on the sidel nikov sequences as frequency hopping sequences a v l lambda fhs denotes a frequency hopping sequence of length v over a frequency set of size l with maximum out of phase hamming autocorrelation lambda recently ding and yin constructed two fhs families for a prime power q satisfying q ef 1 with positive integers e and f theorems 4 and 5 in their paper claim that these two fhs families include optimal q 1 e f fhss and q 1 e 1 f 1 fhss with respect to the lempel greenberger bound respectively in this paper we give counterexamples and make corrections to them furthermore we observe that these fhss are closely related to sidel nikov sequences based on our results on the spectrum of their hamming autocorrelation values we also correct the theorem on the spectrum of hamming distances of nearly equidistant codes derived by sidel nikov

new bound on frequency hopping sequence sets and its optimal constructions in this paper we derive a new bound on maximum nontrivial hamming correlation of frequency hopping fh sequences from the singleton bound in error correcting code literature and we discuss the relation between the new bound and the known ones on fh sequences further we construct two classes of fh sequences from punctured reed solomon codes and one class of fh sequences from polynomial functions which meet the new bound

a class of optimal frequency hopping sequences with new parameters in this paper we propose an interleaving construction of new sets of frequency hopping sequences from the known ones by choosing suitable known optimal frequency hopping sequences and sets of frequency hopping sequences and then recursively applying the proposed construction optimal frequency hopping sequences and sets of frequency hopping sequences with new parameters can be obtained

stability radius and internal versus external stability in banach spaces an evolution semigroup approach in this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems these include autonomous and nonautonomous systems modeled with unbounded state space operators acting on banach spaces this approach allows one to apply the classical theory of strongly continuous semigroups to time varying systems in particular the complex stability radius may be expressed explicitly in terms of the generator of an evolution semigroup examples are given to show that classical formulas for the stability radius of an autonomous hilbert space system fail in more general settings upper and lower bounds on the stability radius are proven for banach space systems in addition it is shown that the theory of evolution semigroups allows for a straightforward operator theoretic analysis of internal stability as determined by classical frequency domain and input output operators even for nonautonomous banach space systems in particular for the nonautonomous setting internal stability is shown to be equivalent to input output stability for stabilizable and detectable systems for the autonomous setting an explicit formula for the norm of input output operator is given

frequency hopping code sequence designs having large linear span in frequency hopping spread spectrum multiple access communication systems it is desirable to use sets of hopping patterns that in addition to having good hamming correlation properties and large period are also derived from sequences having large linear span here two such frequency hopping code sequence designs that are based on generalized bent functions and generalized bent sequences are presented the hamming correlation properties of the designs are optimal in the first case and close to optimal in the second in terms of the alphabet size p required to be prime in both cases the period and family size of the two designs are given by p sup 2 p and p sup n p sup n 2 1 n an even integer respectively the finite field sequences underlying the patterns in the first design have linear span exceeding p whereas still larger linear spans when compared to the sequence period can be obtained using the second design method

strong no hit zone sequences for improved quasi orthogonal fhma systems sequence design and performance analysis this paper is focused on the optimal design and performance analysis of a novel class of no hit zone frequency hopping sequences nhz fhss in quasi synchronous fh multiple access qs fhma systems although traditional nhz fhss can offer interference free fhma performance when the signal arrival delay tau does not exceed the width of nhz z mathrm nh i e tau leq z mathrm nh the same performance cannot be guaranteed for tau z mathrm nh in which traditional nhz fhzs may have large hamming correlation which denotes the total number of frequency hits of sequences and consequently poor error probability performance since the strict quasi synchronization i e tau leq z mathrm nh may be hard to maintain at all times in practical fhma networks e g infrastructureless ad hoc networks it is also important to minimize the hamming correlation for time shifts outside of the nhz such fhss are called strong nhz fhss snhz fhss in this paper we derive a lower bound on the maximum hamming correlation outside of the nhz and then present a design algorithm for the optimal snhz fhs set meeting our proposed lower bound with equality we analyze the bit error rate ber performance of the fhma system employing the proposed snhz fhs sets using the average hamming correlation function the theoretical analysis and simulation results show that the proposed optimal snhz fhs sets are feasible for practical fhma networks with relaxed timing requirement and enhanced ber performance

exponential stability of laminated timoshenko beams with boundary internal controls abstract for a laminated timoshenko system with slip along the interface we study existence and boundary interior stabilization of solutions our first main result using resolvent estimates in the frequency domain is to show that interior damping created by the interfacial slip in companion with boundary feedback controls acting on the complementary displacements traverse and rotation angle drives the solution to zero with exponential decay rate we impose neither conditions on the physical parameters of the model nor on the damping coefficients our second main result is to investigate the asymptotic behavior of solutions for partially dissipative problems assuming the condition that the waves travel at the same speed we prove the decay of solutions with exponential rate finally the same condition allows us to show that dissipative effect created by the interfacial slip is strong enough to exponentially stabilizes the solutions to zero

the hartman grobman theorem for semilinear hyperbolic evolution equations abstract the famous hartman grobman theorem for ordinary differential equations is extended to abstract semilinear hyperbolic evolution equations in banach spaces by means of simple direct proof it is also shown that the linearising map is holder continuous several applications to abstract and specific damped wave equations are given to demonstrate the strength of our results

new classes of optimal frequency hopping sequences by interleaving techniques in this paper we construct new classes of optimal frequency hopping sequences fhss with respect to the lempel greenberger bound and the peng fan bound by interleaving techniques which are used to construct a sequence of length kn from k sequences of length n we first give two generic constructions for optimal fhs sets from some known optimal fhs sets by interleaving techniques and present some examples of new optimal fhs sets we then design new optimal fhss whose parameters include those of the known optimal constructions with length kn and frequency set size n for some positive integers k and n we also construct optimal fhs sets of length kp from power residue sequences for any odd prime p and 2 les k p in particular our constructions give several new parameters not covered in the literature which are summarized in i and ii

optimal sets of frequency hopping sequences with large linear spans frequency hopping fh is one of the basic spread coding technologies in spread spectrum communications fh sequences are needed in fh code division multiple access cdma systems for the anti jamming purpose fh sequences are required to have a large linear span a few optimal sets of fh sequences are available in the literature however their sequences have very small linear spans it is known that an optimal set of fh sequences could be transformed to another optimal set of fh sequences with large linear spans by a power permutation if the power is chosen properly see c ding and j yin ieee trans inf theory vol it 54 pp 3741 3745 2008 the objective of this paper is to investigate this idea of c ding and j yin further and determine the linear span of the fh sequences in the optimal sets obtained by applying a power permutation to some existing optimal sets of fh sequences

a new construction of frequency hopping sequences with optimal partial hamming correlation frequency hopping sequences fhss with favorable partial hamming correlation properties have important applications in many synchronization and multiple access systems in this paper lower bounds on the partial hamming correlation of fhss and fhs sets are proposed they slightly improve the known bounds by eun et al and zhou et al a construction of fhss and fhs sets having optimal partial hamming correlation with respect to the improved bounds is also presented based on the theory of generalized cyclotomy our construction yields optimal fhss and fhs sets with new and flexible parameters not covered in this paper

cyclic codes and self dual codes over f sub 2 uf sub 2 we introduce linear cyclic codes over the ring f sub 2 uf sub 2 0 1 u u u 1 where u sup 2 0 and study them by analogy with the z sub 4 case we give the structure of these codes on this new alphabet self dual codes of odd length exist as in the case of z sub 4 codes unlike the z sub 4 case here free codes are not interesting some nonfree codes give rise to optimal binary linear codes and extremal self dual codes through a linear gray map

strictly optimal frequency hopping sequence sets with optimal family sizes frequency hopping sequences fhss with favorable partial hamming correlation properties are desirable in many synchronization and multiple access systems an fhs set is said to be strictly optimal if it has optimal partial hamming correlation for any correlation window in this paper we derive upper bounds on the family sizes of fhs sets with respect to partial hamming correlation from some classical bounds on error correcting codes we then present strictly optimal fhs sets having optimal family sizes with respect to one of the new bounds in particular our construction gives new parameters not covered in the literature

decay of solutions for a mixture of thermoelastic one dimensional solids we study a pde system modeling thermomechanical deformations for a mixture of thermoelastic solids in particular we investigate the asymptotic behavior of the solutions first we identify conditions on the constitutive coefficients to guarantee that the imaginary axis is contained in the resolvent subsequently we find the necessary and sufficient conditions to guarantee the exponential decay of solutions when the decay is not of exponential type we prove that the solutions decay polynomially and we find the optimal polynomial decay rate

mixed precision block fused multiply add error analysis and application to gpu tensor cores computing units that carry out a fused multiply add fma operation with matrix arguments referred to as tensor units by some vendors have great potential for use in scientific computing however

zero difference balanced functions with new parameters and their applications as an optimal combinatorial object zero difference balanced zdb functions introduced by ding in 2008 are a generalization of the well known perfect nonlinear functions zdb functions have received much attention in recent years due to its important applications in coding theory and sequence design one objective of this paper is to present a construction of zdb functions based on a kind of generalized cyclotomy it generates zdb functions over cyclic group with new parameters which can not be produced by earlier constructions another objective of this paper is to employ these zdb functions to obtain at the same time 1 optimal constant composition codes 2 perfect difference systems of sets and 3 optimal frequency hopping sequences all with new parameters

the lack of exponential stability in certain transmission problems with localized kelvin voigt dissipation in this paper we consider the transmission problem of a material composed of three components one of them is a kelvin voigt viscoelastic material the second is an elastic material no dissipation and the third is an elastic material inserted with a frictional damping mechanism the main result of this paper is that the rate of decay will depend on the position of each component when the viscoelastic component is not in the middle of the material then there exists exponential stability of the solution instead when the viscoelastic part is in the middle of the material there is not exponential stability in this case we show that the corresponding solution decays polynomially as 1 t 2 moreover we show that the rate of decay is optimal over the domain of the infinitesimal generator finally using a second order scheme that ensures the decay of energy newmark beta method we give some numerical examples which demonstrate this asymptotic behavior

optimal frequency hopping sequences with new parameters a frequency hopping sequence fhs of length v and frequency set size m is called a v m fhs if its maximum out of phase hamming autocorrelation is three new classes of optimal fhss with respect to the lempel greenberger bound are presented in this paper first new optimal p m f fhss are constructed when p mf 1 is an odd prime such that f is even and p 3 mod 4 and then a construction for optimal kp p k fhss is given for any odd prime p and a positive integer k p such that k 2 4 p1 p1 p1 2 2m 1 or p1 m 1 where p1 and p1 2 are odd primes finally several new optimal fhss with maximum out of phase hamming autocorrelation 1 or 2 are also presented in particular the existence of optimal v n 1 fhss is proven for any integer n 3 and any integer v with n 1 v 2 n 1 as well as the existence of optimal 2n 1 n 2 fhss is shown for any integer n 3 these classes of optimal fhss have new parameters which are not covered in the literature

algebraic constructions of optimal frequency hopping sequences frequency hopping fh spread spectrum and direct sequence spread spectrum are two main spread coding technologies frequency hopping sequences are needed in fh code division multiple access cdma systems in this correspondence three classes of optimal frequency hopping sequences are constructed with algebraic methods the three classes are based on perfect nonlinear functions power functions and norm functions respectively both individual optimal frequency hopping sequences and optimal families of frequency hopping sequences are presented

optimal biphase sequences with large linear complexity derived from sequences over z sub 4 new families of biphase sequences of size 2 sup r 1 1 r being a positive integer are derived from families of interleaved maximal length sequences over z sub 4 of period 2 2 sup r 1 these sequences have applications in code division spread spectrum multiuser communication systems the families satisfy the sidelnikov bound with equality on spl theta sub max which denotes the maximum magnitude of the periodic cross correlation and out of phase autocorrelation values one of the families satisfies the welch bound on spl theta sub max with equality the linear complexity and the period of all sequences are equal to r r 3 2 and 2 2 sup r 1 respectively with an exception of the single m sequence which has linear complexity r and period 2 sup r 1 sequence imbalance and correlation distributions are also computed

optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings we construct new sequences over finite rings having optimal hamming correlation properties these sequences are useful in frequency hopping multiple access fhma spread spectrum communication systems our constructions can be classified into linear and nonlinear categories both giving optimal hamming correlations according to lempel greenberger 1974 bound the nonlinear sequences have large linear complexity and can be seen as a generalized version of gmw sequences over fields

decay rates for 1 d mixed type ii and type iii thermoelastic system with localized viscous damping abstract this work is devoted to discussing that how the locations of the thermal and viscous damping affect the stability of the 1 d elastic systems the spatial domain of the 1 d thermoelastic system under consideration can be divided into three sub intervals that is the thermoelastic region of type ii the one of type ii with viscous damping and the one of type iii the following two kinds of energy decay rates for the system are obtained 1 if the thermoelastic region of type iii includes one exterior point of the spatial domain of the system the energy of the system decays exponentially 2 if not that is the thermoelastic region of type iii is strictly inside the spatial domain the system always lacks of exponential decay however the optimal polynomial decay rate is further estimated for this system with smooth initial states finally some numerical simulations are presented to verify the stability results obtained in this work

decoding of cyclic codes over f sub 2 uf sub 2 we give a simple decoding algorithm to decode linear cyclic codes of odd length over the ring r f sub 2 uf sub 2 0 1 u u u 1 where u sup 2 0 a spectral representation of the cyclic codes over r is given and a bch like bound is given for the lee distance of the codes the ring r shares many properties of z sub 4 and f sub 4 and admits a linear gray map

a new analysis of iterative refinement and its application to accurate solution of ill conditioned sparse linear systems iterative refinement is a long standing technique for improving the accuracy of a computed solution to a nonsingular linear system ax b obtained via lu factorization it makes use of residuals computed in extra precision typically at twice the working precision and existing results guarantee convergence if the matrix a has condition number safely less than the reciprocal of the unit roundoff u we identify a mechanism that allows iterative refinement to produce solutions with normwise relative error of order u to systems with condition numbers of order u 1 or larger provided that the update equation is solved with a relative error sufficiently less than 1 a new rounding error analysis is given and its implications are analyzed building on the analysis we develop a gmres based iterative refinement method gmres ir that makes use of the computed lu factors as preconditioners gmres ir exploits the fact that even if a is extremely ill conditioned the lu factors contain enough information that preconditioning can greatly reduce the condition number of a our rounding error analysis and numerical experiments show that gmres ir can succeed where standard refinement fails and that it can provide accurate solutions to systems with condition numbers of order u 1 and greater indeed in our experiments with such matrices both random and from the university of florida sparse matrix collection gmres ir yields a normwise relative error of order u in at most 3 steps in every case

conditional stability of unstable viscous shock waves in compressible gas dynamics and mhd extending our previous work in the strictly parabolic case we show that a linearly unstable lax type viscous shock solution of a general quasilinear hyperbolic parabolic system of conservation laws possesses a translation invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small l 1 h 3 perturbations converging time asymptotically to a translate of the unperturbed wave that is for a shock with p unstable eigenvalues we establish conditional stability on a codimension p manifold of initial data with sharp rates of decay in all l p for p 0 we recover the result of unconditional stability obtained by mascia and zumbrun the main new difficulty in the hyperbolic parabolic case is to construct an invariant manifold in the absence of parabolic smoothing

optimal sets of frequency hopping sequences from linear cyclic codes in communication systems frequency hopping spread spectrum and direct sequence spread spectrum are two main spread coding technologies frequency hopping sequences are used in fh cdma systems in this paper an earlier idea of constructing optimal sets of frequency hopping sequences is further investigated new optimal parameters of sets of frequency hopping sequences are obtained with subcodes of the reed solomon codes optimal sets of frequency hopping sequences are constructed with a class of irreducible cyclic codes as a byproduct the weight distribution of a subclass of irreducible cyclic codes is determined

three precision gmres based iterative refinement for least squares problems the standard iterative refinement procedure for improving an approximate solution to the least squares problem min x b ax 2 where a in mathbb r m times n with m ge n has full rank

on uniform decay of a nonsimple thermoelastic bar with memory abstract in this paper we investigate the asymptotic behavior of a one dimensional problem of linear theory of nonsimple thermoelasticity with hereditary heat conduction we show that the corresponding semigroup is exponentially stable when the thermal memory kernel decays exponentially for large time but not analytic we conclude by showing the impossibility of localization in time of the solutions

new constructions for optimal sets of frequency hopping sequences in this paper two generic constructions of optimal frequency hopping sequence fhs sets employing d form functions with difference balanced property are presented they generalize the previous constructions of optimal fhs sets using m sequences and produce new optimal fhs sets that cannot be produced by the earlier constructions by choosing appropriate d form functions with difference balanced property both constructions lead to fhss with large linear complexity in addition one of the proposed constructions gives new optimal parameters of fhs sets

4 phase sequences with near optimum correlation properties two families of four phase sequences are constructed using irreducible polynomials over z sub 4 family a has period l 2 sup r 1 size l 2 and maximum nontrivial correlation magnitude c sub max

stability of post fertilization traveling waves article history this paper studies the stability of a family of traveling wave solutions to the system proposed by lane et al d c lane j d murray v s manoranjan analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post fertilization waves on eggs ima j math appl med biol 4 4 1987 309 331 to model a pair of mechanochemical phenomena known as post fertilization waves on eggs the waves consist of an elastic deformation pulse on the egg s surface and a free calcium concentration front the family is indexed by a coupling parameter measuring contraction stress effects on the calcium concentration this work establishes the spectral linear and nonlinear orbital stability of these post fertilization waves for small values of the coupling parameter the usual methods for the spectral and evolution equations cannot be applied because of the presence of mixed partial derivatives in the elastic equation nonetheless exponential decay of the directly constructed semigroup on the complement of the zero eigenspace is established we show that small perturbations of the waves yield solutions to the nonlinear equations decaying exponentially to a phase modulated traveling

gmw sequences corresp the difference set design of gordon mills and welch gmw is adapted for use as a pseudorandom number generator statistical properties of the generated binary sequences including periodic correlation linear span and k tuple statistics are derived one mechanization of a gmw sequence generator is suggested and the number of sequences that can be generated with a fixed number of shift register stages and read only memory rom size is evaluated

a hybrid incomplete exponential sum with application to aperiodic hamming correlation of some frequency hopping sequences in this paper an upper bound for a hybrid incomplete exponential sum over finite fields is derived this bound is then used to obtain lower and upper bounds for aperiodic hamming correlation of frequency hopping sequences based on power functions

on the energy decay of the linear thermoelastic plate with memory abstract we analyze the longterm properties of a c 0 semigroup describing the solutions to a linear evolution system that models a thermoelastic thin plate with memory effects in the heat flux law under reasonably general assumptions on the memory kernel all single trajectories are shown to decay to zero in spite of that the semigroup is not exponentially stable

new classes of optimal low hit zone frequency hopping sequence sets by cartesian product in quasi synchronous frequency hopping multiple access systems where relative delays between different users are restricted within a zone around the origin low hit zone frequency hopping sequences lhz fhss are employed as spreading sequences in this paper we study lhz fhs sets obtained from the cartesian product of some fhs sets we first derive an upper bound on the hamming correlation of fhss constructed by the cartesian product we also give a general method to construct lhz fhs sets by the cartesian product we then present four new classes of optimal lhz fhs sets the first three classes of sets are obtained from the product of solomon s fhs sets and kumar s fhs sets the last one is constructed by the product of fhs sets based on interleaving techniques these lhz fhs sets have new parameters not covered in the literature

periodic solutions of second order differential equations in banach spaces we use operator valued fourier multiplier theorems to study second order differential equations in banach spaces we establish maximal regularity results in l p and c s for strong solutions of a complete second order equation

mild solutions to integro differential equations in banach spaces abstract in this paper we study the existence and uniqueness of mild solutions to integro differential equations in terms of a resolvent operator on the interval 0 2 and on the real line moreover we characterize the spectrum of the resolvent family that solves the volterra equation u a u a a u f in terms of their mild periodic solutions

exponential stability in thermoviscoelastic mixtures of solids in this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a one dimensional mixture of thermoviscoelastic solids our main result is to establish the exponential stability of the corresponding semigroup and the lack of exponential stability of the corresponding semigroup

accelerating the solution of linear systems by iterative refinement in three precisions we propose a general algorithm for solving a n times n nonsingular linear system ax b based on iterative refinement with three precisions the working precision is combined with possibly different precisions for solving for the correction term and for computing the residuals via rounding error analysis of the algorithm we derive sufficient conditions for convergence and bounds for the attainable normwise forward error and normwise and componentwise backward errors our results generalize and unify many existing rounding error analyses for iterative refinement with single precision as the working precision we show that by using lu factorization in ieee half precision as the solver and calculating the residuals in double precision it is possible to solve ax b to full single precision accuracy for condition numbers kappa 2 a le 10 4 with the o n 3 part of the computations carried out entirely in half precision we show further that by solving the correction equations by gmres preconditioned by the lu factors the restriction on the condition number can be weakened to kappa 2 a le 10 8 although in general there is no guarantee that gmres will converge quickly taking for comparison a standard ax b solver that uses lu factorization in single precision these results suggest that on architectures for which half precision is efficiently implemented it will be possible to solve certain linear systems ax b up to twice as fast emph and to greater accuracy analogous results are given with double precision as the working precision

frequency hopping sequences with optimal partial hamming correlation frequency hopping sequences fhss with favorable partial hamming correlation properties have important applications in many synchronization and multiple access systems in this paper we investigate constructions of fhss and fhs sets with optimal partial hamming correlation we first establish a correspondence between fhs sets with optimal partial hamming correlation and multiple partition type balanced nested cyclic difference packings with a special property by virtue of this correspondence some fhss and fhs sets with optimal partial hamming correlation are constructed from various combinatorial structures such as cyclic difference packings and cyclic relative difference families as a consequence our constructions yield new fhss and fhs sets with optimal partial hamming correlation

spectral conditions for admissibility of evolution equations in hilbert space abstract we study properties of solutions of the evolution equation u t b u t f t where b is a closable operator on the space ap r h of almost periodic functions with values in a hilbert space h such that b commutes with translations the operator b generates a family b of closed operators on h such that b e i t x e i t b x whenever e i t x d b for a closed subset r we prove that the following properties i and ii are equivalent i for every function f ap r h such that f there exists a unique mild solution u ap r h of eq such that u ii b i is invertible for all and sup b i 1

new classes of frequency hopping sequences with optimal partial correlation in this paper the partial hamming correlation properties of frequency hopping sequences fhss are discussed the peng fan bounds on sets of fhss are generalized to the case of partial correlation both individual fhss with optimal partial autocorrelation and sets of fhss with optimal partial correlation are presented the former has more new parameters compared with the known individual fhss with optimal partial autocorrelation while the later is obtained in the literature for the first time

a new class of balanced near perfect nonlinear mappings and its application to sequence design a mapping from zn to zm can be directly applied for the design of a sequence of period n with alphabet size m where zn denotes the ring of integers modulo n the nonlinearity of such a mapping is closely related to the autocorrelation of the corresponding sequence when m is a divisor of n the sequence corresponding to a perfect nonlinear mapping has perfect autocorrelation but it is not balanced in this paper we study balanced near perfect nonlinear npn mappings applicable for the design of sequence sets with low correlation we first construct a new class of balanced npn mappings from z p2 p to zp for an odd prime p we then present a general method to construct a frequency hopping sequence fhs set from a nonlinear mapping by applying it to the new class we obtain a new optimal fhs set of period p2 p with respect to the peng fan bound whose fhss are balanced and optimal with respect to the lempel greenberger bound moreover we construct a low correlation sequence set with size p period p2 p and maximum correlation magnitude p from the new class of balanced npn mappings which is asymptotically optimal with respect to the welch bound

lower bounds on the hamming auto and cross correlations of frequency hopping sequences frequency hopping fh sequences have found wide applications in various modern fh spread spectrum communications and radar systems in fh spread spectrum communications the interference occurs when two distinct transmitters use the same frequency simultaneously in order to evaluate the goodness of fh sequence design the hamming correlation function is used as an important measure in this correspondence by considering separately the maximum hamming autocorrelation sidelobe h sub a and the maximum hamming cross correlation h sub c several new lower bounds on the size p of the frequency slot set f the sequence length l the family size m and correlation properties are established the new periodic bounds include the known lempel greenberger bounds as special case when m 2 and are tighter than the seay bounds under certain conditions when m 2 furthermore the new bounds disclose more information on the relationship between the maximum autocorrelation sidelobe and the maximum cross correlation compared with the lempel greenberger bounds and seay bounds besides the aperiodic fh bounds which have not yet been previously reported are also presented and discussed in this correspondence

stability of bright solitary wave solutions to perturbed nonlinear schrodinger equations abstract the propagation of pulses in ideal nonlinear optical fibers without loss is governed by the nonlinear schrodinger equation nls when considering realistic fibers one must examine perturbed nls equations with the particular perturbation depending on the physical situation that is being modeled a common example is the complex ginzburg landau equation cgl which is a dissipative perturbation it is known that some of the stable bright solitons of the nls survive a dissipative perturbation such as the cgl given that a wave persists it is then important to determine its stability with respect to the perturbed nls a major difficulty in analyzing the stability of solitary waves upon adding dissipative terms is that eigenvalues may bifurcate out of the essential spectrum since the essential spectrum of the nls is located on the imaginary axis such eigenvalues may lead to an unstable wave in fact eigenvalues can pop out of the essential spectrum even if the unperturbed problem has no eigenvalue embedded in the essential spectrum here we present a technique which can be used to track these bifurcating eigenvalues as a consequence we are able to locate the spectrum for bright solitary wave solutions to various perturbed nonlinear schrodinger equations and determine precise conditions on parameters for which the waves are stable in addition we show that a particular perturbation the parametrically forced nls equation supports stable multi bump solitary waves the technique for tracking eigenvalues which bifurcate from the essential spectrum is very general and should therefore be applicable to a larger class of problems than those presented here

stability and stabilizability of infinite dimensional systems in this paper we are concerned with stability problems for infinite dimensional systems first we review the theory for linear systems where the dynamics are governed by strongly continuous semigro

logarithmic well posed approximation of the backward heat equation in banach space abstract in this paper we apply a logarithmic approximation introduced by boussetila and rebbani in order to study an ill posed cauchy problem in banach space the proposed method induces a well posed problem whose approximation parameter yields continuous dependence on modeling throughout properties of holomorphic semigroups are utilized culminating in the motivating application which is the backward heat equation in l p r 1 p

new optimal quadriphase sequences with larger linear span in this paper two new optimal families s and u of quadriphase sequences are presented compared to the family a constructed by boztas and the family d investigated by tang respectively the proposed families have the same optimal correlation properties and family size but larger linear spans

frequency domain approach for the polynomial stability of a system of partially damped wave equations in this paper we study the stability of a system of wave equations which are weakly coupled and partially damped using a frequency domain approach based on the growth of the resolvent on the imaginary axis we establish the polynomial energy decay rate for smooth initial data we show that the behavior of the system is sensitive to the arithmetic property of the ratio of the wave propagation speeds of the two equations

the operator valued marcinkiewicz multiplier theorem and maximal regularity given a closed linear operator on a umd space we characterize maximal regularity of the non homogeneous problem

exponential decay of solutions in type ii porous thermo elasticity with quasi static microvoids abstract in this note we study the problem proposed by the one dimensional thermo porous elasticity of type ii with quasi static microvoids or in mathematical terms when the second time derivative of the volume fraction is so small that it can be negligible it is known that the isothermal deformations decay in a slow way here we prove that the introduction of a conservative mechanism as it is the type ii heat conduction makes the deformations damp generically in an exponential way which is a striking fact

optimal frequency hopping sequences a combinatorial approach frequency hopping multiple access fhma spread spectrum communication systems employing multiple frequency shift keying mfsk as data modulation technique are investigated from a combinatorial approach a correspondence between optimal frequency hopping fh sequences and partition type difference packings is first established by virtue of this correspondence fhma systems with a single optimal fh sequence each are constructed from various combinatorial structures such as affine geometries cyclic designs and difference families combinatorial recursive constructions are also presented many new infinite series of optimal fh sequences are thus obtained these new fh sequences are also useful in ultra wideband uwb communication systems

optimal frequency hopping sequences of odd length in this paper a new generalized cyclotomy with respect to a positive odd integer is introduced and a construction of frequency hopping sequence sets and two constructions of frequency hopping sequences are proposed as its applications the frequency hopping sequence sets and frequency hopping sequences obtained in this paper can be optimal with respect to the peng fan bound and lempel greenberger bound respectively further the length of sequences in the optimal frequency hopping sequence sets can be any odd integer larger than 3 some of them have new parameters

squeezing a matrix into half precision with an application to solving linear systems motivated by the demand in machine learning modern computer hardware is increas ingly supporting reduced precision floating point arithmetic which provides advantages in speed energy and memory usage over single and double precision given the availability of such hardware mixed precision algorithms that work in single or double precision but carry out part of a compu tation in half precision are now of great interest for general scientific computing tasks because of the limited range of half precision arithmetic in which positive numbers lie between 6 10 8 and 7 104 a straightforward rounding of single or double precision data into half precision can lead to overflow underflow or subnormal numbers being generated all of which are undesirable we develop an algorithm for converting a matrix from single or double precision to half precision it first applies two sided diagonal scaling in order to equilibrate the matrix that is to ensure that every row and column has norm 1 then multiplies by a scalar to bring the largest element within a factor 1 of the overflow level and finally rounds to half precision the second step ensures that full use is made of the limited range of half precision arithmetic and must be chosen to allow sufficient headroom for subsequent computations we apply the new algorithm to gmres based iterative re finement gmres ir which solves a linear system ax b with single or double precision data by lu factorizing a in half precision and carrying out iterative refinement with the correction equations solved by gmres preconditioned with the low precision lu factors previous implementations of this algorithm have used a crude conversion to half precision that our experiments show can cause slow convergence of gmres ir for badly scaled matrices or failure to converge at all the new conversion algorithm computes norms of rows and columns of the matrix and its cost is negligible in the context of lu factorization we show that it leads to faster convergence of gmres ir for badly scaled matrices and thereby allows a much wider class of problems to be solved

mild almost periodic solutions of abstract differential equations abstract necessary and sufficient conditions are established for the existence of mild almost periodic solutions of cauchy problems u au and u au f where a is the infinitesimal generator of a strongly continuous semigroup respectively a cosine function on a hilbert space and an almost periodic function

new families of optimal frequency hopping sequences of composite lengths frequency hopping sequences fhss are employed to mitigate the interferences caused by the hits of frequencies in frequency hopping spread spectrum systems in this paper we present two new constructions for fhs sets we first give a new construction for fhs sets of length nn for two positive integers n and n with gcd n n 1 we then present another construction for fhs sets of length q 1 n where q is a prime power satisfying gcd q 1 n 1 by these two constructions we obtain infinitely many new optimal fhs sets with respect to the peng fan bound as well as new optimal fhss with respect to the lempel greenberger bound which have length nn or n q 1 n as a result a great deal of flexibility may be provided in the choice of fhs sets for a given frequency hopping spread spectrum system

robustness with respect to delays for exponential stability of distributed parameter systems in this paper we address the question of whether the open loop exponential growth rate of a linear system can be improved by a feedback in such a way that this improvement is robust with respect to small delays in the feedback loop when the input operator is admissible and the class of possible feedbacks consists of compact operators we find that if a feedback can improve the exponential growth rate then it can do so robustly furthermore we find that if the control space is finite dimensional and a bounded feedback cannot be found to improve exponential stability then a large class of unbounded feedbacks cannot improve the exponential growth rate robustly even if such feedbacks can improve the exponential growth rate in the absence of delays

evolutionary semigroups and dichotomy of linear skew product flows on locally compact spaces with banach fibers abstract we study evolutionary semigroups generated by a strongly continuous semi cocycle over a locally compact metric space acting on banach fibers this setting simultaneously covers evolutionary semigroups arising from non autonomous abstract cauchy problems and c 0 semigroups and linear skew product flows the spectral mapping theorem for these semigroups is proved the hyperbolicity of the semigroup is related to the exponential dichotomy of the corresponding linear skew product flow to this end a banach algebra of weighted composition operators is studied the results are applied in the study of roughness of the dichotomy dichotomy and solutions of nonhomogeneous equations green s function for a linear skew product flow pointwise dichotomy versus global dichotomy and evolutionary semigroups along trajectories of the flow

a combinatorial construction for strictly optimal frequency hopping sequences frequency hopping sequences fhss with favorable partial hamming correlation properties have important applications in many synchronization and multiple access systems strictly optimal fhss are those fhss with optimal partial hamming autocorrelation irrespective of the correlation window length in this paper strictly optimal fhss are investigated from a combinatorial approach a generic connection between strictly optimal fhss and disjoint cyclic perfect mendelsohn difference families is established by virtue of this connection new strictly optimal fhss are generated from some disjoint cpmdfs these strictly optimal fhss have new parameters not covered in the literature

asymptotic stability of semigroups associated with linear weak dissipative systems with memory we study the asymptotic behavior of the solutions of a class of linear dissipative integral differential equations we show in the abstract setting a necessary and sufficient condition to get an exponential decay of the solution in the case of the lack of exponential decay we find the polynomial rate of decay of the solution some examples are given

optimal frequency hopping sequences auto and cross correlation properties frequency hopping fh sequences play a key role in frequency hopping spread spectrum communication systems in order to evaluate the performance of fh sequences lempel and greenberger 1974 and peng and fan 2004 derived lower bounds on their hamming auto and cross correlations in this paper we construct families of fh sequences with hamming correlations meeting those bounds by combinatorial and algebraic techniques we first construct optimal families consisting of a single fh sequence with maximum hamming correlation equal to 2 from a combinatorial approach then we investigate families consisting of multiple fh sequences we provide a combinatorial characterization for such families and present a recursive method to construct them by means of this characterization we also describe two algebraic constructions for such families of fh sequences generalizing those of ding moisio and yuan 2007 as a consequence many new optimal families of fh sequences are obtained

asymptotic behavior of the energy for a class of weakly dissipative second order systems with memory a class of second order abstract systems with memory and dirichlet boundary conditions is investigated by suitable liapunov functionals existence of solutions as well as asymptotic behavior are determined in particular when the memory kernel decays exponentially the polynomially decay of the solutions is proved

frequency hopping sequences with optimal partial autocorrelation properties we classify some p sup k ary p prime k integer generalized m sequences and generalized gordon mills welch gmw sequences of period p sup 2k 1 over a residue class ring r gf p spl xi spl xi sup k having optimal partial hamming autocorrelation properties in frequency hopping fh spread spectrum systems these sequences are useful for synchronizing process suppose for example that a transmitting p sup k ary fh patterns of period p sup 2k 1 are correlated at a receiver usually the length of a correlation window denoted by l is shorter than the pattern s overall period in that case the maximum value of the out of phase hamming autocorrelation is lower bounded by spl lceil l p sup k 1 spl rceil but the classified sequences achieve this bound with equality for any positive integer l

indirect stabilization of weakly coupled kirchhoff plate and wave equations with frictional damping abstract we investigate the indirect stabilization of a weakly coupled system consisting of a kirchhoff plate equation involving free boundary conditions and the wave equation with dirichlet boundary conditions in a bounded domain the distributed damping is frictional and appears in one of the equations only first we consider the case where the damping occurs in the wave equation and using the frequency domain method combined with an interpolation inequality we derive a polynomial decay estimate for the associated semigroup afterwards we consider the case where the frictional damping occurs in the kirchhoff plate equation and we use the same technique to derive a polynomial decay estimate for the underlying semigroup that latter polynomial decay estimate is similar to the one obtained earlier by different authors in the case of a coupling between a frictionally damped euler bernoulli plate equation and an undamped wave equation which is quite surprising since the operator defining the damping in the kirchhoff plate equation is compact

simulating low precision floating point arithmetic the half precision fp16 floating point format defined in the 2008 revision of the ieee standard for floating point arithmetic and a more recently proposed half precision format bfloat16 are in

high rate self synchronizing codes self synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization difference systems of sets are combinatorial designs which specify the positions of synchronization markers in codewords in such a way that the resulting error tolerant self synchronizing codes may be realized as cosets of linear codes ideally difference systems of sets should sacrifice as few bits as possible for a given code length alphabet size and error tolerance capability however it seems difficult to attain optimality with respect to known bounds when the noise level is relatively low in fact the majority of known optimal difference systems of sets are for exceptionally noisy channels requiring a substantial amount of bits for synchronization to address this problem we present constructions for difference systems of sets that allow for higher information rates while sacrificing optimality to only a small extent our constructions utilize optimal difference systems of sets as ingredients and when applied carefully generate asymptotically optimal ones with higher information rates we also give direct constructions for optimal difference systems of sets with high information rates and error tolerance that generate binary and ternary self synchronizing codes

complex sequences over gf p sup m with a two level autocorrelation function and a large linear span new complex sequences with elements are proposed that have constant absolute values of 1 the periodic autocorrelation functions of these sequences are shown to be two level the sequences are generated by three consecutive mapping processes the number of sequences of fixed length is determined which is larger than the number of binary sequences for cryptographical reasons the large linear span of the sequences is of great interest the linear span of the new sequences is examined and is proven to be larger than the linear span of complex m sequences if the parameters of the mapping processes are appropriately chosen the formula for generating the sequences is generalized to enlarge the linear span of sequences

a new method to construct strictly optimal frequency hopping sequences with new parameters in order to evaluate the goodness of frequency hopping fh sequence design the periodic hamming correlation function is used as an important measure usually the length of correlation window is shorter than the period of the chosen fh sequence so the study of the partial hamming correlation of fh sequence is particularly important if an fh sequence or an fh sequence set has an optimal partial hamming correlation with respect to the partial hamming correlation bound for all length of correlation window then the fh sequence or the fh sequence set is said to be strictly optimal in this paper we first prove that there is no strictly optimal fh sequence set of family size m and sequence length n over a frequency slot set of size q with respect to the partial hamming correlation bound derived by niu et al when n q 2 m and q geq 2 and that by cai et al when n q 2 m and q geq 2n n 2 furthermore we define a special partition type difference packing dp called n nabla h a l pdp and give several classes of n nabla h a l pdps then we present a new construction of strictly optimal fh sequences by choosing different pdps the fh sequences constructed can give new and flexible parameters by utilizing this construction method recursively we can obtain new n nabla h a l pdps which lead to infinitely many classes of strictly optimal fh sequences with new parameters moreover based upon an n nabla h a l pdp we present a construction of strictly optimal fh sequence sets by preceding construction method and recursive construction we can also obtain infinite classes of strictly optimal fh sequence sets which can give new and flexible parameters

cyclic codes over r f p uf p u k 1 f p with length p s n in this paper all cyclic codes with length p sn n prime to p over the ring r f p uf p u k 1f p are classified it is first proved that tor j c is an ideal of s f p m w so that the structure of ideals over extension ring s u k m w gr u k m w is determined then an isomorphism between r x and a direct sum h is u k m h w can be obtained using discrete fourier transform the generator polynomial representation of the corresponding ideals over f p uf p u k 1f p is calculated via the inverse isomorphism moreover torsion codes ms polynomial and inversion formula are described

stability of perturbed linear distributed parameter systems we present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup when this estimate is satisfied then the perturbed operator still generates an exponentially stable semigroup for generators of holomorhic semigroups the class of allowed perturbations contains unbounded operators of the form ha with the estimate is given in terms of the norm of the solution of the lyapunov equation which corresponds to the unperturbed system

on the spectrum of cosine functions abstract in this paper we give characterizations of the resolvent set of the generatoraof a strongly continuous cosine functionc t in terms of certain solution properties of the differential equationu t au t f t