relaxation of three solenoidal wells and characterization of extremal three phase h measures we fully characterize quasiconvex hulls for three arbitrary solenoidal divergence free wells in dimension three with this aim we establish weak lower semicontinuity of certain functionals with integrands restricted to generic two dimensional planes and convex in up to three rank 2 directions within the planes within the framework of the theory of compensated compactness the latter represents an example when the differential constraints fail the constant rank condition but nevertheless the so called convexity still implies lower semicontinuity and fancyscript a quasiconvexity which essentially means that rank 2 convexity implies s quasiconvexity that is quasiconvexity in the sense of the divergence free differential constraints on the planes the proof employs a version of muller s estimates of haar wavelet projections in terms of the riesz transform the above semicontinuity result is then applied to the three solenoidal wells problem via analogs of sverak s nontrivial quasiconvex functions and connectedness properties of the rank 2 envelopes as another application of the semicontinuity result we obtain a geometric result of a more general nature characterization of certain extremal three point h measures for three phase mixtures of three characteristic functions in dimension three we also discuss the applicability of the results to problems with other differential constrains in particular to three linear elastic wells and further generalizations

alleviating sensor position error in source localization using calibration emitters at inaccurate locations a previous study shows that the use of a calibration emitter whose position is known exactly can significantly reduce the loss in time differences of arrival tdoa based source localization accuracy when the available sensor positions have random errors this paper extends the previous work to a more practical scenario where the exact position of a calibration emitter is not known by modeling the calibration position error as additive gaussian noise the amount of reduction in localization accuracy due to calibration position error is derived through cramer rao lower bound crlb analysis in addition the analysis also affirms the previous studies on bayesian sensor network localization that it remains possible to improve the localization accuracy even if the calibration position is completely unknown next a performance analysis illustrates that the penalty could be very high if one simply pretends the calibration position is accurate and ignores its error a closed form solution is then developed by accounting for the calibration position error and it is proved analytically to reach the crlb accuracy when the sensor and calibration position errors are small relative to the distance between the calibration emitter and the sensor finally the results are generalized to the case where multiple calibration emitters are available when deploying multiple calibration emitters although their positions may not be known exactly we show that it is possible to completely eliminate the sensor position error and recover the best localization accuracy that is limited by the measurement noise in tdoas only all the theoretical developments are corroborated by simulations

improved bounds for the overall properties of a nonlinear composite dielectric the construction of generalized hashin shtrikman bounds for nonlinear composite problems relies on the introduction of a comparison material in recent work a nonlinear comparison medium has been used however this requires detailed knowledge of the properties of the trial fields that are employed the fields used have the property of bounded mean oscillation and this enables the size of the penalty exacted by using a nonlinear comparison material to be controlled some recent results concerning riesz transforms and the beurling operator are used here to reduce the effect of the penalty and hence to generate improved bounds in addition an exact solution is established for a particular class of composites

h measures a new approach for studying homogenisation oscillations and concentration effects in partial differential equations new mathematical objects called h measures are introduced for studying oscillations and concentration effects in partial differential equations applications to transport properties and to homogenisation are given as an example of the new results which can be obtained by this approach

on the relation of a three well energy this paper studies the relaxation of multi well non convex energies in the context of infinitesimal geometrically linear elasticity and the analogous problem for gradient fields a dual variational principle of hashin shtrikman type is developed for the relaxed energy under the assumption that the original energy function is a difference of a quadratic function and of another convex function in the particular case of linear elastic wells sharing the same elastic modulus this reduces to the approach of r v kohn and leads to the need to minimize an energy functional with respect to matrix measures on the unit sphere the h measures which are subject to certain constraints it is shown that for the three well linearized energy the minimizing measure subject to these constraints can be chosen as a sum of no more than three dirac masses a subclass of such three point measures realizable by microstructures is described it is demonstrated by means of examples that the minimizing measures do fall within this subclass in some cases thereby providing an exact value for the three well non convex relaxed energy more generally the minimization algorithm leads to an improved lower bound for the relaxed energy if the three phases are pairwise compatible the relaxed energy is a convexification of the original energy

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

an approximately efficient tdoa localization algorithm in closed form for locating multiple disjoint sources with erroneous sensor positions this paper considers the problem of time difference of arrival tdoa source localization when the tdoa measurements from multiple disjoint sources are subject to the same sensor position displacements from the available sensor positions this is a challenging problem and closed form solution with good localization accuracy has yet to be found this paper proposes an estimator that can achieve this purpose the proposed algorithm jointly estimates the unknown source and sensor positions to take the advantage that the tdoas from different sources have the same sensor position displacements the joint estimation is a highly nonlinear problem due to the coupling of source and sensor positions in the measurement equations we introduce the novel idea of hypothesized source locations in the algorithm development to enable the formulation of psuedolinear equations thereby leading to the establishment of closed form solution for source location estimates besides the advantage of closed form the newly developed algorithm is shown analytically under the condition that the tdoa measurement noise and the sensor position errors are sufficiently small to reach the crlb accuracy for clarity the localization of two disjoint sources is used in the algorithm development the developed algorithm is then examined under the special case of a single source and extended to the more general case of more than two unknown sources the theoretical developments are supported by simulations

variational second order estimates for nonlinear composites it is shown here that the approximate second order method of ponte castaneda for estimating the effective behaviour of nonlinear composite materials can be given a variational status this is accomplished by means of a slight generalization of the variational structure of talbot and willis consisting of the replacement of the infimum over the polarization field by the more general corresponding stationary operation since the relevant functions are not convex in general this replacement provides additional flexibility that can be exploited advantageously the net result is a stationary principle from which stationary variational estimates can be generated under certain hypotheses on the choice of the linear comparison composite it is shown that the resulting estimates are identical to the second order estimates thus showing that these second order estimates are indeed variational in character although only of the stationary variety the connection of these second order estimates to earlier bounds obtained from related extremum variational principles is also explored

cayley bacharach theorems and conjectures a theorem of pappus of alexandria proved in the fourth century a d began a long development in algebraic geometry in its changing expressions one can see reflected the changing concerns of the field from synthetic geometry to projective plane curves to riemann surfaces to the modern development of schemes and duality we survey this development historically and use it to motivate a brief treatment of a part of duality theory we then explain one of the modern developments arising from it a series of conjectures about the linear conditions imposed by a set of points in projective space on the forms that vanish on them we give a proof of the conjectures in a new

on effective resistivity and related parameters for periodic checkerboard composites an approach for finding the effective properties of two dimensional periodic rectangular checkerboard media is presented it is demonstrated that one can take a relatively simple model problem an appropriate system of joined quarter planes and that after appropriate conformal transformation one can use this to solve for either periodic or doubly periodic structures illustrative calculations involving three phase media are presented that in limiting cases recover earlier analyses useful asymptotic relations are also given

on the cohomology of galois groups determined by witt rings let f denote a field of characteristic different from two in this paper we describe the mod 2 cohomology of a galois group gf called the w group of f which is known to essentially characterize the witt ring wf of anisotropic quadratic modules over f we show that h gf f2 contains the mod 2 galois cohomology of f and that its structure will reflect important properties of the field we construct a space xf endowed with an action of an elementary abelian group e such that the computation of the cohomology of gf reduces to calculating the equivariant cohomology h e xf f2 for the case of a field which is not formally real this amounts to computing the cohomology of an explicit euclidean space form an object which is interesting in its own right we provide a number of examples and a substantial combinatorial computation for the cohomology of the universal w groups

a generalized subspace approach for mobile positioning with time of arrival measurements the problem of locating mobile terminals has received considerable attention particularly in the field of wireless communications in this correspondence a simple subspace based algorithm for mobile positioning with the use of time of arrival measurements deduced from signals received at three or more reference base stations is derived and analyzed it is shown that the proposed approach is a generalization of the mobile localization method based on multidimensional similarity analysis computer simulations are included to contrast the estimator performance with cramer rao lower bound

array shape calibration using sources in unknown locations part i far field sources this paper deals with source localization using a two dimensional array of sensors whose locations are not known precisely if only a single source is observed uncertainties in sensor location increase errors in source bearing and range by an amount which is independent of signal to noise ratio and which can easily dominate over all localization accuracy major performance gains could therefore result from successful calibration of array geometry the paper derives cramer rao bounds on calibration and source location accuracies achievable with far field sources whose bearings are not initially known the sources are assumed to radiate gaussian noise and to be spectrally disjoint of each other when the location of one sensor and the direction to a second sensor is known three noncollinear sources are sufficient to calibrate sensor positions with errors which decrease to zero as calibrating source strength or time bandwidth products tend to infinity the sole exception to this statement is a nominally linear array for which such calibration is not possible when one sensor location is known but no directional reference is available three noncollinear sources can determine array shape but there remains a residual error in angular orientation which is irremovable by the calibration procedure when no sensor locations are known a priori one adds to the residual error in rotation a translational component in the far field the latter should be unimportant in addition to the asymptotic results cramer rao bounds are computed for finite signal to noise ratios and observation times one finds that calibration permits significant reductions in localization errors for parameter values well within the practical range

correctors and field fluctuations for the p x laplacian with rough exponents we provide a corrector theory for the strong approximation of fields inside composites made from two materials with different power law behavior the correctors are used to develop bounds on the local singularity strength for gradient fields inside micro structured media the bounds are multi scale in nature and can be used to measure the amplification of applied macroscopic fields by the micro structure

array shape calibration using sources in unknown locations part ii near field sources and estimator implementation uncertainty concerning sensor locations can seriously degrade the ability of an array to estimate the location of radiating sources array calibration then becomes an important issue this paper deals with array calibration using spectrally disjoint near field sources whose locations are not known a priori it calculates cramer rao bounds on source location and array shape errors it shows that with mild restrictions on source array geometry the array shape errors can be made arbitrarily small by using a sufficient number of sufficiently strong calibrating sources the required number of calibrating sources is five for a four sensor array four for a five sensor array and three for an array of six or more sensors accurate calibration is not possible for a three sensor array while calibration can establish array shape with great accuracy it cannot resolve a rotational uncertainty in array orientation this uncertainty translates into a residual error in source bearings but not in source ranges thus incremental errors in target range due to sensor location uncertainty can be reduced to any desired extent the paper also proposes an actual calibration procedure and presents simulation results indicating that useful calibration can be obtained with calibrating sources of very moderate signal to noise ratio

focussing matrices for coherent signal subspace processing a class of focussing matrices is proposed for use in the coherent signal subspace method csm h wang and m kaveh ibid vol assp 33 aug 1985 when the directions of arrival of wideband sources fall into more than one group of one beamwidth each this class leads to performance substantially better than those suggested in previous studies on direction of arrival estimation new insight into the structures of various focussing matrices and their effect on the performance of csm is presented the performance of csm is compared for several classes of these matrices on the simulations as well as relative sufficiency analyses

maximum likelihood source localization and unknown sensor location estimation for wideband signals in the near field in this paper we derive the maximum likelihood ml location estimator for wideband sources in the near field of the sensor array the ml estimator is optimized in a single step as opposed to other estimators that are optimized separately in relative time delay and source location estimations for the multisource case we propose and demonstrate an efficient alternating projection procedure based on sequential iterative search on single source parameters the proposed algorithm is shown to yield superior performance over other suboptimal techniques including the wideband music and the two step least squares methods and is efficient with respect to the derived cramer rao bound crb from the crb analysis we find that better source location estimates can be obtained for high frequency signals than low frequency signals in addition large range estimation error results when the source signal is unknown but such unknown parameter does not have much impact on angle estimation in some applications the locations of some sensors may be unknown and must be estimated the proposed method is extended to estimate the range from a source to an unknown sensor location after a number of source location frames the location of the uncalibrated sensor can be determined based on a least squares unknown sensor location estimator

on energy based acoustic source localization for sensor networks in this paper energy based localization methods for source localization in sensor networks are examined the focus is on least squares based approaches due to a good tradeoff between performance and complexity a suite of methods are developed and compared first two previously proposed methods quadratic elimination and one step are shown to yield the same location estimate for a source next it is shown that as the errors which perturb the least squares equations are nonidentically distributed it is more appropriate to consider weighted least squares methods which are observed to yield significant performance gains over the unweighted methods finally a new weighted direct least squares formulation is presented and shown to outperform the previous methods with much less computational complexity unlike the quadratic elimination method the weighted direct least squares method is amenable to a correction technique which incorporates the dependence of unknown parameters leading to further performance gains for a sufficiently large number of samples simulations show that the weighted direct solution with correction wdc can be more accurate with significantly less computational complexity than the maximum likelihood estimator and approaches cramer rao bound crb furthermore it is shown that wdc attains crb for the case of a white source

upper and lower bounds for the overall properties of a nonlinear composite dielectric ii periodic microgeometry the study of the effective properties of a nonlinear composite dielectric begun in the companion to this paper is continued in the context of a simple cubic array of inclusions embedded in a matrix use of a nonlinear comparison material in the nonlinear hashin shtrikman variational principles permits the generation of both upper and lower bounds for any composite it is straightforward to apply the new approach to the simple composite considered here as the trial electric field which is substituted into the hashin shtrikman variational principle is finite everywhere the results obtained indicate the likely improvement over the simple classical bounds that can be obtained using the hashin shtrikman principles

rigidity and lack of rigidity for solenoidal matrix fields the problem of finding a curl free matrix valued field e with values in an assigned set of matrices has received considerable attention given a bounded connected open set and a compact set of m n matrices in this paper we establish existence or non existence results for the following problem find b l m n such that div b 0 in in the sense of distributions under the constraint that b x almost everywhere in we consider the case of a b rank a b n and we establish non existence both for the case of exact solutions described above and for the case of approximate solutions described in 1 we also prove existence of approximate solutions for a suitably chosen triple a 1 a 2 a 3 of matrices with rank a i a j n i j and i j 1 2 3 we give examples when the differential constraints are of a different type and present some applications to composites

parametric sensor array calibration using measured steering vectors of uncertain locations we consider the problem of sensor array calibration using a set of unique measured steering vectors of uncertain locations to estimate the unknown deterministic array perturbation parameters in a maximum likelihood framework the array perturbations are parameterized by the sensor locations mutual coupling coefficients and receiver channel mismatch we introduce a hybrid optimizer based on the amalgamation of gradient based algorithms and the genetic algorithm this optimizer is capable of coping with the problem of local extrema attractors particularly initial estimates with large deviations from their true values numerical examples are provided to demonstrate the effectiveness and behavior of the proposed algorithms

bounds and estimates for the overall plastic behaviour of composites with strain gradient effects the macroscopic plastic response is estimated for a composite with each phase satisfying a strain gradient constitutive description in a j 2 deformation theory of strain gradient plasticity the strain energy function is assumed to depend on both the von mises strain invariant epsilon e and on a curvature invariant chi e for a general coupling between epsilon e and chi e a nonlinear variational principle is formulated generalizing that of ponte castaneda 1992 j mech phys solids 40 1757 the minimum principle is used to derive bounds and estimates for the overall plastic response of statistically homogeneous and isotropic strain gradient composites an essential ingredient of the strategy is the use of previous results of the authors 1994 j mech phys solids 42 1851 for a linear comparison composite for a particular coupling between epsilon e and chi e suggested earlier by fleck hutchinson 1993 the hashin shtrikman upper bounds and lower estimates are calculated for a power law hardening solid including the rigid perfectly plastic limit the results demonstrate a size effect

a weighted linear prediction method for near field source localization this paper proposes a low computational cost method for the near field narrowband source localization problem which does not require multidimensional search or high order statistics the proposed method is based on the second order statistics sos of the outputs of a uniform linear array ula more precisely the range and angle parameters are estimated through a weighted linear prediction lp algorithm applied to a properly chosen array output correlation sequence detailed performance analysis and derivation of the optimal weightings are provided simulation results are finally presented to validate the theoretical analysis results and to assess the performance of the proposed method

maximum likelihood localization of multiple sources by alternating projection an algorithm referred to as apm for computing the maximum likelihood estimator of the locations of simple sources in passive sensor arrays is presented the algorithm is equally applicable to the case of coherent signals and to the case of a single snapshot the algorithm is iterative the maximum of the likelihood function is computed by successive approximations the convergence of the algorithm to the global maximum is demonstrated for a variety of scenarios the key to this global convergence is the initialization scheme

new bounds on the effective thermal conductivity of n phase materials based on the perturbation solution to the effective thermal conductivity problem for an n component material we derive new third and fourth order bounds for the effective thermal conductivity of the composite the new third order bounds are accurate to third order in epsilon a epsilon b where epsilon a is the thermal conductivity of phase a and require a total of frac 1 2 n 1 2 third order correlation parameters in their evaluation for two phase composites these bounds require only one geometrical parameter and are identical to beran s bounds for n geqslant 3 the third order bounds use the same information as beran s bounds but always more restrictive than beran s bounds the new fourth order bounds are accurate to fourth order in epsilon a epsilon b and require an additional frac 1 4 n 2 n 1 2 fourth order correlation parameters for n 2 only two parameters are needed and the fourth order bounds are shown to be more restrictive than the third order beran s bounds and the second order hashin shtrikman s bounds the application of the third order bounds to a spherical cell material of miller is illustrated

direction finding for wide band signals using an interpolated array the authors derive a new direction finding algorithm for multiple wideband signals received by an arbitrary array and analyze its performance using an interpolation technique they generate a set of virtual arrays each for a different frequency band having the same array manifold the convergence matrices of these arrays are added to produce a composite covariance matrix direction of arrival doa estimates are obtained by eigendecomposition of this composite covariance matrix using the narrowband music algorithm or its variants closed form expressions for the asymptotic covariance matrix of the doa estimation errors are derived using a perturbation analysis evaluated for specific cases and compared with the cramer rao lower bound special attention is given to correlated and coherent signals the formulas for the error covariance are quite general and can be modified to provide results for other wideband doa estimation algorithms

bounds which incorporate morphological information for a nonlinear composite dielectric the nonlinear hashin shtrikman variational structure relies on the introduction of a comparison material in recent work a nonlinear comparison composite has been employed this has enabled both upper and lower bounds to be found that depend on the three point statistics of the microstructure through a parameter introduced by g w milton at least one of the bounds requires an estimate of the size of the trial field to be known and even if the best estimate available is used and the milton parameter is known for a particular microstructure the bounds can still be widely separated o p bruno has obtained bounds for a linear composite consisting of a matrix containing spherical inclusions where the inclusions are coated with the matrix phase the bounds remain non trivial even when the properties of the inclusions tend to either zero or infinity these bounds are used to improve the bounds for a nonlinear composite comprising either a nonlinear matrix containing linear inclusions or a linear matrix containing nonlinear inclusions for the microgeometry considered here it is possible to construct a bounded trial field and a simple example involving this approach is also described

high resolution multiple wideband and nonstationary source localization with unknown number of sources in this paper a new algorithm for high resolution multiple wideband and nonstationary source localization using a sensor array is proposed the received signals of the sensor array are first converted into the time frequency domain via short time fourier transform stft and we find that a set of short time power spectrum matrices at different time instants have the joint diagonalization structure in each frequency bin based on such joint diagonalization structure a novel cost function is designed and a new spatial spectrum for direction of arrival doa estimation at hand is derived compared to the maximum likelihood ml method with high computational complexity the proposed algorithm obtains the doa estimates via one dimensional 1 d search instead of multidimensional search therefore its computational complexity is much lower than the ml method unlike the subspace based high resolution doa estimation techniques it is not necessary to determine the number of sources in advance for the proposed algorithm moreover the proposed method is robust to the effects of reverberation caused by multipath reflections hence it is suitable for multiple acoustic source localization in a reverberant room the results of numerical simulations and experiments in a real room with a moderate reverberation are provided to demonstrate the good performance of the proposed approach

dielectric breakdown optimal bounds we study dielectric breakdown for composites made of two isotropic phases we show that sachs s bound is optimal this simple example is used to illustrate a variational principle which departs from the traditional one we also derive the usual variational principle by elementary means without appealing to the technology of convex duality

a novel weighted multidimensional scaling analysis for time of arrival based mobile location recently multidimensional scaling mds algorithms have been verified to be robust for the mobile localization however they do not achieve the cramer rao lower bound crlb even though the measurement noise is small in this paper a novel weighted mds method is proposed for time of arrival based mobile location it can achieve the crlb at moderate noise level before the threshold effect occurs in addition unlike the classical mds methods depending on the eigendecomposition of the scalar product matrix the proposed method is based on the matrix itself directly which in turn decreases the computational complexity

some simple explicit bounds for the overall behaviour of nonlinear composites abstract variational expressions developed over the last few years provide bounds for the overall energy functions of a range of nonlinear composite materials the evaluation of a bound requires the solution of a system of nonlinear algebraic equations and this generally involves a computation there are however certain simple composites comprising a nonlinear matrix containing either rigid inclusions or cavities for which very simple explicit formulae can be given these formulae are displayed here at a level of generality greater than in any previous presentation the energy density function of the matrix is arbitrary and the microgeometry of the composite appears through an expression which bounds the energy of a linear composite with the same geometry to the extent that such linear bounds can be developed making allowance for any amount of statistical information on the composite the new nonlinear bounds collect this new results at the level of employing bounds of hashin shtrikman type for the linear problem are given for an incompressible matrix reinforced by aligned rigid platelets or weakened by aligned cracks in the course of the work a recently derived formula more general than any available previously is presented and developed explicitly for any two phase composite

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

laplacian and homology of free two step nilpotent lie algebras abstract in this paper we determine the homology with trivial coefficients of the free two step nilpotent lie algebras over the complex numbers this is done by working out the structure of the homology as a module under the general linear group the main tool is a laplacian for the free two step nilpotent lie algebras which turns out to be closely related to the casimir operator of the general linear group we are able to compute all eigenvalues of the laplacian on the chain complex

homogenization and optimal bounds in linear elasticity in their celebrated paper of 1963 hashin shtrikman 1 addressed the problem of determining optimal bounds for the bulk and shear moduli of a statistically isotropic elastic composite material with arbitrary isotropic phase geometry they derived a set of bounds for these moduli in the physically meaningful case of three dimensional elasticity in the case of a two phase composite let k 1 1 and k 2 2 respectively denote the bulk and shear moduli for the first and the second phase let k denote their analogues for the composite and let 0 stand for the volume fraction of the first phase in the composite under the ordering restriction that both

localizing multiple events using times of arrival a parallelized hierarchical approach to the association problem a fundamental problem in localizing multiple events based on times of arrival toas at a number of sensors is that of associating toas with events we consider this problem in the context of acoustic sensors monitoring events that are closely spaced in time due to the relatively low speed of propagation of sound the order in which the events arrive at a sensor need not be the same as the order in which they occur potentially creating fundamental ambiguities we first explore such ambiguities in an idealized setting with two events and noiseless observations showing that it is possible to localize both events with nine or more sensors as long as degenerate sensor placement is avoided but that we can construct examples with six sensors for which unambiguous space time localization is not possible we then show that these potential ambiguities are not a bottleneck in typical practical settings proposing and evaluating an algorithm that successfully localizes multiple events using noisy observations the algorithm employs parallelism and hierarchical processing to avoid the excessive complexity of naively trying all possible associations of events with toas we use discretization of hypothesized event times to enable us to efficiently generate a set of candidate event locations which contain noisy versions of true events as well as phantom events we refine these estimates iteratively discarding obvious phantoms and then solve a linear programming formulation for matching true events to toas while identifying outliers and misses simulation results indicate excellent performance that is comparable to a genie based algorithm which is given the correct association between toas and events

wideband array processing using a two sided correlation transformation a new method for broadband array processing is proposed the method is based on unitary transformation of the signal subspaces we apply a two sided transformation on the correlation matrices of the array it is shown that the two sided correlation transformation tct has a smaller subspace fitting error than the coherent signal subspace method csm it is also shown that unlike csm the tct algorithm can generate unbiased estimates of the directions of arrival regardless of the bandwidth of the signals the capability of the tct and csm methods for resolving two closely spaced sources is compared the resolution threshold for the new technique is much smaller than that for csm

a variational approach to the overall sink strength of a nonlinear lossy composite medium an extension of the hashin shtrikman variational structure to nonlinear problems initiated by j r willis j appl mech 50 1202 1209 1983 and developed generally by d r s talbot j r willis ima j appl math 35 39 54 1985 is applied to the problem of homogenization of the semilinear steady state diffusion equation nabla 2c partial w partial c c x k x 0 where the function tilde w is convex in c but varies randomly with position x a strict definition for an overall function w which defines the homogenized medium is given and its properties are discussed bounds for tilde w are then developed from variational principles classical energy principles yield bounds analogous to the voigt and reuss bounds of elasticity theory while the new hashin shtrikman structure yields tighter bounds which are sensitive to the two point statistics of the medium explicit results are presented for a particular two phase composite medium for which one phase is linear so that w is quadratic whereas the second has a quadratic nonlinearity so that w is cubic

a simple and efficient estimator for hyperbolic location an effective technique in locating a source based on intersections of hyperbolic curves defined by the time differences of arrival of a signal received at a number of sensors is proposed the approach is noniterative and gives an explicit solution it is an approximate realization of the maximum likelihood estimator and is shown to attain the cramer rao lower bound near the small error region comparisons of performance with existing techniques of beamformer spherical interpolation divide and conquer and iterative taylor series methods are made the proposed technique performs significantly better than spherical interpolation and has a higher noise threshold than divide and conquer before performance breaks away from the cramer rao lower bound it provides an explicit solution form that is not available in the beamforming and taylor series methods computational complexity is comparable to spherical interpolation but substantially less than the taylor series method