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摘要:The most intense and catastrophic hurricanes on record to hit the Florida Keys during 1900 to 1950 were in 1919, and 1935. From 1950 to 2000, the most intense hurricanes to hit or affect the Florida Keys were in 1960, 1965, and 1992. In this paper, we will present a brief parametric analysis of the hurricanes that have hit the Florida Keys in the last 100 years. This analysis will include the descriptive statistics, best fit probability distribution of the latitude of the catastrophic hurricanes and a confidence interval that detects the average latitude of hurricanes (category 3 or higher) style="font-family:Verdana;">which style="font-family:Verdana;"> have hit the Florida Keys in the last 100 years....
摘要:A topological structural design approach is presented which is based upon the implementation of a two phase evolutionary optimization algorithm in conjunction with a finite element analysis code. The first phase utilizes a conventional genetic style="font-family:Verdana;">approach which performs a global search for the optimal design topology. Dual level material properties are specified within the genetic encoding and are applied to each individual element in the design mesh to represent either design material or a void. The second phase introduces style="font-family:Verdana;"> a style="font-family:Verdana;"> rule based refinement which allows for user design intent to accelerate the solution process and eliminate obvious design discrepancies resulting from the phase one search. A series of plate design problems are presented where the objective is to minimize the overall volume of the structure under predefined loading and constraint conditions. The constraints include both stress and deflection considerations where stress is calculated through the use of a commercial finite element package. The initial plate example incorporates a coarse mesh, but a gradual decrease in element size was employed for the remaining cases examined. Replacement of the phase one search with a set of randomly generated designs is demonstrated in order to form a greatly reduced design space which drastically increases the efficiency of the solution process. Comparison results are drawn between the conventional genetic algorithm and the two phase procedure....
摘要: style="text-align:justify;"> In this paper, the fluid examined was electrically conducting. The presence of a uniform transverse magnetic field at the plate was also taken into cognizance. The flow was governed by a modeled coupled nonlinear system of partial differential equations (PDEs) in dimensional form which was transformed into non-dimensional form using some non-dimensional variables. Explicit finite difference method (EFDM) was employed to approximate the fluid velocity, temperature and concentration. The effects of embedded thermo physical parameters of engineering interests on the flow quantities viz. velocity, temperature, concentration field presented through graphs were also examined through a series of numerical experiments and discussed. During the course of the numerical computations, it was found that heat generation has a tendency to enhance the fluid velocity as an opposite result is seen with chemical reaction parameter. A comparison was conducted of present results with the previous literature to show the accuracy of the results.
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摘要: style="text-align:justify;"> In this paper, we study the class of one-dimensional singular integrals that converge in the sense of Cauchy principal value. In addition, we present a simple method for approximating such integrals.
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摘要: style="text-align:justify;"> A Fast Fourier transform approach has been presented by Carr & Madan (2009) on a single underlying asset. In this current research paper, we present fast Fourier transform algorithm for the valuation of Multi-asset Options under Economic Recession Induced Uncertainties. The issue of multi-dimension in both finite and infinite case of Options is part of the focus of this research. The notion of economic recession was incorporated. An intuition behind the introduction of recession induced volatility uncertainty is revealed by huge volatility variation during the period of economic recession compared to the period of recession-free. Nigeria economic recession outbreak in 2016 and its effects on the uncertainty of the payoffs of Nigeria Stocks Exchange (NSE) among other investments was among the motivating factors for proposing economic recession induced volatility in options pricing. The application of the proposed Fast Fourier Transform algorithm in handling multi-assets options was shown. A new result on options pricing was achieved and capable of yielding efficient option prices during and out of recession. Numerical results were presented on assets in 3-dimensions as an illustration taking Black Scholes prices as a bench mark for method effectiveness comparison. The key findings of this research paper among other crucial contributions could be seen in computational procedure of options valuation in multi-dimensions and uncertainties in options payoffs under the exposure of economic recession.
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摘要: style="text-align:justify;"> We develop a dynamical model to understand the underlying dynamics of TUBERCULOSIS infection at population level. The model, which integrates the treatment of individuals, the infections of latent and recovery individuals, is rigorously analyzed to acquire insight into its dynamical features. The phenomenon resulted due to the exogenous infection of TUBERCULOSIS disease. The mathematical analysis reveals that the model exhibits a backward bifurcation when TB treatment remains of infected class. It is shown that, in the absence of treatment, the model has a disease-free equilibrium (DEF) which is globally asymptotically stable (GAS) and the associated reproduction threshold is less than unity. Further, the model has a unique endemic equilibrium (EEP), for a special case, whenever the associated reproduction threshold quantity exceeds unity. For a special case, the EEP is GAS using the central manifold theorem of Castillo-Chavez.
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摘要: style="text-align:justify;"> We present a fourth-order finite difference scheme for the Helmholtz equation in polar coordinates. We employ the finite difference format in the interior of the region and derive a nine-point fourth-order scheme. Specially, ghost points outside the region are applied to obtain the approximation for the Neumann boundary condition. We obtain the matrix form of the linear system and the sparsity of the coefficient matrix is favorable for the computation of the Helmholtz equation. The feasibility and accuracy of the method are validated by two test examples which have exact solutions.
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摘要: style="text-align:justify;"> The diagnosability of a multiprocessor system or an interconnection network is an important research topic. The system and an interconnection network have an underlying topology, which is usually presented by a graph. In this paper, we show proof for the g-good-neighbor diagnosability of the exchanged hypercube EH (s,t) under the PMC model and MM* model.
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摘要: style="text-align:justify;"> In this paper, we study the global regularity of the classical solution of the 2D incompressible magnetohydrodynamic equation with vertical dissipation and vertical magnetic dissipation. We show that any solution of the second component (u2, b2) has a global L2r -bound, where r satisfies src="Edit_c8e493af-5432-4efd-877a-4eeaad6c46fc.jpg" width="53" height="14" alt="" /> and the boundary does not grow faster than  src="Edit_ab64ca78-7019-4e9b-aa04-8acf4b040145.jpg" width="40" height="18" alt="" /> as r increases.
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摘要: style="text-align:justify;"> In this paper, we will establish a formula for calculating the 3144 coefficients coe(n, i) of the first hundred cyclotomic of index n in xi. We will only determine 1003 for an index n odd and a degree src="Edit_d01042e4-ce05-4f1a-b86f-92f22d811e94.jpg" width="50" height="32" alt="" /> . The others will be deduced, we’ll see how. The formula is src="Edit_48e2a59f-d74f-42e1-a652-a1462f8eda4e.jpg" width="130" height="35" alt="" /> , without exception if u(n)=-1 or if 4 doesn’t divide src="Edit_37249895-4092-4e0c-9a4f-25ed03f3b47f.jpg" width="40" height="23" alt="" /> and with its 165 exceptions of which 7 when u(n)=0 and 158 when u(n)=1 that will be shared in 154 and 4 pairs (n, i), which we will specify the conditions and values of the coefficients. According to u(n), according to the class of i modulo p, the first factor of the prime factor decomposition of n when u(n)=1 and according to gcd(n, i), the formula will or will not be valid and replaced otherwise by the good value that will be 0 for 152 pairs (n,i) or 1 in the 13 other exceptions.
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摘要: style="text-align:justify;"> In this article, the model of a non-Newtonian fluid (Thixotropic) flow past a vertical surface in the presence of exponential space and temperature dependent heat source in a thermally stratified medium is studied. It is assumed that free convection is induced by buoyancy and exponentially decaying internal heat source across the space. The dynamic viscosity is taken to be constant and thermal conductivity of this particular fluid model is assumed to vary linearly with temperature. Thermal stratification has been properly incorporated into the governing equation so that its effect can be revealed and properly reported. The governing partial differential equations describing the model are transformed and parameterized to a system of non-linear ordinary differential equation using similarity transformations. Approximate analytic solutions were obtained by adopting Optimal Homotopy Analysis Method (OHAM). The results show that for both cases of non-Newtonian parameters (Thixotropic) (K1=K2=0 & K1=K2=1.0), increasing stratification parameters, relate to decreasing in the heat energy entering into the fluid region and thus reducing the temperature of the Thixotropic fluid as it flows.
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摘要: style="text-align:justify;"> This paper focuses on the development of a hybrid method with block extension for direct solution of initial value problems (IVPs) of general third-order ordinary differential equations. Power series was used as the basis function for the solution of the IVP. An approximate solution from the basis function was interpolated at some selected off-grid points while the third derivative of the approximate solution was collocated at all grid and off-grid points to generate a system of linear equations for the determination of the unknown parameters. The derived method was tested for consistency, zero stability, convergence and absolute stability. The method was implemented with five test problems including the Genesio equation to confirm its accuracy and usability. The rate of convergence (ROC) reveals that the method is consistent with the theoretical order of the proposed method. Comparison of the results with some existing methods shows the superiority of the accuracy of the method.
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摘要: style="text-align:justify;"> In this paper we applicate the Hungarian algorithm for assignment problem to solve traveling salesman problem. Tree examples of application of algorithm are included.
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摘要: style="text-align:justify;"> A quasi-exactly solvable model refers to any second order differential equation with polynomial coefficients of the form A(x)y’’(x)+B(x)y’(x)+C(x)y(x)=0 where a pair of exact polynomials {y(x), C(x)} with respective degrees {deg[y]=n, deg[C]=p} are to be found simultaneously in terms of the coefficients of two given polynomials {A(x), B(x)}. The existing methods for solving quasi-exactly solvable models require the solution of a system of nonlinear algebraic equations of which the dimensions depend on n, the degree of the exact polynomial solution y(x). In this paper, a new method employing a set of polynomials, called canonical polynomials, is proposed. This method requires solving a system of nonlinear algebraic equations of which the dimensions depend only on p, the degree of C(x), and do not vary with n. Several examples are implemented to testify the efficiency of the proposed method.
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摘要: style="text-align:justify;"> It is well known that the full compressible Navier-Stokes equations with viscosity and heat conductivity coefficients of order of the Knudsen number ò>0 can be deduced from the Boltzmann equation via the Chapman-Enskog expansion. In this paper, we carry out the rigorous mathematical study of the compressible Navier-Stokes equation with the initial-boundary value problems. We construct the existence and most importantly obtain the higher regularities of the solutions of the full compressible Navier-Stokes system with weak viscosity and heat conductivity in a general bounded domain.
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摘要: style="text-align:justify;"> In this study we discuss the use of the simplex method to solve allocation problems whose flow matrices are doubly stochastic. Although these problems can be solved via a 0 - 1 integer programming method, H. W. Kuhn href="#ref1">[1] suggested the use of linear programming in addition to the Hungarian method. Specifically, we use the existence theorem of the solution along with partially total unimodularity and nonnegativeness of the incidence matrix to prove that the simplex method facilitates solving these problems. We also provide insights as to how a partition including a particular unit may be obtained.
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摘要:Introductory Statistics is a course taught in various community colleges, state colleges, and universities. Implementation of projects in this course has been shown to enhance students' learning; in addition to increasing the ability of educators to assess students' learning outcomes in detail. These projects are often inquiry-based and require a balance between flexibility and efficiency. Maintaining balance has provided the students' opportunities through exploration and learner autonomy. In exploration, a student seeks new methods and options through experimenting. In this paper, we will discuss the benefits of exploration required by projects given in an introductory statistics course. The details of five different projects discussed in this paper—illustrate the practical influence that they could have on higher statistics courses....
摘要:The paper is devised to combine the approximated semi-Lagrange weighted essentially non-oscillatory scheme and flux vector splitting. The approximated finite volume semi-Lagrange that is weighted essentially non-oscillatory scheme with Roe flux had been proposed. The methods using Roe speed to construct the flux probably generates entropy-violating solutions. More seriously, the methods maybe perform numerical instability in two-dimensional cases. A robust and simply remedy is to use a global flux splitting to substitute Roe flux. The combination is tested by several numerical examples. In addition, the comparisons of computing time and resolution between the classical weighted essentially non-oscillatory scheme (WENOJS-LF) and the semi-Lagrange weighted essentially non-oscillatory scheme (WENOEL-LF) which is presented (both combining with the flux vector splitting)....
摘要:In this article I conduct a short review of the proofs of the area inside a circle. These include intuitive as well as rigorous analytic proofs. This discussion is important not just from mathematical view point but also because pedagogically the calculus books still use circular reasoning today to prove the area inside a circle (also that of an ellipse) on this important historical topic, first illustrated by Archimedes. I offer an innovative approach through the introduction of a theorem, which will lead to proving the area inside a circle avoiding circular argumentation....
摘要:In this work, the peristaltic motion of a nano non-Newtonian fluid which obeys Carreau model through a porous medium inside an asymmetric channel is investigated. The hall current effects with Joule heating and viscous dissipation are considered. The problem is modulated mathematically by a set of nonlinear partial differential equations which describe the conservation of mass, momentum, energy and concentration of nanoparticles. The non-dimensional form of these equations is simplified under the assumption of long wavelength and low Reynolds number, and then resulting equations of coupled nonlinear differential equations are tackled numerically with appropriate boundary conditions. Graphical results are presented for dimensionless velocity, temperature, concentration and pressure gradient in order to illustrate the variations of various parameters of this problem on these obtained solutions....
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