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Articles 61 - 90 of 158
Full-Text Articles in Applied Mathematics
On A-Ary Subdivision For Curve Design: I. 4-Point And 6-Point Interpolatory Schemes, Jian-Ao Lian
On A-Ary Subdivision For Curve Design: I. 4-Point And 6-Point Interpolatory Schemes, Jian-Ao Lian
Applications and Applied Mathematics: An International Journal (AAM)
The classical binary 4-point and 6-point interpolatery subdivision schemes are generalized to a-ary setting for any integer a greater than or equal to 3. These new a-ary subdivision schemes for curve design are derived easily from their corresponding two-scale scaling functions, a notion from the context of wavelets.
A Further Result On The Instability Of Solutions To A Class Of Non-Autonomous Ordinary Differential Equations Of Sixth Order, Cemil Tunç
Applications and Applied Mathematics: An International Journal (AAM)
The aim of the present paper is to establish a new result, which guarantees the instability of zero solution to a certain class of non-autonomous ordinary differential equations of sixth order. Our result includes and improves some well-known results in the literature.
Variational Iteration Method For Solving Initial And Boundary Value Problems Of Bratu-Type, Muhammad A. Noor, Syed T. Mohyud-Din
Variational Iteration Method For Solving Initial And Boundary Value Problems Of Bratu-Type, Muhammad A. Noor, Syed T. Mohyud-Din
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we present a reliable framework to solve the initial and boundary value problems of Bratu-type which are widely applicable in fuel ignition of the combustion theory and heat transfer. The algorithm rests mainly on a relatively new technique, the variational iteration method. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm.
Remarks On The Stability Of Some Size-Structured Population Models Ii: Changes In Vital Rates Due To Size And Population Size, Mohammed El-Doma
Remarks On The Stability Of Some Size-Structured Population Models Ii: Changes In Vital Rates Due To Size And Population Size, Mohammed El-Doma
Applications and Applied Mathematics: An International Journal (AAM)
The stability of some size-structured population dynamics models are investigated. We determine the steady states and study their stability. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. (2003) and El-Doma (2006).
Neural Network Models For Solving The Maximum Flow Problem, S. Effati, M. Ranjbar
Neural Network Models For Solving The Maximum Flow Problem, S. Effati, M. Ranjbar
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, two new neural network models for solving the maximum flow problem are presented. The maximum flow problem in networks is formulated as a special type of linear programming problem and it is solved by appropriately defined neural networks. The nonlinear neural networks are able to generate optimal solution for maximum flow problem. We solve neural network models by one of the numerical method. Finally, some numerical examples are provided for the sake of illustration.
Oscillatory Behavior Of Second Order Neutral Differential Equations With Positive And Negative Coefficients, Jelena Manojlović, Yutaka Shoukaku, Tomoyuki Tanigawa, Norio Yoshida
Oscillatory Behavior Of Second Order Neutral Differential Equations With Positive And Negative Coefficients, Jelena Manojlović, Yutaka Shoukaku, Tomoyuki Tanigawa, Norio Yoshida
Applications and Applied Mathematics: An International Journal (AAM)
Oscillation criteria are obtained for solutions of forced and unforced second order neutral differential equations with positive and negative coefficients. These criteria generalize those of Manojlović, Shoukaku, Tanigawa and Yoshida (2006).
A Comparison Of Several Algorithms And Models For Analyzing Multivariate Normal Data With Missing Responses, Mojtaba Ganjali, H. Ranji
A Comparison Of Several Algorithms And Models For Analyzing Multivariate Normal Data With Missing Responses, Mojtaba Ganjali, H. Ranji
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we compare some modern algorithms i.e. Direct Maximization of the Likelihood (DML), the EM algorithm, and Multiple Imputation (MI) for analyzing multivariate normal data with missing responses. We also compare two approaches for modeling incomplete data (1) ignoring missing data and (2) joint modeling of response and non-response mechanisms. Several types of Software which can be used to implement the above algorithms are also mentioned. We used these algorithms for a simulation study and to analyze a data set where outliers affect the parameter estimates and final conclusion. As the variance of the estimates cannot be obtained …
Signed Decomposition Of Fully Fuzzy Linear Systems, Tofigh Allahviranloo, Nasser Mikaeilvand, Narsis A. Kiani, Rasol M. Shabestari
Signed Decomposition Of Fully Fuzzy Linear Systems, Tofigh Allahviranloo, Nasser Mikaeilvand, Narsis A. Kiani, Rasol M. Shabestari
Applications and Applied Mathematics: An International Journal (AAM)
System of linear equations is applied for solving many problems in various areas of applied sciences. Fuzzy methods constitute an important mathematical and computational tool for modeling real-world systems with uncertainties of parameters. In this paper, we discuss about fully fuzzy linear systems in the form AX = b (FFLS). A novel method for finding the non-zero fuzzy solutions of these systems is proposed. We suppose that all elements of coefficient matrix A are positive and we employ parametric form linear system. Finally, Numerical examples are presented to illustrate this approach and its results are compared with other methods.
Some Applications Of Dirac's Delta Function In Statistics For More Than One Random Variable, Santanu Chakraborty
Some Applications Of Dirac's Delta Function In Statistics For More Than One Random Variable, Santanu Chakraborty
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we discuss some interesting applications of Dirac's delta function in Statistics. We have tried to extend some of the existing results to the more than one variable case. While doing that, we particularly concentrate on the bivariate case.
The Survivability Of Symmetrical Hierarchical Networks With Radial Reserve, Mohammad B. Ahmadi
The Survivability Of Symmetrical Hierarchical Networks With Radial Reserve, Mohammad B. Ahmadi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we shall consider the Symmetrical Hierarchical Network (SHN) and show that SHN possesses poor properties of survivability. There are several methods for raising the survivability of SHN. Here we consider the effectiveness of radial reserve to raise the survivability of SHN taking account of destruction of the main radial edges, and radial reserve.
Peristaltic Pumping Of A Non-Newtonian Fluid, Amit Medhavi
Peristaltic Pumping Of A Non-Newtonian Fluid, Amit Medhavi
Applications and Applied Mathematics: An International Journal (AAM)
The flow induced by sinusoidal peristaltic motion of the tube wall of a non-Newtonian fluid obeying Herschel-Bulkley equation (a general rheological equation that represents a powerlaw, Bingham and Newtonian fluid for particular choice of parameters) under long wavelength and low Reynolds number approximation is investigated. The results obtained for flow rate, pressure drop and friction force are discussed both qualitatively and quantitatively and compared with other related studies. It is found that the pressure drop increases with the flow rate and yield stress but decreases with the increasing amplitude ratio. The flow behaviour index shows significant impact on the magnitude …
Rethinking Pythagorean Triples, William J. Spezeski
Rethinking Pythagorean Triples, William J. Spezeski
Applications and Applied Mathematics: An International Journal (AAM)
It has been known for some 2000 years how to generate Pythagorean Triples. While the classical formulas generate all of the primitive triples, they do not generate all of the triples. For example, the triple (9, 12, 15) can’t be generated from the formulas, but it can be produced by introducing a multiplier to the primitive triple (3, 4, 5). And while the classical formulas produce the triple (3, 4, 5), they don’t produce the triple (4, 3, 5); a transposition is needed. This paper explores a new set of formulas that, in fact, do produce all of the triples …
Certain Expansion Formulae Involving A Basic Analogue Of Fox’S H-Function, S. D. Purohit, R. K. Yadav, S. L. Kalla
Certain Expansion Formulae Involving A Basic Analogue Of Fox’S H-Function, S. D. Purohit, R. K. Yadav, S. L. Kalla
Applications and Applied Mathematics: An International Journal (AAM)
Certain expansion formulae for a basic analogue of the Fox’s H-function have been derived by the applications of the q-Leibniz rule for the Weyl type q-derivatives of a product of two functions. Expansion formulae involving a basic analogue of Meijer’s G-function and MacRobert’s E-function have been derived as special cases of the main results.
The Square Threshold Problem In Number Fields, Matt Lafferty
The Square Threshold Problem In Number Fields, Matt Lafferty
All Theses
Let K be a degree n extension of Q, and let O_K be the ring of algebraic integers in K. Let x >= 2. Suppose we were to generate an ideal sequence by choosing ideals with norm at most x from O_K, independently and with uniform probability. How long would our sequence of ideals need to be before we obtain a subsequence whose terms have a product that is a square ideal in O_K? We show that the answer is about exp((2\ln(x)\ln\ln(x))^(1/2)).
The Weak Euler Scheme For Stochastic Delay Equations, Evelyn Buckwar, Rachel Kuske, Salah-Eldin A. Mohammed, Tony Shardlow
The Weak Euler Scheme For Stochastic Delay Equations, Evelyn Buckwar, Rachel Kuske, Salah-Eldin A. Mohammed, Tony Shardlow
Articles and Preprints
We study weak convergence of an Euler scheme for non-linear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The Euler scheme has weak order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay). The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.
Methods Of Assessing And Ranking Probable Sources Of Error, Nataniel Greene
Methods Of Assessing And Ranking Probable Sources Of Error, Nataniel Greene
Publications and Research
A classical method for ranking n potential events as sources of error is Bayes' theorem. However, a ranking based on Bayes' theorem lacks a fundamental symmetry: the ranking in terms of blame for error will not be the reverse of the ranking in terms of credit for lack of error. While this is not a flaw in Bayes' theorem, it does lead one to inquire whether there are related methods which have such symmetry. Related methods explored here include the logical version of Bayes' theorem based on probabilities of conditionals, probabilities of biconditionals, and ratios or differences of credit to …
A Monte Carlo Power Analysis Of Traditional Repeated Measures And Hierarchical Multivariate Linear Models In Longitudinal Data Analysis, Hua Fang, Gordon P. Brooks, Maria L. Rizzo, Kimberly A. Espy, Robert S. Barcikowski
A Monte Carlo Power Analysis Of Traditional Repeated Measures And Hierarchical Multivariate Linear Models In Longitudinal Data Analysis, Hua Fang, Gordon P. Brooks, Maria L. Rizzo, Kimberly A. Espy, Robert S. Barcikowski
Developmental Cognitive Neuroscience Laboratory: Faculty Publications
The power properties of traditional repeated measures and hierarchical linear models have not been clearly determined in the balanced design for longitudinal studies in the current literature. A Monte Carlo power analysis of traditional repeated measures and hierarchical multivariate linear models are presented under three variance-covariance structures. Results suggest that traditional repeated measures have higher power than hierarchical linear models for main effects, but lower power for interaction effects. Significant power differences are also exhibited when power is compared across different covariance structures. Results also supplement more comprehensive empirical indexes for estimating model precision via bootstrap estimates and the approximate …
Connectivity In Frame Matroids, Dan Slilaty, Hongxun Qin
Connectivity In Frame Matroids, Dan Slilaty, Hongxun Qin
Mathematics and Statistics Faculty Publications
We discuss the relationship between the vertical connectivity of a biased graph Ω and the Tutte connectivity of the frame matroid of Ω (also known as the bias matroid of Ω).
The Signed-Graphic Representations Of Wheels And Whirls, Dan Slilaty, Hongxun Qin
The Signed-Graphic Representations Of Wheels And Whirls, Dan Slilaty, Hongxun Qin
Mathematics and Statistics Faculty Publications
We characterize all of the ways to represent the wheel matroids and whirl matroids using frame matroids of signed graphs. The characterization of wheels is in terms of topological duality in the projective plane and the characterization of whirls is in terms of topological duality in the annulus.
Ordered Matrices Of Prescribed Row And Column Sum, Janine Janoski
Ordered Matrices Of Prescribed Row And Column Sum, Janine Janoski
All Theses
Let M(n,s) be the number of nxn matrices with binary entries, row and column sum s, and whose rows are in lexicographical order. Let S(n) be the number of nxn matrices with entries from {0,1,2}, symmetric, with trace 0, and row sum 2. (The sequence S(n) appears as A002137 in N.J.A. Sloane's Online Encyclopedia of Integer Sequences.)
We give two proofs to show that M(n,2)=S(n). First, we show they satisfy the same recurrence. Second, we give an explicit bijection between the two sets. We also show that the bijection maintains the cycle structure of our matrices.
Let M_s(n,2) be the …
Dow Jones Index, Garch(1,1) And Change-Points, Tharanga Wickramarachchi
Dow Jones Index, Garch(1,1) And Change-Points, Tharanga Wickramarachchi
All Theses
Many econometric time series data sets, such as log returns of stocks, exhibit evidence of the so called stylized facts. Namely it is generally observed that the data itself is uncorrelated with heavy tails, but the squared data has signicant autocorrelation. For such data sets, there appears to be little or no linear information in the past about the future values of the series. Thus the class of Autoregressive Integrated moving average models (ARIMA) are not appropriate. However, there does in general appear to be information in past values of the squared data about future values of the squared data. …
Caching And Distributing Statistical Analyses In R, Roger D. Peng
Caching And Distributing Statistical Analyses In R, Roger D. Peng
Johns Hopkins University, Dept. of Biostatistics Working Papers
We present the cacher package for \proglang{R}, which provides tools for caching statistical analyses and for distributing these analyses to others in an efficient manner. The cacher package takes objects created by evaluating R expressions and stores them in key-value databases. These databases of cached objects can subsequently be assembled into packages for distribution over the web. The cacher package also provides tools to help readers examine the data and code in a statistical analysis and reproduce, modify, or improve upon the results. In addition, readers can easily conduct alternate analyses of the data. We describe the design and implementation …
Traveling Waves And Shocks In A Viscoelastic Generalization Of Burgers' Equation, Victor Camacho '07, Robert D. Guy, Jon T. Jacobsen
Traveling Waves And Shocks In A Viscoelastic Generalization Of Burgers' Equation, Victor Camacho '07, Robert D. Guy, Jon T. Jacobsen
All HMC Faculty Publications and Research
We consider traveling wave phenomena for a viscoelastic generalization of Burgers' equation. For asymptotically constant velocity profiles we find three classes of solutions corresponding to smooth traveling waves, piecewise smooth waves, and piecewise constant (shock) solutions. Each solution type is possible for a given pair of asymptotic limits, and we characterize the dynamics in terms of the relaxation time and viscosity.
Yupanchis: La Matemática Inca Y Su Incorporación A La Clase, Yonit Bousany
Yupanchis: La Matemática Inca Y Su Incorporación A La Clase, Yonit Bousany
Independent Study Project (ISP) Collection
Este diálogo tuve con una estudiante de quinto grado de la escuela intercultural-bilingüe Wiñaypaq, a quien veía cada día luchando con la matemática. Sus respuestas señalan bastante sobre su experiencia escolar, especialmente porque, desafortunadamente, la mayoría de experiencias de niños quechua-hablantes en clases de matemática son indeseables en el Perú. Por una variedad de razones, niños peruanos quechua-hablantes raras veces suceden en alcanzar un nivel avanzado en el aprendizaje de las Matemáticas. Podemos atribuir este hecho a variables sociológicos, políticos, lingüísticos y/o económicos, pero no, como es una opinión popular, a una falta de una fuerte base de conceptos matemáticos …
Study Of Multibody Dynamics Using Matlab, Kalyani Soman
Study Of Multibody Dynamics Using Matlab, Kalyani Soman
Mechanical & Aerospace Engineering Theses & Dissertations
Research in computational dynamics has gained importance in the past few years because of the demand for analysis and simulation of various multi-body systems in the growing mechanical and aerospace industry. These multi-body systems are made of individual bodies that are interconnected via mechanical joints. Mathematically, these joints that connect the bodies can be described as constraint equations imposed upon the motions of the involved free bodies. This process will result in an equation of motion expressed in the form of a differential-algebraic equation. It is the main objective of this thesis to develop a solution algorithm that can take …
A Wavelet-Based Method For Overcoming The Gibbs Phenomenon, Nataniel Greene
A Wavelet-Based Method For Overcoming The Gibbs Phenomenon, Nataniel Greene
Publications and Research
The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities. Here we describe a numerical procedure for overcoming the Gibbs phenomenon called the inverse wavelet reconstruction method. The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series.
Estimation Of The Number Of Microbial Species Comprising A Population, Melanie R. Slattery
Estimation Of The Number Of Microbial Species Comprising A Population, Melanie R. Slattery
Theses and Dissertations
The purpose of this research was to evaluate the appropriateness of using non-parametric estimators, specifically the Chao1, ACES, and Jackknife methods, for estimation of the number of unique species comprising a population. It goes on to develop a parametric method for the above stated problem. This research consisted of creating diverse populations, with known numbers of species, and applying the aforementioned non-parametric and parametric methods to samples drawn from the constructed populations. The parametric fitting of several different distributions to the sample data, including the lognormal, gamma, and Weibull was considered. Both types of methodologies were then applied to sample …
Delay-Induced Instabilities In Self-Propelling Swarms, Eric Forgoston, Ira B. Schwartz
Delay-Induced Instabilities In Self-Propelling Swarms, Eric Forgoston, Ira B. Schwartz
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
We consider a general model of self-propelling particles interacting through a pairwise attractive force in the presence of noise and communication time delay. Previous work by Erdmann [Phys. Rev. E 71, 051904 (2005)] has shown that a large enough noise intensity will cause a translating swarm of individuals to transition to a rotating swarm with a stationary center of mass. We show that with the addition of a time delay, the model possesses a transition that depends on the size of the coupling amplitude. This transition is independent of the initial swarm state (traveling or rotating) and is characterized by …
Failure Of Metric Regularity For Major Classes Of Variational Systems, Boris S. Mordukhovich
Failure Of Metric Regularity For Major Classes Of Variational Systems, Boris S. Mordukhovich
Mathematics Research Reports
The paper is devoted to the study of metric regularity, which is a remarkable property of set-valued mappings playing an important role in many aspects of nonlinear analysis and its applications. We pay the main attention to metric regularity of the so- called parametric variational systems that contain, in particular, various classes of parameterized/perturbed variational and hemivariational inequalities, complementarity systems, sets of optimal solutions and corresponding Lagrange multipliers in problems of parametric optimization and equilibria, etc. Based on the advanced machinery of generalized differentiation1 we surprisingly reveal that metric regularity fails for certain major classes of parametric variational systems, which …
Hardware Algorithm Implementation For Mission Specific Processing, Jason W. Shirley
Hardware Algorithm Implementation For Mission Specific Processing, Jason W. Shirley
Theses and Dissertations
There is a need to expedite the process of designing military hardware to stay ahead of the adversary. The core of this project was to build reusable, synthesizeable libraries to make this a possibility. In order to build these libraries, Matlab® commands and functions, such as Conv2, Round, Floor, Pinv, etc., had to be converted into reusable VHDL modules. These modules make up reusable libraries for the Mission Specific Process (MSP) which will support AFRL/RY. The MSP allows the VLSI design process to be completed in a mere matter of days or months using an FPGA or ASIC design, as …