Search results for: Modigliani and Miller theorem

Authors: Fengxia Zheng, Chuanyun Gu

Abstract:

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.

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Authors: Meng Hu, Lili Wang

Abstract:

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.

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Authors: Yanling Zhu, Kai Wang

Abstract:

In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model.

Keywords: Predator-prey model, Holling II type functional response, positive periodic solution, coincidence degree theorem.

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Authors: Chuanyun Gu, Shouming Zhong

Abstract:

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

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Authors: Zainab M. Musa, Nordin M. A. Rahman, Julaily A. Jusoh

Abstract:

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.

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Authors: Yongzhi Liao

Abstract:

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

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Authors: Lina Yan, Jingjing Di, Ke Wang

Abstract:

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

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Authors: Xiaomei Wang, Shouming Zhong

Abstract:

In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known results. One example is given to show the feasibility and effectiveness of our results.

Keywords: Bi-directional associative memory (BAM) neural networks, mixed delays, Lyapunov stability theory, contraction mapping theorem, existence, equilibrium, globally exponential stability.

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Authors: Nadia M. G. AL-Sa'idi, Muhammad Rushdan Md. Sd., Adil M. Ahmed

Abstract:

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.

Keywords: Fuzzy metric space, Fuzzy fractal space, Multi fuzzy fractal space.

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Authors: Edem K. Bankas, Kazeem A. Gbolagade

Abstract:

In this paper, we propose a new efficient reverse converter for the 4-moduli set {2ⁿ, 2ⁿ + 1, 2ⁿ − 1, 2²ⁿ⁺¹ – 1} based on a modified Chinese Remainder Theorem and Mixed Radix Conversion. Additionally, the resulting architecture is further reduced to obtain a reverse converter that utilizes only carry save adders, a multiplexer and carry propagate adders. The proposed converter has an area cost of (12n + 2) FAs and (5n + 1) HAs with a delay of (9n + 6)t_FA + t_MUX. When compared with state of the art, our proposal demonstrates to be faster, at the expense of slightly more hardware resources. Further, the Area-Time square metric was computed which indicated that our proposed scheme outperforms the state of the art reverse converter.

Keywords: Modified Chinese Remainder Theorem, Mixed Radix Conversion, Reverse Converter, Carry Save Adder, Carry Propagate Adder.

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Authors: Yunquan Ke, Chunfang Miao

Abstract:

In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.

Keywords: Inertial neural networks, unbounded delay, fixed-point theorem, Lyapunov function, periodic solutions, exponential stability.

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Authors: Yongkun Li, Meng Hu

Abstract:

A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results. Based on the global Hopf bifurcation theorem for general functional differential equations, the global existence of periodic solutions is established.

Keywords: Predator-prey system, stage structure, time delay, HOPF bifurcation, periodic solution, stability.

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Authors: T. C. Kuo, Y. J. Huang, B. W. Hong

Abstract:

This paper proposes an adaptive sliding mode controller which combines adaptive control and sliding mode control to control a nonlinear robotic manipulator with uncertain parameters. We use an adaptive algorithm based on the concept of sliding mode control to alleviate the chattering phenomenon of control input. Adaptive laws are developed to obtain the gain of switching input and the boundary layer parameters. The stability and convergence of the robotic manipulator control system are guaranteed by applying the Lyapunov theorem. Simulation results demonstrate that the chattering of control input can be alleviated effectively. The proposed controller scheme can assure robustness against a large class of uncertainties and achieve good trajectory tracking performance.

Keywords: Robotic manipulators, sliding mode control, adaptive law, Lyapunov theorem, robustness.

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Authors: Mohd.F.Shabir, P. Tamilporai, B. Rajendra Prasath

Abstract:

The fundamental aim of extended expansion concept is to achieve higher work done which in turn leads to higher thermal efficiency. This concept is compatible with the application of turbocharger and LHR engine. The Low Heat Rejection engine was developed by coating the piston crown, cylinder head inside with valves and cylinder liner with partially stabilized zirconia coating of 0.5 mm thickness. Extended expansion in diesel engines is termed as Miller cycle in which the expansion ratio is increased by reducing the compression ratio by modifying the inlet cam for late inlet valve closing. The specific fuel consumption reduces to an appreciable level and the thermal efficiency of the extended expansion turbocharged LHR engine is improved. In this work, a thermodynamic model was formulated and developed to simulate the LHR based extended expansion turbocharged direct injection diesel engine. It includes a gas flow model, a heat transfer model, and a two zone combustion model. Gas exchange model is modified by incorporating the Miller cycle, by delaying inlet valve closing timing which had resulted in considerable improvement in thermal efficiency of turbocharged LHR engines. The heat transfer model, calculates the convective and radiative heat transfer between the gas and wall by taking into account of the combustion chamber surface temperature swings. Using the two-zone combustion model, the combustion parameters and the chemical equilibrium compositions were determined. The chemical equilibrium compositions were used to calculate the Nitric oxide formation rate by assuming a modified Zeldovich mechanism. The accuracy of this model is scrutinized against actual test results from the engine. The factors which affect thermal efficiency and exhaust emissions were deduced and their influences were discussed. In the final analysis it is seen that there is an excellent agreement in all of these evaluations.

Keywords: Low Heat Rejection, Miller cycle.

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Authors: Jenn-Yih Chen, Bean-Yin Lee, Yuan-Chuan Hsu, Jui-Cheng Lin, Kuang-Chyi Lee

Abstract:

In this paper, a sliding mode control method based on the passivity approach is proposed to control the position of surface-mounted permanent magnet synchronous motors (PMSMs). Firstly, the dynamics of a PMSM was proved to be strictly passive. The position controller with an adaptive law was used to estimate the load torque to eliminate the chattering effects associated with the conventional sliding mode controller. The stability analysis of the overall position control system was carried out by adopting the passivity theorem instead of Lyapunov-type arguments. Finally, experimental results were provided to show that the good position tracking can be obtained, and exhibit robustness in the variations of the motor parameters and load torque disturbances.

Keywords: Adaptive law, passivity theorem, permanent magnet synchronous motor, sliding mode control.

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Authors: Markus Kaiser, Johannes Buchmann

Abstract:

In this article we explore the application of a formal proof system to verification problems in cryptography. Cryptographic properties concerning correctness or security of some cryptographic algorithms are of great interest. Beside some basic lemmata, we explore an implementation of a complex function that is used in cryptography. More precisely, we describe formal properties of this implementation that we computer prove. We describe formalized probability distributions (σ-algebras, probability spaces and conditional probabilities). These are given in the formal language of the formal proof system Isabelle/HOL. Moreover, we computer prove Bayes- Formula. Besides, we describe an application of the presented formalized probability distributions to cryptography. Furthermore, this article shows that computer proofs of complex cryptographic functions are possible by presenting an implementation of the Miller- Rabin primality test that admits formal verification. Our achievements are a step towards computer verification of cryptographic primitives. They describe a basis for computer verification in cryptography. Computer verification can be applied to further problems in cryptographic research, if the corresponding basic mathematical knowledge is available in a database.

Keywords: prime numbers, primality tests, (conditional) probabilitydistributions, formal proof system, higher-order logic, formalverification, Bayes' Formula, Miller-Rabin primality test.

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Authors: Markus Kaiser, Johannes Buchmann

Abstract:

In this paper we explore the application of a formal proof system to verification problems in cryptography. Cryptographic properties concerning correctness or security of some cryptographic algorithms are of great interest. Beside some basic lemmata, we explore an implementation of a complex function that is used in cryptography. More precisely, we describe formal properties of this implementation that we computer prove. We describe formalized probability distributions (o--algebras, probability spaces and condi¬tional probabilities). These are given in the formal language of the formal proof system Isabelle/HOL. Moreover, we computer prove Bayes' Formula. Besides we describe an application of the presented formalized probability distributions to cryptography. Furthermore, this paper shows that computer proofs of complex cryptographic functions are possible by presenting an implementation of the Miller- Rabin primality test that admits formal verification. Our achievements are a step towards computer verification of cryptographic primitives. They describe a basis for computer verification in cryptography. Computer verification can be applied to further problems in crypto-graphic research, if the corresponding basic mathematical knowledge is available in a database.

Keywords: prime numbers, primality tests, (conditional) proba¬bility distributions, formal proof system, higher-order logic, formal verification, Bayes' Formula, Miller-Rabin primality test.

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Authors: Usha Sridhar, Sridhar Mandyam

Abstract:

We propose a multi-agent based utilitarian approach to model and understand information flows in social networks that lead to Pareto optimal informational exchanges. We model the individual expected utility function of the agents to reflect the net value of information received. We show how this model, adapted from a theorem by Karl Borch dealing with an actuarial Risk Exchange concept in the Insurance industry, can be used for social network analysis. We develop a utilitarian framework that allows us to interpret Pareto optimal exchanges of value as potential information flows, while achieving a maximization of a sum of expected utilities of information of the group of agents. We examine some interesting conditions on the utility function under which the flows are optimal. We illustrate the promise of this new approach to attach economic value to information in networks with a synthetic example.

Keywords: Borch's Theorem , Economic value of information, Information Exchange, Pareto Optimal Solution, Social Networks, Utility Functions

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Authors: A. Pouhassani

Abstract:

The aim of this paper is to exhibit some properties of local topologies of an IVS. Also, we Introduce ISG structure as an interesting structure of semigroups in IVSs.

Keywords: IVS, ISG, Local topology, Lebesgue number, Lindelof theorem

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Authors: Ruiheng Li, Amir Parsa Anvar, Amir M. Anvar, Tien-Fu Lu

Abstract:

High redundancy and strong uncertainty are two main characteristics for underwater robotic manipulators with unlimited workspace and mobility, but they also make the motion planning and control difficult and complex. In order to setup the groundwork for the research on control schemes, the mathematical representation is built by using the Denavit-Hartenberg (D-H) method [9]&[12]; in addition to the geometry of the manipulator which was studied for establishing the direct and inverse kinematics. Then, the dynamic model is developed and used by employing the Lagrange theorem. Furthermore, derivation and computer simulation is accomplished using the MATLAB environment. The result obtained is compared with mechanical system dynamics analysis software, ADAMS. In addition, the creation of intelligent artificial skin using Interlink Force Sensing ResistorTM technology is presented as groundwork for future work

Keywords: Manipulator System, Robot, AUV, Denavit- Hartenberg method Lagrange theorem, MALTAB, ADAMS, Direct and Inverse Kinematics, Dynamics, PD Control-law, Interlink Force Sensing ResistorTM, intelligent artificial skin system.

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Authors: Hao-Hsi Tseng, Hsin-Yun Lee

Abstract:

Adopting Most Advantageous Tender (MAT) for the government procurement projects has become popular in Taiwan. As time pass by, the problems of MAT has appeared gradually. People condemn two points that are the result might be manipulated by a single committee member’s partiality and how to make a fair decision when the winner has two or more. Arrow’s Impossibility Theorem proposed that the best scoring method should meet the four reasonable criteria. According to these four criteria this paper constructed an “Illegitimate Scores Checking Scheme” for a scoring method and used the scheme to find out the illegitimate of the current evaluation method of MAT. This paper also proposed a new scoring method that is called the “Standardizing Overall Evaluated Score Method”. This method makes each committee member’s influence tend to be identical. Thus, the committee members can scoring freely according to their partiality without losing the fairness. Finally, it was examined by a large-scale simulation, and the experiment revealed that the it improved the problem of dictatorship and perfectly avoided the situation of cyclical majorities, simultaneously. This result verified that the Standardizing Overall Evaluated Score Method is better than any current evaluation method of MAT.

Keywords: Arrow’s impossibility theorem, most advantageous tender, illegitimate scores checking scheme, standard score.

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Authors: Muhammad Liaquat Ali, Nasir-uddin Khan, Mushtaq Hussain, Asif Mansoor, Muhammad Shahid

Abstract:

Population in rural areas are scattered in the form of different villages or settlements. The proper selection of land to launch any educational or health activities to equally facilitate both the genders is the sticky situation, both for Govt. and Private organizations. Govt. spends substantial funds for the establishment of education institution/health centre at the place which is feasible and accessible to general public. However for specific gender, the gender population is also considered so that both the gender may be benefited equally. In this research, efforts have been made to illustrate how one can choose or locate the best central place/ area in Taluka Kunri of district Umerkot Sindh Pakistan where the Educational or Health activity is to be initiated. For the purpose the concept of centre of mass theorem is used as a tool to develop mathematical model, subsequently utilize in achieving the objectives.

Keywords: Centre of mass theorem, Establishment of technical/ vocational/ health care centre, Gender population of taluka Kunri of District Umerkot, Graphical interpretation of town committee/villages.

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Authors: D. Allison, A. Didenko, G. Miller

Abstract:

The link between coordinate transformations in the plane and their effects on the graph of a function can be difficult for students studying college level mathematics to comprehend. To solidify this conceptual link in the mind of a student Microsoft Excel can serve as a convenient graphing tool and pedagogical aid. The authors of this paper describe how various transformations and their related functional symmetry properties can be graphically displayed with an Excel spreadsheet.

Keywords: Mathematics education, Microsoft Excel spreadsheet, technology.

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Authors: Isaac Mugume, Charles Basalirwa, Daniel Waiswa, Triphonia Ngailo

Abstract:

Rainfall is a major climatic parameter affecting many sectors such as health, agriculture and water resources. Its quantitative prediction remains a challenge to weather forecasters although numerical weather prediction models are increasingly being used for rainfall prediction. The performance of six convective parameterization schemes, namely the Kain-Fritsch scheme, the Betts-Miller-Janjic scheme, the Grell-Deveny scheme, the Grell-3D scheme, the Grell-Fretas scheme, the New Tiedke scheme of the weather research and forecast (WRF) model regarding quantitative rainfall prediction over Uganda is investigated using the root mean square error for the March-May (MAM) 2013 season. The MAM 2013 seasonal rainfall amount ranged from 200 mm to 900 mm over Uganda with northern region receiving comparatively lower rainfall amount (200–500 mm); western Uganda (270–550 mm); eastern Uganda (400–900 mm) and the lake Victoria basin (400–650 mm). A spatial variation in simulated rainfall amount by different convective parameterization schemes was noted with the Kain-Fritsch scheme over estimating the rainfall amount over northern Uganda (300–750 mm) but also presented comparable rainfall amounts over the eastern Uganda (400–900 mm). The Betts-Miller-Janjic, the Grell-Deveny, and the Grell-3D underestimated the rainfall amount over most parts of the country especially the eastern region (300–600 mm). The Grell-Fretas captured rainfall amount over the northern region (250–450 mm) but also underestimated rainfall over the lake Victoria Basin (150–300 mm) while the New Tiedke generally underestimated rainfall amount over many areas of Uganda. For deterministic rainfall prediction, the Grell-Fretas is recommended for rainfall prediction over northern Uganda while the Kain-Fritsch scheme is recommended over eastern region.

Keywords: Convective parameterization schemes, March-May 2013 rainfall season, spatial variation of parameterization schemes over Uganda, WRF model.

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Authors: Wen-Fang Peng, Justie Su-Tzu Juan

Abstract:

The balanced Hamiltonian cycle problemis a quiet new topic of graph theorem. Given a graph G = (V, E), whose edge set can be partitioned into k dimensions, for positive integer k and a Hamiltonian cycle C on G. The set of all i-dimensional edge of C, which is a subset by E(C), is denoted as Ei(C).

Keywords: Hamiltonian cycle, balanced, Cartesian product.

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Authors: A. Basiri, S. Rahmany, D. Khatibi

Abstract:

The aim of this paper is to review some of standard fact on Miura curves. We give some easy theorem in number theory to define Miura curves, then we present a new implementation of Arita algorithm for Miura curves.

Keywords: Miura curve, discrete logarithm problem, algebraic curve cryptography, Jacobian group.

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Authors: Xiguang Li

Abstract:

In this paper , by using fixed point theorem , upper and lower solution-s method and monotone iterative technique , we prove the existence of maximum and minimum solutions of differential equations with delay , which improved and generalize the result of related paper.

Keywords: Banach space, boundary value problem, differential equation, delay.

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Authors: Yilun Shang

Abstract:

We consider a heterogeneously mixing SIR stochastic epidemic process in populations described by a general graph. Likelihood theory is developed to facilitate statistic inference for the parameters of the model under complete observation. We show that these estimators are asymptotically Gaussian unbiased estimates by using a martingale central limit theorem.

Keywords: statistic inference, maximum likelihood, epidemicmodel, heterogeneous mixing.

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Authors: A. Arockia Selvakumar, R. Sivaramakrishnan, Srinivasa Karthik.T.V, Valluri Siva Ramakrishna, B.Vinodh.

Abstract:

Industrial robots play a vital role in automation however only little effort are taken for the application of robots in machining work such as Grinding, Cutting, Milling, Drilling, Polishing etc. Robot parallel manipulators have high stiffness, rigidity and accuracy, which cannot be provided by conventional serial robot manipulators. The aim of this paper is to perform the modeling and the workspace analysis of a 3 DOF Parallel Manipulator (3 DOF PM). The 3 DOF PM was modeled and simulated using 'ADAMS'. The concept involved is based on the transformation of motion from a screw joint to a spherical joint through a connecting link. This paper work has been planned to model the Parallel Manipulator (PM) using screw joints for very accurate positioning. A workspace analysis has been done for the determination of work volume of the 3 DOF PM. The position of the spherical joints connected to the moving platform and the circumferential points of the moving platform were considered for finding the workspace. After the simulation, the position of the joints of the moving platform was noted with respect to simulation time and these points were given as input to the 'MATLAB' for getting the work envelope. Then 'AUTOCAD' is used for determining the work volume. The obtained values were compared with analytical approach by using Pappus-Guldinus Theorem. The analysis had been dealt by considering the parameters, link length and radius of the moving platform. From the results it is found that the radius of moving platform is directly proportional to the work volume for a constant link length and the link length is also directly proportional to the work volume, at a constant radius of the moving platform.

Keywords: Three Degrees of freedom Parallel Manipulator (3DOF PM), ADAMS, Work volume, MATLAB, AUTOCAD, Pappus- Guldinus Theorem.

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Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su

Abstract:

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.

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