harnack inequalities and discrete continuous error estimates for a chain of atoms with two body interactions we consider deformations in r 3 of an infinite linear chain of atoms where each atom interacts with all others through a two body potential we compute the effect of an external force applied to the chain at equilibrium the positions of the particles satisfy an euler lagrange equation for large classes of potentials we prove that every solution is well approximated by the solution of a continuous model we establish an error estimate between the discrete and the continuous solution based on a harnack lemma of indepen dent interest finally we apply our results to some lennard jones potentials

digital computation of linear canonical transforms we deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform lct of a function from the samples of the original function two approaches are presented and compared the first is based on decomposition of the lct into chirp multiplication fourier transformation and scaling operations the second is based on decomposition of the lct into a fractional fourier transform followed by scaling and chirp multiplication both algorithms take n log n time where n is the time bandwidth product of the signals the only essential deviation from exactness arises from the approximation of a continuous fourier transform with the discrete fourier transform thus the algorithms compute lcts with a performance similar to that of the fast fourier transform algorithm in computing the fourier transform both in terms of speed and accuracy

group gradings on associative algebras abstract let r g g rg be a g graded ring we describe all types of gradings on r if g is torsion free and r is artinian semisimple if r is a matrix algebra over an algebraically closed field f then we give a description of all g gradings on r provided that g is an abelian group in the case of an abelian group g we also classify all finite dimensional graded simple algebras and finite dimensional graded division algebras over an algebraically closed field of characteristic zero

numerical approximation of the solution of variational problem with a double well potential variational problems with a double well potential are not lower semicontinuous and can fail to attain a minimum value rather the gradients of minimizing sequences do not converge pointwise and can have oscillations however the gradients do converge in the weak topology i e their local spatial averages converge such functionals arise in the description of equilibria of crystals or other ordered materials stable configurations for solid crystals which have symmetry related martensitic energy wells have a fine scale microstructure which can be related to the oscillations that energy minimizing sequences for the bulk energy exhibit an analysis is given of approximation methods for variational problems with a double well potential to give a rigorous justification for the use of such numerical methods to model the behavior of this class of solid crystals

repeated filtering in consecutive fractional fourier domains and its application to signal restoration filtering in a single time domain or in a single frequency domain has been generalized to filtering in a single fractional fourier domain we generalize this to repeated filtering in consecutive fractional fourier domains and discuss its applications to signal restoration through an illustrative example

elementary gradings on the lie algebra utn the algebras utn k utn k of the upper triangular matrices over a field k are of significant importance in the theory of algebras with polynomial identities group gradings on algebras appear in various areas and provide an indispensable tool in the study of the algebraic and combinatorial properties of the algebras in question in this paper we consider the lie algebra utn k utn k of all upper triangular matrices of order n we study the group gradings on this algebra it turns out that the gradings on the lie algebra utn k utn k are much more intricate than those in the associative case in this paper we describe the elementary gradings on the lie algebra utn k utn k finally we study the canonical grading on utn k utn k by the cyclic group znzn of order n we produce a finite basis of the graded polynomial identities satisfied by this grading

basis of the identities of the matrix algebra of order two over a field of characteristic p 2 abstract in this paper we prove that the polynomial identities of the matrix algebra of order 2 over an infinite field of characteristic p 2 admit a finite basis we exhibit a finite basis consisting of four identities and in almost all cases for p we describe a minimal basis consisting of two identities the only possibilities for p where we do not exhibit minimal bases of these identities are p 3 and p 5 we show that when p 3 one needs at least three identities and we conjecture a minimal basis in this case in the course of the proof we construct an explicit basis of the vector space of the central commutator polynomials modulo the ideal of the identities of the matrix algebra of order two

interpolating between periodicity and discreteness through the fractional fourier transform periodicity and discreteness are fourier duals in the same sense as operators such as coordinate multiplication and differentiation and translation and phase shift the fractional fourier transform allows interpolation between such operators which gradually evolve from one member of the dual pair to the other as the fractional order goes from zero to one here we similarly discuss the interpolation between the dual properties of periodicity and discreteness showing how one evolves into the other as the order goes from zero to one we also discuss the concepts of partial discreteness and partial periodicity and relate them to fractional discreteness and periodicity

low dimensional lattice groups for the continuum mechanics of phase transitions in crystals first i review and adapt some classical and recent formulations of problems relating to the classification of two and three dimensional lattices then i use these methods to calculate lattice groups that are of interest in the continuum mechanics of phase transitions in crystals and to construct invariant neighbourhoods that are useful in the same context the paper is designed to provide a perspective of similar calculations which employ methods of traditional crystallography

from molecular models to continuum mechanics we present here a limiting process allowing us to write some continuum mechanics models as a natural asymptotic of molecular models the approach is based on the hypothesis that the macroscopic displacement is equal to the microscopic one we carry out the corresponding calculations in the case of two body energies including higher order terms and also in the case of thomas fermi type models

identities and isomorphisms of graded simple algebras abstract let g be an arbitrary abelian group and let a and b be two finite dimensional g graded simple algebras over an algebraically closed field f such that the orders of all finite subgroups of g are invertible in f we prove that a and b are isomorphic if and only if they satisfy the same g graded identities we also describe all isomorphism classes of finite dimensional g graded simple algebras

material symmetry and singularities in solids we examine the relations between the symmetry group of a crystalline or solid body and the line singularities in the deformation or microstructural field which the material can support a method is developed which in some relevant cases allows us to describe a singularity by means of a suitable derham current supported on the defect submanifold this current measures the obstruction to the extension of the local deformation or microstructure to a globally defined field the procedure described here yields the basis of a formulation of weak field equations for a defective material and clarifies the structure of the compatibility relations for virtually any class of material symmetry

optimal stochastic parameter design for estimation problems in this study the aim is to perform optimal stochastic parameter design in order to minimize the cost of a given estimator optimal probability distributions of signals corresponding to different parameters are obtained in the presence and absence of an average power constraint it is shown that the optimal parameter design results in either a deterministic signal or a randomization between two different signal levels in addition sufficient conditions are obtained to specify the cases in which improvements over the deterministic parameter design can or cannot be achieved via the stochastic parameter design numerical examples are presented in order to provide illustrations of theoretical results

on the role of the number of degrees of freedom of the field in mimo channels the aim of this paper is to investigate the relationship between the effective number of degrees of freedom endf of a multiple input multiple output mimo channel and the number of degrees of freedom ndf of the field in particular the ndf of the field represents an upperbound for the endf of a mimo channel consequently the evaluation of the maximum endf can be carried out by adopting the literature on the ndf based on the spatial bandlimitation properties of the field this approach allows a simple and intuitive explanation of the maximum endf in a mimo channel based on a geometrical interpretation of the spatial channel in terms of spatial nyquist intervals

low dimensional lattices vi voronoi reduction of three dimensional lattices the aim of this paper is to describe how the voronoi cell of a lattice changes as that lattice is continuously varied the usual treatment is simplified by the introduction of new parameters called the vonorms and conorms of the lattice the present paper deals with dimensions n leq 3 a sequel will treat four dimensional lattices an elegant algorithm is given for the voronoi reduction of a three dimensional lattice leading to a new proof of voronoi s theorem that every lattice of dimension n leq 3 is of the first kind and of fedorov s classification of the three dimensional lattices into five types there is a very simple formula for the determinant of a three dimensional lattice in terms of its conorms

statistics of the log compressed echo envelope log compression of a lines to produce b scan images in clinical ultrasound imaging systems is a standard procedure to control the dynamic range of the images the statistics of such compressed images in terms of underlying scatterer statistics have not been derived the statistics are analyzed for partially formed speckle using a general k distribution model of envelope statistics to derive the density function for the log compressed envelope this density function is used to elucidate the relation between the moments of the compressed envelope the compression parameters and the statistics of the scatterers the analysis shows that the mean of the log compressed envelope is an increasing function of both the backscattered energy and the effective scatterer density the variance of the log compressed envelope is a decreasing function of the effective scatterer density and is independent of the backscattered energy

one bit distributed sensing and coding for field estimation in sensor networks this paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy one bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution a constructive quantization coding and field reconstruction scheme is developed and an upper bound to the associated mean squared error mse at any point and any snapshot is derived in terms of the local spatio temporal smoothness properties of the underlying field it is shown that when the noise sensor placement pattern and the sensor schedule satisfy certain weak technical requirements it is possible to drive the mse to zero with increasing sensor density at points of field continuity while ensuring that the per sensor bit rate and sensing related network overhead rate simultaneously go to zero a general condition for the optimization of the rate of decay of the mse upper bound with sensor density is derived specific mse versus sensor density decay rates are illustrated for the constant and lipschitz 1 fields with the former attaining order optimal scaling behavior

on the material symmetry group of elastic crystals and the born rule the aim of this paper is to investigate the extent to which non linear elasticity theory can be used for describing the behavior of crystalline solids the results we obtain show that some strict and definite boundaries must be set to the possibility of actually doing so specifically we address here a twofold problem on one hand we pose the question of the validity of the socalled born rule a fundamental hypothesis due to cauchy and in a weaker form to born by means of which continuum theories of crystal mechanics are formulated on the other hand we explore the possibility of developing an effective elastic model independently of the rule in those cases in which the rule itself does not work our results are based on a close study of the implications of the phenomenon of mechanical twinning with regard to the symmetry properties of the energy function of an elastic crystal these are summarized by the choice of a material symmetry group g the main experimental features of twinning lead one to consider a class of twinning subgroups of g that are particular reflection groups in fact particular linear representations possibly unfaithful of abstract coxeter groups in the generic case the properties of such groups prevent the born rule from holding only when some very special non generic conditions are met by the twinning modes of a crystalline substance is the rule valid the development of an elastic model is then possible by following a well known procedure the analysis of relevant experimental data confirms that while basically all crystals exhibit twins most of them do exhibit generic twinning modes for which the hypothesis of born is violated we also show that in such generic cases any tentative thermoelastic approach developed independently of the rule does not give physically sound results and thus cannot be usefully adopted because some quite undesirable conclusions regarding the symmetry of the energy can be drawn that definitely make elasticity inadequate for our purposes experimental data point out nonetheless two quite remarkable classes of nongeneric materials for which the born rule is never violated and to which an elastic model safely applies

real time calculation of a limiting form of the renyi entropy applied to detection of subtle changes in scattering architecture previously a new method for ultrasound signal characterization using entropy hf was reported and it was demonstrated that in certain settings further improvements in signal characterization could be obtained by generalizing to renyi entropy based signal characterization if r with values of r near 2 specifically r 1 99 m s hughes et al j acoust soc am 125 3141 3145 2009 it was speculated that further improvements in sensitivity might be realized at the limit r 2 at that time such investigation was not feasible due to excessive computational time required to calculate if r near this limit in this paper an asymptotic expression for the limiting behavior of if r as r 2 is derived and used to present results analogous to those obtained with if 1 99 moreover the limiting form if is computable directly from the experimentally measured waveform f t by an algorithm that is suitable for real time calculation and implementation

decentralized estimation in an inhomogeneous sensing environment we consider decentralized estimation of a noise corrupted deterministic parameter by a bandwidth constrained sensor network with a fusion center the sensor noises are assumed to be additive zero mean spatially uncorrelated but otherwise unknown and possibly different across sensors due to varying sensor quality and inhomogeneous sensing environment the classical best linear unbiased estimator blue linearly combines the real valued sensor observations to minimize the mean square error mse unfortunately such a scheme cannot be implemented in a practical bandwidth constrained sensor network due to its requirement to transmit real valued messages in this paper we construct a decentralized estimation scheme des where each sensor compresses its observation to a small number of bits with length proportional to the logarithm of its local signal to noise ratio snr the resulting compressed bits from different sensors are then collected and combined by the fusion center to estimate the unknown parameter the proposed des is universal in the sense that each sensor compression scheme requires only the knowledge of local snr rather than the noise probability distribution functions pdf while the final fusion step is also independent of the local noise pdfs we show that the mse of the proposed des is within a constant factor of 25 8 of that achieved by the classical centralized blue estimator

statistical signal analysis for the inverse source problem of electromagnetics a statistical signal analysis for the inverse source problem of electromagnetics is given this correspondence considers the problem of estimating either the near field or the radiating current distribution from a measurement of the far field the solution is derived via a linear operator formalism and the ill posedness of the reconstruction is quantified by using the cramer rao lower bound which is explicitly given in terms of the multipole expansion of the electromagnetic field a numerical study is included to illustrate the theoretical results

signal recovery with cost constrained measurements we are concerned with the problem of optimally measuring an accessible signal under a total cost constraint in order to estimate a signal which is not directly accessible an important aspect of our formulation is the inclusion of a measurement device model where each device has a cost depending on the number of amplitude levels that the device can reliably distinguish we also assume that there is a cost budget so that it is not possible to make a high amplitude resolution measurement at every point we investigate the optimal allocation of cost budget to the measurement devices so as to minimize estimation error this problem differs from standard estimation problems in that we are allowed to design the number and noise levels of the measurement devices subject to the cost constraint our main results are presented in the form of tradeoff curves between the estimation error and the cost budget although our primary motivation and numerical examples come from wave propagation problems our formulation is also valid for other measurement problems with similar budget limitations where the observed variables are related to the unknown variables through a linear relation we discuss the effects of signal to noise ratio distance of propagation and the degree of coherence correlation of the waves on these tradeoffs and the optimum cost allocation our conclusions not only yield practical strategies for designing optimal measurement systems under cost constraints but also provide insights into measurement aspects of certain inverse problems

bandwidth constrained distributed estimation for wireless sensor networks part i gaussian case we study deterministic mean location parameter estimation when only quantized versions of the original observations are available due to bandwidth constraints when the dynamic range of the parameter is small or comparable with the noise variance we introduce a class of maximum likelihood estimators that require transmitting just one bit per sensor to achieve an estimation variance close to that of the clairvoyant sample mean estimator when the dynamic range is comparable or larger than the noise standard deviation we show that an optimum quantization step exists to achieve the best possible variance for a given bandwidth constraint we will also establish that in certain cases the sample mean estimator formed by quantized observations is preferable for complexity reasons we finally touch upon algorithm implementation issues and guarantee that all the numerical maximizations required by the proposed estimators are concave

analysis of digitized waveforms using shannon entropy a novel symbol oriented information theoretic approach to signal analysis is described based on application of shannon entropy it is shown that this can be a preferred alternate to conventional digital signal energy analysis by making an experimental comparison of scanned ultrasonic images formed from shannon entropy signal energy and log signal energy measurements in these images which were made by c scanning a plexiglas bar with drill hole defects the shannon entropy exhibits approximately two to three times the sensitivity of the two energy measures however the shannon entropy analysis of waveforms suffers from a severe fundamental defect it depends on the properties of the analog to digital converter adc used to acquire the waveform as well as the properties of the waveform itself as digitizer dynamic range is increased the shannon entropy ultimately saturates at a level governed by the properties of the digitizer alone this effect arises from the necessary limited bandwidth of a real adc if adc bandwidth were not limited the shannon entropy would grow without bound with increasing dynamic range to overcome this difficulty a variant of the shannon entropy is defined that depends only on the properties of the waveform it is then shown that this variant is sensitive to the same scattering features as is the shannon entropy for data acquired from the plexiglas specimen discussed initially furthermore the variant offers the same sensitivity improvements obtained from the shannon entropy analysis finally computation of this variant for waveforms having noise is described derivation of the variant is given in appendix a of this work several of its more interesting features are also discussed there derivation of the procedure required to compute the variant is given in appendix b

graded identities for tensor products of matrix super algebras over the grassmann algebra abstract in this paper we study the graded identities satisfied by the superalgebras m a b over the grassmann algebra and by their tensor products these algebras play a crucial role in the theory developed by a kemer that led to the solution of the long standing specht problem it is well known that over a field of characteristic 0 the algebras m pr qs ps qr and m p q m r s satisfy the same ordinary polynomial identities by means of describing the corresponding graded identities we prove that the t ideal of the former algebra is contained in the t ideal of the latter furthermore the inclusion is proper at least in case r s 1 1 finally we deal with the graded identities satisfied by algebras of type m 2 n 1 2 n 1 and relate these graded identities to the ones of tensor powers of the grassmann algebra our proofs are combinatorial and rely on the relationship between graded and ordinary identities as well as on appropriate models for the corresponding relatively free graded algebras

electromagnetic degrees of freedom in 2 d scattering environments the electromagnetic em degrees of freedom dof of a noise limited system in two dimensions with random multiple scattering is evaluated numerically following a rigorous dof theory first developed by miller and piestun for optical systems the received em fields are efficiently calculated by fast multipole method fmm and the ensemble average of the dof number is obtained through monte carlo simulation technique the results show that the average em dof number is strongly dependent on the sizes of the transmit volume the receive volume and the scattering region in particular the average number of dof generally increases with both the transmit and receive volumes however this increase is a non linear process and will not continue indefinitely as the transmit volume or the receive volume expands an upper bound of the average dof number is expected due to noise effects due to the lack of criteria for choosing a critical parameter involved in miller and piestun s original dof definition a modified definition is also considered even though the modified definition is snr dependent it provides a clearer physical meaning of the dof in addition the simulations also suggest that it might not be appropriate to ignore the influence of the snr on the dof number when the system concerned is of general form and relative small where no critical point of the channel quality can be identified a logarithmic dependence of the dof number on the total source power is demonstrated for such systems

fractional chirp scaling algorithm mathematical model in this paper the new fractional chirp scaling algorithm frcsa is mathematically derived and analyzed from high resolution sar imaging point of view the frcsa is based on the use of the fractional fourier transform within the chirp scaling algorithm csa the performance of the frcsa is compared to that of the classical csa that is based on the fast fourier transform fft simulation results for airborne sar systems show that the frcsa offers enhanced signal to noise ratio snr better focusing capabilities sharpened main lobe with extra power concentration and greater side lobe reduction ratio slrr and all of these without the need for any additional focusing or enhancement techniques that are required in the classical fft based csa

relations between gabor transforms and fractional fourier transforms and their applications for signal processing many useful relations between the gabor transform gt and the fractional fourier transform frft have been derived first we find that like the wigner distribution function wdf the frft is also equivalent to the rotation operation of the gt then we show that performing the scaled inverse fourier transform ift along an oblique line of the gt of f t can yield its frft since the gt is closely related to the frft we can use it for analyzing the characteristics of the frft compared with the wdf the gt does not have the cross term problem this advantage is important for the applications of filter design sampling and multiplexing in the frft domain moreover we find that if the gt is combined with the wdf the resultant operation called the gabor wigner transform gwt also has rotation relation with the frft we also derive the general form of the linear distribution that has rotation relation with the frft

interference suppression in the wigner distribution using fractional fourier transformation and signal synthesis a novel method for the suppression of cross terms in the time frequency domain is introduced first interference is identified using a fractional fourier transform based technique then auto terms are detected synthesized and subtracted from the original signal the process is repeated until all signal components are extracted finally the wigner distributions of pure auto terms are superimposed to yield a high readability representation

gradings on simple jordan and lie algebras abstract in this paper we describe all group gradings by a finite abelian group g of several types of simple jordan and lie algebras over an algebraically closed field f of characteristic zero

group gradings on the lie algebra of upper triangular matrices abstract the algebras u t n of the n n upper triangular matrices over a field k are of significant importance in the theory of algebras with polynomial identities group gradings on algebras appear in various areas and provide an indispensable tool in the study of the algebraic and combinatorial properties of the algebras in question we classify the group gradings on the lie algebra u t n it was proved by valenti and zaicev in 2007 that every group grading on the associative algebra u t n is isomorphic to an elementary grading the elementary gradings on u t n are also well understood see 6 it follows from our results that there are nonelementary gradings on u t n thus the gradings on the lie algebra u t n are much more intricate than those in the associative case

on the degrees of freedom of scattered fields starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities the degrees of freedom of the scattered field are introduced and then computed the degrees of freedom are shown to be practically equal to the nyquist number appropriate to the effective spatial bandwidth of the scattered field and to the extension of the observation domain accordingly a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error it is also shown that the field representation can be made in terms of field values and simple sampling functions provided that a marginal increase in the approximation error is tolerated the results not only completely justify the use of sampling interpolation for representing scattering fields but also demonstrate that such representation is practically an optimal one an algorithm for the reconstruction of scattered fields given the maximum allowed error is then produced

a note on the model of crystalline defects in ericksen pitteri neighborhoods abstract we apply here the topological theory of defects to a simple model of crystalline microstructure appropriate to the study of elastic crystals the model is obtained by restricting the range of the map describing the local lattice to the neighborhood of a given reference bravais lattice this set may be described as the quotient of a neighborhood of the identity in gl r3 the ericksen pitteri neighborhood by a finite subgroup of the symmetry group of the reference lattice containing the point group we show that the topological structure of this set is sufficiently rich to describe disclinations related to point group symmetries and twins related to non rotational symmetries but excludes defects corresponding to simple shear symmetries intuitively related to plastic deformations we also discuss the dependence of the description from the choice of the reference lattice

constrained decentralized estimation over noisy channels for sensor networks decentralized estimation of a noise corrupted source parameter by a bandwidth constrained sensor network feeding through a noisy channel a fusion center is considered the sensors due to bandwidth constraints provide binary representatives of a noise corrupted source parameter recently proposed decentralized distributed estimation and power scheduling methods do no consider errors occurring during the transmission of binary observations from the sensors to fusion center in this paper we extend the decentralized estimation model to the case where imperfect transmission channels are considered the proposed estimator which operates on additive channel noise corrupted versions of quantized noisy sensor observations is approached from maximum likelihood ml perspective the resulting ml estimate is a root in the region of interest roi of a derivative polynomial function we analyze the natural logarithm of the polynomial within the roi showing that the function is log concave thereby indicating that numerical methods such as newton s algorithm can be utilized to obtain the optimal solution due to complexity and implementation issues associated with the numerical methods we derive and analyze simpler suboptimal solutions i e the two stage and mean estimators the two stage estimator first estimates the binary observations from noisy fusion center observations utilizing a threshold operation followed by an estimate of the source parameter the optimal threshold is the maximum a posteriori map detector for binary detection and minimizes the probability of binary observation estimation error optimal threshold expressions for commonly utilized light gaussian and heavy tailed cauchy channel noise models are derived the mean estimator simply averages the noisy fusion center observations the output variances of means of the proposed suboptimal estimators are derived in addition a computational complexity analysis is presented comparing the proposed ml optimal and suboptimal two stage and mean estimators numerical examples evaluating and comparing the performance of proposed ml two stage and mean estimators are also presented

joint entropy of continuously differentiable ultrasonic waveforms this study is based on an extension of the concept of joint entropy of two random variables to continuous functions such as backscattered ultrasound for two continuous random variables x and y the joint probability density p x y is ordinarily a continuous function of x and y that takes on values in a two dimensional region of the real plane however in the case where x f t and y g t are both continuously differentiable functions x and y are concentrated exclusively on a curve t f t g t in the x y plane this concentration can only be represented using a mathematically singular object such as a schwartz distribution its use for imaging requires a coarse graining operation which is described in this study subsequently removal of the coarse graining parameter is accomplished using the ergodic theorem the resulting expression for joint entropy is applied to several data sets showing the utility of the concept for both materials characterization and detection of targeted liquid nanoparticle ultrasonic contrast agents in all cases the sensitivity of these techniques matches or exceeds sometimes by a factor of two that demonstrated in previous studies that employed signal energy or alternate entropic quantities

quantizer precision for distributed estimation in a large sensor network we investigate the design of simple noncooperative quantizers for distributed estimation of a common random variable it is assumed that there is a budget of aggregate rate a criterion of fisher information and a large population of sensors it is further assumed that sensor quantizers are uniform and that rate is determined by the entropy of the outputs of these the key question asked is whether it is better to quantize a relatively few sensors finely or as many as possible coarsely

a comparison of shannon entropy versus signal energy for acoustic detection of artificially induced defects in plexiglas an experimental comparison of scanned images formed from shannon entropy total energy and log energy measurements of acoustic wave propagation in a plexiglas bar with drill hole defects shows that shannon entropy in the instance investigated is approximately two to three times as sensitive to the presence of small defects than are the two energy measures this suggests that the shannon entropy technique may be useful for flaw detection in materials that are too thick or lossy for the conventional use of acoustic energy for flaw detection

on electromagnetics and information theory some connections are described between electromagnetic theory and information theory identifying some unavoidable limitations imposed by the laws of electromagnetism to communication systems starting from this result the role of the degrees of freedom of the field in radiating systems is investigated different classes of antennas use the available degrees of freedom in different ways in particular a multiple input multiple output antenna is a radiating system conveying statistically independent information on more than one degree of freedom of the field applications of the theory to antenna synthesis and antenna characterization in complex environments are shown

degrees of freedom in multiple antenna channels a signal space approach multiple antenna systems that are limited by the area and geometry of antenna arrays are considered given these physical constraints the limit on the available number of spatial degrees of freedom is derived the commonly used statistical multiple input multiple output mimo model is inadequate antenna theory is applied to take into account the area and geometry constraints and to define the spatial signal space so as to interpret experimental channel measurements in an array independent but manageable description of the physical environment based on these modeling strategies for a spherical array of effective aperture a in a physical environment of angular spread spl omega in solid angle the number of spatial degrees of freedom is shown to be a spl omega for uni polarized antennas and 2a spl omega for tri polarized antennas together with the 2wt degrees of freedom for a system of bandwidth w transmitting in an interval t the total degrees of freedom of a multiple antenna channel is therefore 4wta spl omega

optimal channel switching over gaussian channels under average power and cost constraints optimal channel switching that provides the highest performance over a set of gaussian channels with variable utilization costs is investigated in the presence of average power and average cost constraints first generic cost functions are considered and it is shown that the optimal channel switching strategy performs channel switching time sharing among at most three different channels and always operates at the average power and average cost limits also for channel switching between two channels relations between the optimal power levels are obtained depending on the average power limit and it is proved that the ratio of the optimal power levels is upper bounded by the ratio of the larger noise variance to the smaller one in addition for logarithmic cost functions the convexity properties of the error probability are investigated as a function of power and cost and the optimal channel switching strategy is shown to employ at most two channels which can easily be determined based on specific formulas when the average power limit is larger than a certain threshold numerical examples are presented to provide illustrations of the theoretical results

uncertainty principle for real signals in the linear canonical transform domains the linear canonical transform lct is a generalization of the fractional fourier transform frft having applications in several areas of signal processing and optics in this paper we extend the uncertainty principle for real signals in the fractional fourier domains to the linear canonical transform domains giving us the tighter lower bound on the product of the spreads of the signal in two specific lct domains than the existing lower bounds in the lct domains it is seen that this lower bound can be achieved by a gaussian signal the effect of time shifting and scaling the signal on the uncertainty principle is also discussed it is shown here that a signal bandlimited in one lct domain can be bandlimited in some other lct domains also the exceptions to the uncertainty principle in the lct domains arising out of this are also discussed

a variational model for reconstructive phase transformations in crystals and their relation to dislocations and plasticity 1we study the reconstructive martensitic transformations in crystalline solids i e martensitic transformations in which the parent and product lattices have arithmetic symmetry groups admitting no finite supergroup the best known example of which is the bcc fcc transformation in iron we first describe the maximal ericksen pitteri neighborhoods in the space of lattice metrics thereby obtaining a quantitative characterization of the weak transformations which occur within these domains then focusing for simplicity on a two dimensional setting we construct a class of strain energy functions admitting large strains in their domain and which are invariant under the full symmetry group of the lattice in particular we exhibit an explicit energy suitable for the square to hexagonal reconstructive transformation in planar lattices we present a numerical scheme based on atomic scale finite elements and by means of our constitutive function we use it to analyze the effects of transformation cycling on a planar crystal this example illustrates the main phenomena related to the reconstructive martensitic phase changes in crystals in particular the formation of dislocations vacancies and interstitials in the lattice

capacity of the continuous space electromagnetic channel constructing the capacity bound of a multiple input multiple output wireless system is often performed by assuming specified antenna configurations and a propagation environment and determining the signaling strategy which maximizes throughput this paper extends this approach to further determine the optimal antenna characteristics which maximize the capacity for the propagation scenario with the resulting capacity bound representing the ultimate maximum achievable value if optimal antenna design and signaling are used in this approach the spatially continuous transmit currents and receive fields are represented using eigenfunctions of appropriate operators it is shown that except under certain conditions where array supergain solutions emerge the capacity remains bounded for finite transmit power the approach also shows how to limit supergain effects using practical constraints model problems and numerical computations are provided for different power constraints at the transmitter and noise characteristics at the receiver

gradings on the algebra of upper triangular matrices and their graded identities abstract let k be an infinite field and let ut n k denote the algebra of n n upper triangular matrices over k we describe all elementary gradings on this algebra further we describe the generators of the ideals of graded polynomial identities of ut n k and we produce linear bases of the corresponding relatively free graded algebras we prove that one can distinguish the elementary gradings by their graded identities we describe bases of the graded polynomial identities in several typical cases although in these cases we consider elementary gradings by cyclic groups the same methods serve for elementary gradings by any finite group

on parameter estimates of the lossy wave equation the cramer rao bound crb and maximum likelihood estimates in gaussian noise for the parameters of a sampled signal that satisfies the lossy wave equation such as the voltage sampled along a transmission line are derived results for both equally and unequally spaced samples are given it is shown that for certain values of the wave number frequency the estimates are sensitive to the amount of the ldquoreflected waverdquo in the signal while for other values of the wave number the estimates are insensitive it is also shown that for certain special cases it is possible to improve on standard frequency estimation up to 3 6 db by reflecting some of the noise free signal energy into a backward propagating wave and applying the maximum likelihood estimator mle to the new measured signal

time delay estimation of chirp signals in the fractional fourier domain a new time delay estimator is presented in this paper it is evaluated based on the delay property of the fractional fourier transform with less computation and is suitable for chirp signals the statistical analysis in terms of signal to noise ratio snr and estimation accuracy for this estimation is also studied the proposed method for the time delay yields a variance which is theoretically equal to the cramer rao lower bound the validity of this estimation method is demonstrated via simulations

the discrete fractional fourier transform we propose and consolidate a definition of the discrete fractional fourier transform that generalizes the discrete fourier transform dft in the same sense that the continuous fractional fourier transform generalizes the continuous ordinary fourier transform this definition is based on a particular set of eigenvectors of the dft matrix which constitutes the discrete counterpart of the set of hermite gaussian functions the definition is exactly unitary index additive and reduces to the dft for unit order the fact that this definition satisfies all the desirable properties expected of the discrete fractional fourier transform supports our confidence that it will be accepted as the definitive definition of this transform

intrinsic limits of dimensionality and richness in random multipath fields we study the dimensions or degrees of freedom of farfield multipath that is observed in a limited source free region of space the multipath fields are studied as solutions to the wave equation in an infinite dimensional vector space we prove two universal upper bounds on the truncation error of fixed and random multipath fields a direct consequence of the derived bounds is that both fixed and random multipath fields have an effective finite dimension for circular and spherical spatial regions we show that this finite dimension is proportional to the radius and area of the region respectively we use the karhunen loegraveve kl expansion of random multipath fields to quantify the notion of multipath richness the multipath richness is defined as the number of significant eigenvalues in the kl expansion that achieve 99 of the total multipath energy we establish a lower bound on the largest eigenvalue this lower bound quantifies to some extent the well known reduction of multipath richness with reducing the angular power spread of multipath angular power spectrum

analysis of digitized waveforms using shannon entropy ii high speed algorithms based on green s functions an improved approach for calculating continuous waveform entropy hc is described this approach is based on the use of the green s function for the one dimensional differential operator l u u with boundary conditions u 1 u 0 0 the method is applied to data acquired from a plexiglas block having artificial defects in order to produce an entropy image the defect contrast obtained with the new green s function computation is then compared with that obtained from a previously described fourier series approach it is found that the new approach produces the same or higher image contrast in a time that is roughly three orders of magnitude smaller than that required by the fourier series method this speedup arises from two sources the green s function approach has greater inherent immunity to noise and the number of calculations required in the green s function approach is much smaller than the number required in the fourier series approach

properties of an entropy based signal receiver with an application to ultrasonic molecular imaging qualitative and quantitative properties of the finite part hf of the shannon entropy of a continuous waveform f t in the continuum limit are derived in order to illuminate its use for waveform characterization simple upper and lower bounds on hf based on features of f t are defined quantitative criteria for a priori estimation of the average case variation of hf and logef where ef is the signal energy of f t are also derived these provide relative sensitivity estimates that could be used to prospectively choose optimal imaging strategies in real time ultrasonic imaging machines where system bandwidth is often pushed to its limits to demonstrate the utility of these sensitivity relations for this application a study designed to assess the feasibility of identification of angiogenic neovasculature targeted with perfluorocarbon nanoparticles that specifically bind to v 3 integrin expression in tumors was performed the outcome of this study agrees with the prospective sensitivity estimates tha

on z2 graded polynomial identities of the grassmann algebra abstract let f be a field of characteristic zero and let e be the grassmann algebra of an infinite dimensional f vector space l in this paper we study the z 2 graded polynomial identities of e with respect to any fixed z 2 grading such that l is an homogeneous subspace we found explicit generators for the ideal t 2 e of graded polynomial identities of e and we determine its cocharacter and codimension sequences

new aspects of electromagnetic information theory for wireless and antenna systems this paper investigates information theoretic characterization via shannon s information capacity and number of degrees of freedom of wave radiation antenna and wireless propagation systems specifically the paper derives from the fundamental physical point of view of maxwell s equations describing electromagnetic fields the shannon information capacity of space time wireless channels formed by electromagnetic sources and receivers in a known background medium the theory is developed first for the case of sources working at a fixed frequency time harmonic case and is expanded later to the more general case of temporally bandlimited systems time domain fields in the bandlimited case we consider separately the two cases of time limited and essentially bandlimited systems and of purely bandlimited systems the developments take into account the physical radiated power constraint in addition to a constraint in the source l 2 norm which acts to avoid antenna superdirectivity based on such radiated power and current l 2 norm constraints we derive the shannon information capacity of canonical wireless and antenna systems in free space for a given additive gaussian noise level as well as an associated number of degrees of freedom resulting from such capacity calculations the derived results also illustrate from a new information theoretic point of view the transition from near to far fields