on the construction of equiangular frames from graphs abstract we give details of the 1 1 correspondence between equiangular frames of n vectors for r d and graphs with n vertices this has been studied recently for tight equiangular frames because of applications to signal processing and quantum information theory the nontight examples given here which correspond to graphs with more than 2 eigenvalues have the potential for similar applications e g the frame corresponding to the 5 cycle graph is the unique grassmannian frame of 5 vectors in openr 3 further the associated canonical tight frames have a small number of angles in many cases

on oscillation of nonlinear second order differential equation with damping term we present new oscillation criteria for the second order nonlinear differential equation with damping our theorems are stated in general form they complement and extend related results known in the literature the relevance of our results is illustrated with a number of examples to facilitate computations in these examples we use mathematica r a symbolic computer language

designing structured tight frames via an alternating projection method tight frames also known as general welch bound equality sequences generalize orthonormal systems numerous applications including communications coding and sparse approximation require finite dimensional tight frames that possess additional structural properties this paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems ieps which includes the frame design problem to apply this method one needs only to solve a matrix nearness problem that arises naturally from the design specifications therefore it is the fast and easy to develop versions of the algorithm that target new design problems alternating projection will often succeed even if algebraic constructions are unavailable to demonstrate that alternating projection is an effective tool for frame design the paper studies some important structural properties in detail first it addresses the most basic design problem constructing tight frames with prescribed vector norms then it discusses equiangular tight frames which are natural dictionaries for sparse approximation finally it examines tight frames whose individual vectors have low peak to average power ratio par which is a valuable property for code division multiple access cdma applications numerical experiments show that the proposed algorithm succeeds in each of these three cases the appendices investigate the convergence properties of the algorithm

two constructions of asymptotically optimal codebooks according to the welch bound abstract in a number of applications the codebook that minimizes the maximal cross correlation amplitude imax is often desirable there are two major ingredients in this paper these two contents are to propose two constructions of codebooks the codebooks generated by these constructions asymptotically meet the welch bound what we find is the codebook constructed in section 2 can also asymptotically meet the levenshtein bound the parameters of these codebooks are new

equiangular tight frames and signature sets in groups abstract quiangular frames are an important class of finite dimensional frames because of their superior performance and numerous applications the objective of this paper is to present a new tool to construct equiangular tight frames from groups we prove that many equiangular tight frames arise from subsets of groups which we call signature sets subsequently we define quasi signature sets and examine real equiangular tight frames associated with these subsets of groups this approach yields further results and establishes new correspondences we extend these results to complex equiangular tight frames where the inner product between any pair of vectors is a common multiple of a cube root of unity and exhibit equiangular tight frames that arise from groups in this manner

a monte carlo form finding method for large scale regular and irregular tensegrity structures we propose a monte carlo form finding method that employs a stochastic procedure to determine equilibrium configurations of a tensegrity structure this method does not involve complicated matrix operations or symmetry analysis works for arbitrary initial configurations and can handle large scale regular or irregular tensegrity structures with or without material geometrical constraints

oscillation results for a second order damped differential equation with nonmonotonous nonlinearity abstract we present new oscillation criteria for a nonlinear second order differential equation with a damping term an essential feature of our results is that we do not require the nonlinearity to be nondecreasing furthermore as opposed to the recent results by s r grace 1989 math nachr 141 117 127 1992 j math anal appl 171 220 241 and s r grace and b s lalli 1990 j math anal appl 149 277 311 we do not impose any additional condition on the damping term p t consequently our theorems apply to new classes of equations which are not covered by the known criteria the relevance of the results obtained is illustrated with a number of carefully selected examples

oscillation criteria for second order matrix differential equations new oscillation criteria are presented for second order matrix differential equation px qx rf x 0 which extend and improve the recent results of li and agarwal for scalar cases and the results of meng wang and zheng for matrix cases

nonlinear functionals and a theorem of sun we use a recently developed theory of nonlinear functionals in the study of oscillations of second order symmetric vector differential systems to extend a number of theorems of sun new kamenev type theorems for second order linear matrix differential systems appl math lett 2004 in press under a common theme the criteria presented here are of the form the integral of the coefficient matrix is bounded at infinity in a sense to be made explicit in the paper and bounded away from a positive absolute constant implies oscillation at infinity

new kamenev type oscillation criteria for second order nonlinear advanced dynamic equations this paper presents a new kamenev type oscillation criterion for a second order advanced dynamic equation on a time scale two examples are included to show that the result obtained complements and improves those reported in the literature

interval criteria for oscillation of second order half linear differential equations by employing a generalized riccati technique and an integral averaging method interval oscillation criteria are established for the second order half linear differential equation r t x t 1x t q t x t 1x t 0 these criteria are different from most known ones in the sense that they are based on information only on a sequence of subintervals of t0 rather than on the whole half line they also extend improve and complement a number of existing results and can be applied to extreme cases such as t0 q s ds in particular several interesting examples that illustrate the importance of our results are included

oscillation criteria for second order nonlinear damped differential equations abstract this paper discusses a class of second order nonlinear damped differential equations by using the generalized riccati technique and the integral averaging technique new oscillation criteria are obtained

oscillation and global attractivity in a delay periodic host macroparasite model abstract in this paper we shall consider the nonlinear delay host macroparasite model with periodic coefficients with common period by means of a continuation theorem in coincidence degree theory we establish a sufficient condition for the existence of a positive periodic solution m t with strictly positive components also we establish some sufficient conditions for oscillation of all positive solutions about the positive periodic solution m t and establish a sufficient condition for the global attractivity of m t

asymptotic behavior of solutions of second order nonlinear delay differential equations with impulses this paper is concerned with second order nonlinear delay differential equations with impulses of the form r t x t p t x t f t x email protected 0 t t k x t k i k x t k x t k j k x t k t t k k 1 2 t t 0 by impulsive differential inequality and riccati transformation sufficient conditions of asymptotic behavior of all solutions of second order nonlinear delay differential equations with impulses are obtained some examples are also inserted to illustrate the impulsive effect

properties of real and complex etfs and their application to the design of low coherence frames certain properties of an equiangular tight frame are contained in the sign or phase of its corresponding gram matrix in this paper we convey new properties for gram matrices of equiangular tight frames and use them to construct new frames with low average and worst case coherences based on these results we also provide properties of the synthesis matrix of equiangular tight frames

oscillation criteria for nonlinear differential equations with damping oscillation criteria are established for the nonlinear second order damped differential equation rx px qf x 0 which are different from most known results

addendum to lattices from equiangular tight frames linear algebra appl 510 2016 395 420 abstract this note supplies additions to our paper quoted in the title on integral spans of tight frames in euclidean spaces in that previous paper we considered the case of an equiangular tight frame etf proving that if its integral span is a lattice then the frame must be rational but overlooking a simple argument in the reverse direction thus our first result here is that the integral span of an etf is a lattice if and only if the frame is rational further we discuss conditions under which such lattices are eutactic and perfect and consequently are local maxima of the packing density function in the dimension of their span in particular the unit 276 23 equiangular tight frame is shown to be eutactic and perfect more general tight frames and their norm forms are considered as well and definitive results are obtained in dimensions two and three

oscillation of certain second order nonlinear differential equations abstract in this paper we consider the second order nonlinear differential equation formula where 0 is any quotient of odd integers a c 1 r 0 q c r r f c r r xf x 0 f x 0 for x 0 some new sufficient conditions for the oscillation of all solutions of are obtained several examples that dwell upon the importance of our results are also included

oscillation theorems for self adjoint matrix hamiltonian systems involving general means by use of monotone functionals and positive linear functionals a generalized riccati transformation and the general means technique some new oscillation criteria for the following self adjoint hamiltonian matrix system e x t a t x t b t y t y t c t x t a t y t are obtained the results obtained improve and complement that of kumari et al 2000 on kamenev type theorems moreover these results generalize and improve earlier results due to meng 2002 for e erbe et al 1993 meng et al 1998 and wang 2001 for p t x t q t x t 0 or its special cases and wong 2001 for the scalar system x t q t x t 0

a tight degree 4 sum of squares lower bound for the sherrington kirkpatrick hamiltonian we show that if varvec w is an n times n matrix drawn from the gaussian orthogonal ensemble then with high probability the degree 4 sum of squares relaxation cannot certify an upper bound on the objective n 1 cdot varvec x top varvec w varvec x under the constraints x i 2 1 0 i e varvec x in pm 1 n that is asymptotically smaller than lambda max varvec w approx 2 we also conjecture a proof technique for lower bounds against sum of squares relaxations of any degree held constant as n rightarrow infty by proposing an approximate pseudomoment construction

equiangular tight frames and unistochastic matrices we demonstrate that a complex equiangular tight frame composed of n vectors in dimension d denoted etf d n exists if and only if a certain bistochastic matrix univocally determined by n and d belongs to a special class of unistochastic matrices this connection allows us to find new complex etfs in infinitely many dimensions and to derive a method to introduce non trivial free parameters in etfs we present an explicit six parametric family of complex etf 6 16 which defines a family of symmetric povms minimal and maximal possible average entanglement of the vectors within this qubit qutrit family are described furthermore we propose an efficient numerical procedure to compute the unitary matrix underlying a unistochastic matrix which we apply to find all existing classes of complex etfs containing up to 20 vectors

oscillation theorems for certain nonlinear differential equations of second order abstract we present new oscillation criteria for the second order nonlinear differential equations these criteria involve the use of averaging functions our theorems are stated in general form they complement and extend related results known in the literature also the relevance of our results is to show that some of manojlovic s results contain the superfluous condition

frames graphs and erasures two uniform frames and their use for the coding of vectors are the main subject of this paper these frames are known to be optimal for handling up to two erasures in the sense that they minimize the largest possible error when up to two frame coefficients are set to zero here we consider various numerical measures for the reconstruction error associated with a frame when an arbitrary number of the frame coefficients of a vector are lost we derive general error bounds for two uniform frames when more than two erasures occur and apply these to concrete examples we show that among the 227 known equivalence classes of two uniform 36 15 frames arising from hadamard matrices there are 5 that give smallest error bounds for up to 8 erasures

finite two distance tight frames abstract a finite collection of unit vectors s r n is called a spherical two distance set if there are two numbers a and b such that the inner products of distinct vectors from s are either a or b we prove that if a b then a two distance set that forms a tight frame for r n is a spherical embedding of a strongly regular graph we also describe all two distance tight frames obtained from a given graph together with an earlier work by s waldron 2009 22 on the equiangular case this completely characterizes two distance tight frames as an intermediate result we obtain a classification of all two distance 2 designs

interval criteria for oscillation of second order functional differential equations by using averaging functions new interval oscillation criteria are established for the second order functional differential equation r t x t a 1x t f t x t x t t x t x t t 0 t t 0that are different from most known ones in the sense that they are based on information only on a sequence of subintervals of t 0 rather than on the whole half line our results can be applied to three cases ordinary delay and advance differential equations in the case of half linear functional differential equations our criteria implies that the t t t delay and gt t t advance cases do not affect the oscillation in particular several examples are given to illustrate the importance of our results

achieving the welch bound with difference sets consider a codebook containing n unit norm complex vectors in a k dimensional space in a number of applications the codebook that minimizes the maximal cross correlation amplitude i sub max is often desirable relying on tools from combinatorial number theory we construct analytically optimal codebooks meeting in certain cases the welch lower bound when analytical constructions are not available we develop an efficient numerical search method based on a generalized lloyd algorithm which leads to considerable improvement on the achieved i sub max over existing alternatives we also derive a composite lower bound on the minimum achievable i sub max that is effective for any codebook size n

an asymptotic existence result on compressed sensing matrices abstract for any rational number h and all sufficiently large n we give a deterministic construction for an n h n compressed sensing matrix with l 1 t recoverability where t o n our method uses pairwise balanced designs and complex hadamard matrices in the construction of equiangular frames which we introduce as a generalisation of equiangular tight frames the method is general and produces good compressed sensing matrices from any appropriately chosen pairwise balanced design the l 1 t recoverability performance is specified as a simple function of the parameters of the design to obtain our asymptotic existence result we prove new results on the existence of pairwise balanced designs in which the numbers of blocks of each size are specified

kirkman equiangular tight frames and codes an equiangular tight frame etf is a set of unit vectors in a euclidean space whose coherence is as small as possible equaling the welch bound also known as welch bound equality sequences such frames arise in various applications such as waveform design and compressed sensing at the moment there are only two known flexible methods for constructing etfs harmonic etfs are formed by carefully extracting rows from a discrete fourier transform steiner etfs arise from a tensor like combination of a combinatorial design and a regular simplex these two classes seem very different the vectors in harmonic etfs have constant amplitude whereas steiner etfs are extremely sparse we show that they are actually intimately connected a large class of steiner etfs can be unitarily transformed into constant amplitude frames dubbed kirkman etfs moreover we show that an important class of harmonic etfs is a subset of an important class of kirkman etfs this connection informs the discussion of both types of frames some steiner etfs can be transformed into constant amplitude waveforms making them more useful in waveform design some harmonic etfs have low spark making them less desirable for compressed sensing we conclude by showing that real valued constant amplitude etfs are equivalent to binary codes that achieve the grey rankin bound and then construct such codes using kirkman etfs

new kamenev type oscillation criteria for second order nonlinear differential equations with damping abstract some new oscillation criteria are established for the nonlinear damped differential equation r t y p t y q t f y 0 that are different from most known ones in the sense that they are based on a class of new functions t s r defined in the sequel our results are sharper than some previous results which can be seen by the examples at the end of this paper

optimal frames for erasures we study frames from the viewpoint of coding theory we introduce a numerical measure of how well a frame reconstructs vectors when some of the frame coefficients of a vector are lost and then attempt to find and classify the frames that are optimal in this setting

interval criteria for oscillation of second order linear ordinary differential equations abstract new oscillation criteria are established for the equation py qy 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are more natural according to the sturm separation theorem and sharper than some previous results and can be applied to extreme cases such as t 0 q t dt

equiangular tight frames that contain regular simplices abstract an equiangular tight frame etf is a type of optimal packing of lines in euclidean space a regular simplex is a special type of etf in which the number of vectors is one more than the dimension of the space they span in this paper we consider etfs that contain a regular simplex that is have the property that a subset of its vectors forms a regular simplex as we explain such etfs are characterized as those that achieve equality in a certain well known bound from the theory of compressed sensing we then consider the so called binder of such an etf namely the set of all regular simplices that it contains we provide a new algorithm for computing this binder in terms of products of entries of the etf s gram matrix in certain circumstances we show this binder can be used to produce a particularly elegant naimark complement of the corresponding etf other times an etf is a disjoint union of regular simplices and we show this leads to a certain type of optimal packing of subspaces known as an equichordal tight fusion frame we conclude by considering the extent to which these ideas can be applied to numerous known constructions of etfs including harmonic etfs

interval oscillation criteria for second order linear differential equations with impulsive effects abstract this paper discusses how the oscillation of solutions changes by adding an impulsive term to a second order linear differential equation having only a restoring force term but no damping term due to the effect of this impulsive term the moving speed of a mass point of the equation of motion described by the second order linear differential equation changes discontinuously oscillation theorems are given for this impulsive differential equation as is well known when the restoring force term is small all nontrivial solutions of the equation with no impulsive effects do not oscillate even when the restoring force term is small if the action of the impulsive term compensates the oscillation criteria obtained are satisfied and all nontrivial solutions oscillate several examples are given to confirm this fact and some figures are shown to depict the solution curves of these examples as shown by the obtained oscillation theorems there are cases that the impulsive effect promotes the oscillation of solutions but on the contrary it may suppress the oscillation of solutions it is shown by a simulation that there is a case where the impulsive effect suppress the oscillation of solutions finally the obtained results are compared with the previous ones

oscillation criteria for second order functional differential equations in this paper oscillation criteria for general second order functional differential equations are given integral criterion for oscillation using recent nth primitive method introduced by cheh chih yeh is considered

compressive framework for demosaicing of natural images typical consumer digital cameras sense only one out of three color components per image pixel the problem of demosaicing deals with interpolating those missing color components in this paper we present compressive demosaicing cd a framework for demosaicing natural images based on the theory of compressed sensing cs given sensed samples of an image cd employs a cs solver to find the sparse representation of that image under a fixed sparsifying dictionary as opposed to state of the art cs based demosaicing approaches we consider a clear distinction between the interchannel color and interpixel correlations of natural images utilizing some well known facts about the human visual system those two types of correlations are utilized in a nonseparable format to construct the sparsifying transform our simulation results verify that cd performs better both visually and in terms of psnr than leading demosaicing approaches when applied to the majority of standard test images

oscillation criteria for second order sublinear differential equation abstract the basic purpose of this paper is to present a new oscillation criteria for second order sublinear differential equation a t x t x t q t t 0 t t 0 0 where a a c 1 t 0 is positive function q c t 0 has no restriction on its sign c 1 r are such that x 0 x x 0 for x 0

interval oscillation criteria for second order nonlinear differential equations with damping new oscillation criteria are established for the nonlinear damped differential equation ry py qf y 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are sharper than some previous results and extend and improve the recent interval criteria of kong and huang and can be applied to extreme cases such as t0 q s ds in particular several examples that dwell upon the sharp conditions of our results are also included

on the singularities of a constrained incompressible like tensegrity cytoskeleton model under equitriaxial loading singularity theory is applied for the study of the characteristic three dimensional tensegrity cytoskeleton model after adopting an incompressibility constraint the model comprises six elastic bars interconnected with 24 elastic string members previous studies have already been performed on non constrained systems however the present one allows for general non symmetric equilibrium configurations critical conditions for branching of the equilibrium are derived and post critical behaviour is discussed classification of the simple and compound singularities of the total potential energy function is effected the theory is implemented into the cusp catastrophe for the case of one dimensional branching of the buckling allowed tensegrity model and an elliptic umbilic singularity for compound branching of a rigid bar model it is pointed out that singularity studies with constraints demand a quite different mathematical approach than those without constraints

complex codebooks from combinatorial designs codebooks also called signal sets meeting the welch bounds are desirable in code division multiple access cdma systems in 2003 binary codebooks meeting welch s bounds were constructed using difference sets by ding golin and kloslashve recently a generic construction of codebooks with cyclic difference sets meeting welch s bound on the maximum cross correlation amplitude was developed by xia in this correspondence the idea of xia is extended and related constructions of optimal codebooks with both cyclic and noncyclic difference sets are presented these codebooks are optimal in the sense that they also meet this welch bound in addition complex codebooks that almost meet welch s bound on the maximum cross correlation amplitude are also constructed with almost difference sets

equiangular tight frames from paley tournaments abstract we prove the existence of equiangular tight frames having n 2 d 1 elements drawn from either c d or c d 1 whenever n is either 2 k 1 for k n or a power of a prime such that n 3 mod 4 we also find a simple explicit expression for the prime power case by establishing a connection to a 2 d element equiangular tight frame based on quadratic residues

note on wong s paper using the method of interval integral average we establish some new oscillation criteria which improve the oscillation criteria due to james s w wong

oscillation criteria for second order nonlinear perturbed differential equations abstract we present new oscillation criteria for the second order nonlinear perturbed differential equations these criteria are of a high degree of generality and they extend and unify a number of existing results

oscillation criteria of second order nonlinear matrix differential systems in this paper the second order nonlinear matrix differential systems p t y t f t y t y t 0 t t 0is considered where p t y t and f t y t y t are nxn real continuous matrix functions and p t 0 are positive definite and symmetric one some new oscillation criteria for the systems are established and some known results in the literature are improved and generalized

oscillation and global attractivity in hematopoiesis model with periodic coefficients in this paper we shall consider the nonlinear delay differential equation p t email protected t p m email protected 1 p n email protected email protected t p t where k is a positive integer b t and c t are positive periodic functions of period w in the nondelay case we shall show that has a unique positive periodic solution email protected t and we will study the global attractivity of email protected t in the delay case we shall establish some sufficient conditions for oscillation of all positive solutions of about email protected t and establish some sufficient conditions for the global attractivity of email protected t our results in this paper extend as well as improve the results in the autonomous case

upper bounds for s distance sets and equiangular lines abstract the set of points in a metric space is called an s distance set if pairwise distances between these points admit only s distinct values two distance spherical sets with the set of scalar products 0 1 are called equiangular the problem of determining the maximum size of s distance sets in various spaces has a long history in mathematics we suggest a new method of bounding the size of an s distance set in compact two point homogeneous spaces via zonal spherical functions this method allows us to prove that the maximum size of a spherical two distance set in r n n 7 is n n 1 2 with possible exceptions for some n 2 k 1 2 3 k n we also prove the universal upper bound 2 3 n a 2 for equiangular sets with 1 a and employing this bound prove a new upper bound on the size of equiangular sets in all dimensions finally we classify all equiangular sets reaching this new bound

oscillation criteria related to integral averaging technique for linear matrix hamiltonian systems by employing a generalized riccati technique and an integral averaging technique new oscillation criteria are established for the linear matrix hamiltonian system u a x u b x v v c x u a x v under the assumption that all a x b x b x 0 and c x c x are n n matrices of real valued continuous functions on the interval i x0 x0 these criteria extend improve and unify a number of existing results and also handle cases not covered by known criteria several interesting examples that illustrate the importance of our results are included

a note on equiangular tight frames we settle a conjecture of joseph renes about the existence and construction of certain equiangular tight frames

oscillation and asymptotics for second order half linear differential equations this paper discusses a class of second order half linear differential equations by using the generalized riccati technique and the averaging technique new oscillation criteria are obtained for all solutions of the equations to be oscillatory asymptotic behavior for forced equations is also discussed

oscillation criteria for second order nonlinear differential equations with damping abstract for a second order nonlinear differential equation with a damping term we obtain new oscillation criteria without an assumption that has been required for related results reported in the literature over the last two decades two approaches refining the standard integral averaging technique suggested in the paper can be used to derive a variety of simpler oscillation theorems for different classes of nonlinear differential equations and both sets of oscillation criteria established in the paper are of independent interest several examples are provided to illustrate the relevance of the new theorems

interval oscillation criteria related to integral averaging technique for certain nonlinear differential equations abstract we present new interval oscillation criteria related to integral averaging technique for certain classes of second order nonlinear differential equations that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are sharper than some previous results and handle the cases which are not covered by known criteria in particular several examples that dwell upon the sharp conditions of our results are also included

on the existence of equiangular tight frames abstract an equiangular tight frame etf is a d n matrix that has unit norm columns and orthogonal rows of norm n d its key property is that the absolute inner products between pairs of columns are i identical and ii as small as possible etfs have applications in communications coding theory and sparse approximation numerical experiments indicate that etfs arise for very few pairs d n and it is an important challenge to develop restrictions on the pairs for which they can exist this article uses field theory to provide detailed conditions on real and complex etfs in particular it describes restrictions on harmonic etfs a specific type of complex etf that appears in applications finally the article offers empirical evidence that these conditions are sharp or nearly sharp especially in the real case

oscillation and asymptotics for nonlinear second order differential equations this paper discusses a class of second order nonlinear differential equations by using the generalized riccati technique and the averaging technique new oscillation criteria are obtained for all solutions of the equation to be oscillatory asymptotic behavior for forced equations is also discussed

oscillation of nonlinear dynamic equations on time scales by means of riccati transformation techniques we establish some new oscillation criteria for the second order nonlinear dynamic equation p t x d t d q t f x s t 0 email protected a b on time scales in terms of the coefficients and the graininess function we illustrate our results with a nontrivial example

complex equiangular tight frames and erasures in this paper we demonstrate that there are distinct dierences between real and complex equiangular tight frames etfs with regards to erasures for example we prove that there exist arbitrarily large non trivial complex equiangular tight frames which are robust against three erasures and that such frames come from a unique class of complex etfs in addition we extend certain results in 1 to complex vector spaces as well as show that other results regarding real etfs are not valid for complex etfs

on maximal relative projection constants abstract this article focuses on the maximum of relative projection constants over all m dimensional subspaces of the n dimensional coordinate space equipped with the max norm this quantity called maximal relative projection constant is studied in parallel with a lower bound dubbed quasimaximal relative projection constant exploiting alternative expressions for these quantities we show how they can be computed when n is small and how to reverse the kadec snobar inequality when n does not tend to infinity precisely we first prove that the quasi maximal relative projection constant can be lower bounded by c m with c arbitrarily close to one when n is superlinear in m the main ingredient is a connection with equiangular tight frames by using the semicircle law we then prove that the lower bound c m holds with c 1 when n is linear in m

on discontinuous strain fields in incompressible finite elastostatics abstract piece wise homogeneous three dimensional deformations in incompressible materials in finite elasticity are considered the emergence of discontinuous strain fields in incompressible materials is studied via singularity theory since the simplest singularities including maxwell s sets are the cusp singularities cusp conditions for the total energy function of homogeneous deformations for incompressible materials in finite elasticity will be derived compatible with strain jumping the proposed method yields simple criteria for the study of discontinuous deformations in three dimensional problems and for any homogeneous incompressible material furthermore the homogeneous stress tensor is also not restricted neither fictitious nor simplified constitutive relations are invoked the theory is implemented in a simple shearing problem

oscillation criteria for second order nonlinear differential equations with nonlinear damping this paper is concerned with the oscillation of a class of general type second order differential equations with nonlinear damping several new oscillation criteria are established under quite general assumptions which improve and extend the known results in the literature

oscillation criteria for second order linear differential equations abstract some oscillation criteria are given for the second order linear differential equation r t u t c t u t 0 where r t c 1 t 0 0 and c t c t 0 r these results improve oscillation criteria of wintner hartman kamenev yan and philos by using a generalized riccati transformation t a t r t u t u t f t where f c 1 is a given function on t 0 and a t exp 2 t f s ds

interval oscillation of a general class of second order nonlinear differential equations with nonlinear damping abstract the paper is concerned with the oscillation of a class of general type second order differential equations with nonlinear damping terms several new interval oscillation criteria are established for such a class of differential equations under quite general assumptions examples are also given to illustrate the results in particular it is shown that under some very mild conditions on k 1 k 2 and f the equation k 1 x x cos tk 2 x x x sin tf x 0 is oscillatory which extends the result obtained by kwong and wong j math anal appl 288 2003 15

steiner equiangular tight frames abstract we provide a new method for constructing equiangular tight frames etfs the construction is valid in both the real and complex settings and shows that many of the few previously known examples of etfs are but the first representatives of infinite families of such frames it provides great freedom in terms of the frame s size and redundancy this method also explicitly constructs the frame vectors in their native domain as opposed to implicitly defining them via their gram matrix moreover in this domain the frame vectors are very sparse the construction is extremely simple a tensor like combination of a steiner system and a regular simplex this simplicity permits us to resolve an open question regarding etfs and the restricted isometry property rip we show that the rip behavior of some etfs is unfortunately no better than their coherence indicates

geometry of the welch bounds abstract a geometric perspective involving grammian and frame operators is used to derive the entire family of welch bounds this perspective unifies a number of observations that have been made regarding tightness of the bounds and their connections to symmetric k tensors tight frames homogeneous polynomials and t designs in particular a connection has been drawn between sampling of homogeneous polynomials and frames of symmetric k tensors it is also shown that tightness of the bounds requires tight frames the lack of tight frames of symmetric k tensors in many cases however leads to consideration of sets that come as close as possible to attaining the bounds the geometric derivation is then extended in the setting of generalized or continuous frames the welch bounds for finite sets and countably infinite sets become special cases of this general setting

kamenev type and interval oscillation criteria for second order linear differential equations on a measure chain abstract we establish kamenev type criteria and interval criteria for oscillation of the second order scalar differential equation p t x t q t x t 0 on a measure chain our results cover those for differential equations and provide new oscillation criteria for difference equations several examples are given to show the significance of the results

equiangular tight frames and fourth root seidel matrices in this paper we construct complex equiangular tight frames etfs in particular we study the grammian associated with an etf whose off diagonal entries consist entirely of fourth roots of unity these etfs are classified and we also provide some computational techniques which give rise to previously undiscovered etfs

lattices from equiangular tight frames abstract we consider the set of all linear combinations with integer coefficients of the vectors of a unit equiangular tight k n frame and are interested in the question whether this set is a lattice that is a discrete additive subgroup of the k dimensional euclidean space we show that this is not the case if the cosine of the angle of the frame is irrational we also prove that the set is a lattice for n k 1 and that there are infinitely many k such that a lattice emerges for n 2 k we dispose of all cases in dimensions k at most 9 in particular we show that a 7 28 frame generates a strongly eutactic lattice and give an alternative proof of roland bacher s recent observation that this lattice is perfect

integral averaging technique for the interval oscillation criteria of certain second order nonlinear differential equations abstract we present new interval oscillation criteria related to integral averaging technique for certain classes of second order nonlinear differential equations which are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line they generalize and improve some known results examples are also given to illustrate the importance of our results

on quasi orthogonal signatures for cdma systems sum capacity optimal signatures in synchronous code division multiple access cdma systems are functions of the codebook length as well as the number of active users a new signature set must be assigned every time the number of active users changes this correspondence considers signature sets that are less sensitive to changes in the number of active users equiangular signature sequences are proven to solve a certain max min signal to interference plus noise problem which results from their interference invariance unions of orthonormal bases have subsets that come close to satisfying the welch bound bounds on the maximum number of bases with minimum maximum correlation are derived and a new construction algorithm is provided connections are made between these signature design problems grassmannian line packing frame theory and algebraic geometry

interval criteria for oscillation of certain matrix differential systems by employing a generalized riccati technique and an averaging technique interval oscillation criteria are established for the second order matrix differential system of the form p t y q t y 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are presented in the form of a high degree of generality handle the cases which are not covered by known criteria and can be applied to extreme cases such as limt 1 t0tq s ds in particular several interesting examples that dwell upon the importance of our results are included

oscillation criteria for second order nonlinear delay dynamic equations abstract in this paper we consider the second order nonlinear delay dynamic equation r t x t p t f x t 0 on a time scale t by employing the generalized riccati technique we will establish some new sufficient conditions which ensure that every solution oscillates or converges to zero the obtained results improve the well known oscillation results for dynamic equations and include as special cases the oscillation results for differential equations some applications and examples are considered to illustrate the main results

frames of uniform subframe bounds with applications to erasures abstract we introduce a class of frames called usb frames frames of uniform subframe bounds which mean that any subsequence of the frame is a frame for the subspace it spans and the frame bounds depend only on the cardinality of the subsequence we give several necessary and sufficient conditions for a frame to be a usb frame as an application we show that a tight usb frame is optimal for erasures in the sense that the reconstruction error is independent of the position of erasures we give several explicit construction of usb frames

riccati techniques and oscillation for self adjoint matrix hamiltonian systems the purpose of this paper is to develop a generalized matrix riccati technique for the self adjoint matrix hamiltonian system u a x u b x v v c x u a x v together with the integral averaging technique and monotone functionals new oscillation and interval oscillation criteria are established for the system these criteria extend improve complement a number of existing results and handle some cases not covered by known criteria in particular two interesting examples are included to illustrate the versatility of our results