Analytic steady-state solutions to dynamic grating envelope

Abstract

The photorefractive holographic recording is a dynamic grating formulation process, where the grating is induced by the interference modulation of two beams, and the energies of the beams are exchanged with each other owing to their interaction in the induced grating. The grating modulation envelope is a comprehensive analysis for holographic dynamic recording and non-destructive readout, but analytic solutions can only be obtained by simultaneously solving the materials equations and the coupled wave equations. In this paper, based on Kukhtarev's model and Moharam's field function exact steady-state analytic expressions for dynamic grating envelopes are deduced for any constant values of light modulation depth and light excitation efficiency. Thus their approximations for straight formulation instead of parametric formulation are then obtained. These steady-state analytic solutions to envelopes describe the dynamic holographic recording and readout more clearly and exactly.     

An algorithm for profilometry by white-light phase-shifting interferometry

Abstract

In the case of white-light interferometry, the usual phase shifting methods cannot be used because the modulation in the interference intensity is due to both the phase variation and to the coherence envelope. We propose a practical approach in which the coherence envelope is considered as locally linear. The classical four-point calculation algorithm is adapted to a set of seven intensities which are weighted with adapted coefficients in order to compensate for the effect of the coherence envelope. The capabilities of this method are described theoretically.     

Determination of r‐curves of steel fiber reinforced concrete from size effect tests

Abstract

A developed size effect law for blunt fracture is used to determine the R‐Curves and related parameters of steel fiber reinforced concrete. Geometrically similar single‐edge notched beams of different sizes made of cementitious mixes at various fiber volume fractions and different maximum aggregate sizes were used for the tests. Fracture energy of concrete is identified by linear regression using the size effect law. From the experimentally calibrated size effect law, the R‐curve is obtained as the envelope of the family of fracture equilibrium curves for different specimen sizes.     

Determination of optical constants and inhomogeneity of optical films by two-step film envelope method

A simple two-step film envelope method has been proposed to determine the optical constants and small inhomogeneity of the optical films, which uses maximum envelopes and minimum envelope of the normal incidence transmittance of the two-step film. The two-step films were prepared by stopping the deposition process in the middle of the designed sputtering time, and then, after a full cooling down to room temperature, repeating the same deposition process again to complete the whole preparation of the films. The optical constants of Nb₂O₅-TiO₂ mixed films were calculated by two-step film envelope method and traditional envelope method. The experimental results demonstrate that the average refractive index and extinction coefficient calculated by two-step film envelope method are more accurate than those calculated by the traditional envelope method.     

Piecewise constant solutions of integral equations via Walsh functions

Abstract

Double Walsh series is used to obtain the piecewise‐constant solutions of integral equations as well as convolution integral. Some special properties of the Walsh functions are derived. The Volterra and Fredholm integral equations are transformed, respectively, into simultaneous linear algebraic equations, which are then solved to obtain the piecewise constant solutions.     

Efficient Integration of Sufficient Dimension Reduction and Prediction in Discriminant Analysis

Sufficient dimension reduction (SDR) methods are popular model-free tools for preprocessing and data visualization in regression problems where the number of variables is large. Unfortunately, reduce-and-classify approaches in discriminant analysis usually cannot guarantee improvement in classification accuracy, mainly due to the different nature of the two stages. On the other hand, envelope methods construct targeted dimension reduction subspaces that achieve dimension reduction and improve parameter estimation efficiency at the same time. However, little is known about how to construct envelopes in discriminant analysis models. In this article, we introduce the notion of the envelope discriminant subspace (ENDS) as a natural inferential and estimative object in discriminant analysis that incorporates these considerations. We develop the ENDS estimators that simultaneously achieve sufficient dimension reduction and classification. Consistency and asymptotic normality of the ENDS estimators are established, where we carefully examine the asymptotic efficiency gain under the classical linear and quadratic discriminant analysis models. Simulations and real data examples show superb performance of the proposed method. Supplementary materials for this article are available online.     

Biaxial testing of continuous fibre reinforced aluminium tubes

Abstract

Composite tubes of aluminium and aluminium alloy containing hoop wound alumina (Altex) fibres were fabricated using a liquid metal infiltration method. The tubes were well consolidated, with low porosity, and good bonding between fibre and matrix, as confirmed using ‘rule of mixtures’ calculations of elastic modulus. Mechanical properties were evaluated in the principal directions of the tube under uniaxial and biaxial stress loading conditions, and damage modes were studied. Stress quarter diagrams were constructed on the basis of a maximum stress failure mechanism, and failure envelopes were produced using the measured values of yield stress and failure strength. The composition and condition of the matrix was shown to influence the shape of the failure envelope and, in turn, the mode of failure of the tube for a given biaxial stress ratio. Good correlation was obtained between predictions made from the stress quarter diagrams and the fracture paths observed in tested tubes.     

Influence of substrate absorption on accuracy of determination of refractive index and thickness of uniform thin chalcogenide Cu1[As2(S0.5Se0.5)3]99 film

The envelope method is a commonly used method for determination of some important optical constants, by using the envelopes of the transmittance T(λ) and/or reflectance R(λ) spectrum of the thin film deposited on transparent substrate. Two envelope methods were carried out in this paper: standard—method which assumes that substrate is absolutely transparent and modified—method which takes substrate absorption into account.The investigated sample is a uniform thin chalcogenide Cu₁[As₂(S_0.5Se_0.5)₃]₉₉ film, deposited onto two kinds of a weakly absorbing substrates that differ in thickness.It was shown that the degree of accuracy in determination of chosen optical parameters for both investigated samples is notably improved when the absorbance of the bare substrates is considered in the expressions for the envelopes.     

Split Regularized Regression

Abstract

We propose an approach for fitting linear regression models that splits the set of covariates into groups. The optimal split of the variables into groups and the regularized estimation of the regression coefficients are performed by minimizing an objective function that encourages sparsity within each group and diversity among them. The estimated coefficients are then pooled together to form the final fit. Our procedure works on top of a given penalized linear regression estimator (e.g., Lasso, elastic net) by fitting it to possibly overlapping groups of features, encouraging diversity among these groups to reduce the correlation of the corresponding predictions. For the case of two groups, elastic net penalty and orthogonal predictors, we give a closed form solution for the regression coefficients in each group. We establish the consistency of our method with the number of predictors possibly increasing with the sample size. An extensive simulation study and real-data applications show that in general the proposed method improves the prediction accuracy of the base estimator used in the procedure. Possible extensions to GLMs and other models are discussed. The supplemental material for this article, available online, contains the proofs of our theoretical results and the full results of our simulation study.     

Relaxed Simultaneous Congruences

 In certain digital signal processing applications, residues of an input integer signal x are measured with respect to integer moduli . The signal x is then recovered by solving the system of simultaneous linear congruences . Since the residues r _i are measured quantities, they are subject to noise contamination. To provide noise protection, the moduli m _i may be chosen to possess common factors. Accurate approximations for x may then be determined by solving approximate or ``relaxed" simultaneous congruences. This paper presents a coherent mathematical theory for the approximate solution of simultaneous congruences with inaccurate residues when no exact solution exists. After precisely formulating the notion of relaxed congruences, it is found that, under nonrestrictive technical assumptions, unique solutions to these congruences always exist. A variety of examples illustrating characteristics of solutions of relaxed congruences are provided, and a fast, efficient algorithm for solving them numerically is presented. The problem of finding an optimal approximate solution is then discussed. Several optimality criteria are proposed and procedures for finding optimal approximate solutions are outlined. Error bounds are derived which specify the maximum amount that an approximate solution based upon inaccurate residues may differ from the corresponding true solution based upon the exact residues. Received: January 12, 2001; revised version: December 23, 2002 Keywords: Residue number systems, Error correction, Error detection, Measurement noise, Linear simultaneous congruences.     

Nonlinearity-induced Modes and the Frequency Response of Coupled Nonlinear Fabry-Pérot Cavities

Abstract

We study the frequency response of a system of two coupled Kerr nonlinear cavities with the same or opposite signs of nonlinearity. In the framework of a slowly varying envelope approximation, we show the possibility of having various hysteresis loops in the transmission characteristics of the structure. We also investigate the power-dependent modes of the structure. For large powers we demonstrate the existence of new modes which do not have any linear analogue. These nonlinearity-induced modes show up in the multistable output when the input power is varied.     

The Fabry-Perot Interferometer. History,Theory, Practice and Applications

Abstract

A simple algebraic algorithm is proposed as a computational tool for the thin-lens design of a triplet which consists of a singlet and a cemented doublet. The triplet is required to yield specified amounts of lens power, primary spherical aberration, central coma, longitudinal chromatic aberration and secondary spectrum. The three element powers of the triplet are first obtained by solving the simultaneous linear equations of the total lens power, longitudinal chromatic aberration and secondary spectrum. A quadratic equation is obtained by combining the equations of spherical aberration and central coma, and the lens shapes are then obtained by solving this quadratic equation. The solving process is purely algebraic and is therefore easy to calculate and guarantees that all the solutions can be found.     

Superconducting telecommunication cable studies in Japan

Large capacity and long distance telecommunications media are fields in which full use of the excellent properties of superconducting coaxial cables may be applied. By employing a new conductor structure, characteristics of a 1.6 mm miniature superconducting coaxial pair were remarkably improved in a short time. Features such as low-loss (of the order of 1 dB km^?1 at 1 GHz), broad-band and low cross-talk etc. were demonstrated for these coaxial pairs.In cryogenic envelope studies, the 20–200 m long envelopes have been manufactured for evaluating thermal insulation and investigating cable cooling performance. Cooling experiments on the envelope, including cable splice, are now in progress.     

Development of cooling load temperature differential values for building envelopes in Thailand

Abstract

This article describes the development of cooling load temperature differential (CLTD) values for building envelopes made of materials commonly used in Thailand and using Bangkok weather data. The Bangkok design weather data are selected from 12 years of data collected by the meteorological department. Two sets of weather data for Bangkok are chosen. The first weather data set was selected based on dry bulb temperature of 0.4% annual cumulative frequency of occurrence. The second weather data set was selected based on dry bulb temperature of 0.4% hourly cumulative frequency of occurrence and solar radiation obtained from the ASHRAE mathematical model. The room parameters which have effects on thermal response, such as building envelope material, room decoration, and room conditions are investigated. 288 different room types for each exterior wall type and each roof type were checked. The values of amplitude and delay based on conduction weighting factors for a sinusoidal heat gain are analyzed. The distribution of the amplitude and delay of similar thermal response are grouped together and represented by a single point in the group. For each set of design weather data, 7 CLTD tables for exterior walls and 6 CLTD tables for roofs are developed.     

Optimization of laminated composite structure considering uncertainty effects

In this paper, the most conservative Tsai–Wu failure envelopes are obtained for laminated composite considering material as well as ply angle uncertainty. The uncertainty analysis is performed using Monte Carlo simulation (MCS). The obtained failure envelopes are then used as the constraint functions to perform the minimum weight design optimization problem using particle swarm optimization (PSO). Results show increase in weight of the laminate from the deterministic results and it varies from 4% to 50% depending upon the stacking sequence and loading condition. Substantial effects of uncertainty on the failure envelope and optimal design are quantified.     

大信号网络分析中的包络域

超越S参数的大信号网络分析是解决非线性问题的一个行之有效的方法,包络域是该分析法的一个重要概念,是指能同时表征载波基波和载波各高次谐波的包络的一种方法,它充分而形象地表征了系统的非线性特性.作者从基本原理出发详细分析了包络域的概念.     

Optical-constant calculation over an extended spectral region: application to titanium dioxide film

An iterative algorithm has been developed that takes starting values derived by an envelope method but then minimizes the influence of the envelopes and emphasizes the actual measured data. This combination avoids the difficulties inherent in the accurate drawing of the envelopes and makes it possible to extract the thickness and the optical constants of semiconducting and dielectric films over a wide spectral region, including regions of high absorption.     

A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test

We establish a joint central limit theorem for sums of squares and the fourth powers of residuals in a high-dimensional regression model. We then apply this CLT to detect the existence of heteroscedasticity for linear regression models without assuming randomness of covariates when the sample size n tends to infinity and the number of covariates p may be fixed or tend to infinity.     

Parameter identification of discrete systems via discrete Chebyshev transformation

Abstract

A new method is proposed for the parameter identification of linear time‐invariant discrete single‐input‐single‐output systems by the application of the discrete Chebyshev transformation. The input and output data sequences of a system represented by difference equation are first transformed into discrete Chebyshev spectra. Using spectrum matching, the parameter identification problem becomes the solution of a set of overdetermined simultaneous linear algebraic equations. Examples with and without noise contamination are given to illustrate the new method.     

Matrix Linear Discriminant Analysis

Abstract

We propose a novel linear discriminant analysis (LDA) approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional LDA and the ordinary least squares, we consider an efficient nuclear norm penalized regression that encourages a low-rank structure. Theoretical properties including a nonasymptotic risk bound and a rank consistency result are established. Simulation studies and an application to electroencephalography data show the superior performance of the proposed method over the existing approaches.