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Search Results: 1 - 10 of 327849 matches for " Adem K l man "
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On the Fresnel sine integral and the convolution
Adem K l man
International Journal of Mathematics and Mathematical Sciences , 2003, DOI: 10.1155/s0161171203211510
Abstract: The Fresnel sine integral S(x), the Fresnel cosine integral C(x), and the associated functions S
On the -Invariance Property for -Flows
Amin Saif,Adem Kl??man
Abstract and Applied Analysis , 2010, DOI: 10.1155/2010/375014
Abstract: We define an equivalence relation on a topological space which is acted by topological monoid as a transformation semigroup. Then, we give some results about the -invariant classes for this relation. We also provide a condition for the existence of relative -invariant classes. 1. Introduction The invariance theory is one of the principal concepts in the topological dynamics system, see [1, 2]. In [3], Colonius and Kliemann introduced the concept of a control set which is relatively invariant with respect to a subset of the phase space of the control system. From a more general point of view, the theory of control sets for semigroup actions was developed by San Martin and Tonelli in [4]. In this paper, we define an equivalence relation on a topological space which is acted by topological monoid as a transformation semigroup. Then, we provide the necessary and sufficient conditions for the equivalence classes to be -invariant classes which correspond with the control sets for control systems. Then, we study the -invariant classes for this relation in , in particular, and we provide the conditions for the existence and uniqueness of invariant classes. Throughout this paper, will denote the closure set of a set , and will denote the interior set of and all topological spaces involved Hausdorff. Definition 1.1 (see [2]). Let be a monoid with the identity element and also a topological space. Then, will be called a topological monoid if the multiplication operation of: is continuous mapping from to . Definition 1.2 (see [4]). Let be a topological monoid and a topological space. We say that acts on as a transformation semigroup if there is a continuous map between the product space and satisfying we further require that for all . The triple is called an flow; will denote . In particular, an flow is called phase flow if is a compact space. The orbit of under is the set . For a subset of , denotes the set . And a subset is called an invariant set if and . A control set for on is a subset of which satisfies(1) ,(2)for all ,(3) is a maximal with these properties. Then, we say that a subset , satisfies the no-return condition if for some and , then . Lemma 1.3 (see [5, Zorn's Lemma]). If each chain in a partially ordered set has an upper bound, then there is a maximal element of the set. 2. Invariant Classes Let be an flow. From the action on , we can define the relation ~ on by It is clear that the relation ~ is an equivalence relation, and will denote the set of all equivalence classes induced by ~ on . We observe that for all , and if , then for all . The
A Note on Some Strongly Sequence Spaces
Ekrem Sava ,Adem K l man
Abstract and Applied Analysis , 2011, DOI: 10.1155/2011/598393
Abstract: We introduce and study new sequence spaces which arise from the notions of generalized de la Vallée-Poussin means, invariant means, and modulus functions.
Pairwise Weakly Regular-Lindel?f Spaces
Adem K l man,Zabidin Salleh
Abstract and Applied Analysis , 2008, DOI: 10.1155/2008/184243
Abstract: We will introduce and study the pairwise weakly regular-Lindelöf bitopological spaces and obtain some results. Furthermore, we study the pairwise weakly regular-Lindelöf subspaces and subsets, and investigate some of their characterizations. We also show that a pairwise weakly regular-Lindelöf property is not a hereditary property. Some counterexamples will be considered in order to establish some of their relations.
Application of Sumudu Decomposition Method to Solve Nonlinear System of Partial Differential Equations
Hassan Eltayeb,Adem K l man
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/412948
Abstract: We develop a method to obtain approximate solutions of nonlinear system of partial differential equations with the help of Sumudu decomposition method (SDM). The technique is based on the application of Sumudu transform to nonlinear coupled partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of threeexamples, and results of the present technique have close agreement with approximate solutions obtained with the help of Adomian decomposition method (ADM).
Note on the Numerical Solutions of the General Matrix ConvolutionEquations by Using the Iterative Methods and Box Convolution Product
Adem K l man,Zeyad Al zhour
Abstract and Applied Analysis , 2010, DOI: 10.1155/2010/106192
Abstract: We define the so-called box convolution product and study their properties in order to present the approximate solutions for the general coupled matrix convolution equations by using iterative methods. Furthermore, we prove that these solutions consistently converge to the exact solutions and independent of the initial value.
A Note on the Class of Functions with Bounded Turning
Rabha W. Ibrahim,Adem K l man
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/820696
Abstract: We consider subclasses of functions with bounded turning for normalized analytic functions in the unit disk. The geometric representation is introduced, some subordination relations are suggested, and the upper bound of the pre-Schwarzian norm for these functions is computed. Moreover, by employing Jack's lemma, we obtain a convex class in the class of functions ofbounded turning and relations with other classes are posed.
On Lower Separation and Regularity Axioms in Fuzzy Topological Spaces
Amin Saif,Adem Kl??man
Advances in Fuzzy Systems , 2011, DOI: 10.1155/2011/941982
Abstract: We use the concepts of the quasicoincident relation to introduce and investigate some lower separation axioms such as , , , and as well as the regularity axioms and . Further we study some of their properties and the relations among them in the general framework of fuzzy topological spaces. 1. Introduction The fundamental concept of a fuzzy set was introduced by Zadeh in 1965, [1]. Subsequently, in 1968, Chang [2] introduced fuzzy topological spaces (in short, fts). In Chang’s fuzzy topological spaces, each fuzzy set is either open or not. Later on, Chang’s idea was developed by Goguen [3], who replaced the closed interval by a more general lattice L. In 1985, Kubiak [4], and ?ostak [5], in separated works, made topology itself fuzzy besides their dependence on fuzzy sets. In 1991, from a logical point of view, Ying [6] studied Hohles topology and called it fuzzifying topology. This fuzzification opened a rich field for research. As it is well known, the neighborhood structure is not suitable to -topology, and Pu and Liu [7] broke through the classical theory of neighborhood system and established the strong and powerful method of quasicoincident neighborhood system in -topology. Zhang and Xu [8] established the neighborhood structure in fuzzifying topological spaces. Considering the completeness and usefulness of theory of -fuzzy topologies, Fang [9] established -fuzzy quasicoincident neighborhood system in -fuzzy topological spaces and gave a useful tool to study -fuzzy topologies. In ordinary topology, -open sets were introduced and studied by Njastad [10]. Bin Shahna [11], in the same spirit, defined fuzzy -open and fuzzy -closed. Separation is an essential part of fuzzy topology, on which a lot of work has been done. In the framework of fuzzifying topologies, Shen [12], Yue and Fang [13], Li and Shi [14], and Khedr et al. [15] introduced some separation axioms and their separation axioms are discussed on crisp points not on fuzzy points. In 2004, Mahmoud et al. [16] introduced fuzzy semicontinuity and fuzzy semiseparation axioms and examined the validity of some characterization of these concepts. Further, they also defined fuzzy generalized semiopen set and introduced fuzzy separation axioms by using thew semiopen sets concept. In the same paper, the authors also discussed fuzzy semiconnected and fuzzy semicompact spaces and some of their properties. The present paper is organized as follows. It consists of four sections. After this introduction, Section 2 is devoted to some preliminaries. In Section 3, we introduce the notions of some lower
Portfolio Optimization of Equity Mutual Funds—Malaysian Case Study
Adem Kl??man,Jaisree Sivalingam
Advances in Fuzzy Systems , 2010, DOI: 10.1155/2010/879453
Abstract: We focus on the equity mutual funds offered by three Malaysian banks, namely Public Bank Berhad, CIMB, and Malayan Banking Berhad. The equity mutual funds or equity trust is grouped into four clusters based on their characteristics and categorized as inferior, stable, good performing, and aggressive funds based on their return rates, variance and treynor index. Based on the cluster analysis, the return rates and variance of clusters are represented as triangular fuzzy numbers in order to reflect the uncertainty of financial market. To find the optimal asset allocation in each cluster we develop a hybrid model of optimization and fuzzy based on return rates, variance. This was done by maximizing the fuzzy return for a tolerable fuzzy risk and minimizing the fuzzy risk for a desirable fuzzy return separately at different confidence levels. 1. Introduction The portfolio optimization is also known as a risk management, and how to obtain the optimal solution of portfolio allocation has atracted many researchers on portfolio decision-making in the recent years. Thus the objective for models, either the return model or the risk model, is to maximize the profit or to minimize the cost for portfolio selection based on mean-variance (MV) theorem that was proposed by Markowitz. Nowadays, mutual funds have become an ideal form of investment for many people since they have the ability to separate risks to the smallest degree. Therefore, it is not surprising at all to have many banks offering equity mutual fund schemes since it is investors’ preference. However, selecting the best equity mutual fund is a difficult process. In the selection process, investors normally analyze the past performance of funds in order to evaluate the future performance. But sometimes, this method cannot be used for prediction of the future performance of funds due to the high volatility of market environment that is there is no assurance past trends will continue. Thus Ammar and Khalifa [1] introduced the formulation of fuzzy portfolio optimization problem as a convex quadratic programming approach and gave an acceptable solution to such problems. They determined how much money should be allocated to each investment so that the total expected return would be greater than or equal to some lowest fuzzy return or the total fuzzy variance less than or equal to some greatest fuzzy variance. In a recent study, by Chen and Huang [2], the uncertainty of future return rates and risk was considered and presented in triangular fuzzy numbers in contrast with the previous research whereby return rates
On Certain Classes of -Valent Functions by Using Complex-Order and Differential Subordination
Abdolreza Tehranchi,Adem Kl??man
International Journal of Mathematics and Mathematical Sciences , 2010, DOI: 10.1155/2010/275935
Abstract: The aim of the present paper is to study the -valent analytic functions in the unit disk and satisfy the differential subordinations where is an operator defined by S l gean and is a complex number. Further we define a new related integral operator and also study the Fekete-Szego problem by proving some interesting properties. 1. Introduction Let be the class of analytic functions in . Let denote the class of all analytic functions in the form of where is Gaussian hypergeometric function defined by Note that it is easy to see that these functions are analytic in the unit disk ; for more details on hypergeometric functions , see [1, 2]. Definition 1.1. A function is said to be in the class , -valently starlike functions of order , if it satisfies . We write , the class of -valently starlike functions in . Similarly, a function is said to be in the class , -valently convex of order , if it satisfies . Let be analytic and . A function is in the class if The class and a corresponding convex class were defined by Ma and Minda in [3]. Similar results which are related to the convex class can also be obtained easily from the corresponding functions in . For example, (i)if and then the classes reduce to the usual classes of starlike and convex functions; (ii)if where , then the classes are reduced to the usual classes of starlike and convex functions of order ;(iii)if , where , then the classes are reduced to the class of Janowski starlike functions which is defined by (iv)if where and , then the classes reduce to the classes of strongly starlike and convex functions of order that consists of univalent functions satisfing or equivalently we have In the literature, there are several works and many researchers have been studying the related problems. For example, Obradovi? and Owa [4], Silverman [5], Obradowi? and Tuneski [6], and Tuneski [7] have studied the properties of classes of functions which are defined in terms of the ratio of . Definition 1.2. A function is said to be -valent Bazilevic of type and order if there exists a function such that for some and . We denote by , the subclass of consisting of all such functions. In particular, a function in is said to be -valently close-to-convex of order in . Definition 1.3. Let and be analytic functions in , then we say is subordinate to and denoted by if there exists a Schwarz function , analytic in with and , such that . In particular, if the function is univalent in , the above subordination is equivalent to and . Also, we say that is superordinate to ; see [8]. Definition 1.4. Motivated by the multiplier
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