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Universal functions of Two Variables for Special Values of k

Computational Mathematics and Modeling 2019年第1期30卷 1-6页

作者： Voronenko, A.V. Shchurova, A.A. Faculty of Computational Mathematics and Cybernetics Moscow State University and MIPT Moscow Russian Federation Tinkoff Bank Moscow Russian Federation

We consider the notion of universal function such that a subset of the function’s values defines any function from some set. For the set of linear functions, we consider all the combinations of the number of variables and the number of values, except four-valued functions of two variables. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

关键词： linear function universal function

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Densities and distribution functions of the ratio of two linear functions and the product of Gamma variates: A saddlepoint approach

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2017年第15期46卷 7327-7336页

作者： Abd-Elfattah, Ehab F. Ain Shams Univ Dept Math Fac Educ Cairo Egypt

Saddlepoint approximations for the densities and the distribution functions of the ratio of two linear functions of gamma random variables and the product of gamma random variables are derived. Ratios of linear functions with positive and negative weights and non identical gamma variables are considered. The saddlepoint approximations are very accurate in the tails as in the center of the distribution. Extensive simulation studies are used to evaluate the accuracy of the proposed methods.

关键词： Gamma distribution linear function product saddlepoint approximation

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Integrating Deep Learning and Explicit MPC for Advanced Process Control

Integrating Deep Learning and Explicit MPC for Advanced Proc...

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American Control Conference

作者： Justin Katz Iosif Pappas Styliani Avraamidou Efstratios N. Pistikopoulos Artie McFerrin Department of Chemical Engineering Texas A&M University College Station TX USA Texas A&M Energy Institute Texas A&M University College Station TX USA

ISBN: (数字)9781538682661

ISBN: (纸本)9781538682678

For highly nonlinear systems, using deep learning models to capture complex dynamics is a promising feature for advanced control applications. Recently it has been shown that a particular class of deep learning models can be exactly recast in a mixed-integer linear programming formulation. Recasting a deep learning model as a set of piecewise linear functions enables the incorporation of advanced predictive models in model-based control strategies such as model predictive control. To alleviate the computational burden of solving the piecewise linear optimization problem online, multiparametric programming is utilized to obtain the full, offline, explicit solution of the optimal control problem. In this work, a strategy is presented for the integration of deep learning models, specifically neural networks with rectified linear units, and explicit model predictive control. The proposed strategy is demonstrated on the advanced control of a benchmark chemical process involving multiple reactors, a flash separator, and a recycle stream. The positive results showcase the relevance and strength of the proposed methodology.

关键词： Process control Advanced controls linear function Model predictive control Predictive control Machine Learning Explicit Mixed integer linear programming linear unit Piecewise Optimal control

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An Ionosphere Specification Technique Based on Data Ingestion Algorithm and Empirical Orthogonal function Analysis Method

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SPACE WEATHER-THE INTERNATIONAL JOURNAL OF RESEARCH AND APPLICATIONS 2018年第9期16卷 1410-1423页

作者： Aa, Ercha Ridley, Aaron Huang, Wengeng Zou, Shasha Liu, Siqing Coster, Anthea J. Zhang, Shunrong Chinese Acad Sci Natl Space Sci Ctr Beijing Peoples R China Univ Michigan Dept Climate & Space Sci & Engn Ann Arbor MI 48109 USA Univ Chinese Acar ly Sci Coll Earth & Planetary Sci Beijing Peoples R China MIT Haystack Observ 77 Massachusetts Ave Cambridge MA 02139 USA

A data ingestion method in reproducing ionospheric electron density and total electron content (TEC) was developed to incorporate TEC products from the Madrigal Database into the NeQuick 2 model. The method is based on retrieving an appropriate global distribution of effective ionization parameter (Az) to drive the NeQuick 2 model, which can be implemented through minimizing the difference between the measured and modeled TEC at each grid in the local time-modified dip latitude coordinates. The performance of this Madrigal TEC-driven-NeQuick 2 result is validated through the comparison with various International Global Navigation Satellite Systems Services global ionospheric maps and ionosonde data. The validation results show that a general accuracy improvement of 30-50% can be achieved after data ingestion. In addition, the empirical orthogonal function (EOF) analysis technique is used to construct a parameterized time-varying global Az model. The quick convergence of EOF decomposition makes it possible to use the first six EOF series to represent over 90% of the total variances. The intrinsic diurnal variation and spatial distribution in the original data set can be well reflected by the constructed EOF base functions. The associated EOF coefficients can be expressed as a set of linear functions of F-10.7 and Ap indices, combined with a series of trigonometric functions with annual/seasonal variation components. The NeQuick TEC driven by EOF-modeled Az shows 10-15% improvement in accuracy over the standard ionosphere correction algorithm in the Galileo navigation system. These preliminary results demonstrate the effectiveness of the combined data ingestion and EOF modeling technique in improving the specifications of ionospheric density variations.

关键词： Ionosphere Specification Technique Data Ingestion Algorithm ionospheres correction algorithm Dataset TEC gene Ingestion EOF Orthogonal functions linear function Circular functions

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Using Dynamic Representations to Strengthen Understanding of linear functions among Seventh Graders

台湾数学教育期刊

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台湾数学教育期刊 2018年第2期5卷 1-17页

作者：呂鳳琳李健恆蕭淑娟

In this study, we investigated the effectiveness of computer-assisted learning when used by students in the seventh grade to learn the linear function y = mx + b. The proposed instructional approach is based on the dynamic linking of multiple representations. The aim of this linking is to provide clarification of the mathematical structure of linear functions and the meaning of parameters m and b. We adopted a quasi-experimental design involving two classes from a junior high school in Taiwan. None of the students possessed prior knowledge of linear functions. The experiment group was exposed to linear functions within a digital learning environment, whereas the control group was subjected to the conventional paper and pencil approach. Results from pre-tests and post-tests revealed significant improvements in both groups; however, the experiment group significantly outperformed those in the control group. In fact, the experiment group obtained higher scores on a delayed posttest than on the initial posttest. This is a clear demonstration of the benefits of computer-assisted learning in terms of concept retention.

关键词： computer aided instruction dynamic representations linear function

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More secure version of a Cayley hash function

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GROUPS COMPLEXITY CRYPTOLOGY 2018年第1期10卷 29-32页

作者： Ghaffari, Mohammad Hossein Mostaghim, Zohreh Iran Univ Sci & Technol Sch Math Cryptog & Data Secur Lab Tehran Iran

In this paper, we propose a more secure version of a Cayley hash function which is based on the linear functions. It is a practical parallelizable hash function.

关键词： Cayley hash function linear function Cayley graph hash function

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Split credibility: A two-dimensional semi-linear credibility model

Split credibility: A two-dimensional semi-linear credibility...

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作者： Jingbing Qiu University of Western Ontario

学位级别：硕士

In the thesis, we introduce a two-dimensional semi-linear credibility model, which is an extension of the classical credibility or split credibility models used by practicing actuaries. Our model predicts the future expected losses of a policyholder by considering its historical primary and excess losses. The optimal split point is derived based on the mean squared error criterion. We show when and why splitting a policyholder's historical losses into primary and excess parts work analytically. In addition, we derived formulas for estimating our model parameters nonparametrically. Finally, we show the application of our model through three examples.

关键词： Two-dimensional semi-linear credibility model split credibility primary and excess credibility linear function mean square error

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Saddlepoint density and distribution functions for the ratio of two linear functions and the product of generalized gamma variates

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2017年第23期46卷 11745-11755页

作者： Abd-Elfattah, Ehab F. Ain Shams Univ Dept Math Cairo Egypt

The generalized gamma distribution is a flexible and attractive distribution because it incorporates several well-known distributions, i.e., gamma, Weibull, Rayleigh, and Maxwell. This article derives saddlepoint density and distribution functions for the ratio of two linear functions of generalized gamma variables and the product of n independent generalized gamma variables. Simulation studies are used to evaluate the accuracy of the saddlepoint approximations. The saddlepoint approximations are fast, easy, and very accurate.

关键词： Generalized gamma distribution linear function product Ratio of two linear functions Saddlepoint approximation 62E17 60E05 6008

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An arc-shaped crack in nonlinear fully coupled thermoelectric materials

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ACTA MECHANICA 2018年第5期229卷 1989-2008页

作者： Yu, Chuanbin Zou, Daifeng Li, Yu-Hao Yang, Hai-Bing Gao, Cun-Fa Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Nanjing 210016 Jiangsu Peoples R China Chinese Acad Sci Shenzhen Inst Adv Technol Shenzhen Key Lab Nanobiomech Shenzhen 518055 Guangdong Peoples R China

We present a rigorous treatment to the problem of a circular-arc crack in an infinite thermoelectric solid subjected to a combined electrical and thermal loading. Formulating the problem in terms of the complex potentials and reducing it to the Hilbert arc problem, the solutions of quantities in both thermoelectric field and the associated thermoelastic field are presented in a closed form based on the electrically permeable and thermally insulated crack model. The results show that the fields of heat flux, energy flux, and stress exhibit the traditional square-root singularity at tips of arc crack. The applied electric current and energy flux generate both mode I and mode II stress intensity factors (SIFs), which are dependent on the loading direction, electric conductivity, thermal conductivity, central angle of the crack, and thermoelastic isotropy. Electrically induced SIF is a quadratic function of applied electric current density, and thermally induced SIF is a linear function of the imposed total energy flux. In addition, the effects of the loading direction and half crack angle on the thermal SIFs are also presented in a graphic form. This is the first theoretical paper to study the effect of the crack shape on the fracture of fully coupled thermoelectric materials by a rigorous inference of physics and mathematics.

关键词： complex potential Thermal loading Quadratics corrosion current density closed forms thermoelectric materials ENERGY FLUX cracks Electricity linear function

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Energy efficient power allocation approach to asymmetric analogue network coding with rate-dependent circuit power

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IET COMMUNICATIONS 2018年第18期12卷 2324-2331页

作者： Zheng, Fangyuan Li, Jing Yu, Xiangbin Ge, Jianhua Xidian Univ State Key Lab Integrated Serv Networks Xian 710071 Shaanxi Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Elect & Informat Engn Nanjing 210016 Jiangsu Peoples R China

Energy efficiency (EE) plays an indispensable role in the battery constrained systems. In this study, the EE optimisation problem for asymmetric analogue network coding (ANC) protocol is analysed in a two-way relaying network, where the two sources have different transmission rate requirements. A generalised power consumption model is applied consisting of not only the transmit power and fixed circuit power, but also the most general rate-dependent dynamic circuit power, with which a power allocation problem is formulated to achieve the maximal EE constrained by the rate requirements as well as the total transmit power budget. By exploiting the two-layer optimisation method and non-linear fractional programming theorem, the original EE maximisation problem is solved in an efficient way. Specially, when the rate-dependent circuit power is modelled as the linear function of transmission rate, a closed-form solution is obtained. Through simulations, the proposed power allocation algorithm is verified and the impacts of some system parameters such as relay location, transmit power and transmission rate asymmetry are also provided to gain useful insights, which facilitates the energy-efficient design for the practical asymmetric ANC protocol.

关键词： relay networks (telecommunication) telecommunication power management energy conservation power consumption network coding resource allocation protocols nonlinear programming energy efficient power allocation approach battery constrained systems EE optimisation problem asymmetric analogue network coding protocol two-way relaying network generalised power consumption model fixed circuit power power allocation problem total transmit power budget two-layer optimisation method transmission rate asymmetry energy-efficient design transmission rate requirements general rate-dependent dynamic circuit power asymmetric ANC protocol nonlinear fractional programming theorem EE maximisation problem closed-form solution linear function system parameters

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