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On the stability of a hyperbolic fractional partial differential equation

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arXiv 2018年

作者： da C. Sousa, J. Vanterler Capelas De Oliveira, E. Department of Applied Mathematics Institute of Mathematics Statistics and Scientific Computation University of Campinas - UNICAMP rua Sérgio Buarque de Holanda 651 Campinas SP13083-859 Brazil

In this paper, by means of the Gronwall inequality, the ψ-Riemann-Liouville fractional partial integral and the ψ-Hilfer fractional partial derivative are introduced and some of its particular cases are recovered. Using these results, we investigate the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the solutions of a fractional partial differential equation of hyperbolic type in a Banach space (B, |·|), real or complex.26A33, 35B35, 35R11, 35LXX Copyright © 2018, The Authors. All rights reserved.

关键词： Banach spaces

On the ψ-hilfer fractional derivative

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arXiv 2017年

作者： Sousa, Vanterler Da J.C. de Oliveira, E. Capelas Department of Applied Mathematics Institute of Mathematics Statistics and Scientific Computation University of Campinas – UNICAMP rua Sérgio Buarque de Holanda 651 Campinas SP13083–859 Brazil

In this paper we introduce a new fractional derivative with respect to another function the so-called ψ-Hilfer fractional derivative. We discuss some properties and important results of the fractional calculus. In this sense, we present some uniformly convergent sequence of function results and examples involving the Mittag-Leffler function with one parameter. Finally, we present a wide class of integrals and fractional derivatives, by means of the fractional integral with respect to another function and the ψ-Hilfer fractional derivative.26A03;26A15;26A33;26A46 .MSC Codes 26A03, 26A15, 26A33, 26A46 Copyright © 2017, The Authors. All rights reserved.

关键词： Calculations

A new truncated m-fractional derivative type unifying some fractional derivative types with classical properties

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arXiv 2017年

作者： Sousa, J. Vanterler Da C. De Oliveira, E. Capelas Department of Applied Mathematics Institute of Mathematics Statistics and Scientific Computation University of Campinas - UNICAMP rua Sérgio Buarque de Holanda 651 Campinas SP13083-859 Brazil

We introduce a truncated M-fractional derivative type for α-differentiable functions that generalizes four other fractional derivatives types recently introduced by Khalil et al., Katugampola and Sousa et al., the so-called conformable fractional derivative, alternative fractional derivative, generalized alternative fractional derivative and M-fractional derivative, respectively. We denote this new differential operator by iDMα,β, where the parameter α, associated with the order of the derivative is such that 0 0 and M is the notation to designate that the function to be derived involves the truncated Mittag-Leffler function with one parameter. The definition of this truncated M-fractional derivative type satisfies the properties of the integer-order calculus. We also present, the respective fractional integral from which emerges, as a natural consequence, the result, which can be interpreted as an inverse property. Finally, we obtain the analytical solution of the M-fractional heat equation and present a graphical analysis. Copyright © 2017, The Authors. All rights reserved.

关键词： Mathematical operators

Gruss-type inequality by mean of a fractional integral

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arXiv 2017年

作者： Vanterler Da Sousa, J.C. Oliveira, D.S. Capelas De Oliveira, E. Department of Applied Mathematics Institute of Mathematics Statistics and Scientific Computation University of Campinas – UNICAMP rua Sérgio Buarque de Holanda 651 Campinas SP13083–859 Brazil

In this paper, using a fractional integral as proposed by Katugampola we establish a generalization of integral inequalities of Gruss-type. We prove two theorems associated with these inequalities and then immediately we enunciate and prove others inequalities associated with these fractional operator.26A33;26A39;26A42 Copyright © 2017, The Authors. All rights reserved.

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A Physical-Constraint-Preserving Finite Volume WENO Method for Special Relativistic Hydrodynamics on Unstructured Meshes

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arXiv 2022年

作者： Chen, Yaping Wu, Kailiang School of Mathematics and Statistics Xi'an Key Laboratory of Scientific Computation and Applied Statistics NPU-UoG International Cooperative Lab for Computation and Application in Cardiology Northwestern Polytechnical University Shaanxi Province Xi'An710129 China Guangdong Shenzhen518055 China

This paper presents a highly robust third-order accurate finite volume weighted essentially nonoscillatory (WENO) method for special relativistic hydrodynamics on unstructured triangular meshes. We rigorously prove that the proposed method is physical-constraint-preserving (PCP), namely, always preserves the positivity of the pressure and the rest-mass density as well as the subluminal constraint on the fluid velocity. The method is built on a highly efficient compact WENO reconstruction on unstructured meshes, a simple PCP limiter, the provably PCP property of the Harten-Lax-van Leer flux, and third-order strong-stability-preserving time discretization. Due to the relativistic effects, the primitive variables (namely, the rest-mass density, velocity, and pressure) are highly nonlinear implicit functions in terms of the conservative variables, making the design and analysis of our method nontrivial. To address the difficulties arising from the strong nonlinearity, we adopt a novel quasilinear technique for the theoretical proof of the PCP property. Three provable convergence-guaranteed iterative algorithms are also introduced for the robust recovery of primitive quantities from admissible conservative variables. We also propose a slight modification to an existing WENO reconstruction to ensure the scaling invariance of the nonlinear weights and thus to accommodate the homogeneity of the evolution operator, leading to the advantages of the modified WENO reconstruction in resolving multi-scale wave structures. Extensive numerical examples are presented to demonstrate the robustness, expected accuracy, and high resolution of the proposed method. Copyright © 2022, The Authors. All rights reserved.

关键词： Hydrodynamics

STATISTICAL ISSUES AND PROBLEMS IN GROUND-WATER DETECTION MONITORING AT HAZARDOUS-WASTE FACILITIES

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GROUND WATER MONITORING AND REMEDIATION 1988年第4期8卷 135-150页

作者： MCNICHOLS, RJ DAVIS, CB Roger J. McNichols is a professor of industrial engineering at the University of Toledo (Department of Industrial Engineering University of Toledo Toledo OH 43606). After receiving his Ph.D in industrial engineering from The Ohio State University he joined the faculty of Texas A and M University where he directed the Maintainability Engineering Graduate Program at Red River Army Depot. At UT he has served as associate dean of engineering and as chairman of the Systems engineering doctoral program. His research and consulting interests include reliability quality control manufacturing mathematical modeling and applied statistics. Charles B. Davis is an associate professor of mathematics at the University of Toledo (Department of Mathematics University of Toledo Toledo OH 43606). After receiving his M.S. in mathematics and statistics and his Ph.D. in statistics from the University of New Mexico he joined the Mathematics Department at UT where he established the graduate program in statistics. His research and consulting interests include statistical modeling statistical computation simultaneous inference and data analysis.

Ground water monitoring presents interesting statistical challenges, including controlling the risk of entering compliance monitoring, incorporating all modes of inherent variability into the statistical model on which tests are based, and taming the detection limit problem, all while maintaining demonstrable sensitivity to real contamination. Some of these challenges exceed textbook statistics considerably, even when considered alone, and good solutions are scarce. When these challenges are combined, the task of developing good statistical procedures or good regulations can be formidable. This article presents a number of realities of ground water monitoring that should be considered when developing statistical procedures. Recommendations made for addressing these realities include the following: (1) the false positive rate should be controlled on a facility-wide basis, rather than per well or per parameter as required in the proposed regulation (40 CFR §264); (2) multiple comparisons with control procedures are preferable to analysis of variance (ANOVA) for controlling the overall false positive rate; (3) retests can be made an explicit part of the statistical procedure in order to increase power and decrease sensitivity to distribution shape assumptions; (4) commonly used simple methods of handling below detection limit data with parametric tests, including Cohen's procedure as implemented in the U.S. EPA's Technical Enforcement Guidance Document (TEGD), should probably be avoided; (5) the statistical properties of practical quantitation limits for non-naturally occurring compounds should be studied carefully; and (6) so long as the facility-wide false positive rate is controlled, better sensitivity to real contamination is obtained by monitoring fewer well-chosen parameters at a smaller number of well-chosen locations. An evaluation of the proposed revised §264 regulation with respect to these realities reveals that it seems to be a definite improvement over the

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Using Cluster Analysis and Dynamic programming for Demand Response applied to Electricity Load in Residential Homes

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Journal of Engineering for Sustainable Buildings and Cities 2020年第1期1卷 011006页

作者： Chanpiwat, Pattanun Gabriel, Steven A. Moglen, Rachel L. Siemann, Michael J. Department of Mechanical Engineering University of Maryland College Park 20742 MD United States Department of Mechanical Engineering and the Applied Mathematics Statistics and Scientific Computation Program University of Maryland College Park 20742 MD United States Department of Industrial Economics and Technology Management Norwegian University of Science and Technology Trondheim NO-7491 Norway Operations Research and Industrial Engineering The University of Texas at Austin Austin 78712 TX United States Resideo Technologies Austin 78702 TX United States

This paper develops means to analyze and cluster residential households into homogeneous groups based on the electricity load. Classifying customers by electricity load profiles is a top priority for retail electric providers (REPs), so they can plan and conduct demand response (DR) effectively. We present a practical method to identify the most DR-profitable customer groups as opposed to tailoring DR programs for each separate household, which may be computationally prohibitive. Electricity load data of 10,000 residential households from 2017 located in Texas was used. The study proposed the clustered load-profile method (CLPM) to classify residential customers based on their electricity load profiles in combination with a dynamic program for DR scheduling to optimize DR profits. The main conclusions are that the proposed approach has an average 2.3% profitability improvement over a business-as-usual heuristic. In addition, the proposed method on average is approximately 70 times faster than running the DR dynamic programming separately for each household. Thus, our method not only is an important application to provide computational business insights for REPs and other power market participants but also enhances resilience for power grid with an advanced DR scheduling tool. Copyright © 2020 by ASME.

关键词： cluster analysis customer classification demand response dynamic programming energy efficiency integrated systems occupant behavior optimization residential household

PERMUTATION INVARIANT REPRESENTATIONS with APPLICATIONS to GRAPH DEEP LEARNING

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arXiv 2022年

作者： Balan, Radu Haghani, Naveed Singh, Maneesh Department of Mathematics University of Maryland College ParkMD20742 United States Applied Mathematics and Statistics and Scientific Computation Program University of Maryland College ParkMD20742 United States Verisk Analytics Jersey CityNJ07310 United States

This paper presents primarily two Euclidean embeddings of the quotient space generated by matrices that are identified modulo arbitrary row permutations. The original application is in deep learning on graphs where the learning task is invariant to node relabeling. Two embedding schemes are introduced, one based on sorting and the other based on algebras of multivariate polynomials. While both embeddings exhibit a computational complexity exponential in problem size, the sorting based embedding is globally bi-Lipschitz and admits a low dimensional target space. Additionally, an almost everywhere injective scheme can be implemented with minimal redundancy and low computational cost. In turn, this proves that almost any classifier can be implemented with an arbitrary small loss of performance. Numerical experiments are carried out on two data sets, a chemical compound data set (QM9) and a proteins data set (PROTEINS FULL).MSC Codes 05C62, 20C32, 68R12 © 2022, CC BY.

关键词： Embeddings

Bootstrap Confidence Regions for Directional Data

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Journal of the American Statistical Association 1989年第408期84卷 996-996页

作者： Fisher, Nicholas I. Hall, Peter Program Leader Applied and Industrial Statistics Division of Mathematics and Statistics Commonwealth Scientific and Industrial Research Organisation Lindfield New South Wales 2070 Australia. Professor Department of Statistics Australian National University Canberra Australian Capital Territory 2601 Australia

Methods are proposed for constructing bootstrap confidence regions for the mean direction of a random p-dimensional unit vector X with an arbitrary unimodal distribution on the p sphere. The approach of this article differs from that of other authors in that it is based on pivotal statistics. A general pivotal method is introduced that produces a wide variety of confidence regions on general p-dimensional spheres; included are confidence cones and likelihood-based regions. It can readily be modified to incorporate extra assumptions about the underlying distribution, such as rotational symmetry. The general method leads to confidence pictures, which present information about the estimated posterior likelihood of mean orientation by shading spherical surfaces. An application is given to a sample of spherical cross-bed measurements. The methods extend to the case where X has random length, and to calculation of confidence regions for reference directions of axial bipolar or girdle distributions. [ABSTRACT FROM AUTHOR]

关键词： Axial data Circular data Confidence picture Gray-level image Pivotal statistic Studentization Weighted vectors.