Partial Higher-Order Specifications1

1992 ◽  
Vol 16 (2) ◽  
pp. 101-126
Author(s):  
Egidio Astesiano ◽  
Maura Cerioli
Keyword(s):  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Important Case ◽  
Deduction System ◽  
Closure Properties ◽  
Inference System ◽  
Conditional Specification ◽  
Necessary And Sufficient

In this paper the classes of extensional models of higher-order partial conditional specifications are studied, with the emphasis on the closure properties of these classes. Further it is shown that any equationally complete inference system for partial conditional specifications may be extended to an inference system for partial higher-order conditional specifications, which is equationally complete w.r.t. the class of all extensional models. Then, applying some previous results, a deduction system is proposed, equationally complete for the class of extensional models of a partial conditional specification. Finally, turning the attention to the special important case of termextensional models, it is first shown a sound and equationally complete inference system and then necessary and sufficient conditions are given for the existence of free models, which are also free in the class of term-generated extensional models.

scholarly journals Approximation on the sphere by weighted Fourier expansions

2005 ◽  
Vol 2005 (4) ◽  
pp. 321-339 ◽  
Author(s):  
V. A. Menegatto ◽  
A. C. Piantella
Keyword(s):  
Spherical Harmonics ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Important Case ◽  
Weighted Sums ◽  
Main Theme ◽  
Fourier Expansions ◽  
Necessary And Sufficient

The main theme of this paper is the approximation on the sphere by weighted sums of spherical harmonics. We give necessary and sufficient conditions on the weights for convergence in both the continuous and theLPcases. Approximation by spherical convolution is a particular and important case that fits into our setting.

scholarly journals Convex sequences of higher order

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4655-4663
Author(s):  
Daniel Sofonea ◽  
Ioan Ţincu ◽  
Ana Acu
Keyword(s):  
Real Number ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Difference Operators ◽  
Real Sequence ◽  
Convex Sequence ◽  
Different Types ◽  
The Difference ◽  
Necessary And Sufficient

In this paper we study the class of convex sequences of higher order defined using the difference operators and investigate their properties. The notion of the convex sequence of order r ? N will be extended for r a real number. Some necessary and sufficient conditions such that a real sequence belongs to the class of convex sequences of higher order r ? R are introduced. Using different types of means we will investigate the convexity of higher order for real sequences.

scholarly journals Characterizations of weighted dynamic Hardy-type inequalities with higher-order derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. H. Saker ◽  
R. R. Mahmoud ◽  
K. R. Abdo
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Type Inequality ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Hardy Type Inequality ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Weighted Functions ◽  
Necessary And Sufficient

AbstractIn this paper, we establish some necessary and sufficient conditions for the validity of a generalized dynamic Hardy-type inequality with higher-order derivatives with two different weighted functions on time scales. The corresponding continuous and discrete cases are captured when $\mathbb{T=R}$ T = R and $\mathbb{T=N}$ T = N , respectively. Finally, some applications to our main result are added to conclude some continuous results known in the literature and some other discrete results which are essentially new.

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 Optimality conditions for higher order polyhedral discrete and differential inclusions

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4533-4553
Author(s):  
Sevilay Demir Sağlam ◽  
Elimhan Mahmudov
Keyword(s):  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Inequality Constraints ◽  
Approximation Problem ◽  
Numerical Approach ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Transversality Conditions ◽  
Linear Inequality Constraints ◽  
Necessary And Sufficient

The problems considered in this paper are described in polyhedral multi-valued mappings for higher order(s-th) discrete (PDSIs) and differential inclusions (PDFIs). The present paper focuses on the necessary and sufficient conditions of optimality for optimization of these problems. By converting the PDSIs problem into a geometric constraint problem, we formulate the necessary and sufficient conditions of optimality for a convex minimization problem with linear inequality constraints. Then, in terms of the Euler-Lagrange type PDSIs and the specially formulated transversality conditions, we are able to obtain conditions of optimality for the PDSIs. In order to obtain the necessary and sufficient conditions of optimality for the discrete-approximation problem PDSIs, we reduce this problem to the form of a problem with higher order discrete inclusions. Finally, by formally passing to the limit, we establish the sufficient conditions of optimality for the problem with higher order PDFIs. Numerical approach is developed to solve a polyhedral problem with second order polyhedral discrete inclusions.

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