Vol 82 ◽  
pp. 113-129 ◽  
Author(s):  
Stephen S.-T. Yau
Keyword(s):  
Unit Ball ◽  
Deformation Theory ◽  
Complex Analysis ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Order Perturbation ◽  
First Order ◽  
Finite Dimensional ◽  
Necessary And Sufficient ◽  
First Order Perturbation

One of the main problems in complex analysis has been to determine when two open sets D1, D2 in Cn are biholomorphically equivalent. In [26] Poincaré studied perturbations of the unit ball B2 in C2 of a particular kind, and found necessary and sufficient conditions on a first order perturbation that the perturbed domain be biholomorphically equivalent to B2. Recently Burns, Shnider and Wells [7] (cf. also Chern-Moser [9]) have studied the deformations of strongly pseudoconvex manifolds. They proved that there is no finite-dimensional deformation theory for M if one keeps track of the boundary.

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