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infinite STRONG CODES

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Chinese Science Bulletin 1987年第24期32卷 1669-1672页

作者：张洛新郭聿琦 Lanzhou University Lanzhou University Let ∑~* be the free monoid generated by (finite) alphabet ∑. An dement of ∑is called a letter an dement of ∑~* and a subset of ∑~* are respectively called a word and a language. The identity of ∑~* is called an empty word which is denoted by A we use the notation ∑~+=∑~*-{A}. For any word x we define lg(x) as the number of letters in x which is called the length of x.

Let ∑~* be the free monoid generated by (finite) alphabet ∑. An dement of ∑ is called a letter, an dement of ∑~* and a subset of ∑~* are respectively called a word and a language. The identity of ∑~* is called an empty word which is denoted by A; we use the notation ∑^+=∑~*-{A}. For any word x, we define lg(x) as the number of letters in x, which is called the length of x.

关键词： letters notation monoid congruence proof prefix infinite empty satisfy length

Modulated Hydrothermal Chemistry of Metal−Organic Frameworks

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Accounts of Materials Research 2022年第11期3卷 1106-1114页

作者： Zhigang Hu Yuxiang Wang Dan Zhao Shanghai Key Laboratory of Hydrogen Science&Center of Hydrogen Science School of Materials Science and EngineeringShanghai Jiao Tong UniversityShanghai 200240China Department of Chemical&Biomolecular Engineering National University of Singapore117585Singapore

CONSPECTUS:Metal−organic frameworks(MOFs)are infinite networks composed of inorganic metals and organic linkers,and have demonstrated superior advantages over traditional porous materials in gas storage,separation,catalysis,etc.,because of possessing ultrahigh surface areas and tunability in pore sizes,topologies,shapes,and functionalities.Although tremendous progress has been made in the fundamental research and applications of MOFs,developing a green and large-scale approach to synthesizing MOFs with repeatably high quality remains a key step for their massive production and industrial applications.

关键词： catalysis infinite sizes

infinite Sets of Solutions and Almost Solutions of the Equation N⋅M= reversal(N⋅M)

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Open Journal of Discrete Mathematics 2019年第3期9卷 63-67页

作者： Viorel Niţ ică Premalata Junius Department of Mathematics West Chester University of Pennsylvania West Chester USA

Motivated by their intrinsic interest and by applications to the study of numeric palindromes and other sequences of integers, we discover infinite sets of solutions and almost solutions of the equation N?⋅?M=reversal... 详细信息

关键词： Sequences of Integers infinite Sets

The Dynamics of an Impulsive Competitive System with infinite Delay and Diffusion

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Journal of Applied Mathematics and Physics 2018年第6期6卷 1388-1407页

作者： Hairu Chen Yuanfu Shao College of Science Guilin University of Technology Guilin China

In this paper, we consider an impulsive competitive system with infinite delay and diffusion. Firstly, on basis of inequality estimation techniques and comparison theorem of impulsive differential equations, we obtain some sufficient conditions for the permanence and extinction of the system. Then, we establish sufficient conditions for the globally attractive of the system by constructing appropriate Lyapunov function. Besides, under different impulsive conditions, we discuss the effect of time delay and diffusion on dynamic behavior of the competitive system.

关键词： Diffusion infinite Delay Permanence Extinction Attractive

Asymptotic Approximation of the Eigenvalues and the Eigenfunctions for the Orr-Sommerfeld Equation on infinite Intervals

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Advances in Pure Mathematics 2019年第12期9卷 967-989页

作者： Victor Nijimbere School of Mathematics and Statistics Carleton University Ottawa Canada

Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a short-wave limit approximation is used, and another in which a long-wave limit approximation is used. In the short-wave limit, Wentzel-Kramers-Brillouin (WKB) methods are utilized to estimate the eigenvalues, and the eigenfunctions are approximated in terms of Green’s functions. The procedure consists of transforming the Orr-Sommerfeld equation into a system of two second order ordinary differential equations for which the eigenvalues and the eigenfunctions can be approximated. In the long-wave limit approximation, solutions are expressed in terms of generalized hypergeometric functions. Our procedure works regardless of the values of the Reynolds number.

关键词： Eigenvalues Eigenfunctions infinite Intervals WKB Methods Long-Wave Limit Approximation Short-Wave Limit Approximation Generalized Hypergeometric Functions

Theories on the Propulsion System for Lithium-ion Battery Electric Vehicles with infinite Cruising Range

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Journal of Traffic and Transportation Engineering 2018年第3期6卷 134-147页

作者： Katsutoshi Ono Department of Energy Science&Technology Kyoto UniversityKyoto 6068317Japan

On-board electric power generation in the absence of external energy may be sufficient to realize tough electric vehicles.The method to charge the Li-ion battery modules in the present investigation differs from the conventional single voltage source scheme in that the power requirement is only 12%of the power required for typical direct voltage applications.This method utilizes the ESI-PSC(electrostatic-induction potential-superposed electrolytic charge).The on-board electric power generation system is an identical twin of battery modules that function in ESI-PSC mode,in which the performance can be explained through consecutive cycles of field-induced charge and discharge between two batteries.When the charge of one battery is terminated,it becomes responsible for both the power to recharge the other battery and the power to drive the motor.This power generation system works with zero energy input,zero matter input and zero emission,without violating the laws of thermodynamics.The commercially available Li-ion battery modules and power control systems enable the realization of this type of EVs(electric vehicles).A simulation based on the official standard cruising mode(JCO08)showed that an electric vehicle with an on-board twin of 13.2 kWh energy capacity modules can travel 132 km before switching from charge to discharge.

关键词： EVs lithium-ion battery infinite cruising range electrostatic induction charge electrostatic energy discharge capacity

A finite difference scheme for magneto-thermo analysis of an infinite cylinder

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Natural Science 2010年第11期2卷 1312-1317页

作者： Daoud S. Mashat 不详

A finite different scheme as well as least-square method is presented for the magneto-thermo analysis of an infinite functionally graded hollow cylinder. The radial displacement, mechanical stresses and temperature as well as the electromagnetic stress are investigated along the radial direction of the cylinder. Material properties are assumed to be graded in the radial direction according to a novel exponential-law distribution in terms of the volume fractions of the metal and ceramic constituents. The governing second-order differential equations are derived from the equations of motion and the heat-conduction equation. The system of differential equations is solved numerically and some plots for displacement, radial stress, and temperature are presented.

关键词： infinite Cylinder Electro-Magneto-Thermoelastic Finite Difference Method

infinite GROUPS OF SYMMETRIES OF BURGERS EQUATION

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Chinese Science Bulletin 1988年第5期33卷 433-434页

作者：田畴 Department of Mathematics University of Science and Technology of China Hefei

We discuss the symmetries and the strong symmetries of Bugers equation ut=uxx + 2uux. （1） As is known, there is a strong

关键词： symmetry infinite linearized algebra arbitrary checked

A Maximum Principle for Smooth infinite Horizon Optimal Control Problems with State Constraints and with Terminal Constraints at Infinity

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Open Journal of Optimization 2015年第3期4卷 100-130页

作者： Atle Seierstad University of Oslo Oslo Norway

Necessary conditions for optimality are proved for smooth infinite horizon optimal control problems with unilateral state constraints (pathwise constraints) and with terminal conditions on the states at the infinite horizon. The aim of the paper is to obtain strong necessary conditions including transversality conditions at infinity, which in many cases lead to a set of candidates for optimality containing only a few elements, similar to what is the case in finite horizon problems. However, strong growth conditions are needed for the results to hold.

关键词： infinite Horizon Optimal Control State Constraints