Numerical Analysis and Computational Mathematics

We study the relationship between finite volume and mixed finite element methods for the the hyperbolic conservation laws, and the closely related convection-diffusion equations. A general framework is proposed for the derivation and a functional framework is developed which could allow the analysis of relating finite volume (FV) schemes. We show via two non-standard formulations, that numerous FV schemes, including

A common observation is that large groups of oscillatory biological units often have the ability to synchronize. A paradigmatic model of such behavior is provided by the Kuramoto model, which achieves synchronization through coupling of the phase dynamics of individual oscillators, while each oscillator maintains a different constant inherent natural frequency. Here we consider the biologically likely possibility that the oscillatory units may be capable of enhancing their synchronization ability by adaptive frequency dynamics. We propose a simple augmentation of the Kuramoto model which does this. We also show that, by the use of a previously developed technique [Ott and Antonsen, Chaos 18, 037113 (2008)], it is possible to reduce the resulting dynamics to a lower dimensional system for the macroscopic evolution of the oscillator ensemble. By employing this reduction, we investigate the dynamics of our system, finding a characteristic hysteretic behavior and enhancement of the qual...

Unto Others (UO) is an important book for all with a genuine interest in evolutionary biology, and right on target for everyone interested in human behavior. It is also of great relevance for those interested in the effects of the global human population increase, and the interaction of population and environment, aspects which will be emphasized in this review. UO is a truly interdisciplinary exploration of the paradox of explaining the existence of both the egoistic (i.e., selfish) and the altruistic (unselfish) behaviors and motives. UO draws upon data and arguments from biology, philosophy, psychology, and anthropology.

In this note we generalize an upper bound given in Guggenheimer et al. (College Math. J. 26(1) (1995) 2) for the condition number of a matrix as a function of the determinant, the Frobenius norm and of k singular values. If no singular value is known it is possible to derive an upper bound for the condition number applying lower and upper bounds for the product of a subset of singular values.

In this paper, we review decision support models for the design of global supply chains, and assess the fit between the research literature in this area and the practical issues of global supply chain design. The classification scheme for this review is based on ongoing and emerging issues in global supply chain management and includes review dimensions for (1) decisions addressed in the model, (2) performance metrics, (3) the degree to which the model supports integrated decision processes, and (4) globalization considerations. We conclude that although most models resolve a difficult feature associated with globalization, few models address the practical global supply chain design problem in its entirety. We close the paper with recommendations for future research in global supply chain modeling that is both forward-looking and practically oriented.

This article addresses the question of validating the homogeneous Lanchestrian square law of attrition by the use of historical data (and by extension, other attrition models). Validating an attrition model means testing that model against reality. In this case, Lanchester's square law is tested against the data from the Inchon-Seoul campaign of the Korean War. The data are examined using three analysis techniques: linear regression, the Akaike Information Criterion (AIC), and Bozdogan's Consistent AIC (CAIC). The data do not fit the assumption of a single, constant coefficient, homogeneous square law battle. The data do fit a set of three such battles (a new one every six or seven days); however, the data fit three constantcasualty-model battles just as well. The homogeneous Lanchester square law cannot be regarded as a proven attrition algorithm for warfare; however, the square law cannot be regarded as disproved either. Data on more battles are required to validate the square law or any other proposed attrition law. Q 1995 John Wiley & Sons, Inc.* Attrition is a euphemism for killing, wounding, destroying, or otherwise rendering hors de combat enemy personnel or equipment. Attrition is at the heart of every general discussion of warfare. Regardless of claims of prior or parallel discovery, Lanchester's equations for attrition provided the origin for modeling of attrition in the United States. Attrition models are referred to as extensions of the Lanchester "laws" or as replacements to those equations. Lanchester proposed that attrition could be mathematically modeled and stated his thoughts on the matter. With the advent of computers, models of warfare have become required in the decision process for research, development, and acquisition of weapons systems, for force mix decisions, and often for operational plans development. Decision makers realize that computer model results are factors for consideration rather than final answers; however, the model results still carry considerable weight in the decision processes.

Let ϕ denote Euler's phi function. For a fixed odd prime q we investigate the first and second order terms of the asymptotic series expansion for the number of n x such that q ∤ ϕ(n). Part of the analysis involves a careful study of the Euler-Kronecker constants for cyclotomic fields. In particular, we show that the Extended Riemann Hypothesis, the prime k-tuples conjecture and a conjecture of Ihara about the distribution of these Euler-Kronecker constants cannot be all true.

This paper considers the strategic routing of a fleet of unmanned combat aerial vehicles (UCAVs) to service a set of predetermined targets from a prior surveillance mission. Targets are characterized by their priority or importance level, and minimum and maximum service levels that, respectively, represent the lower bound of munitions for destruction and upper bound of munitions to limit collateral damage. Additional constraints to be respected are the payload capacities of the (possibly heterogeneous) UCAV fleet and the range based on fuel capacity and payload transported. The vital aspect of this paper is the integrated optimal utilization of available resources-weaponry and flight time-while allocating targets to UCAVs and sequencing them to maximize service to targets based on their criticality.

Any dynamic decision model needs to deal with conditional events and conditional uncertainty measures. Moreover, to avoid the introduction of not available information in decision processes, we should refer to domains containing only the elements of interest. According to the aforementioned guidelines we study the comparative uncertainty framework for decision models referring to possibility and necessity measures: we consider binary relations, defined on an arbitrary set of conditional events and we provide a complete characterization in terms of necessary and sufficient conditions for their representability by a conditional possibility and by a conditional necessity.

We study how changes to the composition and employment of the US Navy combat logistic force (CLF) influence our ability to supply our navy worldwide. The CLF consists of about 30 special transport ships that carry ship and aircraft fuel, ordnance, dry stores, and food, and deliver these to client combatant ships underway, making it possible for our naval forces to operate at sea for extended periods. We have modeled CLF operations to evaluate a number of transforming initiatives that simplify its operation while supporting an even larger number of client ships for a greater variety of missions. Our input is an employment schedule for navy battle groups of ships operating worldwide, extending over a planning horizon of 90-180 days. We show how we use optimization to advise how to sustain these ships. We have used this model to evaluate new CLF ship designs, advise what number of ships in a new ship class would be needed, test concepts for forward at-sea logistics bases in lieu of conventional ports, demonstrate the effects of changes to operating policy, and generally try to show whether and how the CLF can support planned naval operations.

We investigate the 3-edge coloring problem, based on the idea to give an algorithm, that attempts to minimize the use of color 4 (in a 4-edge coloring), and to study the factors that force it to fail. More specific, we introduce the notion of the ”position” of crossing points (or crossing edges) and the notion of the ”connection by bicolor paths”. A first result of this approach is that we can always assign a 4-edge coloring in a connected, bridgeless and cubic graph G using the fourth color only in crossing edges. Furthermore, color 4 is needed at most in half of these pairs of crossing edges. Finally, we bound the number of times color 4 is required in terms of the distance between the crossing points in the drawing of the graph.

In this paper, we consider the problem of computing the region visible to a query point located in a given polygonal domain. The polygonal domain is specified by a simple polygon with m holes and a total of n vertices. We provide two bounds on the complexity of this problem. One approach constructs a data structure with space complexity O (n 2) in time O (n 2 lg n) and yields a query time of O ((1 + min(m, |V (q)|)) lg 2 n + m + |V (q)|). Here, V (q) represents the set of vertices of the visibility polygon of a query point q, and |E| denotes the number of edges in the visibility graph. The other approach provides a data structure with space complexity O (min(|E|, mn) + n) in time O (T + |E| + n lg n) with the query time of O (|V (q)| lg n + m). Here, T is the time to triangulate the given polygonal region (which is O (n + m lg 1+ m) for a small positive constant > 0). In both of these approaches, O (m) additive factor in the query time is eliminated with an additional O ((min(|E|, mn)) 2) space and an additional O (m(min(|E|, mn)) 2) preprocessing time.

We develop a geometric approach to complexity based on the principle that complexity requires interactions at different scales of description. Complex systems are more than the sum of their parts of any size, and not just more than the sum of their elements. Using information geometry, we therefore analyze the decomposition of a system in terms of an interaction hierarchy. In mathematical terms, we present a theory of complexity measures for finite random fields using the geometric framework of hierarchies of exponential families. Within our framework, previously proposed complexity measures find their natural place and gain a new interpretation.

In the COVID-19 pandemic situation, the need to adopt cloud computing (CC) applications by education institutions, in general, and higher education (HE) institutions, in particular, has especially increased to engage students in an online mode and remotely carrying out research. The adoption of CC across various sectors, including HE, has been picking momentum in the developing countries in the last few years. In the Indian context, the CC adaptation in the HE sector (HES) remains a less thoroughly explored sector, and no comprehensive study is reported in the literature. Therefore, the aim of the present study is to overcome this research vacuum and examine the factors that impact the CC adoption (CCA) by HE institutions (HEIs) in India. The scope of the study is limited to public universities (PUs) in India. There are, in total, 465 Indian PUs and among these 304 PUs, (i.e., 65% PUs) are surveyed using questionnaire-based research. The study has put forth a novel integrated technology adoption framework consisting of the Technology Acceptance Model (TAM), Technology-Organization-Environment (TOE), and Diffusion of Innovation (DOI) in the context of the HES. This integrated TAM-TOE-DOI framework is utilized in the study to analyze eleven hypotheses concerning factors of CCA that have been tested using structural equation modelling (SEM) and confirmatory factor analysis (CFA). The findings reveal that competitive advantage (CA), technology compatibility (TC), technology readiness (TR), senior leadership support, security concerns, government support, and vendor support are the significant contributing factors of CCA by Indian PUs. The study contends that whereas the rest of the factors positively affect the PUs' intention towards CCA, security concerns are a significant reason for the reluctance of these universities against adopting CC. The findings demonstrated the application of an integrated TAM-TOE-DOI framework to assess determining factors of CCA in Indian PUs. Further, the study has given useful insights into the successful CCA by Indian PUs, which will facilitate eLearning and remote working during COVID-19 or similar outbreak.

The nonlinear Poisson-Boltzmann equation is solved in the region between a sphere and a plane, which models the electrolyte solution interface between the tip and the substrate in a scanning tunneling microscope. A finite difference method is used with the domain transformed into bispherical coordinates. Picard iteration with relaxation is used to achieve convergence for this highly nonlinear problem. An adsorbed molecule on the substrate can also be modelled by a superposition of a perturbing potential in a small region of the plane. An approximate analytical solution using a superposition of individual solutions for plane, the adsorbed molecule, and the sphere is also attempted. Results for cases of different potential values on the boundary surfaces and different distances of the sphere from the plane are presented. The results of the numerical method, the approximate analytical method, as well as the previous solutions of the linearized equation are compared.

We studied convolution properties of spirallike, starlike and convex functions, and some special cases of the main results are also pointed out. Further, we also obtained inclusion and convolution properties for some new subclasses on p-valent functions defined by using the Dziok-Srivastava operator.

The rapid development in the information technology field has introduced digital watermark technologies as a solution to prevent unauthorized copying and redistribution of data. This article introduces a self-embedded image verification and integrity scheme. The images are firstly split into dedicated segments of the same block sizes. Then, different Analytic Beta-Wavelet (ABW) orthogonal filters are utilized for embedding a self-segment watermark for image segment using a predefined method. ABW orthogonal filter coefficients are estimated to improve image reconstruction under different block sizes. We conduct a comparative study comparing the watermarked images using three kinds of ABW filters for block sizes 64 × 64, 128 × 128, and 256 × 256. We embed the watermark using the ABW-based image watermarking method in the 2-level middle frequency sub-bands of the ABW digital image coefficients. The imperceptibility and robustness of the ABW-based image watermarking method image is evaluated based on the Peak Signal to Noise Ratio (PSNR) and Correlation coefficient values. From the implementation results, we came to know that this ABW-based image watermarking method can withstand many image manipulations compared to other existing methods.

We study possible interrelations between the 300-year record of the yearly sunspot numbers and the solar inertial motion (SIM) using the recently developed technique of synchronization analysis. Phase synchronization of the sunspot cycle and the SIM is found and statistically confirmed in three epochs (1734-1790, 1855-1875 and 1907-1960) of the whole period 1700-2000. These results give quantitative support to the hypothesis that there is a weak interaction between the solar activity and the SIM.

Stable and efficient updates to the basis matrix factors are vital to the simplex method. The "best" updating method depends on the machine in use and how the update is implemented. For example, the classical product-form update can take advantage of the vector hardware on current supercomputers, and this helps compensate for its well-known drawbacks. Conversely, the method of Bartels and Golub performs well on conventional machines, but is difficult to vectorize.

Boundary value methods for the solution of differential-algebraic equations are described. We consider both initial and boundary value problems and derive an algorithm that does not require additional information from the user, but only the initial or boundary conditions needed in theory to obtain a unique solution.

The virtual warehouse (VW) is a state of real-time global visibility for logistics assets such as inventory and vehicles. The eciency of the VW is comparable to that achieved in a local warehouse facility. We assess the enabling technologies, develop a conceptual framework, and identify the essential decisionsupport modules of a virtual warehouse. A case study for ®eld repair service illustrates potential bene®ts of perfect information, in terms of reduced transportation, labor costs and service times. The case study pertains to ®eld logistics support for business telephone systems. The productivity and utilization of highly skilled ®eld technicians are improved substantially. A ®eld scrap policy supported by VW reduces the volume of returns to the repair depot by over 20%. Ó

The implementation of global optimization algorithms, using the arithmetic of infinity, is considered. A relatively simple version of implementation is proposed for the algorithms that possess the introduced property of strong homogeneity. It is shown that the P-algorithm and the one-step Bayesian algorithm are strongly homogeneous.

In this paper we address the issue of privacy preserving data mining. Specifically, we consider a scenario in which two parties owning confidential databases wish to run a data mining algorithm on the union of their databases, without revealing any unnecessary information. Our work is motivated by the need both to protect privileged information and to enable its use for research or other purposes.

We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness for two applications. First, the characterization yields a singular value formula for determining the nearest pencil whose eigenvalues lie in a specified region in the complex plane. For instance, this enables the numerical computation of the nearest stable descriptor system in control theory. Second, the characterization partially solves the problem posed in ] regarding the distance from a general rectangular pencil to the nearest pencil with a complete set of eigenvalues. The involved singular value optimization problems are solved by means of BFGS and Lipschitz-based global optimization algorithms.

In Part I of this series of articles, we introduced a general framework of exploiting the aggregate sparsity pattern over all data matrices of large scale and sparse semidefinite programs (SDPs) when solving them by primal-dual interior-point methods. This framework is based on some results about positive semidefinite matrix completion, and it can be embodied in two different ways. One is by a conversion of a given sparse SDP having a large scale positive semidefinite matrix variable into an SDP having multiple but smaller positive semidefinite matrix variables. The other is by incorporating a positive definite matrix completion itself in a primal-dual interior-point method. The current article presents the details of their implementations. We introduce new techniques to deal with the sparsity through a clique tree in the former method and through new computational formulae in the latter one. Numerical results over different classes of SDPs show that these methods can be very efficient for some problems.

The concept of a Morse decomposition consisting of nonautonomous sets is reviewed for linear cocycle mappings w.r.t. to past, future and all-time convergences. In each case, the set of accumulation points of the finite-time Lyapunov exponents corresponding to points in a nonautonomous set is shown to be an interval. For a finest Morse decomposition, the Morse spectrum is defined as the union of all of the above accumulation point intervals over the different nonautonomous sets in such a finest Morse decomposition. In addition, Morse spectrum is shown to be independent of which finest Morse decomposition is used, when more than one exists.

We study the multivariate approximation by certain partial sums (hyperbolic wavelet sums) of wavelet bases formed by tensor products of univariate wavelets. We characterize spaces of functions which have a prescribed approximation error by hyperbolic wavelet sums in terms of a K -functional and interpolation spaces. The results parallel those for hyperbolic trigonometric cross approximation of periodic functions [DPT].

A multicompartment mathematical model is presented with the goal of studying the role of dose-dense protocols in the context of combination cancer chemotherapy. Dose-dense protocols aim at reducing the period between courses of chemotherapy from three to two weeks or less, in order to avoid the regrowth of the tumor during the meantime and achieve maximum cell kill at the end of the treatment. Inspired by clinical trials, we carry out a randomized computational study to systematically compare a variety of protocols using two drugs of different specificity. Our results suggest that cycle specific drugs can be administered at low doses between courses of treatment to arrest the relapse of the tumor. This might be a better strategy than reducing the period between cycles.

In this paper, we study a multi-period portfolio selection model in which a generic class of probability distributions is assumed for the returns of the risky asset. An investor with a power utility function rebalances a portfolio comprising a risk-free and risky asset at the beginning of each time period in order to maximize expected utility of terminal wealth. Trading the risky asset incurs a cost that is proportional to the value of the transaction. At each time period, the optimal investment strategy involves buying or selling the risky asset to reach the boundaries of a certain no-transaction region. In the limit of small transaction costs, dynamic programming and perturbation analysis are applied to obtain explicit approximations to the optimal boundaries and optimal value function of the portfolio at each stage of a multi-period investment process of any length.

In the area of broad-band antenna array signal processing, the global minimum of a quadratic equality constrained quadratic cost minimization problem is often required. The problem posed is usually characterized by a large optimization space (around 50-90 tuples), a large number of linear equality constraints, and a few quadratic equality constraints each having very low rank quadratic constraint matrices. Two main difficulties arise in this class of problem. Firstly, the feasibility region is nonconvex and multiple local minima abound. This makes conventional numerical search techniques unattractive as they are unable to locate the global optimum consistently (unless a finite search area is specified). Secondly, the large optimization space makes the use of decision-method algorithms for the theory of the reals unattractive. This is because these algorithms involve the solution of the roots of univariate polynomials of order to the square of the optimization space. In this paper we present a new algorithm which exploits the structure of the constraints to reduce the optimization space to a more manageable size. The new algorithm relies on linear-algebra concepts, basic optimization theory, and a multivariate polynomial root-solving tool often used by decision-method algorithms.

A new nonlinear integral-equation model is derived in terms of hodograph variables for free-surface flow past an arbitrary bottom obstruction. A numerical method, carefully chosen to solve the resulting nonlinear algebraic equations and a simple, yet effective radiation condition have led to some very encouraging results. In this paper, results are presented for a semi-circular obstruction and are compared with

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

Surface reconstruction from large unorganized data sets is very challenging, especially if the data present undesired holes. This is usually the case when the data come from laser scanner 3D acquisitions or if they represent damaged objects to be restored. An attractive field of research focuses on situations in which these holes are too geometrically and topologically complex to fill using triangulation algorithms. In this work a local approach to surface reconstruction from point-clouds based on positive definite Radial Basis Functions (RBF) is presented that progressively fills the holes by expanding the neighbouring information. The method is based on the algorithm introduced in [7] which has been successfully tested for the smooth multivariate interpolation of large scattered data sets. The local nature of the algorithm allows for real time handling of large amounts of data, since the computation is limited to suitable small areas, thus avoiding the critical efficiency problem involved in RBF multivariate interpolation. Several tests on simulated and real data sets demonstrate the efficiency and the quality of the reconstructions obtained using the proposed algorithm.