Search

This paper presents a semester-long bottle design project for an undergraduate Numerical Analysis course. Students implement numerical methods in MATLAB to design and 3D print a bottle. Employing mathematical methods to compute features of their designs enhances students' understanding of numerical techniques in design applications. Student feedback highlights the project's efficacy in demonstrating the intersection of mathematics and design, fostering creativity, and instilling a deeper appreciation for mathematical principles in real-world contexts. [ABSTRACT FROM AUTHOR]

Abstract. In this paper, we study the interpolation properties of anisotropic net spaces Np,q(M), where p = (p1; ...., pn), q = (q1 ...., qn). It is shown that, with respect to the multidimensional interpolation method, the following equality holds [ABSTRACT FROM AUTHOR]

Network modeling in electromagnetics is an effective technique in treating scattering problems by canonical and complex structures. Geometries constituted of angular regions (wedges) together with planar layers can now be approached with the Generalized Wiener-Hopf Technique supported by network representation in spectral domain. Even if the network representations in spectral planes are of great importance by themselves, the aim of this paper is to present a theoretical base and a general procedure for the formulation of complex scattering problems using network representation for the Generalized Wiener Hopf Technique starting basically from the wave equation. In particular while the spectral network representations are relatively well known for planar layers, the network modelling for an angular region requires a new theory that will be developed in this paper. With this theory we complete the formulation of a network methodology whose effectiveness is demonstrated by the application to a complex scattering problem with practical solutions given in terms of GTD/UTD diffraction coefficients and total far fields for engineering applications. The methodology can be applied to other physics fields. [ABSTRACT FROM AUTHOR]

This paper mainly considered the finite-time lag synchronization for two-layer complex networks with impulsive effects. Different types of controllers were designed to achieve the lag synchronization of two-layer complex networks. Several sufficient conditions on lag synchronization in the sense of finite time were derived. The time for synchronization was also estimated. It is important to note that synchronization time was influenced by the initial value, as well as the impulses and impulse sequence. This implied that different impulse effects result in varying synchronization times. Additionally, desynchronizing impulses can extend the synchronization time, whereas synchronizing impulses have the opposite effect. Finally, a numerical example was presented to showcase the practicality and validity of the proposed theoretical criteria. [ABSTRACT FROM AUTHOR]

This paper discussed the synchronization of impulsive fuzzy neural networks (FNNs) with uncertainty of information exchange. Since the data of neural networks (NNs) cannot be completely measured in reality, we designed an observer-based impulsive controller on the basis of the partial measurement results and achieved the purpose of reducing the communication load and the controller load of FNNs. In terms of the Lyapunov stability theory, an impulsive augmented error system (IAES) was established and two sufficient criteria to guarantee the synchronization of our FNNs system were obtained. Finally, we demonstrated the validity of the results by a numerical example. [ABSTRACT FROM AUTHOR]

Traffic congestion in freeway network is a prevalent transportation problem and leads to a strong degradation of freeway network facilities. This paper proposes a new coordinated optimization approach for freeway network, aiming to relieve the traffic congestion in freeway network equipped with the coordinated traffic controllers. The challenge is how to solve the problem between the traffic control goals of each path and those of the network. In this paper, the bi-level programming theory is used to address this problem. More exactly, in the path level, the optimal control model is designed to relieve congestion in each path of the test network. Furthermore, in the network level, the optimal model considers the traffic equilibrium and cost optimization. The efficiency of the proposed approach is tested on a well-known traffic network calibrated by the field test data of freeway network. The results show that the proposed approach has positive effects in balancing traffic load and improving the service level of freeway networks. [ABSTRACT FROM AUTHOR]

In this paper, a class of matrices, namely, Drazin-dagger ma- trices, in which the Drazin inverse and the Moore-Penrose inverse com- mute, is introduced. Also, some properties of the generalized inverses of these matrices, are investigated. Moreover, some results about the Moore- Penrose inverse, the Drazin inverse and the numerical range of some re- ciprocal matrices are obtained. In particular, the relations between re- ciprocal matrices, Drazin-Dagger matrices and star order are established. Also, some properties of the generalized inverses of the conjugate EP ma- trices are studied. To illustrate the results, some numerical examples are also given. [ABSTRACT FROM AUTHOR]

Despite the variety of methods available to solve nonlinear optimal control problems, numerical methods are still evolving to solve these problems. This paper deals with the numerical solution of nonlinear optimal control affine problems by the interpolated variational iteration method, which was introduced in 2016 to improve the variational iteration method. For this purpose, the optimality conditions are first derived as a two-point boundary value problem and then converted to an initial value problem with the unknown initial values for costates. The speed and convergence of the method are compared with the existing methods in the form of three examples, and the initial values of the costates are obtained by an efficient technique in each iteration. [ABSTRACT FROM AUTHOR]

The construction of weak solutions to compressible Navier–Stokes equations via a numerical method (including a rigorous proof of the convergence) is in a short supply, and so far, available only for one sole numerical scheme suggested in Karper (Numer Math, 125(3):441–510, 2013) for the no slip boundary conditions and the isentropic pressure with adiabatic coefficient γ > 3 . Here we consider the same problem for the general non zero inflow–outflow boundary conditions, which is definitely more appropriate setting from the point of view of applications, but which is essentially more involved as far as the existence of weak solutions is concerned. There is a few recent proofs of existence of weak solutions in this setting, but none of them is performed via a numerical method. The goal of this paper is to fill this gap. The existence of weak solutions on the continuous level requires several tools of functional and harmonic analysis and differential geometry whose numerical counterparts are not known. Our main strategy therefore consists in rewriting of the numerical scheme in its variational form modulo remainders and to apply and/or to adapt to the new variational formulation the tools developed in the theoretical analysis. In addition to the result, which is new, the synergy between numerical and theoretical analysis is the main originality of the present paper. [ABSTRACT FROM AUTHOR]

Subdivision schemes are widely used in numerical mathematics such as signal/image approximation, analysis and control of data or numerical analysis. However, to develop their full power, subdivision schemes should be incorporated into a multiresolution analysis that, mimicking wavelet analyses, provides a multi-scale decomposition of a function, a curve, or a surface. The ingredients needed to define a multiresolution analysis associated to a subdivision scheme are a decimation scheme and detail operators. Their construction is not straightforward as soon as the subdivision scheme is non-interpolatory. This paper is devoted to the construction of decimation schemes and detail operators compatible with general subdivision schemes, including non-linear ones. Analysis of the performances of the constructed analyses is carried out. Some numerical applications are presented in the framework of image approximation. [ABSTRACT FROM AUTHOR]

Numerical literacy refers to the knowledge and ability to use various numbers and basic mathematical symbols to solve problems, while math self-concept means the assessment of students' skills, abilities, enjoyment, and interest in the subject. However, children with special needs and normal students in inclusive Elementary Schools are yet to sufficiently acquire learning that accommodates literacy and maths self-concept. This causes a need for the implementation of a children-friendly learning process. Therefore, this study aimed to identify the factors influencing the numeracy level and math self-concept, and also explore the obstacles in implementing children-friendly learning in order to facilitate students' abilities. A qualitative method was applied because of in-depth data exploration regarding children with special needs, while the utilized instruments include tests, questionnaires, and interviews. Both the data collected and the analysis are qualitative, which are obtained through excavation, identification, and description. Consequently, this paper was able to (a) describe the factors influencing the numeracy level and math self-concept in inclusive elementary schools; (b) explore the barriers to implementing children-friendly learning; and (c) identify the relationship between students' numeracy and math self-concept. [ABSTRACT FROM AUTHOR]

In this paper, fast fixed-time (FDT) synchronization of T--S fuzzy (TSF) complex networks (CNs) is considered. The given control schemes can make the CNs synchronize with the given isolated system more fleetly than the most of existing results. By constructing comparison system and applying new analytical techniques, sufficient conditions are established to derive fast FDT synchronization speedily. In order to give some comparisons, FDT synchronization of the considered CNs is also presented by designing FDT fuzzy controller. Numerical examples are given to illustrate our new results. [ABSTRACT FROM AUTHOR]

Linear operators with off‐diagonal decay appear in many areas of mathematics including harmonic and numerical analysis, and their stability is one of the basic assumptions. In this paper, we consider a family of localized integral operators in the Beurling algebra with kernels having mild singularity near the diagonal and certain Hölder continuity property, and prove that their weighted stabilities for different exponents and Muckenhoupt weights are equivalent to each other on a space of homogeneous type with Ahlfors regular measure. [ABSTRACT FROM AUTHOR]

This paper introduces a novel nonlocal partial difference equation (G-PDE) for labeling metric data on graphs. The G-PDE is derived as a nonlocal reparametrization of the assignment flow approach that was introduced in [J. Math. Imaging Vision, 58 (2017), pp. 211-238]. Due to this parameterization, solving the G-PDE numerically is shown to be equivalent to computing the Riemannian gradient flow with respect to a nonconvex potential. We devise an entropy-regularized difference of convex (DC) functions decomposition of this potential and show that the basic geometric Euler scheme for integrating the assignment flow is equivalent to solving the G-PDE by an established DC programming scheme. Moreover, the viewpoint of geometric integration reveals a basic way to exploit higher-order information of the vector field that drives the assignment flow, in order to devise a novel accelerated DC programming scheme. A detailed convergence analysis of both numerical schemes is provided and illustrated by numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper the probability of ruin is investigated under the influence of a premium rate which varies according to the intensity of claims, and the occurrence of claims is described by a Cox process in the considered risk model. The idea is originally enlightened by Jasiulewicz (2001). We make a slight modification on the model and a generalization on the intensity process. By a "backward differential argument" and the Markov property of the intensity process we strictly derive the integral equation satisfied by the probability of ruin. Further, we solve the equation when the intensity process is a homogeneous n -state Markov process by Laplace transforms. At the end of the paper, an example is given. [ABSTRACT FROM AUTHOR]

The paper investigates how the order of numerical data in word problems on division of a whole into unequal parts affects achievement and reasoning of 14-16-year old pupils. The variable was altered in two word problems, in one of which also the context was changed (psychological variable) and in the latter "if-clause" is or is not used (linguistic variable). 182 pupils were involved in the experiment. The solutions were analysed quantitatively using Item Response Theory as well as qualitatively. The data suggest that pupils' success is affected by the order of numerical data in the statement in an unfamiliar context. The presence of "if-clause" in the statement was studied in a two-level problem. The order of numerical data played its role in case of formulations without "if". The results of the experiment are of interest for mathematics education as well as for construction of tests. The paper is an extended version of the paper by Novotná (2018). [ABSTRACT FROM AUTHOR]

Wind and temperature data are important parameters in aircraft performance studies. The lack of accurate measurements of these parameters forces researchers to rely on numerical weather prediction models, which are often filtered for a larger area with decreased local accuracy. Aircraft, however, also transmit information related to weather conditions, in response to interrogation by air traffic controller surveillance radars. Although not intended for this purpose, aircraft surveillance data contains information that can be used for weather models. This paper presents a method that can be used to reconstruct a weather field from surveillance data that can be received with a simple 1090 MHz receiver. Throughout the paper, we answer two main research questions: how to accurately infer wind and temperature from aircraft surveillance data, and how to reconstruct a real-time weather grid efficiently. We consider aircraft as moving sensors that measure wind and temperature conditions indirectly at different locations and flight levels. To address the first question, aircraft barometric altitude, ground velocity, and airspeed are decoded from down-linked surveillance data. Then, temperature and wind observations are computed based on aeronautical speed conversion equations. To address the second question, we propose a novel Meteo-Particle (MP) model for constructing the wind and temperature fields. Short-term local prediction is also possible by employing a predictor layer. Using an unseen observation test dataset, we are able to validate that the mean absolute errors of inferred wind and temperature using MP model are 67% and 26% less than using the interpolated model based on GFS reanalysis data. [ABSTRACT FROM AUTHOR]

Hessenberg matrices frequently arise in many application areas and have been attracted much attention in recent years. In the current paper, we present two numerical algorithms of $$O(n^2)$$ for computing the determinant of an n-by- n general Hessenberg matrix. The algorithms are all suited for implementation using Computer Algebra Systems such as MATLAB and MAPLE. Some numerical examples are provided in order to demonstrate the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, the initial condition independence property of Grünwald-Letnikov fractional difference is revealed for the first time. For example, the solution x(k) of equation Ga..., cannot be calculated with initial condition x(a). First, the initial condition independence property is carefully investigated in both time domain and frequency domain. Afterwards, some possible schemes are formulated to make the considered system connect to initial condition. Armed with this information, the concerned property is examined on three modified Grünwald-Letnikov definitions. Finally, results from illustrative examples demonstrate that the developed schemes are sharp. [ABSTRACT FROM AUTHOR]

In this paper, the fast synchronization problem of 5D Hindmarsh-Rose neuron networks is studied. Firstly, the global predefined-time stability of a class of nonlinear dynamical systems is investigated under the complete beta function. Then an active controller via backstepping design is proposed to achieve predefined-time synchronization of two 5D Hindmarsh-Rose neuron networks in which the synchronization time of each state variable of the master-slave 5D Hindmarsh-Rose neuron networks is different and can be defined in advance, respectively. To show the applicability of the obtained theoretical results, the designed predefined-time backstepping controller is applied to secure communication to realize asynchronous communication of multiple different messages. Three numerical simulations are provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, based on the accelerated over relaxation (AOR) iteration method, a generalization of the AOR iteration method is presented to solve the absolute value equations (AVE), which is called the GAOR method. The convergence conditions of the GAOR method are obtained. Numerical experiments are presented in order to verify the feasibility of the GAOR method. [ABSTRACT FROM AUTHOR]

Price inflation has outbalanced the income of residents and buyers in major post-industrial city-regions, and real estate has become an important driver of these inequalities. In a context of a resilient inflation of home values during the last two decades in the greater Paris Region, it is critical to examine housing price dynamics to get a better understanding of socioeconomic segregation. This paper aims at presenting spatial analysis of the dynamics of segregation pertaining to inflation, analyzing price and sellers and buyers data. Using interpolation techniques and multivariate analysis, the paper presents a spatial analysis of property-level data from the Paris Chamber of Notaries (1996-2012) in a GIS (159,000 transactions in suburban areas, single family homes only). Multivariate analysis capture price change and local trajectories of occupational status, i.e. changes in balance between inward and outward flows of sellers and buyers. We adopt a method that fits the fragmented spatial patterns of suburbanization. To do so, we remove the spatial bias by means of a regular 1-km spatial grid, interpolating the variables within it, using a time-distance matrix. The main results are threefold. We document the spatial patterns of professionalization (a rise of executives, intermediate occupation and employees) to describe the main trends of inward mobility in property ownership in suburbs, offsetting the outward mobility of retired persons. Second, neighborhood trajectories are related the diverging patterns of appreciation, between local contexts of accumulation with a growth of residential prices, and suburbs with declining trends. The maturity of suburbanization yields a diversified structure of segregation between the social groups, that do not simply oppose executives vs. blue collar suburbs. A follow-up research agenda is finally outlined. [ABSTRACT FROM AUTHOR]

In their 2010 (Erkenntnis 73:393-412) paper, Dizadji-Bahmani, Frigg, and Hartmann (henceforth 'DFH') argue that the generalized version of the Nagel-Schaffner model that they have developed (henceforth 'the GNS') is the right one for intertheoretic reduction, i.e. the kind of reduction that involves theories with largely overlapping domains of application. Drawing on the GNS, DFH (Synthese 179:321-338, 2011) presented a Bayesian analysis of the confirmatory relation between the reducing theory and the reduced theory and argued that, post-reduction, evidence confirming the reducing theory also confirms the reduced theory and evidence confirming the reduced theory also confirms the reducing theory, which meets the expectations one has about theories with largely overlapping domains. In this paper, I argue that the Bayesian analysis presented by DFH (Synthese 179:321-338, 2011) faces difficulties. In particular, I argue that the conditional probabilities that DFH introduce to model the bridge law entail consequences that run against the GNS. However, I also argue that, given slight modifications of the analysis that are in agreement with the GNS, one is able to account for these difficulties and, moreover, one is able to more rigorously analyse the confirmatory relation between the reducing and the reduced theory. [ABSTRACT FROM AUTHOR]

In this paper, we show that reproducibility is a severe problem that concerns simulation models. The reproducibility problem challenges the concept of numerical solution and hence the conception of what a simulation actually does. We provide an expanded picture of simulation that makes visible those steps of simulation modeling that are numerically relevant, but often escape notice in accounts of simulation. Examining these steps and analyzing a number of pertinent examples, we argue that numerical solutions are importantly different from usual mathematical solutions. They are do not merely approximate the latter, but introduce new problems, including issues of artificiality, stability, and well-posedness. Consequently, simulation modelling can attain reproducibility only to a certain degree because it is working with numerical solutions (in a sense we specify in the paper). [ABSTRACT FROM AUTHOR]

A map that is defined on the set of all symmetric matrices over a field is rank-one nonincreasing if it maps the matrices of rank one to matrices of rank at most one. In the case of the fields with two or three elements nonstandard examples of such additive maps are known to exist. In this paper, all these maps are characterized. Moreover, the existence of nonstandard maps is understood in a geometric sense since they exist precisely in the two cases, where the whole n-dimensional vector space over can be written as a union of two hyperbolic/parabolic quadrics of low indices. This geometric interpretation enables us to realize that these weird examples represent just a tip of an iceberg that appears in an analogous problem on symmetric tensors, where nonstandard maps exist also over larger fields. A few open problems related to the multilinear analog and to homogeneous polynomials are posed. [ABSTRACT FROM AUTHOR]

Let T and S be two self-adjoint positive invertible operators of a complex Hilbert space H. In this paper, we investigate some inequalities involving the quadratic forms of the weighted arithmetic and harmonic means of T and S. Application for operator entropies is also discussed. [ABSTRACT FROM AUTHOR]

Surface roughness is often considered the main purpose in contemporary computer numerical controlled (CNC) machining industry. Most existing optimization researches for CNC finish turning were either accomplished within certain manufacturing circumstances or achieved through numerous equipment operations. Therefore, a general deduction optimization scheme is deemed to be necessary for the industry. In this paper, the cutting depth, feed rate, speed, and tool nose runoff with low, medium, and high level are considered to optimize the surface roughness for finish turning based on L9(34) orthogonal array. Additionally, nine fuzzy control rules using triangle membership function with respective to five linguistic grades for surface roughness are constructed. Considering four input and twenty output intervals, the defuzzification using center of gravity is then completed. Thus, the optimum general fuzzy linguistic parameters can then be received. The confirmation experiment result showed that the surface roughness from the fuzzy linguistic optimization parameters is significantly advanced compared to that from the benchmark. This paper certainly proposes a general optimization scheme using orthogonal array fuzzy linguistic approach to the surface roughness for CNC turning with profound insight. [ABSTRACT FROM AUTHOR]

In this paper we are interested in the global existence and large time behavior of solutions to the initial- boundary value problem for sub critical nonlinear dissipative equations (Multiple line equation(s) cannot be represented in ASCII text) where the nonlinear term N(u, ux) depends on the unknown function u and its derivative ux and satisfy the estimate (Multiple line equation(s) cannot be represented in ASCII text)The linear operator IK(u) is defined as follows (Multiple line equation(s) cannot be represented in ASCII text) where the constants an, am ϵ R, n, m are integers, m > n. The aim of this paper is to prove the global existence of solutions to the initial-boundary value Problem (1). We find the main term of the asymptotic representation of solutions in sub critical case, when the nonlinear term of equation has the time decay rate less then that of the linear terms. Also we give some general approach to obtain global existence of solution of initial-boundary value problem in sub critical case and elaborate general sufficient conditions to obtain asymptotic expansion of solution. [ABSTRACT FROM AUTHOR]

The present paper continues the study of acceleration of convergence started in the paper [A. Aasma, Proc. Estonian Acad. Sci. Phys. Math., 2006, 55, 4, 195-209]. The new, non-classical convergence acceleration concept, called strong μ-acceleration of convergence (μ is a positive monotonically increasing sequence), is introduced. It is shown that this concept allows to compare the speeds of convergence for a larger set of sequences than the classical convergence acceleration concept. Regular matrix methods are used to accelerate the convergence of sequences. [ABSTRACT FROM AUTHOR]

Stochastic differential equations with Markovian switching (SDEwMSs), one of the important classes of hybrid systems, have been used to model many physical systems that are subject to frequent unpredictable structural changes. The research in this area has been both theoretical and applied. Although the numerical methods for stochastic differential equations (SDEs) have been well studied, there are only a few results on the numerical solutions for SDEwMSs. By this manuscript we continue our series of papers on numerical solutions of SDEwMSs. The main aim of this paper is to investigate the stationary distributions of Euler-Maruyama-type stochastic difference equations with Markovian switching (EMSDEwMSs) and discuss their convergence. [ABSTRACT FROM AUTHOR]

In this paper, an efficient numerical algorithm is proposed for the valuation of unilateral American better-of options with two underlying assets. The pricing model can be described as a backward parabolic variational inequality with variable coefficients on a two-dimensional unbounded domain. It can be transformed into a one-dimensional bounded free boundary problem by some conventional transformations and the far-field truncation technique. With appropriate boundary conditions on the free boundary, a bounded linear complementary problem corresponding to the option pricing is established. Furthermore, the full discretization scheme is obtained by applying the backward Euler method and the finite element method in temporal and spatial directions, respectively. Based on the symmetric positive definite property of the discretized matrix, the value of the option and the free boundary are obtained simultaneously by the primal-dual active-set method. The error estimation is established by the variational theory. Numerical experiments are carried out to verify the efficiency of our method at the end. [ABSTRACT FROM AUTHOR]

We here adapt an extended version of the adaptive cubic regularization method with dynamic inexact Hessian information for nonconvex optimization in Bellavia et al. [Adaptive cubic regularization methods with dynamic inexact hessian information and applications to finite-sum minimization. IMA Journal of Numerical Analysis. 2021;41(1):764–799] to the stochastic optimization setting. While exact function evaluations are still considered, this novel variant inherits the innovative use of adaptive accuracy requirements for Hessian approximations introduced in the just quoted paper and additionally employs inexact computations of the gradient. Without restrictions on the variance of the errors, we assume that these approximations are available within a sufficiently large, but fixed, probability and we extend, in the spirit of Cartis and Scheinberg [Global convergence rate analysis of unconstrained optimization methods based on probabilistic models. Math Program Ser A. 2018;159(2):337–375], the deterministic analysis of the framework to its stochastic counterpart, showing that the expected number of iterations to reach a first-order stationary point matches the well-known worst-case optimal complexity. This is, in fact, still given by O (ϵ − 3 / 2) , with respect to the first-order ϵ tolerance. Finally, numerical tests on nonconvex finite-sum minimization confirm that using inexact first- and second-order derivatives can be beneficial in terms of the computational savings. [ABSTRACT FROM AUTHOR]