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1

On a cubic integral equation of Urysohn type with linear perturbation of second kind

Awad H. K., Darwish M. A., Metwali M. M. A.

Journal of Mathematics and Applications

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2018

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Vol. 41

29--38

EN

In this paper, we concern by a very general cubic integral equation and we prove that this equation has a solution in C[0; 1]. We apply the measure of noncompactness introduced by Banaś and Olszowy and Darbo's fixed point theorem to establish the proof of our main result.

2

On Deadlockability, Liveness and Reversibility in Subclasses of Weighted Petri Nets

Hujsa T., Devillers R.

Fundamenta Informaticae

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2018

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Vol. 161, nr 4

383--421

EN

Liveness, (non-)deadlockability and reversibility are behavioral properties of Petri nets that are fundamental for many real-world systems. Such properties are often required to be monotonic, meaning preserved upon any increase of the marking. However, their checking is intractable in general and their monotonicity is not always satisfied. To simplify the analysis of these features, structural approaches have been fruitfully exploited in particular subclasses of Petri nets, deriving the behavior from the underlying graph and the initial marking only, often in polynomial time. In this paper, we further develop these efficient structural methods to analyze deadlockability, liveness, reversibility and their monotonicity in weighted Petri nets. We focus on the join-free subclass, which forbids synchronizations, and on the homogeneous asymmetric-choice subclass, which allows conflicts and synchronizations in a restricted fashion. For the join-free nets, we provide several structural conditions for checking liveness, (non-)deadlockability, reversibility and their monotonicity. Some of these methods operate in polynomial time. Furthermore, in this class, we show that liveness, non-deadlockability and reversibility, taken together or separately, are not always monotonic, even under the assumptions of structural boundedness and structural liveness. These facts delineate more sharply the frontier between monotonicity and non-monotonicity of the behavior in weighted Petri nets, present already in the join-free subclass. In addition, we use part of this new material to correct a flaw in the proof of a previous characterization of monotonic liveness and boundedness for homogeneous asymmetric-choice nets, published in 2004 and left unnoticed.

3

On types of responsiveness in the theory of voting

Holler M. J., Nurmi H.

Operations Research and Decisions

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2016

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Vol. 26, No. 2

87--106

EN

In mathematics, monotonicity is used to denote the nature of the connection between variables. Hence for example, a variable is said to be a monotonically increasing function of another variable if an increase in the value of the latter is always associated with an increase in the other variable. In the theory of voting and the measurement of a priori voting power one encounters, not one, but several concepts that are closely related to the mathematical notion of monotonicity. We deal with such notions focusing particularly on their role in capturing key aspects of plausible opinion aggregation. Further, we outline approaches to analyzing the relationship of opinion aggregation and voting power and thereby contribute to our understanding of major components that determine the outcome of voting.

4

Convergence Analysis of Inverse Iterative Neural Networks with L₂ Penalty

Wen Y., Wang J., Huang B., Zurada J. M.

Journal of Applied Computer Science Methods

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2016

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Vol. 8 No. 2

85--98

EN

The iterative inversion of neural networks has been used in solving problems of adaptive control due to its good performance of information processing. In this paper an iterative inversion neural network with L₂ penalty term has been presented trained by using the classical gradient descent method. We mainly focus on the theoretical analysis of this proposed algorithm such as monotonicity of error function, boundedness of input sequences and weak (strong) convergence behavior. For bounded property of inputs, we rigorously proved that the feasible solutions of input are restricted in a measurable field. The weak convergence means that the gradient of error function with respect to input tends to zero as the iterations go to infinity while the strong convergence stands for the iterative sequence of input vectors convergence to a fixed optimal point.

5

Convergence Analysis of An Improved Extreme Learning Machine Based on Gradient Descent Method

Yusong L., Zhixun S., Bingjie Y., Xiaoling G., Zhaoyang S.

Journal of Applied Computer Science Methods

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2016

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Vol. 8 No. 1

5--15

EN

Extreme learning machine (ELM) is an efficient algorithm, but it requires more hidden nodes than the BP algorithms to reach the matched performance. Recently, an efficient learning algorithm, the upper-layer-solution-unaware algorithm (USUA), is proposed for the single-hidden layer feed-forward neural network. It needs less number of hidden nodes and testing time than ELM. In this paper, we mainly give the theoretical analysis for USUA. Theoretical results show that the error function monotonously decreases in the training procedure, the gradient of the error function with respect to weights tends to zero (the weak convergence), and the weight sequence goes to a fixed point (the strong convergence) when the iterations approach positive infinity. An illustrated simulation has been implemented on the MNIST database of handwritten digits which effectively verifies the theoretical results.

6

An inequality involving the gamma and digamma functions

Qi F., Guo B.-N.

Journal of Applied Analysis

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2016

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Vol. 22, nr 1

49--54

EN

In the paper, the authors establish an inequality involving the gamma and digamma functions and apply it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.

7

On the number of zeros of a polynomial in a region

Kareem K. A., Mogbademu A. A.

Fasciculi Mathematici

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2016

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Nr 57

53--65

EN

In this paper, we impose restrictions on the complex coefficients of a polynomial in order to give bounds concerning the number of zeros in a specific region of the complex plane. Our results generalize and refine a good number of results in this area of research.

8

Evolution and monotonicity of the first eigenvalue of p-Laplacian under the Ricci-harmonic flow

Abolarinwa A.

Journal of Applied Analysis

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2015

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Vol. 21, nr 2

147--160

EN

We study the evolution and monotonicity of the eigenvalues of p-Laplace operator on an m-dimen-sional compact Riemannian manifold M whose metric g(t) evolves by the Ricci-harmonic flow. The first nonzero eigenvalue is proved to be monotonically nondecreasing along the flow and differentiable almost everywhere. As a corollary, we recover the corresponding results for the usual Laplace-Beltrami operator when p = 2. We also examine the evolution and monotonicity under volume preserving flow and it turns out that the first eigenvalue is not monotone in general.

9

Two semantics of trust management language with negation

Felkner A.

Journal of Telecommunications and Information Technology

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2013

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nr 4

102--108

EN

The family of Role-based Trust management languages is used for representing security policies by defining a formalism, which uses credentials to handle trust in decentralized, distributed access control systems. A credential provides information about the privileges of users and the security policies issued by one or more trusted authorities. The main topic of this paper is RT⊖, a language which provides a carefully controlled form of non-monotonicity. The core part of the paper defines two different semantics of RT⊖ language – a relational, set-theoretic semantics for the language, and an inference system, which is a kind of operational semantics. The set-theoretic semantics maps roles to a set of entity names. In the operational semantics credentials can be derived from an initial set of credentials using a set of inference rules. The soundness and the completeness of the inference system with respect to the set-theoretic semantics of RT⊖ will be proven.

10

Iterative learning control — monotonicity and optimization

Owens D. H., Daley S.

International Journal of Applied Mathematics and Computer Science

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2008

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Vol. 18, no 3

279-293

EN

The area if Iterative Learning Control (ILC) has great potential for applications to systems with a naturally repetitive action where the transfer of data from repetition (trial or iteration) can lead to substantial improvements in tracking performance. There are several serious issues arising from the "2D" structure of ILC and a number of new problems requiring new ways of thinking and design. This paper introduces some of these issues from the point of view of the research group at Sheffield University and concentrates on linear systems and the potential for the use of optimization methods and switching strategies to achieve effective control.

11

Best constant approximants in Orlicz-Lorentz spaces

Levis F.E., Cuenya H.H., Priori A.N.

Commentationes Mathematicae

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2008

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Vol. 48, [Z] 1

59-73

EN

The best constant approximant operator is extended from an Orlicz- Lorentz space [...]to the space[...] , where 0 is the derivative of φ. Monotonicity property of its extension is established.

12

Wartości "proceduralne" gier kooperacyjnych

Malawski M.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

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2004

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Nr 982

1-18

PL

W pracy wprowadzamy nowe pojęcie "wartości proceduralnych" dla gier kooperacyjnych z wypłatami ubocznymi. Wartości takie są wyznaczone przez procedury podziału krańcowych wkładów graczy pomiędzy nich i graczy już obecnych w koalicji powstającej przy losowym uporządkowaniu graczy. Najprostszą wartościąproceduralną jest wartość Shapleya, otrzymywana przy procedurze, według której każdy gracz zachowuje całość swego wkładu; jednak inne zasady podziału prowadzą do różnych interesujących wartości, w tym do podziału równego i do "wartości solidarnej" Nowaka i Radzika. Zbiór wszystkich wartości proceduralnych zawiera się w zbiorze wartości efektywnych, symetrycznych, liniowych i lokalnie monotonicznych; w pracy pokazujemy, że jest jego właściwym podzbiorem. Onawiamy także krótko możliwe kierunki uogólnień.

EN

A new notion of a "procedural" value for cooperative TU games is proposed. A procedural value is determined by an underlying procedurę of sharing marginal contributions to koalicje that form by random ordering of players between the contributing player and his predecessors in the ordering. The simplest procedural value is the Shapley value obtaining under the procedurę of every player j ust re-taining his entire marginal contribution. But different sharing rules lead to other interesting values, including the "egalitarian solution" and the Nowak and Radzik "solidarity value". The set of all procedural values is a subset of all efficient, symmetric, linear and locally monotonie values, and it is shown that the subset is proper. Some possible generalizations arę also briefły discussed.

13

Integral representations of convex and concave set-valued functions

Piszczek M.

Demonstratio Mathematica

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2002

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Vol. 35, nr 4

727-742

EN

We will denote by C+ the family of all convex set-valued functions F denned on [a, b} with nonempty compact values, continuous at a, for which there exist all differences F(t) - F(s) as far as a < s < t < b. The main purpose oh this paper is to show that a function F belongs to the family C+ if and only if it is of the form t F(t)=F(a)+^\G(x)dx a for some decreasing set-valued function G.