scholarly journals Equivalent Locally Martingale Measure for the Deflator Process on Ordered Banach Algebra

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Boushra Y. Hussein
Keyword(s):  
Banach Algebra ◽  
Sufficient Conditions ◽  
Price System ◽  
Martingale Measure ◽  
Free Lunch ◽  
Equivalent Measure ◽  
Equivalent Martingale ◽  
Necessary And Sufficient ◽  
The Given ◽  
Ordered Banach Algebra

This paper aims at determining the measure of Q under necessary and sufficient conditions. The measure is an equivalent measure for identifying the given P such that the process with respect to P is the deflator locally martingale. The martingale and locally martingale measures will coincide for the deflator process discrete time. We define s-viable, s-price system, and no locally free lunch in ordered Banach algebra and identify that the s-price system C,π is s-viable if and only a character functional ψC≤π exists. We further demonstrate that no locally free lunch is a necessary and sufficient condition for the equivalent martingale measure Q to exist for the deflator process and the subcharacter ϕ∈Γ such that φC=π. This paper proves the existence of more than one condition and that all conditions are equivalent.

scholarly journals New Conditions of The Existence of Fixed Point in Δ- Ordered Δ Banach Algebra

2020 ◽  
Vol 18 ◽  
pp. 60-71
Author(s):  
Boushra Hussein
Keyword(s):  
Fixed Point ◽  
Banach Algebra ◽  
Hausdorff Space ◽  
Sufficient Conditions ◽  
Main Idea ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
New Space ◽  
Necessary And Sufficient ◽  
Ordered Banach Algebra

The main idea is to construct a new algebra and find new necessary and sufficient conditions equivalent to the existence of a fixed point. In this work, an algebra is constructed, called Δ - ordered Banach algebra, we define convergent in this new space, Topological structure on  Δ ordered Banach Algebra and prove this as Hausdorff space. Also, we define new conditions as Δ- lipshtiz,, Δ- contraction  contraction , in this algebra construct, we prove this condition is the existence and uniqueness results of the fixed point. In this paper,  we prove a common fixed point if the self-functions satisfy the new condition which is called Ф-contraction.  

scholarly journals Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1026 ◽  
Author(s):  
Martin Gavalec ◽  
Zuzana Němcová
Keyword(s):  
Linear System ◽  
Fuzzy Systems ◽  
Polynomial Algorithm ◽  
Sufficient Conditions ◽  
Recognition Algorithm ◽  
Triangular Norm ◽  
Binary Operations ◽  
Interval Coefficients ◽  
Necessary And Sufficient ◽  
The Given

The max-Łukasiewicz algebra describes fuzzy systems working in discrete time which are based on two binary operations: the maximum and the Łukasiewicz triangular norm. The behavior of such a system in time depends on the solvability of the corresponding bounded parametric max-linear system. The aim of this study is to describe an algorithm recognizing for which values of the parameter the given bounded parametric max-linear system has a solution—represented by an appropriate state of the fuzzy system in consideration. Necessary and sufficient conditions of the solvability have been found and a polynomial recognition algorithm has been described. The correctness of the algorithm has been verified. The presented polynomial algorithm consists of three parts depending on the entries of the transition matrix and the required state vector. The results are illustrated by numerical examples. The presented results can be also applied in the study of the max-Łukasiewicz systems with interval coefficients. Furthermore, Łukasiewicz arithmetical conjunction can be used in various types of models, for example, in cash-flow system.

scholarly journals Minimum energy control of positive 2D continuous-discrete linear systems with bounded inputs

2015 ◽  
Vol 25 (3) ◽  
pp. 319-331
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Discrete Linear Systems ◽  
Minimum Energy Control ◽  
New Formulation ◽  
Necessary And Sufficient ◽  
The Given

AbstractA new formulation of the minimum energy control problem for the positive 2D continuous-discrete linear systems with bounded inputs is proposed. Necessary and sufficient conditions for the reachability of the systems are established. Conditions for the existence of the solution to the minimum energy control problem and a procedure for computation of an input minimizing the given performance index are given. Effectiveness of the procedure is demonstrated on numerical example.

scholarly journals Some quaternion matrix equations involving Φ-Hermicity

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5097-5112 ◽  
Author(s):  
Zhuo-Heng He
Keyword(s):  
Quaternion Algebra ◽  
Sufficient Conditions ◽  
Matrix Decomposition ◽  
Matrix Equations ◽  
Quaternion Matrix ◽  
Existence Of A Solution ◽  
Quaternion Matrices ◽  
Real Quaternion ◽  
Necessary And Sufficient ◽  
The Given

Let H be the real quaternion algebra and Hmxn denote the set of all m x n matrices over H. For A ? Hm x n, we denote by A? the n x m matrix obtained by applying ? entrywise to the transposed matrix At, where ? is a nonstandard involution of H. A ? Hnxn is said to be ?-Hermitian if A = A?. In this paper, we construct a simultaneous decomposition of four real quaternion matrices with the same row number (A,B,C,D), where A is ?-Hermitian, and B,C,D are general matrices. Using this simultaneous matrix decomposition, we derive necessary and sufficient conditions for the existence of a solution to some real quaternion matrix equations involving ?-Hermicity in terms of ranks of the given real quaternion matrices. We also present the general solutions to these real quaternion matrix equations when they are solvable. Finally some numerical examples are presented to illustrate the results of this paper.

Controllability of nonlinear stochastic fractional higher order dynamical systems

2019 ◽  
Vol 22 (4) ◽  
pp. 1063-1085
Author(s):  
R. Mabel Lizzy ◽  
K. Balachandran ◽  
Yong-Ki Ma
Keyword(s):  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Necessary And Sufficient Condition ◽  
Bounded Operators ◽  
Semilinear Systems ◽  
Operator Functions ◽  
Fractional System ◽  
Necessary And Sufficient ◽  
The Given

Abstract This paper deals with the study of controllability of stochastic fractional dynamical systems with 1 < α ≤ 2. Necessary and sufficient condition for controllability of linear stochastic fractional system is obtained. Sufficient conditions for controllability of stochastic fractional semilinear systems, integrodifferential systems, systems with neutral term, systems with delays in control and systems with Lévy noise is formulated and established. The solution is obtained in terms of Mittag-Leffler operator functions by considering bounded operators. The Banach fixed point theorem is used to obtain the desired results from an equivalent nonlinear integral equation of the given system.

scholarly journals Hypersurface Family with a Common Isoasymptotic Curve

Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ergin Bayram ◽  
Emin Kasap
Keyword(s):  
Linear Combination ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Frenet Frame ◽  
Necessary And Sufficient ◽  
The Given

We handle the problem of finding a hypersurface family from a given asymptotic curve in R4. Using the Frenet frame of the given asymptotic curve, we express the hypersurface as a linear combination of this frame and analyze the necessary and sufficient conditions for that curve to be asymptotic. We illustrate this method by presenting some examples.

scholarly journals Minimizing of the quadratic functional on Hopfield networks

2021 ◽  
pp. 1-20
Author(s):  
Oleksandr Boichuk ◽  
Dmytro Bihun ◽  
Victor Feruk ◽  
Oleksandr Pokutnyi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Sufficient Conditions ◽  
Quadratic Functional ◽  
Problem Solution ◽  
Linear Boundary ◽  
System Of Differential Equations ◽  
Hopfield Networks ◽  
Necessary And Sufficient ◽  
The Given

In this paper, we consider the continuous Hopfield model with a weak interaction of network neurons. This model is described by a system of differential equations with linear boundary conditions. Also, we consider the questions of finding necessary and sufficient conditions of solvability and constructive construction of solutions of the given problem, which turn into solutions of the linear generating problem, as the parameter $\varepsilon$ tends to zero. An iterative algorithm for finding solutions has been constructed. The problem of finding the extremum of the target functions on the given problem solution is considered. To minimize a functional, an accelerated method of conjugate gradients is used. Results are illustrated with examples for the case of three neurons.

scholarly journals On the pseudo drazin inverse of the sum of two elements in a Banach algebra

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2011-2022 ◽  
Author(s):  
Honglin Zou ◽  
Jianlong Chen
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Drazin Inverse ◽  
Necessary And Sufficient ◽  
Associative Rings

In this paper, some additive properties of the pseudo Drazin inverse are obtained in a Banach algebra. In addition, we find some new conditions under which the pseudo Drazin inverse of the sum a + b can be explicitly expressed in terms of a, az, b, bz. In particular, necessary and sufficient conditions for the existence as well as the expression for the pseudo Drazin inverse of the sum a+b are obtained under certain conditions. Also, a result of Wang and Chen [Pseudo Drazin inverses in associative rings and Banach algebras, LAA 437(2012) 1332-1345] is extended.

Some Relationships between Filters*

1967 ◽  
Vol 10 (2) ◽  
pp. 257-260
Author(s):  
Ivan Baggs
Keyword(s):  
Sufficient Conditions ◽  
Theoretical Concept ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
The Given

A filter is a set theoretical concept and as such, its structure is independent of any topology which can be put on the given space. However, an O-filter, whose counterpart in the theory of nets is the O-nets of Robertson and Franklin [2], is defined with respect to the topology on the given space. The purpose of this paper is to give necessary and sufficient conditions for every O-filter to be an ultrafilter and for every Cauchy filter to be an O-filter.

scholarly journals The equivalent martingale measure conditions in a general model for interest rates

2005 ◽  
Vol 37 (2) ◽  
pp. 415-434 ◽  
Author(s):  
Kais Hamza ◽  
Saul Jacka ◽  
Fima Klebaner
Keyword(s):  
Interest Rates ◽  
General Model ◽  
Field Model ◽  
Sufficient Conditions ◽  
Martingale Measure ◽  
Equivalent Martingale Measure ◽  
Forward Rates ◽  
No Arbitrage ◽  
Equivalent Martingale ◽  
Integrated Processes

Assuming that the forward rates ftu are semimartingales, we give conditions on their components under which the discounted bond prices are martingales. To achieve this, we give sufficient conditions for the integrated processes ftu=∫0uftvdv to be semimartingales, and identify their various components. We recover the no-arbitrage conditions in models well known in the literature and, finally, we formulate a new random field model for interest rates and give its equivalent martingale measure (no-arbitrage) condition.

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