## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (192.977 recursos)

Journal of Applied Mathematics

1. #### Generation Expansion Models including Technical Constraints and Demand Uncertainty

Deossa, P.; De Vos, K.; Deconinck, G.; Espinosa, J.
This article presents a Generation Expansion Model of the power system taking into account the operational constraints and the uncertainty of long-term electricity demand projections. The model is based on a discretization of the load duration curve and explicitly considers that power plant ramping capabilities must meet demand variations. A model predictive control method is used to improve the long-term planning decisions while considering the uncertainty of demand projections. The model presented in this paper allows integrating technical constraints and uncertainty in the simulations, improving the accuracy of the results, while maintaining feasible computational time. Results are tested over three...

2. #### Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method

Agbolade, Olumuyiwa A.; Anake, Timothy A.
The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobatto collocation points were, respectively, chosen to collocate the approximate solution. Numerical experiments are performed on some sample problems already solved by homotopy analysis method and finite difference methods. Comparison of the absolute error is obtained from the present method and those from aforementioned methods. It is also observed that the absolute errors obtained are very low establishing convergence and computational efficiency.

3. #### Sparse Optimization of Vibration Signal by ADMM

Wanqing, Song
In this paper, the alternating direction method of multipliers (ADMM) algorithm is applied to the compressed sensing theory to realize the sparse optimization of vibration signal. Solving the basis pursuit problem for minimizing the $L1$ norm minimization under the equality constraints, the sparse matrix obtained by the ADMM algorithm can be reconstructed by inverse sparse orthogonal matrix inversion. This paper analyzes common sparse orthogonal basis on the reconstruction results, that is, discrete Fourier orthogonal basis, discrete cosine orthogonal basis, and discrete wavelet orthogonal basis. In particular, we will show that, from the point of view of central tendency, the discrete...

4. #### First Integrals and Hamiltonians of Some Classes of ODEs of Maximal Symmetry

Ndogmo, J. C.
Complete sets of linearly independent first integrals are found for the most general form of linear equations of maximal symmetry algebra of order ranging from two to eight. The corresponding Hamiltonian systems are constructed and it is shown that their general solutions can also be found by a simple superposition formula from the solutions of a scalar second-order source equation.

5. #### Bayesian Analysis for a Fractional Population Growth Model

Ariza-Hernandez, Francisco J.; Sanchez-Ortiz, Jorge; Arciga-Alejandre, Martin P.; Vivas-Cruz, Luis X.
We implement the Bayesian statistical inversion theory to obtain the solution for an inverse problem of growth data, using a fractional population growth model. We estimate the parameters in the model and we make a comparison between this model and an exponential one, based on an approximation of Bayes factor. A simulation study is carried out to show the performance of the estimators and the Bayes factor. Finally, we present a real data example to illustrate the effectiveness of the method proposed here and the pertinence of using a fractional model.

6. #### Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations

A new one-step block method with generalized three hybrid points for solving initial value problems of second-order ordinary differential equations directly is proposed. In deriving this method, a power series approximate function is interpolated at $\{{x}_{n},{x}_{n+r}\}$ while its second and third derivatives are collocated at all points $\{{x}_{n},{x}_{n+r},{x}_{n+s},{x}_{n+t},{x}_{n+\mathrm{1}}\}$ in the given interval. The proposed method is then tested on initial value problems of second-order ordinary differential equations solved by other methods previously. The numerical results confirm the superiority of the new method to the existing methods in terms of accuracy.

7. #### Numerical Solution of Second-Order Fredholm Integrodifferential Equations with Boundary Conditions by Quadrature-Difference Method

Jalius, Chriscella; Abdul Majid, Zanariah
In this research, the quadrature-difference method with Gauss Elimination (GE) method is applied for solving the second-order of linear Fredholm integrodifferential equations (LFIDEs). In order to derive an approximation equation, the combinations of Composite Simpson’s 1/3 rule and second-order finite-difference method are used to discretize the second-order of LFIDEs. This approximation equation will be used to generate a system of linear algebraic equations and will be solved by using Gauss Elimination. In addition, the formulation and the implementation of the quadrature-difference method are explained in detail. Finally, some numerical experiments were carried out to examine the accuracy of the proposed...

8. #### Axioms for Consensus Functions on the $n$ -Cube

Garcia-Martinez, C.; McMorris, F. R.; Ortega, O.; Powers, R. C.
A $p$ value of a sequence $\pi =({x}_{\mathrm{1}},{x}_{\mathrm{2}},\dots ,{x}_{k})$ of elements of a finite metric space $(X,d)$ is an element $x$ for which ${\sum }_{i=\mathrm{1}}^{k}{d}^{p}(x,{x}_{i})$ is minimum. The ${\mathcal{l}}_{p}$ –function with domain the set of all finite sequences on $X$ and defined by ${\mathcal{l}}_{p}(\pi )=\{x\text{:} x$ is a $p$ value of $\pi \}$ is called the ${\mathcal{l}}_{p}$ –function on $(X,d)$ . The ${\mathcal{l}}_{\mathrm{1}}$ and ${\mathcal{l}}_{\mathrm{2}}$ functions are the well-studied median and mean functions, respectively. In this note, simple characterizations of the ${\mathcal{l}}_{p}$ –functions on the $n$ -cube are given. In addition, the center function (using the minimax criterion) is characterized as...

9. #### Viscous Dissipation Effects on the Motion of Casson Fluid over an Upper Horizontal Thermally Stratified Melting Surface of a Paraboloid of Revolution: Boundary Layer Analysis

Ajayi, T. M.; Omowaye, A. J.; Animasaun, I. L.
The problem of a non-Newtonian fluid flow past an upper surface of an object that is neither a perfect horizontal/vertical nor inclined/cone in which dissipation of energy is associated with temperature-dependent plastic dynamic viscosity is considered. An attempt has been made to focus on the case of two-dimensional Casson fluid flow over a horizontal melting surface embedded in a thermally stratified medium. Since the viscosity of the non-Newtonian fluid tends to take energy from the motion (kinetic energy) and transform it into internal energy, the viscous dissipation term is accommodated in the energy equation. Due to the existence of internal...

10. #### On the Usefulness of Cooperation in $N$ Person Games

Nikolskii, Mikhail Sergeevich; Moussa, Aboubacar
The $N$ person games in which each player maximizes his payoff function are considered. We have studied an interesting question for the cooperative game theory about the usefulness of uniting the $N$ players in a union. The aim of such cooperation is for each player to get a positive increase to his guaranteed payoff. We have obtained some effective sufficient conditions under which the joining of the players in union is useful for each player. The linear case, specially, is being considered. In the second part of the paper, we have studied the question about the usefulness of cooperation of...

11. #### Uniqueness of Solutions to a Nonlinear Elliptic Hessian Equation

Li, Siyuan
Through an Alexandrov-Fenchel inequality, we establish the general Brunn-Minkowski inequality. Then we obtain the uniqueness of solutions to a nonlinear elliptic Hessian equation on ${\mathbb{S}}^{n}$ .

12. #### Theoretical Analysis of the Noise Power Ratio of Nonlinear Power Amplifiers

Kumar, Rajendra
This paper presents a theoretical analysis and derives the amplifier output noise power spectral density result in a closed form when the input to the amplifier is a band limited Gaussian noise. From the computed power spectral density the NPR is evaluated by a simple subtraction. The method can be applied to any amplifier with known input-output characteristics. The method may be applied to analyze various other important characteristics of the nonlinear amplifier such as spectral regrowth that refers to the spreading of the signal bandwidth when a band limited signal is inputted to the nonlinear amplifier. The paper presents...

13. #### A New Double Color Image Watermarking Algorithm Based on the SVD and Arnold Scrambling

Li, Ying; Wei, Musheng; Zhang, Fengxia; Zhao, Jianli
We propose a new image watermarking scheme based on the real SVD and Arnold scrambling to embed a color watermarking image into a color host image. Before embedding watermark, the color watermark image $W$ with size of $M\timesM$ is scrambled by Arnold transformation to obtain a meaningless image $\stackrel{~}{W}$ . Then, the color host image $A$ with size of $N\timesN$ is divided into nonoverlapping $N/M\timesN/M$ pixel blocks. In each $(i,j)$ pixel block ${A}_{i,j}$ , we form a real matrix ${C}_{i,j}$ with the red, green, and blue components of ${A}_{i,j}$ and perform the SVD of ${C}_{i,j}$ . We then replace the...

14. #### On Graceful Spider Graphs with at Most Four Legs of Lengths Greater than One

Panpa, A.; Poomsa-ard, T.
A graceful labeling of a tree $T$ with $n$ edges is a bijection $f:V(T)\to \{\mathrm{0,1},\mathrm{2},\dots ,n\}$ such that $\{|f(u)-f(v)|:uv\in E(T)\}$ equal to $\{\mathrm{1,2},\dots ,n\}$ . A spider graph is a tree with at most one vertex of degree greater than $\mathrm{2}$ . We show that all spider graphs with at most four legs of lengths greater than one admit graceful labeling.

15. #### A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices

Caswell, Hal; van Daalen, Silke F.
The vec operator transforms a matrix to a column vector by stacking each column on top of the next. It is useful to write the vec of a block-structured matrix in terms of the vec operator applied to each of its component blocks. We derive a simple formula for doing so, which applies regardless of whether the blocks are of the same or of different sizes.

16. #### The Order Classes of 2-Generator $p$ -Groups

Alhasanat, Mahmoud Bashir; Al-Hasanat, Bilal; Al-Sarairah, Eman
In order to classify a finite group using its elements orders, the order classes are defined. This partition determines the number of elements for each order. The aim of this paper is to find the order classes of 2-generator $p$ -groups of class 2. The results obtained here are supported by Groups, Algorithm and Programming (GAP).

17. #### Bounds on the Spectral Radius of a Nonnegative Matrix and Its Applications

Huang, Danping; You, Lihua
We obtain the sharp bounds for the spectral radius of a nonnegative matrix and then obtain some known results or new results by applying these bounds to a graph or a digraph and revise and improve two known results.

18. #### A Three-State Markov-Modulated Switching Model for Exchange Rates

Ayodeji, Idowu Oluwasayo
Several authors have examined the long swings hypothesis in exchange rates using a two-state Markov switching model. This study developed a model to investigate long swings hypothesis in currencies which may exhibit a $k$ -state $(k\ge \mathrm{2})$ pattern. The proposed model was then applied to euros, British pounds, Japanese yen, and Nigerian naira. Specification measures such as AIC, BIC, and HIC favoured a three-state pattern in Nigerian naira but a two-state one in the other three currencies. For the period January 2004 to May 2016, empirical results suggested the presence of asymmetric swings in naira and yen and long swings...

19. #### An Analytically Tractable Model for Pricing Multiasset Options with Correlated Jump-Diffusion Equity Processes and a Two-Factor Stochastic Yield Curve

Guillaume, Tristan
This paper shows how to value multiasset options analytically in a modeling framework that combines both continuous and discontinuous variations in the underlying equity or foreign exchange processes and a stochastic, two-factor yield curve. All correlations are taken into account, between the factors driving the yield curve, between fixed income and equity as asset classes, and between the individual equity assets themselves. The valuation method is applied to three of the most popular two-asset options.

20. #### A New Algorithm for Positive Semidefinite Matrix Completion

Xu, Fangfang; Pan, Peng
Positive semidefinite matrix completion (PSDMC) aims to recover positive semidefinite and low-rank matrices from a subset of entries of a matrix. It is widely applicable in many fields, such as statistic analysis and system control. This task can be conducted by solving the nuclear norm regularized linear least squares model with positive semidefinite constraints. We apply the widely used alternating direction method of multipliers to solve the model and get a novel algorithm. The applicability and efficiency of the new algorithm are demonstrated in numerical experiments. Recovery results show that our algorithm is helpful.

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