A guide to the literature on the history of engineering available in the cooper union library: Cooper Union Bulletin. Engineering and science series,Number 28, 46 pages, 18 × 2S CMS., paper. New York,The Cooper Union for the Advancement of Science and Art, 1946.

The linear logarithmic relations between deformation and temperature and pressure, previously empirical, have been directly derived from the defining equations for compressibility and thermal expansivity and shown to apply to all three stages of every deformation.Gibbs' thermodynamic potential function is shown to lead directly to simple and exact expressions for the energy of change of phase and of deformation within any one phase. The latter, a general equation of state, amounts to a simple relation between the four internal pressures.The derived deformation and energy functions are applied to some experimental data on steel tape which included thermal and relaxation observations.Thermodynamic relations governing both elastic and viscous behavior are developed. Plastic behavior involves both single phase and multiple phase applications of the second law. Precise thermal measurements should give the constants.     

Representation and realization of operational differential equations with time-varying coefficients

An algebraic treatment of operational differential equations with time-varying coefficients is presented in terms of skew rings of differential polynomials defined over a Noetherian ring. Included in this framework are delay differential equations with time- varying coefficients. The operator equations are characterized by transfer matrices which are utilized to construct realizations given by first-order vector differential equations with operator coefficients. It is shown that the realization of matrix equations can be reduced to the realization of scalar equations. Finally, a simple procedure is derived for realizing scalar equations.     

Diversity incorporated energy adaptation for A-CDMA systems over slow fading channels

In this paper, a theoretical analysis of diversity incorporated Variable Energy Adaptation (VEA) in an Asynchronous Code Division Multiple Access (A-CDMA) system is discussed for Rayleigh, Rician and Nakagami slow fading channels. The adaptation is accomplished by providing the receiver with the capability of measuring the signal energy-to-noise ratio, and controlling the transmitted signal energy by means of a noise-free feedback loop. System parameters such as fading margin, maximum signal-to-noise ratio, and mean transmitter energy gain are derived and plotted for fading channels as a function of the probability of error specification and the probability of unsatisfactory operation. The mean and median probabilities of error are plotted as a function of energy-to-noise ratios for different fading channels. Error probability distribution and density functions are derived and plotted for various signal-fading distributions.     

Equilibrium and duality in electromagnetic field problems

Electromagnetic fields can be treated as systems in which the field equations are the equations of equilibrium. This formulation draws the subject into the unified approach of mechanics. Close analogies to potential and kinetic energy exist and these can be used to provide double bounds to the electromagnetic energy.     

适用于中尺度系统研究的位涡方程

本文通过推导绝热、无摩擦大气方程组，讨论了新方程组的特点；新方程组中，位温 显式出现在动量方程中，有利于探讨倾斜的等熵面（等位温面）对中尺度系统发生和发展的影响。进一步，利用此新方程组，推导出适用于中尺度系统研究的新的位涡方程，新位涡方程突出的特点是，与中尺度系统发生、发展密切相关的散度项显式出现在方程的右端；这为研究中尺度系统演变过程中，辐合、辐散效应对系统位涡收支的影响、进而研究中尺度系统发生、发展的热、动力学过程提供了方法。     

A matrix generalization of heaviside's expansion theorem

Starting with the energy and dissipation functions of the general n mesh linear bilateral network and using the operational methods of the Laplacian transformation, a solution is obtained for the Lagrangian equations of the system subject to initial boundary conditions. The equations take a particularly simple and general form if matrix notation is used.It is noted that the general case bears a close resemblance to the simple, one mesh, series circuit when the scalar factors which appear in this circuit are generalized to matrix form.     

Alternative derivation of equations of motion

Equations of motion in the form of sets of non-linear differential equations are derived for dynamic systems which may exhibit simultaneous changes in their electrical, fluid, mechanical and thermal states. These equations are based on considerations of the physics of components and their eventual topology when forming an assembly. The effect of thermal environment is shown when its capacity is finite and when it is not.     

Reduction of models of large scale lumped structures using normal modes and bond graphs

Bond graphs are an extremely useful modeling procedure for representing the actual energy exchange mechanisms of interacting dynamic systems. Governing state equations are straightforwardly obtained from the bond graph; however, for large structures, a restrictively large number of equations can result. A procedure is developed whereby the original equations are reduced to a form suitable for modal decomposition. The resulting modes are reinterpreted in bond graph form with the resulting model being an extremely accurate system representation while requiring only a fraction of the original number of equations. The procedure is demonstrated through example.     

要素替代及回弹效应视角下中国钢铁行业能源消费研究

基于中国1980~2013年钢铁行业数据,利用超越对数成本函数构建要素成本份额方程,运用动态最小二乘法对模型进行修正,利用似不相关回归对钢铁行业生产要素间的替代关系进行测度,并通过引入价格的非对称性来研究回弹效应.结果表明:钢铁行业的能源和资本自价格弹性均为负;资本和能源的绝对替代弹性和相对替代弹性均为正.能源对资本的绝对替代弹性大于资本对能源的绝对替代弹性,但资本对能源的相对替代弹性自2000年以后逐渐占优于能源对资本的相对替代弹性;钢铁行业的回弹效应高达95.85%,由能源效率提高而节约的能源基本上被回弹效应所抵消.     

Energy conversion in biological systems—part I. chemical reactions and ion transport

Constitutive equations for nonisothermal chemical reactions are derived with attention to temperature dependent parameters. Equations are also developed for the coupling of chemical reactions to ion transport. The equations are shown to be consistent with the laws of thermodynamics.     

A new direct method based on the Chebyshev cardinal functions for variable-order fractional optimal control problems

In this paper, a new direct method based on the Chebyshev cardinal functions is proposed to solve a class of variable-order fractional optimal control problems (V-OFOCPs). To this end, a new operational matrix (OM) of variable-order (V-O) fractional derivative in the Caputo sense is derived for these basis functions and is used to obtain an approximate solution for the problem under study. In the proposed method, the state and the control variables are expanded in terms of the Chebyshev cardinal functions with unknown coefficients, at first. Then, the OM of V-O fractional derivative and some properties of the Chebyshev cardinal functions are employed to achieve a nonlinear algebraic equation corresponding to the performance index and a nonlinear system of algebraic equations corresponding to the dynamical system in terms of the unknown coefficients. Finally, the method of constrained extremum is applied, which consists of adjoining the constraint equations derived from the given dynamical system and the initial conditions to the performance index by a set of undetermined Lagrange multipliers. As a result, the necessary conditions of optimality are derived as a system of algebraic equations in the unknown coefficients of the state variable, control variable, and Lagrange multipliers. Furthermore, some numerical examples of different types are demonstrated with their approximate solutions for confirming the high accuracy and applicability of the proposed method.     

Nonlinear Vibration of Elastic Skew Plates Exhibiting Rectilinear Orthotropy

The governing equations for large amplitude flexural vibrations of orthotropic skew plates are obtained from the corresponding static equations derived in this paper. Making use of an approximation originally due to Berger, corresponding simplified equations are also derived. Considering the large amplitude free flexural vibration of orthotropic skew plates clamped along all the edges, it is shown that the Berger approximation leads to results good enough for engineering purposes. Amplitude vs period curves are presented for different aspect ratios and skew angles of the plate under two in-plane edge conditions. It is observed that the amplitude vs period behaviour is of the hardening type, i.e. period decreases with increasing amplitude.     

Almost sure weak exponential stability with a certain decay function of semilinear stochastic evolutionequations

In this paper the weak exponential stability with decay function of sample path, which are given by mild solution to a class of semilinear stochastic evolution equations, are presented. The analyses consist in using exponential martingale formula, Lyapunov functional and some special inequalities derived for our stability purposes. Two examples are given to illustrate the theory.     

Stability in mean of partial variables for stochastic reaction–diffusion systems with Markovian switching

This paper is denoted to investigating stability in mean of partial variables for stochastic reaction–diffusion equations with Markovian switching (SRDEMS). By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential equations with Markovian switching (SODEMS) and using Itô formula, sufficient criteria on uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, exponential stability in mean of partial variables for SRDEMS are first derived. An example is presented to illustrate the effectiveness and efficiency of the obtained results.     

On the matching equations of kinetic energy shaping in IDA-PBC

Interconnection and damping assignment passivity-based control scheme has been used to stabilize many physical systems such as underactuated mechanical systems through total energy shaping. In this method, some partial differential equations (PDEs) related to kinetic and potential energy shaping shall be solved analytically. Finding a suitable desired inertia matrix as the solution of nonlinear PDEs relevant to kinetic energy shaping is a challenging problem. In this paper, a systematic approach to solving this matching equation for systems with one degree of underactuation is proposed. A special structure for desired inertia matrix is proposed to simplify the solution of the corresponding PDE. It is shown that the proposed method is more general than that of some reported methods in the literature. In order to derive a suitable desired inertia matrix, a necessary condition is also derived. The proposed method is applied to three examples, including pendubot, VTOL aircraft, and 2D SpiderCrane.     

总能量守恒与辛几何算法

以正压大气原始方程为例子,以总能量守恒为主线,介绍动力保守系统两类重要算法———总能量守恒算法和辛几何算法,讨论了两者之间的关系,并给出具体的算例,说明两类算法的有效性.     

A new approach to numerical integration by means of steady-state flux in a slab

The definite integral is generally interpreted geometrically as an “area”. An alternate interpretation as a steady-state “flux” through a unit slab is derived, which leads to a new method of numerical integration. The usual sum of a large number of approximate areas is replaced by the flux through a “single” increment.The method involves the solution of a system of linear finite difference equations. The coefficient matrix is tri-diagonal and is solved efficiently by the Thomas algorithm. During the iterative process the coefficients are determined by simple quadrature schemes applied to each increment.Error analysis revealed that an expression could be derived for the roundoff error associated with the final Thomas iteration. It is shown that the roundoff error is smallest when the matrix coefficients a_k\S>1. The method is shown to be superior to the classical methods due to its simplicity and tolerance for variable increment size. In addition, a new function is determined which is useful in diffusion studies. Numerical data are presented confirming these results.     

Non-Linear Functional Relations and Superposition Principles in Viscoelasticity

Non-linear constitutive functional equations for isotropic viscoelastic materials with small and finite deformations are derived on the basis of tensorial expansions. These equations express the first-order as well as simple and joint second-order effects. Further, the corresponding non-linear superposition principles are formulated.     

The linear Legendre mother wavelets operational matrix of integration and its application

The linear Legendre mother wavelets operational matrix of integration P is derived. A general procedure of forming this matrix P is given. This matrix P can be used to solve problems such as calculus of variations, differential equations, optimal control and integral equations. Illustrative examples are included to demonstrate the validity and applicability of matrix P.