optimal designs for space time linear precoders and decoders we introduce a new paradigm for the design of transmitter space time coding that we refer to as linear precoding it leads to simple closed form solutions for transmission over frequency selective multiple input multiple output mimo channels which are scalable with respect to the number of antennas size of the coding block and transmit average peak power the scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension the specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses under average and peak power constraints the solutions are shown to convert the mimo channel with memory into a set of parallel flat fading subchannels regardless of the design criterion while appropriate power bits loading on the subchannels is the specific signature of the different designs the proposed designs are compared in terms of various performance measures such as information rate ber and symbol mean square error

control of the vorticity mode in the linearized euler equations for hybrid aeroacoustic prediction the issue of vorticity mode perturbation in linearized euler equations lee is addressed in this paper we chose to tackle this question by the point of view of source term formulation it is numerically shown that the use of a rotational free acoustic source term significantly reduces the development of the hydrodynamic mode in accordance with the theory the proposed source term lead to a quasi total absence of vorticity mode in a spatially uniform mean flow and a strong reduction in a sheared mean flow

surjective linear maps preserving local spectra let b x be the algebra of all bounded linear operators on an infinite dimensional complex banach space x we characterize linear surjective and continuous maps on b x preserving different local spectral quantities at a nonzero fixed vector

recursive construction of minimum euclidean distance based precoder for arbitrary dimensional mimo systems the objective of maximizing the minimum euclidean distance between two received data vectors via real valued linear precoding is considered for multiple input multiple output mimo systems with arbitrary dimensions assuming that perfect channel state information csi is available at both the transmitter side and the receiver side a novel low complexity precoding algorithm is proposed to recursively construct the full rank the rank deficient and the rank one precoders with respect to particular channel realization from the lattice theoretical perspective the full rank precoder is generated by using well known dense packing lattices which can also be recursively involved into the construction of higher dimensional rank deficient precoders moreover the optimal solution is clearly figured out for the specific case of rank one precoder the closed form expression of the achievable minimum distance is obtained and the analytical results reveal the performance bounds for different rank constraint precoders simulation results validate the efficiency of the proposed precoder as compared with the state of the art

multiplicative mappings at some points on matrix algebras let mn be the algebra of all n n matrices and let mn mn be a linear mapping we say that is a multiplicative mapping at g if st s t for any s t mn with st g fix g mn we say that g is an all multiplicative point if every multiplicative linear bijection at g with in in is a multiplicative mapping in mn where in is the unit matrix in mn we mainly show in this paper the following two results 1 if g mn with detg 0 then g is an all multiplicative point in mn 2 if is an multiplicative mapping at in then there exists an invertible matrix p mn such that either s psp 1 for any s mn or t pttrp 1 for any t mn

operators preserving the strong birkhoff james orthogonality on b h abstract we characterize the class of surjective conjugate linear mappings b h b h that preserve the strong birkhoff james orthogonality in both directions we also give characterizations of rank one operators as well as coisometries in terms of the strong birkhoff james orthogonality

linear maps preserving the spectral radius abstract let x be a complex banach space if b x b x is a surjective linear map such that a and a have the same spectral radius for every a b x then c where is either an algebra automorphism or an antiautomorphism of b x and c is a complex constant such that c 1

norms of minimal projections it is proved that the projection constants of two and three dimensional spaces are bounded by 43 and 1 5 2 respectively these bounds are attained precisely by the spaces whose unit balls are the regular hexagon and dodecahedron in fact a general inequality for the projection constant of a real or complex n dimensional space is obtained and the question of equality therein is discussed

optimal minimum distance based precoder for mimo spatial multiplexing systems we describe a new precoder based on optimization of the minimum euclidean distance d sub min between signal points at the receiver side and for use in multiple input multiple output mimo spatial multiplexing systems assuming that channel state information csi can be made available at the transmitter the three steps noise whitening channel diagonalization and dimension reduction which are currently used in investigations on mimo systems are performed thanks to this representation an optimal d sub min precoder is derived in the case of two different transmitted data streams for quadrature phase shift keying qpsk modulation a numerical approach shows that the precoder design depends on the channel characteristics comparisons with maximum signal to noise ratio snr strategy and other precoders based on criteria such as water filling wf minimum mean square error mmse and maximization of the minimum singular value of the global channel matrix are performed to illustrate the significant bit error rate ber improvement of the proposed precoder

generalized linear precoder and decoder design for mimo channels using the weighted mmse criterion we address the problem of designing jointly optimum linear precoder and decoder for a mimo channel possibly with delay spread using a weighted minimum mean squared error mmse criterion subject to a transmit power constraint we show that the optimum linear precoder and decoder diagonalize the mimo channel into eigen subchannels for any set of error weights furthermore we derive the optimum linear precoder and decoder as functions of the error weights and consider specialized designs based on specific choices of error weights we show how to obtain 1 the maximum information rate design 2 qos based design we show how to achieve any set of relative snrs across the subchannels and 3 the unweighted mmse and equal error design for fixed rate systems

minimum euclidean distance based precoders for mimo systems using rectangular qam modulations from the feedback of the channel state information csi precoding techniques improve the performance of multiple input multiple output mimo systems by optimizing various criteria in this correspondence an efficient precoder that maximizes the minimum distance dmin of two received vectors is studied this criterion leads to a nondiagonal precoding scheme and allows achieving a full diversity order however the optimized solution for mimo systems using a high order qam modulation is rather complex and changes for different constellations therefore we propose herein a general form of minimum euclidean distance based precoders for all rectangular qam modulations it is shown that the new solution optimizes the distance dmin for small and large dispersive channels

linear maps preserving the minimum and surjectivity moduli of hilbert space operators abstract let b h be the algebra of all bounded linear operators on a complex infinite dimensional hilbert space h for every t b h let m t and q t denote the minimum modulus and surjectivity modulus of t respectively let b h b h be a surjective linear map in this paper we prove that the following assertions are equivalent i m t m t for all t b h ii q t q t for all t b h iii there exist two unitary operators u v b h such that t u t v for all t b h this generalizes the result of mbekhta 7 theorem 3 1 to the non unital case

a spectral characterization of operators having rank k abstract let a b x the algebra of all bounded linear operators on a complex banach space x and let k be a positive integer it is proved that a has rank k if and only if i k 1 m 1 t c m a t for every t b x and some nonzero scalars c 1 c k 1 and ii k m 1 t c m a t for some t b x and some distinct scalars c 1 c k

conservative high order finite difference schemes for low mach number flows three finite difference algorithms are proposed to solve a low mach number approximation for the navier stokes equations these algorithms exhibit fourth order spatial and second order temporal accuracy they are dissipation free and thus well suited for dns and les of turbulent flows the key ingredient common to each of the methods presented is a poisson equation with variable coefficient that is solved for the hydrodynamic pressure this feature ensures that the velocity field is constrained correctly it is shown that this approach is needed to avoid violation of the conservation of kinetic energy in the inviscid limit which would otherwise arise through the pressure term in the momentum equation an existing set of finite difference formulae for incompressible flow is generalized to handle arbitrary large density fluctuations with no violation of conservation through the non linear convective terms an algorithm which conserves mass momentum and kinetic energy fully is obtained when an approximate equation of state is used instead of the exact one results from a model problem are used to show both spatial and temporal convergence rates and several test cases are presented to illustrate the performance of the algorithms

additive maps on standard operator algebras preserving invertibilities or zero divisors let a and b be standard operator algebras on infinite dimensional complex banach spaces x and y respectively and let be an additive surjection from a onto b we prove that if is unital and preserves any one of left right invertibility left right zero divisors left right topological divisors of zero quasi affinity injectivity surjectivity range density lower boundedness and left right maximal ideals in both directions then it has one of the following forms isomorphism conjugate isomorphism anti isomorphism and conjugate anti isomorphism we also show that preserves zero products in both directions if and only if is either an isomorphism or a conjugate isomorphism

computation of flow noise using source terms in linearized euler s equations an acoustic analogy using linearized euler s equations lee forced with aerodynamic source terms is investigated to computetheacousticfare eld thishybridmethod isappliedto threemodelproblemssimulatedby solving navier stokes equations in this way its validity is estimated by comparing the predicted acoustic e eld with the reference solution given directly by the navier stokes equations the noise radiated by two corotating vortices is studied e rst in a medium at rest and second in a mean sheared e ow with no convection velocity then the sound e eld generated by vortex pairings in a subsonic mixing layer is investigated in this case a simplie ed formulation of lee is proposed to prevent the exponential growth of instability waves the acoustic e elds obtained by solving lee are in good agreement with the reference solution this study shows that the source terms introduced into the lee are appropriate for free sheared e ows and that acoustic mean e ow interactions are properly taken into account in the wave operator nomenclature b half width of the monopolar source c sound velocity e f h vectors in linearized euler s equations lee f frequency f0 fundamental frequency of the mixing layer k complex wave number kr ciki m mach number p pressure re reynolds number rc vortex core radius r0 initial half distance between the two vortices s sound source vector in lee si source terms in the momentum equations t period tij lighthill s tensor t time u unknown vector in lee u1 slow stream velocity of the mixing layer u2 rapid stream velocity of the mixing layer u velocity vector u1 u2 v initial tangential velocity of vortices

complexity reduction for the optimization of linear precoders over random mimo channels precoder optimization with full channel state information for finite alphabet signals over multiple input multiple output random channels is investigated in this paper the precoder is represented by a product of power allocation matrix and constellation forming matrix there was an optimal algorithm introduced in the literature to globally maximize the channel mutual information by iteratively optimizing these two matrices however the computational complexity of the optimal algorithm is painfully high especially when it is used with the high order modulation and the high data stream number in this paper we propose a novel sub optimal low complexity precoding algorithm and compare it with the optimal one the new algorithm proceeds in two steps first the constellation forming matrix is fixed in order to maximize the minimum euclidean distance between the received symbols which ensures high channel mutual information then given the constellation forming matrix an iterative algorithm searches for the power allocation matrix that maximizes the channel mutual information since optimizing only one matrix instead of two the new algorithm not only achieves a lower computational complexity but also avoids the use of initial values which must be carefully selected for each channel and signal to noise ratio for fast convergence another advantage of the new algorithm is that the resulting precoder has a fixed form of received constellation thanks to the fixed constellation forming matrix this allows us to optimize the symbol mapping on the received constellation simulation results show that the proposed low complexity precoder achieves error rate performance that is close to performance of the optimal one when the conventional mapping is used in addition the new precoder used with optimized mapping at received constellation shows significant error rate performance improvement

multiplicative maps on matrices that preserve the spectrum abstract let m n denote the set of all n n matrices over the complex numbers n 2 let a n m n be either the set of all invertible matrices the set of all unitary matrices or a multiplicative semigroup containing the singular matrices theorem if a n m n is a spectrum preserving multiplicative map then there exists a matrix r in m n such that s r 1 sr for all s in a n

additive idempotence preservers abstract let a be a local matrix algebra over a field of characteristic different from 2 b an arbitrary algebra and x y banach spaces additive mappings a b which preserve idempotents are characterized the result is then used in classifying additive surjections b x b y which preserve idempotents and do not annihilate finite rank operators

characterizations of automorphisms of operator algebras on banach spaces abstract let x be a complex banach space of dimension greater than one and denote by b x the algebra of all the bounded linear operators on x it is shown that if b x b x is a multiplicative map not assumed linear and if is sufficiently close to a linear automorphism of b x in some uniform sense then it is actually an automorphism

invertibility preserving linear maps on j subspace lattice algebras it is shown that every unital surjective linear map between j subspace lattice algebras which preserves invertibility in both directions is a jordan isomorphism this result can apply to atomic boolean subspace lattice algebras and pentagon subspace lattice algebras

minimum ber block precoders for zero forcing equalization we determine the linear precoder that minimizes the bit error rate ber at moderate to high signal to noise ratios snrs for block transmission systems with zero forcing zf equalization and threshold detection the design is developed for the two standard schemes for eliminating inter block interference viz zero padding zp and cyclic prefix cp we show that both the zp minimum ber precoder and the cp minimum ber precoder provide substantially lower error rates than standard block transmission schemes such as orthogonal frequency division multiplexing ofdm the corresponding snr gains can be on the order of several decibels we also show that the cp minimum ber precoder can be obtained by a two stage modification of the water filling discrete multitone modulation dmt scheme in which the diagonal water filling power loading is replaced by a full matrix consisting of a diagonal minimum mean square error power loading matrix post multiplied by a discrete fourier transform dft matrix

spherical isometries of finite dimensional c algebras abstract in this paper it is shown that every surjective isometry between the unit spheres of two finite dimensional c algebras extends to a real linear jordan isomorphism followed by multiplication operator by a fixed unitary element this gives an affirmative answer to tingley s problem between two finite dimensional c algebras moreover we show that if two finite dimensional c algebras have isometric unit spheres then they are isomorphic

linear additive preservers of rank 2 on spaces of alternate matrices over fields abstract let kn f be the linear space of all n n alternate matrices over a field f and let k n 2 f be its subset consisting of all rank 2 matrices an operator kn f kn f is said to be additive if a b a b for any a b kn f linear if is additive and aa af a for every a f and a kn f and a preserver of rank 2 on kn f if k n 2 f k n 2 f when n 4 we characterize all linear respectively additive preservers of rank 2 on kn f over any field respectively any field that is not isomorphic to a proper subfield of itself

spectrum preserving linear maps abstract let x and y be banach spaces we show that a spectrum preserving surjective linear map from b x to b y is either of the form t ata 1 for an isomorphism a of x onto y or the form t bt b 1 for an isomorphism b of x onto y

direct numerical simulation of a turbulent reactive plume on a parallel computer a computational algorithm is described for direct numerical simulation dns of a reactive plume in spatially evolving grid turbulence the algorithm uses sixth order compact differencing in conjunction with a fifth order compact boundary scheme which has been developed and found to be stable a compact filtering method is discussed as a means of stabilizing calculations where the viscous diffusive terms are differenced in their conservative form this approach serves as an alternative to nonconservative differencing previously advocated as a means of damping the 2 waves in numerically solving the low mach number equations the time derivative of the density field in the pressure poisson equation was found to be the most destabilizing part of the calculation even ordered finite difference approximations to this derivative were found to be more stable allow for larger density gradients than odd ordered approximations turbulence at the inlet boundary is generated by scanning through an existing three dimensional field of fully developed turbulence in scanning through the inlet field it was found that a high order interpolation e g cubic spline interpolation is necessary in order to provide continuous velocity derivatives regarding pressure a neumann inlet condition combined with a dirichlet outlet condition was found to work well the chemistry follows the single step irreversible global reaction fuel r oxidizer 1 r product heat with parameters chosen to match experimental data as far as allowed by resolution constraints simulation results are presented for four different cases in order to examine the effects of heat release damkohler number and arrhenius kinetics on the flow physics statistical data from the dns are compared to theory and wind tunnel data and found in reasonable agreement with regard to growth of turbulent length scales decay of turbulent kinetic energy decay of centerline scalar concentration decrease in scalar rms and spread of plume profile reactive scalar statistics are consistent with expected behavior

approximately spectrum preserving maps let x and y be superreflexive complex banach spaces and let b x and b y be the banach algebras of all bounded linear operators on x and y respectively if a bijective linear map b x b y almost preserves the spectra then it is almost multiplicative or anti multiplicative furthermore in the case where x y is a separable complex hilbert space such a map is a small perturbation of an automorphism or an anti automorphism

preservers of local spectra of matrix sums abstract let m n c be the set of n n complex matrices and for a nonzero vector e c n and t m n c let t e denote the local spectrum of t at e we characterize surjective maps on m n c which satisfy t s e t s e for all matrices t and s we arrive at the same conclusion by supposing that t s e t s e for all matrices t and s without the surjectivity assumption on continuous maps from m n c onto itself that preserve the local spectral radius of the sum of matrices at a nonzero fixed vector are also characterized

linear rank and corank preserving maps on b h and an application to semigroup isomorphisms of operator ideals abstract we characterize linear rank k nonincreasing rank k preserving and corank k preserving maps on b h the algebra of all bounded linear operators on the hilbert space h this unifies and extends finite dimensional results and results on linear rank 1 non increasing and rank 1 preserving maps in the infinite dimensional case we conclude with an application to semigroup isomorphisms of operator ideals

some multiplicative preservers on b h abstract in this paper we describe the form of those continuous multiplicative maps on b h h being a separable complex hilbert space of dimension not less than 3 which preserve the rank or the corank furthermore we characterize those continuous presup semigroup endomorphisms of b h which are spectrum non increasing

on a spectral characterization of rank one matrices abstract let a be an n n complex matrix with a 2 0 it is proved that a has rank one if and only if t a t ca t for every rank one matrix t and some fixed scalar c 0 or 1 the condition a 2 0 cannot be dropped in case n 4

on positive linear maps preserving invertibility theorem a positive linear map 4 between two c algebras is a jordan homomorphism if d preserves invertibility and the range of is a c algebra a counterexample is given for the case that the range of q is not assumed to be a c algebra this answers a question raised by b russo proc amer math sot 17

quantum renyi relative entropies on density spaces of c algebras their symmetries and their essential difference abstract we extend the definitions of different types of quantum renyi relative entropy from the finite dimensional setting of density matrices to density spaces of c algebras we show that those quantities which trivially coincide in the classical commutative case are essentially different on non commutative algebras in the sense that none of them can be transformed to another one by any surjective transformation between density spaces besides we determine the symmetry groups of density spaces corresponding to each of those quantum renyi relative entropies and find that they are identical similar results concerning the umegaki and the belavkin staszewksi relative entropies are also presented