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The instrument line shape (ILS) of a Fourier-transform spectrometer is expressed in a matrix form. For all line shape effects that scale with wavenumber, the ILS matrix is shown to be transposed in the spectral and interferogram domains. The novel representation of the ILS matrix in the interferogram domain yields an insightful physical interpretation of the underlying process producing self-apodization. Working in the interferogram domain circumvents the problem of taking into account the effects of finite optical path difference and permits a proper discretization of the equations. A fast algorithm in O(N [log.sub.2] N), based on the fractional Fourier transform, is introduced that permits the application of a constant resolving power line shape to theoretical spectra or forward models. The ILS integration formalism is validated with experimental data. OCIS codes: 070.6020, 300.6300, 120.6200.

A dynamic model for stiffened composite multicell wing structures is developed. In this model, the extensional, bending, and coupling stiffnesses are calculated not only from the properties of the composite laminates of the wing skin but also from the stringers and spar flanges, which are treated as fibers of a pseudolamina. The arrangement of the wing spar webs and ribs is then treated like a sandwich honeycomb core, from which an equivalent transverse shear modulus of the wing structures is calculated. With these estimated properties, the composite wing structure is modeled, incorporating the effects of bending-torsion coupling, warping restraint, transverse shear deformation, shape of airfoil, rotary inertia, etc. To avoid complexity of formulation, the matrix form representation is introduced, which then makes most of the equations for the vibration analysis bear the same form as those of the classical beam theory. Thus, by following the classical approach, the composite wing structures can be studied analytically.

The Rayleigh-Schrodinger perturbation theory (PT) scheme has been reformulated in matrix notation for purposes of teaching. A recursive algorithm of the usual PT for nondegenerate systems directed to computational practice can be described in matrix form to find eigenvalue and eigenvector corrections to any desired order for Hermitian or symmetrical secular equations. That gives a very simple way to solve the Schrodinger equation in a matrix formalism.

Issues concerning biochemical reaction thermodynamics using Gibbs energy equations at three levels are presented.

The paper presents a matrix representation of filter banks corresponding to spline wavelets with shifted supports. The matrix form of the decomposition and reconstruction filters simplifies the representation of nonuniform nonstationary wavelet transforms built on nonuniform grids on a finite interval. Such a representation of filters is used, for example, in constructing error-correcting codes. Bibliography: 7 titles., 1. THE SPACE OF COORDINATE SPLINES On an interval [a, b] [subset] [R.sup.1], consider a grid [[DELTA].sup.L] with two supplementary nodes outside of [a, b], [Please download the PDF to [...]

In this paper, an approach to computational flutter analysis is presented, which permits the determination of the critical wind velocity that initiates damping- and stiffness-driven flutter of cable-suspended bridges. Dynamic response may be coupled elastically and/or aerodynamically, with the developed algorithm, the so-called pK-F method determining the preflutter and postflutter responses by solution to the modal equations of motion. The entire method is presented in matrix form, so as to be easily implemented into finite element systems. As an example, the pK-F method is applied to the Luling cable-stayed bridge, which was experimentally tested for flutter in the wind tunnel. Also, examples are provided for flutter determination with different deck sections. The pK-F method has proved reliable in its methodology and efficient in its use. The generality of the method permits more flutter scenarios to be examined, including construction stages and different flutter derivatives for different portions of the bridge structure., The pK-F method for the preflutter and postflutter analysis of cable-suspended bridges is presented. The method allows a single algorithm for determining the damping- and stiffness-driven flutter. The method is presented in matrix form for application to finite element systems. The application of the method to the Luling cable-stayed bridge which was tested for flutter in a wind tunnel is also described.

The two-dimensional (2-D) parabolic equation (PE) is widely used for making radiowave propagation predictions in the troposphere. The effects of transverse terrain gradients, propagation around the sides of obstacles, and scattering from large obstacles to the side of the great circle path are not modeled, leading to prediction errors in many situations. In this paper, these errors are addressed by extending the 2-D PE to three dimensions. This changes the matrix form of the PE making it difficult to solve. A novel iterative solver technique, which is highly efficient and guaranteed to converge, is being presented. In order to confine the domain of computation, a three-dimensional (3-D) rectangular box is placed around the region of interest. A new second-order nonreflecting boundary condition is imposed on the surface of this box and its angular validity is established. The boundary condition is shown to keep unwanted fictitious reflections to an acceptable level in the domain of interest. The terrain boundary conditions for this 3-D PE method are developed and an original technique for incorporating them into the matrix form of the iterative solver is described. This is done using the concept of virtual field points below the ground. The prediction accuracy of the 3-D PE in comparison to the 2-D PE is tested both against indoor scaled frequency measurements and very high frequency (VHF) field trials. Index Terms--Mobile radio, parabolic equation, radiowave propagation, terrain.

Mathematical models of a biped and quadruped walking are considered. The planar five-link biped consists of a one-link trunk and two identical two-link legs. In the single support motion (swing phase), the biped has five degrees of freedom and is described by a system of nonlinear ordinary differential equations of the 10th order. These equations are written in a visible matrix form. A seven-link planar biped with massless feet is also considered. In this paper, the swing motion of the biped is assumed a ballistic (passive) one. There are no active torques in the interlink joints during the single support motion--only the gravity force and ground reaction forces are applied to the biped. The problem of design of ballistic swing motion is reduced to the boundary-value problem for the system of nonlinear differential equations with given initial and final configurations and the duration of the half-step. It is assumed that there is no friction in the interlink joints (note that the friction in the human joints is very small). Therefore, in the ballistic swing motion the complete energy of the system (kinetic energy plus potential one) is conserved and the system has the energy integral. Due to this fact some properties of symmetry of ballistic motions are proved. Linearized model can be reduced to the canonical Jordan form. Then the linear boundary-value problem can be solved analytically. Using numerical investigations of the linear model we have animated the biped walking, which occurs 'similar' to the human gait: the transferring leg moves over the support, the legs bend with knees forward, and the trunk makes one vibration during one half-step. All these features have not been prescribed beforehand in the statement of the problem. Iteration process is used to solve the nonlinear boundary-value problem. For some cases, several solutions of this nonlinear problem are found numerically. The symmetry properties of the ballistic motions help to find numerically the solutions of this complex nonlinear problem. The ballistic motion is also designed numerically for the three-dimensional biped model with 6, 8, 9, and finally with 11 degrees of freedom. The double-support phase is assumed an instantaneous one. During this phase there is a collision of the transferring (swing) leg and the support. Active impulsive torques are applied in the interlink joints at this instant. These impulsive torques and ground reaction forces are described by delta functions of Dirac. Thus, with this impulsive control, most of the efforts are applied in the double-support phase. Formulas for the energy cost of impulsive control actions have been found. Some problems of optimal distribution of the impulsive actions between the joints are discussed. A planar seven-link model of biped with arms is considered. This model consists of a one-link trunk, two identical one-link arms, and two identical two-link legs with point feet. Ballistic gait of this biped model is studied. The goal of this study is to find the optimal amplitude of the arms swinging, minimizing the energy consumption. We show numerically the existence of the optimal amplitude of the arms swinging. Ballistic walking of a quadruped is investigated too. Three types of quadruped gaits, bound, amble, and trot, are considered. For each kind of the gait, ballistic locomotion is designed and energy consumption is evaluated. DOI: 10.1061/(ASCE)AS.1943-5525.0000017 CE Database subject headings: Ballast; Mathematical models; Control systems; Design; Aerospace engineering. Author keywords: Locomotion; Ballistic; Control; Impulsive; Biped; Quadruped; Leg; Arm; Torso; Mathematical model; Boundary-value problem.

A method to concisely quantify, compare, and identify mode shapes for flutter analysis using orthogonalized basis vectors is developed. The procedure numerically describes wing structural mode shapes as scalar projections onto a reduced set of basis vectors. The basis vectors are baseline wing shapes derived from the mode shapes of a reference wing model, and mode shapes from other wing models are concisely related to the basis vectors using the scalar projections. The resulting quantifier describes the wing modes in terms of the physical wing shapes from the reference model. The technique is demonstrated on a simple wing model from which the basis vectors are derived. Mass elements are added to the wing in four different configurations to produce various mode shapes for comparison to the basis set. These mode shapes are quantified in terms of basis vector components that are expressed concisely in matrix form. Visual comparisons of the mode shapes to the basis vectors show that the numeric characterizations are consistent with the visual interpretations. Comparison of the four configurations to one another indicates that the numeric components distinguish subtle differences in wing deformation as well as differences in the overall shape of the deformed wing. DOI: 10.2514/1.42591

We consider reconstruction of a wave field distribution in an input/object plane from data in an output/ diffraction (sensor) plane. We provide digital modeling both for the forward and backward wave field propagation. A novel algebraic matrix form of the discrete diffraction transform (DDT) originated in Katkovnik et al. [Appl. Opt. 47, 3481 (2008)] is proposed for the forward modeling that is aliasing free and precise for pixelwise invariant object and sensor plane distributions. This 'matrix DDT' is a base for formalization of the object wave field reconstruction (backward propagation) as an inverse problem. The transfer matrices of the matrix DDT are used for calculations as well as for the analysis of conditions when the perfect reconstruction of the object wave field distribution is possible. We show by simulation that the developed inverse propagation algorithm demonstrates an improved accuracy as compared with the standard convolutional and discrete Fresnel transform algorithms. OCIS codes: 070.2025, 100.3010, 100.3190.

This paper proposes a coupling method involving the finite element (FE) equation of a discretized region and an analytical equation along with the field singularity of line currents in two-dimensional space. The singular field in the interior region is represented by Green's function of the line source, and the exterior region of air, conductor, or ferromagnetic material is represented by using the finite element method (FEM). An analytical expression for a magnetic field that contains unknown coefficients is coupled with the FE formulation for a coupled system equation with a matrix form. A numerical experiment relating to a line current near a ferromagnetic material shows the validity of this coupling method. Index Terms--Analytical solution, coupling schemes finite element method (FEM), Fourier series expansion, singular line current.

The transition from the continuously rotating dielectric ellipsoid approach to the discrete periodic collection of wave plates is investigated by comparing an exact analytic solution found using a Bloch-Lyaponov transformation on the 4 x 4 matrix form of Maxwell's equations and the numerical solution. The validity of the analytic solution depends only on the number of sublayers within the unit cell and not on the number of periods in the sample. The circularly polarized Bragg-type selective reflection peak is shown to exist with helices containing as few as [N.sub.l] = 3 sublayers in a single period, but due to the appearance of higher Fourier harmonics in the dielectric tensor, additional selective reflection peaks appear. The case of [N.sub.l] = 4 corresponds to the folded Solc-type filter case with a twist angle of [pi]/4, but it acts as a reflection filter for unpolarized light. Hence using this fact with liquid crystalline structures, polarization insensitive tunable filters can be built. OCIS codes: 260.2110, 360.2460.

We investigated the effects of surface-treated organophilic clay on the crystallization of poly(L-lactide) (PLLA) in their hybrids. The natural nano-clay in PLLA/clay hybrids acts as a heterogeneous nucleating agent to facilitate crystallization. On the contrary, extensive distributions of induction periods for nucleation are observed in the individual spherulites of neat PLLA and PLLA/organophilic clay hybrids. Therefore, it is suggested that nucleation type of neat PLLA and PLLA/organophilic clay hybrids implies nearly growth geometry as a homogeneous one. Further, under the presence of nano-clay in their composites, PLLA matrix form the orthorhombic lattice structure corresponded to the α-form crystal. Since this experimental fact implies little effect of the clay particles on polymorphism of PLLA crystal, the nucleating effect of the organophilic clay seems weaker than the natural clay itself. However, an increase in clay content enhances the growth rates of spherulite for hybrids. Consequently, most of hybrids exhibit an increase in overall crystallization rates at any crystallization temperature in spite of relatively lower nucleation rate of PLLA crystallites itself. In addition, the Avrami exponents (n) obtained by relatively low crystallization temperature ranged from 4 to 6, implying that the growth geometry was dominated sheaf-like structure in early stage of isothermal crystallization. POLYM. ENG. SCI., 48:1103-1111, 2008. [C] 2008 Society of Plastics Engineers, INTRODUCTION Poly(L-lactide) (PLLA) has been known a biodegradable and biocompatible crystalline polymer with applications such as surgical suture and drug delivery systems [1-4]. The combination of PLLA and low-level loadings [...]

An analysis method for multiconductor transmission lines embedded in inhomogeneous bi-anisotropic media is presented. The Maxwell-Boffi equations, accompanied by the Maxwell-Minkowski ones, are expressed as Taylor series of the operating frequency where the zeroth- and first-order terms are retained. The reduced problem is solved using the potential formulation through the static 2-D free-space Green's function. The method of moments is employed to numerically solve the set of quasi-TEM integral equations, to produce the Telegrapher's equations, and to derive the circuit parameters in matrix form. The procedure is augmented by providing in closed form the field-coupling integrals. Index Terms--Bi-anisotropic media, multiconductor transmission lines, quasi-TEM theory.

This paper presents a suitable method for time-domain identification of synchronous machine parameters from the hybrid state model recently introduced by the authors in a compact matrix form. The saturated version of this model is developed in terms of generator equivalent-circuit parameters. The load rejection test of a combined resistive/inductive load is performed for the parameter identification while the online symmetrical three. phase short-circuit test is carried out for the model cross-validation. For weak power factor initial loads connected to the generator, the rotor speed is quite constant during the full load rejection test. Thus, the mechanical transients do not have any influence on estimated electrical parameters since they are decoupled from the electrical model of the machine. The method is successfully applied for the parameter identification of 380 V, 3 kV.A, four-pole, 50 Hz saturated synchronous generator. Index Terms--Cross-validation, identification, load rejection, nonlinear hybrid state model, saturation, synchronous generator.

The problem of allocation of fuel consumption and carbon-dioxide emissions from transport aircraft is presented. An accurate comprehensive program for transport aircraft has been developed. The model includes a geometry deck with 12 subsystems, a separate engine input deck with basic parameters, a database of engine performance from independent simulation, an aerodynamics model for all flight conditions, and an operational deck. Validation of the model is discussed from the point of view of aerodynamics and payload-range performance. The aircraft considered are the Boeing B-737-500, B-747-400, and B-777-300, and the Airbus A340-300. Parametric studies are shown in terms of flight distance, passenger load, baggage allowance, operation with an en route stop, and direct flight. Calculations of best flight range and average passenger load have been considered. Data are presented in matrix form to be used for allocation of carbon dioxide in carbon trading schemes and for the critical evaluation of emissions from civil and commercial operations. It is shown that emissions per passenger per nautical mile range from 0.5 to 1.5 times the reference conditions, which is taken from the design range at full passenger load. It is also shown that fuel and emission savings can be achieved from optimal flight distance.

This paper derives a simple closed-form expression for computing the power spectral density (PSD) of constrained sequences whose constraints are characterized by a function of an ergodic Markov process specified in terms of a Mealy machine. A suitable matrix description of the stochastic behavior of the constrained sequence is used to express its autocorrelation sequence in a compact matrix form that simplifies the calculation of the PSD. Examples of the application of this technique in cases of practical interest are provided, including differentially encoded binary sequences, source-driven binary Huffman codes, maximum entropy (d, k) codes, and convolutional- or block-encoded sequences. A unified treatment to several widely used constrained sequences is provided. Index Terms--Autocorrelation function, Fourier transform, Markov chain, Mealy machine, Moore machine, power spectral density (PSD).

An affine mapping mathematical expression of the double-random-phase encryption technique has been deduced utilizing the matrix form of discrete fractional Fourier transforms. This expression clearly describes the encryption laws of the double-random-phase encoding techniques based on both the fractional Fourier transform and the ordinary Fourier transform. The encryption process may be regarded as a substantial optical realization of the affine cryptosystem. It has been illustrated that the encryption process converts the original image into a white Gaussian noise with a zero-mean value. Also, the decryption process converts the data deviations of the encrypted image into white Gaussian noises, regardless of the type of data deviations. These noises superimpose on the decrypted image and degrade the signal-to-noise ratio. Numerical simulations have been implemented for the different types of noises introduced into the encrypted image, such as the white noise with uniform distribution probability, the white noise with Gaussian distribution probability, colored noise, and the partial occlusion of the encrypted image.

A novel method for kinematic analysis of parallel-axes epicyclic gear trains is presented, called the incidence and transfer method, which uses the incidence matrices associated with the edge-oriented graph associated to the mechanism and the transfer joints (teeth contact joints). Relative to such joints, a set of independent equations can be generated for calculating the angular positions, velocities, and accelerations. Complete kinematic equations are obtained in matrix form using a base of circuits from a cycle matroid. The analysis uses the relationships between the number of mobile links, number of joints, and number of circuits in the base of circuits, together with the Latin matrix (whose entries are function of the absolute values of the partial gear ratios of the transmission). Calculating the rank of the Latin matrix can identify singularities, like groups of gears that rotate as a whole. Relationships between the output and input angular velocities and accelerations are then determined in a matrix-based approach without using any derivative operations. The proposed method has general applicability and can be employed for systems with any number of gears and degrees of freedom, as illustrated by the numerical examples presented. [DOI: 10.1115/1.2337310]

In order to deal with the stability problem restricted by the finite-difference time-domain (FDTD) and conventional pseudospectral time domain (PSTD), the multidomain PSTD algorithm based on alternating-direction implicit (ADI) technique is proposed in this paper. This algorithm improves the stability and efficiency of conventional PSTD, while it maintains the accuracy and flexibility of conventional PSTD for an accurate treatment of arbitrarily curved objects. A compact matrix form is derived to effectively describe two-dimensional ADI multidomain pseudospectral time domain (ADI-MPSTD) algorithm. Numerical results show an excellent agreement with analytical solutions as well as results obtained by the FDTD algorithm, and fully demonstrate a remarkable improvement in stability and efficiency. Index Terms--Alternating-direction implicit (ADI), multidomain, pseudospectral time domain (PSTD), stability problem.

A unique ultranarrowband fiber-optic phase-shifted Fabry-Perot Bragg grating filter for atmospheric water vapor lidar measurements was designed, fabricated, and successfully tested. Customized optical fiber Bragg gratings were fabricated so that two transmission filter peaks occurred: one (89% transmission, 8 pm FWHM) near the 946-nm water vapor absorption line and the other peak (80% transmission, 4 pm FWHM) at a region of no absorption. Both transmission peaks were within a 2.66-nm stop band. Demonstration of tension tuning to the 946.0003-nm water vapor line was achieved, and the performance characterization of custom-made optical fiber Bragg grating filters are presented. These measurements are successfully compared to theoretical calculations using a piecewise-matrix form of the coupled-mode equations. OCIS codes: 010.3640, 060.2310, 280.1910.

The spectral analysis of an infinite rectangular wave-guide with dielectric-filled transverse corrugations is performed to investigate supporting backward waves in this structure. The corrugations act as a capacitive immittance surface which provides a suitable environment for left-hand propagation to occur in an undersized rectangular waveguide having an inherent shunt inductance of the evanescent transverse electric dominant mode. The analysis of the corrugated waveguide is based on Floquet's theorem, where the problem is solved in terms of a unit cell; then Galerkin's projection technique is applied to reduce the integral equation to the matrix form. The dispersion relation and the modal field expressions are derived and, for the special case of wall-to-wall corrugations with single current harmonic, rather simpler expressions are obtained. The effect of the different design parameters on the dispersion characteristics is studied with emphasis on the left-hand propagation band. Some representative field plots of the dominant mode of the corrugated structure are depicted. Sample results are compared with Ansoft High Frequency Structure Simulator (HFSS) and with an equivalent circuit model developed for the same structure. The results exhibit very good agreement. Index Terms--Corrugated waveguide, left-hand propagation, metamaterial transmission lines, spectral analysis.

Osteocytes, former osteoblasts entombed in the bone matrix, form an extensive cell communication network that is thought to detect microdamage and mechanical strains and to transmit signals leading to repair and compensatory bone augmentation or reduction. Bone active hormones and drugs control the integrity of this network by regulating osteocyte apoptosis, which might be a determinant of bone strength. Herein we demonstrate that mechanical stimulation by stretching activates the ERKs, which in turn are responsible for the attenuation of osteocyte apoptosis. The effect of osteocyte stretching is transmitted by integrins and cytoskeletal and catalytic molecules, such as Src kinases. Stretch-induced antiapoptosis also requires nuclear translocation of ERKs and new gene transcription. The evidence linking mechanical stimulation, activation of an integrin/cytoskeleton/Src/ERK signaling pathway, and osteocyte survival provides a mechanistic basis for the profound role of mechanical forces, or lack thereof, on skeletal health and disease. bone; mechanotransduction; osteoblastic cells; caveolae; stretching

The objective of the present work is to present the numerical analysis of the computer hard disk slider. The air film pressure is calculated using the finite element method. The conjugate-gradient method and the perturbation method are employed in the static analysis of the slider. The steady state attitude of the femto slider is studied for various radial positions and skew angles. It is found that the perturbation method is an efficient method for gradient evaluation. Also, it is shown that optimization of the Hessian matrix form accelerates the search process. [DOI: 10.1115/1.1843168] Keywords: Hard Disk Drive Slider, FEM, Optimization, Static Analysis

A variational full-field method is presented in this paper for the free vibration analysis of open circular cylindrical laminated shells supported at discrete points. A differential equation in matrix form is developed using the first-order shear deformable theory of shells, and rotary inertia is included. The displacement fields are defined by using very high-order interpolating polynomials and a large number of preselected nodal points on the reference surface of the shell. Each nodal point has 5 degrees of freedom, three displacement components, and two components of the rotation of the normal to the reference surface. The stiffness and mass matrices are obtained using the strain and kinetic energy functions. The numerical results are calculated for shallow and deep circular cylindrical panels with four-, six-, and eight-point supports along the two parallel straight edges. The values of the natural frequency obtained from the present method show good agreement with published data in the literature. CE Database subject headings: Vibration; Cylindrical shells; Composite materials; Laminates; Numerical analysis.

We present a semianalytical method for calculating the electromagnetic field distribution in a multilayer slab conductor. This is a very advanced and comprehensive method because there is no limitation for the shape of the exciter and the number of layers (i.e., an exciter of any arbitrary shape and at any distance near the surface of a multilayer conductor with a large number of layers can be modeled). We solve the Helmholtz equation in three dimensions by separation of variables. We develop a two-dimensional fast Fourier transform (FFT) integral model and use exponential functions in the third dimension. We solve this integral model analytically and numerically by using the custom matrix form AX = B and a system of algebraic equations, respectively. To verify this method, we solve a simple example problem both by the new method and a finite-element method (FEM) program. The results are in good agreement with each other. Index Terms--Arbitrary shape exciters, electromagnetic field distribution, fast Fourier transform (FFT), multilayer conductors, semianalytical methods.

In this paper, a new split-radix fast Hartley transform (FHT) algorithm is proposed for computing the discrete Hartley transform (DHT) of an arbitrary length N = q x [2.sup.m], where q is an odd integer. The basic idea behind the proposed FHT algorithm is that a mixture of radix-2 and radix-8 index maps is used in the decomposition of the DHT. This idea and the use of an efficient indexing process lead to a new decomposition different from that of the existing split-radix FHT algorithms, since the existing ones are all based on the use of a mixture of radix-2 and radix-4 index maps. The proposed algorithm reduces substantially the operations such as data transfer, address generation, and twiddle factor evaluation or access to the lookup table, which contribute significantly to the execution time of FHT algorithms. It is shown that the arithmetic complexity (multiplications + additions) of the proposed algorithm is, in almost all cases, the same as that of the existing split-radix FHT algorithm for length- q x [2.sup.m]DHTs. Since the proposed algorithm is expressed in a simple matrix form, it facilitates an easy implementation of the algorithm, and allows for an extension to the multidimensional case. Index Terms--Discrete Hartley transform (DHT), fast Hartley transform (FHT) algorithms, mixed radix, split radix.

In this paper, a new radix-2/8 fast Fourier transform (FFT) algorithm is proposed for computing the discrete Fourier transform of an arbitrary length N = q x [2.sup.m], where q is an odd integer. It reduces substantially the operations such as data transfer, address generation, and twiddle factor evaluation or access to the lookup table, which contribute significantly to the execution time of FFT algorithms. It is shown that the arithmetic complexity (multiplications+additions) of the proposed algorithm is, in most cases, the same as that of the existing split-radix FFT algorithm. The basic idea behind the proposed algorithm is the use of a mixture of radix-2 and radix-8 index maps. The algorithm is expressed in a simple matrix form, thereby facilitating an easy implementation of the algorithm, and allowing for an extension to the multidimensional case. For the structural complexity, the important properties of the Cooley-Tukey approach such as the use of the butterfly scheme and in-place computation are preserved by the proposed algorithm. Index Terms--Fast Fourier transform (FFT), fixed radix, mixed radix, split radix.

The penetration of a wide-brand electromagnetic pulse into a conducting layer is formulated in terms of an implicit time-domain integral equation and cast into matrix form via the method of moments. Though such a wide-band problem indeed calls for a time-domain solution, one may argue that the frequency-dependent attenuation of the field penetrating the conductor could suggest a frequency-domain approach that would greatly reduce the number of unknowns. The proposed via media is to use spatio-temporal wavelength functions instead of the standard pulse basis. Owing to their multiresolution property, both in the spatial and temporal domains, these functions can span the field propagating inwardly with substantially fewer terms. The reduction in the number of basis functions used is effected by the impedance matrix compression technique, which automatically omits the basis functions whose coefficients would be insignificant due to the attenuation. Reducing the number of basis functions renders the matrix equation much smaller and the overall solution for more efficient. Index Terms--Electromagnetic scattering by absorbing media, electromagnetic transient analysis, impedance matrix compression, integral equations, moment methods, time-domain analysis, wavelet transforms.

The purpose of this paper is to estimate the direction of arrival (DOA) of the signal of interest (SOI) in the presence of both coherent and noncoherent interferences and multipath components utilizing a combined temporal and spatial processing technique based on a direct data domain approach. The concept of cyclostationarity, which deals with the temporal information of the SOI, is used to extract signals having the same cycle frequency and null out the co-channel interferences and additive noise. Hence, the signal detection capability can be significantly increased over conventional filtering when the length of the data record is limited. The main contribution of the paper is that by combining temporal and spatial processing based on a direct data domain approach one can handle number of signals along with their various coherent and noncoherent multipaths and interferences which can exceed the number of antenna elements. Hence, this methodology may be advantageous over conventional spatial processing when the number of degrees of freedom can never exceed the number of antenna elements in the array. However, the number of multipaths and interferers at the same cycle frequency has to be less than approximately 66 % of the antenna elements. Since we do not form a covariance matrix of the data, this method is quite suitable for short data lengths or when the environment is quite dynamic. Hence, in the proposed algorithm, while the estimation of the cyclic array covariance matrix is avoided, we develop a new matrix form using extremely short data samples. As a result, the computational load in the proposed approach is relatively reduced and the robustness of the estimation of SOI is significantly improved when the number of available snapshots is extremely limited. Numerical results are presented to illustrate the efficiency and accuracy of this method. Index Terms--Cyclostationarity, direction of arrival (DOA), direct data domain, matrix pencil, phased arrays.

Adaptive structures involving large imposed deformation often go beyond the boundary, of linear theory and they should be treated as 'nonlinear' structures. A generic nonlinear finite element formulation for vibration sensing and control analysis of laminated electro/elastic nonlinear shell structures is derived based on the virtual work principle. A generic curved triangular piezoelectric shell element is proposed based on the layerwise constant shear angle theory. The dynamic system equations, equations of electric potential output and feedback control force defined in a matrix form are derived. The modified Newton-Raphson method is adopted for nonlinear dynamic analysis of large and complex piezoelectric/elastic/control structures. A finite element code for vibration sensing and control analysis of nonlinear active piezoelectric structronic systems is developed. The developed piezoelectric shell element and finite element code are validated and then applied to control analysis of flexible electro-elastic (piezoelectric-elastic) structural systems. Vibration control of constant-curvature electro/elastic beam and plate systems are studied. Time-history responses of free and controlled nonlinear electro/elastic beam and plate systems are presented and nonlinear effects discussed.

The multiplicity of temporal priors proposed for regularization of the bioelectromagnetic source imaging problems [e.g., the inverse electrocardiogram (ECG) and inverse electroencephalogram (EEG) problems], is discordant with the fact that fundamental statistical principles sharply limit the choice. Thus, our objective is to derive the form of the prior consistent with the general unavailability of temporal constraints. Writing linear formulations of the inverse ECG and inverse EEG problems as H = FG + N (where the ith columns of matrices H, G, and N, are data, signal, and noise vectors at time step i, and F is the transfer matrix), and using the noninformative principle that features of the spatiotemporal prior not supplied a posteriori should be invariant under temporal transformations, we show that the implied spatiotemporal signal autocovariance matrix (of the vector formed by the entries of G) is given in block matrix form as [C.sub.G[epsilon][GG']] = [epsilon][G'G][cross product]/[epsilon][[parallel]G[[parallel].sup.2] = ([epsilon][H'H]-[epsilon])[N'N][cross product][C.sub.g]/(F'F) [dot in circle] [C.sub.g] where [C.sub.g] is a matrix of unit trace proportional to the autocovariance matrix of any column of G (representing supplied information regarding the spatial prior), [epsilon][*] denotes expectation, superscript ' indicates transpose, [cross product] is the Kronecker product, [parallel] * [parallel] is Frobenius norm, and the 'matrix scalar product' [dot in circle] indicates the inner product of the two vectors formed by the entries of the two adjacent matrices (i.e., A [dot in circle] B [equivalent to] trace[A'B]). This result eliminates some uncertainties and ambiguities that have characterized spatiotemporal regularization methods--including eight methods previously introduced in this transactions. Ultimately, the result derives from an implied symmetry principle under which the form of a nontrivial noninformative temporal component of the prior can be identified. Among other things, separability of the spatiotemporal prior in terms of the above Kronecker product can be thought of as the expression of the lack of 'entanglement' of the spatial and temporal contributions (a consequence of noninformativity). The approach is generalized to the important cases of non-Gaussian spatial priors, and signal and noise that are not independent (transfer matrix noise). We also demonstrate a means for computational complexity reduction, related to the application of a particular orthogonal transformation, having features dependent on whether or not the transfer matrix represents a surjective mapping. Index Terms--Biomedical electromagnetic imaging, inverse problems, map estimation, stochastic approximation, time domain analysis.