Search results for: coincidence degree theorem.
1034 Weyl Type Theorem and the Fuglede Property
Authors: M. H. M. Rashid
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Given H a Hilbert space and B(H) the algebra of bounded linear operator in H, let δAB denote the generalized derivation defined by A and B. The main objective of this article is to study Weyl type theorems for generalized derivation for (A,B) satisfying a couple of Fuglede.Keywords: Fuglede Property, Weyl’s theorem, generalized derivation, Aluthge Transformation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5461033 Extremal Properties of Generalized Class of Close-to-convex Functions
Authors: Norlyda Mohamed, Daud Mohamad, Shaharuddin Cik Soh
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Let Gα ,β (γ ,δ ) denote the class of function f (z), f (0) = f ′(0)−1= 0 which satisfied e δ {αf ′(z)+ βzf ′′(z)}> γ i Re in the open unit disk D = {z ∈ı : z < 1} for some α ∈ı (α ≠ 0) , β ∈ı and γ ∈ı (0 ≤γ <α ) where δ ≤ π and α cosδ −γ > 0 . In this paper, we determine some extremal properties including distortion theorem and argument of f ′( z ) .Keywords: Argument of f ′(z) , Carathéodory Function, Closeto- convex Function, Distortion Theorem, Extremal Properties
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13501032 A Constructive Proof of the General Brouwer Fixed Point Theorem and Related Computational Results in General Non-Convex sets
Authors: Menglong Su, Shaoyun Shi, Qing Xu
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In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.
Keywords: interior path following method, general Brouwer fixed point theorem, non-convex sets, globally convergent algorithm
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14361031 A Sandwich-type Theorem with Applications to Univalent Functions
Authors: Sukhwinder Singh Billing, Sushma Gupta, Sukhjit Singh Dhaliwal
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In the present paper, we obtain a sandwich-type theorem. As applications of our main result, we discuss the univalence and starlikeness of analytic functions in terms of certain differential subordinations and differential inequalities.Keywords: Univalent function, Starlike function, Differential subordination, Differential superordination.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13131030 A Test to Express Diagnostic Cohesion of Football Team
Authors: Alexandra O. Savinkina
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We proposed to assess the cohesion of a football team by its subject-goal and subject-value unity according to the A.V. Petrovsky theory. Goal unity was measured by the degree of compliance of the priority targets for various players in the team. Values were estimated by the coincidence of the ideas about a perfect football player. On the basis of the provisional diagnosis of the six teams, we had made the lists of goals and values. The tests were piloted on 35 football teams. The results allowed not only to compare quantitatively the cohesion of the different teams, but also to identify subgroups within the team.
Keywords: Cohesion, football, psychodiagnostic, soccer, sports team, value-orientation unity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11551029 On the Central Limit Theorems for Forward and Backward Martingales
Authors: Yilun Shang
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Let {Xi}i≥1 be a martingale difference sequence with Xi = Si - Si-1. Under some regularity conditions, we show that (X2 1+· · ·+X2N n)-1/2SNn is asymptotically normal, where {Ni}i≥1 is a sequence of positive integer-valued random variables tending to infinity. In a similar manner, a backward (or reverse) martingale central limit theorem with random indices is provided.Keywords: central limit theorem, martingale difference sequence, backward martingale.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27761028 Cryptographic Attack on Lucas Based Cryptosystems Using Chinese Remainder Theorem
Authors: Tze Jin Wong, Lee Feng Koo, Pang Hung Yiu
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Lenstra’s attack uses Chinese remainder theorem as a tool and requires a faulty signature to be successful. This paper reports on the security responses of fourth and sixth order Lucas based (LUC4,6) cryptosystem under the Lenstra’s attack as compared to the other two Lucas based cryptosystems such as LUC and LUC3 cryptosystems. All the Lucas based cryptosystems were exposed mathematically to the Lenstra’s attack using Chinese Remainder Theorem and Dickson polynomial. Result shows that the possibility for successful Lenstra’s attack is less against LUC4,6 cryptosystem than LUC3 and LUC cryptosystems. Current study concludes that LUC4,6 cryptosystem is more secure than LUC and LUC3 cryptosystems in sustaining against Lenstra’s attack.Keywords: Lucas sequence, Dickson Polynomial, faulty signature, corresponding signature, congruence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7261027 Reduction of Search Space by Applying Controlled Genetic Operators for Weight Constrained Shortest Path Problem
Authors: A.K.M. Khaled Ahsan Talukder, Taibun Nessa, Kaushik Roy
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The weight constrained shortest path problem (WCSPP) is one of most several known basic problems in combinatorial optimization. Because of its importance in many areas of applications such as computer science, engineering and operations research, many researchers have extensively studied the WCSPP. This paper mainly concentrates on the reduction of total search space for finding WCSP using some existing Genetic Algorithm (GA). For this purpose, some controlled schemes of genetic operators are adopted on list chromosome representation. This approach gives a near optimum solution with smaller elapsed generation than classical GA technique. From further analysis on the matter, a new generalized schema theorem is also developed from the philosophy of Holland-s theorem.Keywords: Genetic Algorithm, Evolutionary Optimization, Multi Objective Optimization, Non-linear Schema Theorem, WCSPP.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14051026 Recursive Wiener-Khintchine Theorem
Authors: Khalid M. Aamir, Mohammad A. Maud
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Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. In this paper, recursive version of the Wiener-Khintchine theorem has been derived by using the sliding DFT approach meant for computation of STFT. The computational complexity of the proposed recursive Wiener-Khintchine algorithm, for a window size of N, is O(N).
Keywords: Power Spectral Density (PSD), Wiener-KhintchineTheorem, Periodogram, Short Time Fourier Transform (STFT), TheSliding DFT.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24771025 Some Applications of Gröbner bases
Authors: Hassan Noori, Abdolali Basiri, Sajjad Rahmany
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In this paper we will introduce a brief introduction to theory of Gr¨obner bases and some applications of Gr¨obner bases to graph coloring problem, automatic geometric theorem proving and cryptography.Keywords: Gr¨obner bases, Application of Gr¨obner bases, Automatic Geometric Theorem Proving, Graph Coloring, Cryptography.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 49071024 Quadrilateral Decomposition by Two-Ear Property Resulting in CAD Segmentation
Authors: Maharavo Randrianarivony
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The objective is to split a simply connected polygon into a set of convex quadrilaterals without inserting new boundary nodes. The presented approach consists in repeatedly removing quadrilaterals from the polygon. Theoretical results pertaining to quadrangulation of simply connected polygons are derived from the usual 2-ear theorem. It produces a quadrangulation technique with O(n) number of quadrilaterals. The theoretical methodology is supplemented by practical results and CAD surface segmentation.Keywords: Quadrangulation, simply connected, two-ear theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12491023 On Chvátal’s Conjecture for the Hamiltonicity of 1-Tough Graphs and Their Complements
Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su
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In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.
Keywords: Complement, degree sum, Hamiltonian, tough.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6911022 Existence of Positive Solutions for Second-Order Difference Equation with Discrete Boundary Value Problem
Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit
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We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.
Keywords: Positive solution, Boundary value problem, Fixed point theorem, Cone.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17231021 Periodic Solutions for a Third-order p-Laplacian Functional Differential Equation
Authors: Yanling Zhu, Kai Wang
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By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g t, 0 −τ x(t + s) dα(s) + e(t), some criteria to guarantee the existence of periodic solutions are obtained.
Keywords: p–Laplacian, distributed delay, periodic solution, Mawhin's continuation theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12801020 Lagrange-s Inversion Theorem and Infiltration
Authors: Pushpa N. Rathie, Prabhata K. Swamee, André L. B. Cavalcante, Luan Carlos de S. M. Ozelim
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Implicit equations play a crucial role in Engineering. Based on this importance, several techniques have been applied to solve this particular class of equations. When it comes to practical applications, in general, iterative procedures are taken into account. On the other hand, with the improvement of computers, other numerical methods have been developed to provide a more straightforward methodology of solution. Analytical exact approaches seem to have been continuously neglected due to the difficulty inherent in their application; notwithstanding, they are indispensable to validate numerical routines. Lagrange-s Inversion Theorem is a simple mathematical tool which has proved to be widely applicable to engineering problems. In short, it provides the solution to implicit equations by means of an infinite series. To show the validity of this method, the tree-parameter infiltration equation is, for the first time, analytically and exactly solved. After manipulating these series, closed-form solutions are presented as H-functions.Keywords: Green-Ampt Equation, Lagrange's Inversion Theorem, Talsma-Parlange Equation, Three-Parameter Infiltration Equation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18811019 The Proof of Analogous Results for Martingales and Partial Differential Equations Options Price Valuation Formulas Using Stochastic Differential Equation Models in Finance
Authors: H. D. Ibrahim, H. C. Chinwenyi, A. H. Usman
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Valuing derivatives (options, futures, swaps, forwards, etc.) is one uneasy task in financial mathematics. The two ways this problem can be effectively resolved in finance is by the use of two methods (Martingales and Partial Differential Equations (PDEs)) to obtain their respective options price valuation formulas. This research paper examined two different stochastic financial models which are Constant Elasticity of Variance (CEV) model and Black-Karasinski term structure model. Assuming their respective option price valuation formulas, we proved the analogous of the Martingales and PDEs options price valuation formulas for the two different Stochastic Differential Equation (SDE) models. This was accomplished by using the applications of Girsanov theorem for defining an Equivalent Martingale Measure (EMM) and the Feynman-Kac theorem. The results obtained show the systematic proof for analogous of the two (Martingales and PDEs) options price valuation formulas beginning with the Martingales option price formula and arriving back at the Black-Scholes parabolic PDEs and vice versa.
Keywords: Option price valuation, Martingales, Partial Differential Equations, PDEs, Equivalent Martingale Measure, Girsanov Theorem, Feyman-Kac Theorem, European Put Option.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3661018 Multiple Positive Periodic Solutions to a Predator-prey system with Harvesting Terms and Holling II Type Functional Response
Authors: Pan Wang, Yongkun Li
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In this paper, a periodic predator-prey system with harvesting terms and Holling II type functional response is considered. Sufficient criteria for the existence of at least sixteen periodic solutions are established by using the well known continuation theorem due to Mawhin. An example is given to illustrate the main result.
Keywords: Periodic solution, predator-prey system, harvesting terms, continuation theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12791017 A new Configurable Decimation Filter using Pascal-s Triangle Theorem
Authors: A. Chahardah Cherik, E. Farshidi
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This paper presents a new configurable decimation filter for sigma-delta modulators. The filter employs the Pascal-s triangle-s theorem for building the coefficients of non-recursive decimation filters. The filter can be connected to the back-end of various modulators with different output accuracy. In this work two methods are shown and then compared from area occupation viewpoint. First method uses the memory and the second one employs Pascal-s triangle-s method, aiming to reduce required gates. XILINX ISE v10 is used for implementation and confirmation the filter.Keywords: Decimation filter, sigma delta, Pascal's triangle'stheorem, memory
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16721016 PI Control for Second Order Delay System with Tuning Parameter Optimization
Authors: R. Farkh, K. Laabidi, M. Ksouri
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In this paper, we consider the control of time delay system by Proportional-Integral (PI) controller. By Using the Hermite- Biehler theorem, which is applicable to quasi-polynomials, we seek a stability region of the controller for first order delay systems. The essence of this work resides in the extension of this approach to second order delay system, in the determination of its stability region and the computation of the PI optimum parameters. We have used the genetic algorithms to lead the complexity of the optimization problem.Keywords: Genetic algorithm, Hermit-Biehler theorem, optimization, PI controller, second order delay system, stability region.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17711015 The Positive Solution for Singular Eigenvalue Problem of One-dimensional p-Laplace Operator
Authors: Lv Yuhua
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In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.
Keywords: Cone, fixed point index, eigenvalue problem, p-Laplace operator, positive solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14221014 Simplified Equations for Rigidity and Lateral Deflection for Reinforced Concrete Cantilever Shear Walls
Authors: Anas M. Fares
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Reinforced concrete shear walls are the most frequently used forms of lateral resisting structural elements. These walls may take many forms due to their functions and locations in the building. In Palestine, the most lateral resisting forces construction forms is the cantilever shear walls system. It is thus of prime importance to study the rigidity of these walls. The virtual work theorem is used to derive the total lateral deflection of cantilever shear walls due to flexural and shear deformation. The case of neglecting the shear deformation in the walls is also studied, and it is found that the wall height to length aspect ratio (H/B) plays a major role in calculating the lateral deflection and the rigidity of such walls. When the H/B is more than or equal to 3.7, the shear deformation may be neglected from the calculation of the lateral deflection. Moreover, the walls with the same material properties, same lateral load value, and same aspect ratio, shall have the same of both the lateral deflection and the rigidity. Finally, an equation to calculate the total rigidity and total deflection of such walls is derived by using the virtual work theorem for a cantilever beam.Keywords: Cantilever shear walls, flexural deformation, lateral deflection, lateral loads, reinforced concrete shear walls, rigidity, shear deformation, virtual work theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 50121013 The Boundary Theory between Laminar and Turbulent Flows
Authors: Tomasz M. Jankowski
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The basis of this paper is the assumption, that graviton is a measurable entity of molecular gravitational acceleration and this is not a hypothetical entity. The adoption of this assumption as an axiom is tantamount to fully opening the previously locked door to the boundary theory between laminar and turbulent flows. It leads to the theorem, that the division of flows of Newtonian (viscous) fluids into laminar and turbulent is true only, if the fluid is influenced by a powerful, external force field. The mathematical interpretation of this theorem, presented in this paper shows, that the boundary between laminar and turbulent flow can be determined theoretically. This is a novelty, because thus far the said boundary was determined empirically only and the reasons for its existence were unknown.Keywords: Freed gravitons, free gravitons.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14561012 Analysis of Permanence and Extinction of Enterprise Cluster Based On Ecology Theory
Authors: Ping Liu, Yongkun Li
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This paper is concerned with the permanence and extinction problem of enterprises cluster constituted by m satellite enterprises and a dominant enterprise. We present the model involving impulsive effect based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environment. Applying comparison theorem of impulsive differential equation, we establish sufficient conditions which ultimately affect the fate of enterprises: permanence, extinction, and co-existence. Finally, we present numerical examples to explain the economical significance of mathematical results.
Keywords: Enterprise cluster, permanence, extinction, impulsive, comparison theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14481011 A Sum Operator Method for Unique Positive Solution to a Class of Boundary Value Problem of Nonlinear Fractional Differential Equation
Authors: Fengxia Zheng, Chuanyun Gu
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By using a fixed point theorem of a sum operator, the existence and uniqueness of positive solution for a class of boundary value problem of nonlinear fractional differential equation is studied. An iterative scheme is constructed to approximate it. Finally, an example is given to illustrate the main result.Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14801010 Existence of Solutions for a Nonlinear Fractional Differential Equation with Integral Boundary Condition
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This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.
Keywords: Fractional differential equation, Integral boundary condition, Schauder fixed point theorem, Banach contraction principle.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16511009 The Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation Boundary Value Problem
Authors: Chuanyun Gu, Shouming Zhong
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In this paper, the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problem is concerned by a fixed point theorem of a sum operator. Our results can not only guarantee the existence and uniqueness of positive solution, but also be applied to construct an iterative scheme for approximating it. Finally, the example is given to illustrate the main result.
Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14851008 Validation of the Formal Model of Web Services Applications for Digital Reference Service of Library Information System
Authors: Zainab M. Musa, Nordin M. A. Rahman, Julaily A. Jusoh
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The web services applications for digital reference service (WSDRS) of LIS model is an informal model that claims to reduce the problems of digital reference services in libraries. It uses web services technology to provide efficient way of satisfying users’ needs in the reference section of libraries. The formal WSDRS model consists of the Z specifications of all the informal specifications of the model. This paper discusses the formal validation of the Z specifications of WSDRS model. The authors formally verify and thus validate the properties of the model using Z/EVES theorem prover.Keywords: Validation, verification, formal, theorem proving.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13161007 Almost Periodicity in a Harvesting Lotka-Volterra Recurrent Neural Networks with Time-Varying Delays
Authors: Yongzhi Liao
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By using the theory of exponential dichotomy and Banach fixed point theorem, this paper is concerned with the problem of the existence and uniqueness of positive almost periodic solution in a delayed Lotka-Volterra recurrent neural networks with harvesting terms. To a certain extent, our work in this paper corrects some result in recent years. Finally, an example is given to illustrate the feasibility and effectiveness of the main result.
Keywords: positive almost periodic solution, Lotka-Volterra, neural networks, Banach fixed point theorem, harvesting
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16151006 Effect of Birks Constant and Defocusing Parameter on Triple-to-Double Coincidence Ratio Parameter in Monte Carlo Simulation-GEANT4
Authors: F. Abubaker, F. Tortorici, M. Capogni, C. Sutera, V. Bellini
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This project concerns with the detection efficiency of the portable Triple-to-Double Coincidence Ratio (TDCR) at the National Institute of Metrology of Ionizing Radiation (INMRI-ENEA) which allows direct activity measurement and radionuclide standardization for pure-beta emitter or pure electron capture radionuclides. The dependency of the simulated detection efficiency of the TDCR, by using Monte Carlo simulation Geant4 code, on the Birks factor (kB) and defocusing parameter has been examined especially for low energy beta-emitter radionuclides such as 3H and 14C, for which this dependency is relevant. The results achieved in this analysis can be used for selecting the best kB factor and the defocusing parameter for computing theoretical TDCR parameter value. The theoretical results were compared with the available ones, measured by the ENEA TDCR portable detector, for some pure-beta emitter radionuclides. This analysis allowed to improve the knowledge of the characteristics of the ENEA TDCR detector that can be used as a traveling instrument for in-situ measurements with particular benefits in many applications in the field of nuclear medicine and in the nuclear energy industry.
Keywords: Birks constant, defocusing parameter, GEANT4 code, TDCR parameter.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5091005 Spline Basis Neural Network Algorithm for Numerical Integration
Authors: Lina Yan, Jingjing Di, Ke Wang
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A new basis function neural network algorithm is proposed for numerical integration. The main idea is to construct neural network model based on spline basis functions, which is used to approximate the integrand by training neural network weights. The convergence theorem of the neural network algorithm, the theorem for numerical integration and one corollary are presented and proved. The numerical examples, compared with other methods, show that the algorithm is effective and has the characteristics such as high precision and the integrand not required known. Thus, the algorithm presented in this paper can be widely applied in many engineering fields.
Keywords: Numerical integration, Spline basis function, Neural network algorithm
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2920