on witten s proof of the positive energy theorem this paper gives a mathematically rigorous proof of the positive energy theorem using spinors this completes and simplifies the original argument presented by edward witten we clarify the geometric aspects of this argument and prove the necessary analytic theorems concerning the relevant dirac operator

generalized chirp like polyphase sequences with optimum correlation properties a new general class of polyphase sequences with ideal periodic autocorrelation function is presented the new class of sequences is based on the application of zadoff chu polyphase sequences of length n sm sup 2 where s and m are any positive integers it is shown that the generalized chirp like sequences of odd length have the optimum crosscorrelation function under certain conditions finally recently proposed generalized p4 codes are derived as a special case of the generalized chirp like sequence

a data bearing approach for pilot embedding frameworks in space time coded mimo systems space time st coded mimo systems employing coherent detectors crucially require channel state information this paper presents a novel pilot embedding framework for channel estimation and data detection by exploiting the null space property and the orthogonality property of the data bearer and pilot matrices the st data matrix is firstly projected onto the data bearer matrix which is a null space of the pilot matrix and the resulting matrix and the pilot matrix are combined for transmitting the data and pilot extractions are achieved independently through linear transformations by exploiting the null space property the unconstrained maximum likelihood ml and linear minimum mean squared error lmmse estimators are explored for channel estimation then the ml approach for data detection is developed by exploiting the orthogonality property the mean squared error mse of channel estimation cramer rao lower bound crlb and the chernoff s bound of a pair wise error probability for st codes are analyzed for examining the performance of the proposed scheme the optimum power allocation scheme for data and pilot parts is also considered three data bearer and pilot structures including time multiplexing tm based st block code stbc based and code multiplexing cm based are proposed simulation results show that the cm based structure provides superior performance for nonquasi static flat rayleigh fading channels while these three structures yield similar performances for quasi static flat rayleigh fading channels

a general class of lower bounds in parameter estimation a general class of bayesian lower bounds on moments of the error in parameter estimation is formulated and it is shown that the cramer rao the bhattacharyya the bobrovsky zakai and the weiss weinstein lower bounds are special cases in the class the bounds can be applied to the estimation of vector parameters and any given function of the parameters the extension of these bounds to multiple parameter is discussed

positivity of quasi local mass ii a spacetime is a four manifold with a pseudo metric of signature a hypersurface or a 2 surface in a spacetime is spacelike if the induced metric is pos itive definite a quasi local energy momentum vector is a vector in r3 1 associated to a spacelike 2 surface which depends on its first and second fundamental forms and the connection to its normal bundle in the spacetime the time component of the four vector is called quasi local energy mass similar to 10 8 we require the quasi local energy momentum vector to satisfy the following properties 1 it should be zero for the flat spacetime 2 the quasi local mass should be equivalent to the standard definition if the spacetime is spherically symmetric and the quasi local mass is evaluated on the spheres 7 we say that two masses mi and m2 are equivalent if there is a universal constant c 0 such that c lm area e 167r 6 the quasi local energy momentum vector should be nonspacelike and the quasi local mass should be nonnegative

tracking performance of least squares mimo channel estimation algorithm in this paper the tracking performance analysis of the least squares ls multiple input multiple output mimo channel estimation and tracking algorithm is presented mimo channel estimation is a novel application of the ls algorithm that presents near optimum performance by karami and shiva in 2003 and 2006 in this paper the mean square error mse of tracking of the ls mimo channel estimator algorithm is derived as a closed form function of the doppler shift forgetting factor channel rank and the length of training sequences in the analysis all training symbols are considered as randomly generated equal power vectors on the unit circle or in other words phase shift keying psk signaling by evaluating this function some insights into the tracking behavior of the ls mimo channel estimator are achieved then the calculated tracking error is compared with the tracking error derived from monte carlo simulation for quaternary psk based training signals to verify the validation of the presented analysis finally the optimum forgetting factor is derived to minimize the error function and it is shown that the optimum forgetting factor is highly dependent on the training length doppler shift and eb no also it is concluded that in low eb no values the number of transmitter antennas has negligible effect on the optimal value of the forgetting factor

maximum likelihood detection for differential unitary space time modulation with carrier frequency offset can conventional differential unitary space time modulation dustm be applied when there is an unknown carrier frequency offset cfo this paper answers this question affirmatively and derives the necessary maximum likelihood ml detection rule the asymptotic performance of the proposed ml rule is analyzed leading to a code design criterion for dustm by using the modified diversity product the resulting proposed decision rule is a new differential modulation scheme in both the temporal and spatial domains two sub optimal multiple symbol decision rules with improved performance are also proposed for the efficient implementation of these we derive a modified bound intersection detector bid a generalization of the previously derived optimal bid for the conventional dustm the simulation results show that the proposed differential modulation scheme is more robust against cfo drifting than the existing double temporal differential modulation

deformations of the hemisphere that increase scalar curvature consider a compact riemannian manifold m of dimension n whose boundary m is totally geodesic and is isometric to the standard sphere s n 1 a natural conjecture of min oo asserts that if the scalar curvature of m is at least n n 1 then m is isometric to the hemisphere s n equipped with its standard metric this conjecture is inspired by the positive mass theorem in general relativity and has been verified in many special cases in this paper we construct counterexamples to min oo s conjecture in dimension n 3

optimal training sequence for mimo wireless systems in colored environments in this paper we design the training signal for a multi input multi output mimo communication system in a colored medium we assume that the known channel covariance matrix cm is a kronecker product of a transmit channel cm and a receive channel cm similarly the cm of the additive gaussian noise is modeled by a kronecker product of a temporal cm and a spatial cm we maximize the differential entropy gained by receiver for a limited energy budget for training at the transmitter using singular value decomposition of the involved cms we turn this problem into a convex optimization problem we prove that the left and right singular vectors of the optimal training matrix are eigenvectors of the channel transmit cm and the noise temporal cm in general case this problem can be solved numerically using efficient methods the impact of the optimal training is more significant in environments with larger eigenvalue spread the expression of the optimal solution is interesting for some specific cases for uncorrelated receive channel the optimal training looks like water filling i e more training power must be invested on the directions which have more impact for high signal to noise ratios snrs any orthogonal training is optimal this means that if large amount of energy is available it must be invested uniformly in all directions in low snr scenarios where low amount of energy is available for channel training all the energy must be allocated to the best mode of channel which has the highest ratio of the received channel variance to the received noise power

local existence of quasispherical space time initial data we consider the system of einstein constraint equations in the special case when the spacelike 3 manifold is assumed to satisfy the quasispherical ansatz of bartnik we introduce two different time slicing conditions under each of which we may view the resulting constraint equations as a parabolic elliptic ode system of partial differential equations we combine recent existence results for parabolic equations in sobolev space with an iterative method to prove local existence results for the quasispherical einstein constraint equations under the two different time slicing conditions

everything you always wanted to know about training guidelines derived using the affine precoding framework and the crb in this paper affine precoding is used to investigate the tradeoffs that exist while using the transmitter resources on training versus information symbols the channel input is a training vector superimposed on a linearly precoded vector of symbols a block fading frequency selective multi input multi output mimo channel is considered to highlight the tradeoffs between training and data symbols the fisher information matrix fim is derived under two circumstances the random parameter vector to be estimated contains 1 only fading channel coefficients and 2 unknown data symbols as well as the channel coefficients while strategy 1 corresponds to the receiver structure in which the channel is estimated initially and the channel measurement is utilized to retrieve the data symbols strategy 2 corresponds to the structure in which channel and symbol estimations are performed jointly the interesting outcome of the study in this paper is that minimizing the channel cramer rao bound crb for strategies 1 and 2 under a total average transmit power constraint leads to different affine precoder design guidelines

on the riemannian penrose inequality in dimensions less than eight the positive mass theorem states that a complete asymptotically flat manifold of nonnegative scalar curvature has nonnegative mass and that equality is achieved only for the euclidean metric the riemannian penrose inequality provides a sharp lower bound for the mass when black holes are present more precisely this lower bound is given in terms of the area of an outermost minimal hypersurface and equality is achieved only for schwarzschild metrics the riemannian penrose inequality was first proved in three dimensions in 1997 by g huisken and t ilmanen for the case of a single black hole see hi in 1999 bray extended this result to the general case of multiple black holes using a different technique see br in this article we extend the technique of br to dimensions less than eight part of the argument is contained in a companion article by lee l the equality case of the theorem requires the added assumption that the manifold be spin

total mean curvature scalar curvature and a variational analog of brown york mass we study the supremum of the total mean curvature on the boundary of compact mean convex 3 manifolds with nonnegative scalar curvature and a prescribed boundary metric we establish an additivity property for this supremum and exhibit rigidity for maximizers assuming the supremum is attained when the boundary consists of 2 spheres we demonstrate that the finiteness of the supremum follows from the previous work of shi tam and wang yau on the quasi local mass problem in general relativity in turn we define a variational analog of brown york quasi local mass without assuming that the boundary 2 sphere has positive gauss curvature

boundary effect of ricci curvature on a compact riemannian manifold with boundary we study how ricci curvature of the interior affects the geometry of the boundary first we establish integral inequalities for functions defined solely on the boundary and apply them to obtain geometric inequalities involving the total mean curvature then we discuss related rigidity questions and prove ricci curvature rigidity results for manifolds with boundary

fading channels how perfect need perfect side information be the analysis of flat fading channels is often performed under the assumption that the additive noise is white and gaussian and that the receiver has precise knowledge of the realization of the fading process these assumptions imply the optimality of gaussian codebooks and of scaled nearest neighbor decoding here we study the robustness of this communication scheme with respect to errors in the estimation of the fading process we quantify the degradation in performance that results from such estimation errors and demonstrate the lack of robustness of this scheme for some situations we suggest the rule of thumb that in order to avoid degradation the estimation error should be negligible compared to the reciprocal of the signal to noise ratio snr

optimal training signals for mimo ofdm channel estimation in the presence of frequency offset and phase noise we develop robust mean square error mse optimal training signal designs for multiple input multiple output orthogonal frequency division multiplexing channel estimation with frequency offset and phase noise pn and present analytical and simulation results for the frequency offset and pn effects on channel estimation the proposed designs are more advantageous for moderate to high values of signal to noise ratio snr residual frequency offset and pn level at snr 10 db the normalized mse reductions of our proposed training signals at normalized frequency offset v 0 1 0 5 are about 9 and 19 db respectively for one transmit antenna and 6 and 11 db for two transmit antennas

quasi spherical metrics and applications in this paper using the idea of bartnik b2 on quasi spherical metrics we continue our study on the boundary behaviors of compact manifolds with nonnegative scalar curvature and nonempty boundary unlike the previous work st of the authors and the work of liu yau ly we only assume each boundary component has nonnegative curvature which is not identically zero we also study the case that the boundary is embedded in the quotient of the infinity of the euclidean space over a finite group the regularity of the black hole boundary condition of quasi spherical metrics is also discussed

foundations for relativistic quantum theory i feynman s operator calculus and the dyson conjectures in this paper we provide a representation theory for the feynman operator calculus this allows us to solve the general initial value problem and construct the dyson series we show that the series is asymptotic thus proving dyson s second conjecture for quantum electrodynamics in addition we show that the expansion may be considered exact to any finite order by producing the remainder term this implies that every nonperturbative solution has a perturbative expansion using a physical analysis of information from experiment versus that implied by our models we reformulate our theory as a sum over paths this allows us to relate our theory to feynman s path integral and to prove dyson s first conjecture that the divergences are in part due to a violation of heisenberg s uncertainly relations

convergence theorems for hl integrable vector valued functions with applications abstract in this paper we prove dominated and monotone convergence theorems for hl integrable banach valued functions these results and a fixed point theorem in ordered spaces are then applied to prove existence and comparison results for integral equations of fredholm type in ordered banach spaces involving kurzweil integrals or improper integrals results are used also to solve concrete second order functional boundary value problems involving discontinuities and singularities

orthogonal space time block code over time varying flat fading channels channel estimation detection and performance analysis this paper studies the channel estimation detection and performance analysis of mobile wireless communication systems employing space time block codes stbc where the channels exhibit flat rayleigh fading with a significant amount of doppler spread pilot symbol assisted modulation psam is developed to estimate the channels the performance of the channel estimation is evaluated maximum likelihood ml detection is first formulated a linear detector called the symmetric linear sl detector is proposed an interference cancellation ic detector is also developed to improve the performance of the sl detector we derive the closed form analytical expressions for the bit error rate ber or symbol error rate ser of pilot sequence assisted stbc with binary phase shift keying psk quaternary psk 16 quadrature amplitude modulation qam and 64 qam when the sl and ic detectors are used some important design issues in the pilot sequence assisted stbc systems including the selection of pilot spacing and interpolator size are discussed simulation results are presented that verify our analytical results the tradeoffs between the performance and complexity for ml sl and ic detection are also discussed

joint cfo and channel estimation for multiuser mimo ofdm systems with optimal training sequences this paper addresses the problem of joint carrier frequency offset cfo and channel estimation in multiuser multiple input multiple output mimo orthogonal frequency division multiplexing ofdm systems to choose the optimal training sequences with the goal of providing the smallest estimation mean square error mse the asymptotic cramer rao bounds ascrbs are derived the optimal training sequences are designed that minimize the ascrbs for both cfo and channel estimation under the constraint that the ascrbs being channel independent a joint cfo and channel estimator is derived based on the maximum likelihood ml criterion a computationally efficient method using importance sampling technique is proposed to solve the highly demanding multidimensional exhaustive search required by the ml multi cfo estimation simulation results illustrate the merits of the proposed training sequences and also verify the effectiveness of the proposed estimation scheme

positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature in this paper we study the boundary behaviors of compact manifolds with nonnegative scalar curvature and nonempty boundary using a general version of positive mass theorem of schoen yau and witten we prove the following theorem for any compact manifold with boundary and nonnegative scalar curvature if it is spin and its boundary can be isometrically embedded into euclidean space as a strictly convex hypersurface then the integral of mean curvature of the boundary of the manifold cannot be greater than the integral of mean curvature of the embedded image as a hypersurface in euclidean space moreover equality holds if and only if the manifold is isometric with a domain in the euclidean space conversely under the assumption that the theorem is true then one can prove the adm mass of an asymptotically flat manifold is nonnegative which is part of the positive mass theorem

stability of the positive mass theorem for rotationally symmetric riemannian manifolds we study the stability of the positive mass theorem using the intrinsic flat distance in particular we consider the class of complete asymptotically flat rotationally symmetric riemannian manifolds with nonnegative scalar curvature and no interior closed minimal surfaces whose boundaries are either outermost minimal hypersurfaces or are empty we prove that a sequence of these manifolds whose adm masses converge to zero must converge to euclidean space in the pointed intrinsic flat sense in fact we provide explicit bounds on the intrinsic flat distance between annular regions in the manifold and annular regions in euclidean space by constructing an explicit filling manifold and estimating its volume in addition we include a variety of propositions that can be used to estimate the intrinsic flat distance between riemannian manifolds without rotationally symmetry conjectures regarding the intrinsic flat stability of the positive mass theorem in the general case are proposed in the final section lee is partially supported by a psc cuny research grant and nsf dms 0903467 sormani is partially supported by a psc cuny research grant and nsf dms 1006059 1 ar x iv 1 10 4 26 57 v1 m at h d g 1 4 a pr 2 01 1 2 dan a lee and christina sormani

the mass of an asymptotically flat manifold we show that the mass of an asymptotically flat n manifold is a geometric invariant the proof is based on harmonic coordinates and to develop a suitable existence theory results about elliptic operators with rough coefficients on weighted sobolev spaces are summarised some relations between the mass scalar curvature and harmonic maps are described and the positive mass theorem for n dimensional spin manifolds is proved

insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds we construct a solution to inverse mean curvature flow on an asymptotically hyperbolic 3 manifold which does not have the convergence properties needed in order to prove a penrose type inequality this contrasts sharply with the asymptotically flat case the main idea consists in combining inverse mean curvature flow with work done by shi tam regarding boundary behavior of compact manifolds assuming the penrose inequality holds we also derive a nontrivial inequality for functions on s

differential and integral equations with henstock kurzweil integrable functions abstract in this paper we apply fixed point theorems for increasing mappings in ordered normed spaces to prove existence and comparison results for solutions of discontinuous functional differential and integral equations containing henstock kurzweil integrable functions

optimal sequences for channel estimation using discrete fourier transform techniques this paper addresses the problem of selecting the optimum training sequence for channel estimation in communication systems over time dispersive channels by processing in the frequency domain a new explicit form of search criterion is found the gain loss factor glf which minimizes the variance of the estimation error and is easy to compute theoretical upper and lower bounds on the glf are derived an efficient directed search strategy and optimal sequences up to length 42 are given these sequences are optimal only for frequency domain estimation not for time domain estimation

quasi local mass and the existence of horizons in this paper we obtain lower bounds for the brown york quasilocal mass and the bartnik quasilocal mass for compact three manifolds with smooth boundaries as a consequence we derive sufficient conditions for the existence of horizons for a certain class of compact manifolds with boundary and some asymptotically flat complete manifolds the method is based on analyzing hawking mass and inverse mean curvature flow

lower bounds for parametric estimation with constraints a chapman robbins form of the barankin bound is used to derive a multiparameter cramer rao cr type lower bound on estimator error covariance when the parameter theta in r sup n is constrained to lie in a subset of the parameter space a simple form for the constrained cr bound is obtained when the constraint set theta sub c can be expressed as a smooth functional inequality constraint it is shown that the constrained cr bound is identical to the unconstrained cr bound at the regular points of theta sub c i e where no equality constraints are active on the other hand at those points theta in theta sub c where pure equality constraints are active the full rank fisher information matrix in the unconstrained cr bound must be replaced by a rank reduced fisher information matrix obtained as a projection of the full rank fisher matrix onto the tangent hyperplane of the full rank fisher matrix onto the tangent hyperplane of the constraint set at theta a necessary and sufficient condition involving the forms of the constraint and the likelihood function is given for the bound to be achievable and examples for which the bound is achieved are presented in addition to providing a useful generalization of the cr bound the results permit analysis of the gain in achievable mse performance due to the imposition of particular constraints on the parameter space without the need for a global reparameterization

unbiased estimation of a sparse vector in white gaussian noise the problem studied in this paper is unbiased estimation of a sparse nonrandom vector corrupted by additive white gaussian noise it is shown that while there are infinitely many unbiased estimators for this problem none of them has uniformly minimum variance therefore the focus is placed on locally minimum variance unbiased lmvu estimators simple closed form lower and upper bounds on the variance of lmvu estimators or equivalently on the barankin bound bb are derived these bounds allow an estimation of the threshold region separating the low signal to noise ratio snr and high snr regimes and they indicate the asymptotic behavior of the bb at high snr in addition numerical lower and upper bounds are derived these are tighter than the closed form bounds and thus characterize the bb more accurately numerical studies compare the proposed characterizations of the bb with established biased estimation schemes and demonstrate that while unbiased estimators perform poorly at low snr they may perform better than biased estimators at high snr an interesting conclusion of this analysis is that the high snr behavior of the bb depends solely on the value of the smallest nonzero entry of the sparse vector and that this type of dependence is also exhibited by the performance of certain practical estimators

the intersymbol interference channel lower bounds on capacity and channel precoding loss the discrete time additive gaussian intersymbol interference isi channel with i i d not necessarily gaussian input signals is considered several new and old lower bounds on the capacity are derived in a unified manner by assuming different front end receiver filters in particular the sampled whitened matched filter swmf and the minimum mean squared error decision feedback equalizer mmse dfe filter the features of the bounds are demonstrated and compared in several examples with binary and quaternary input signals it is also shown that the effect of an ideal post cursor or tail cancellation in an information preserving context depends primarily on the front end filter while as is well known ideal post cursor cancellation at the output of the swmf decreases the information the opposite trend is seen when an mmse dfe front filter is considered this observation reflects the basic theoretical obstacles in precoding i e ideal post cursor cancellation in the presence of a pre cursor it is used to assess the inherent loss in terms of information rates as compared to the rates achievable with the hypothetical ideal post cursor cancellation associated with any post cursor cancellation technique such as precoding dfe or other variants when operating in synergy with the mmse dfe front end filter the effect of the front end filter on an ideally interleaved precoded coded modulation system is also addressed

proof of the positive mass theorem ii the positive mass theorem states that for a nontrivial isolated physical system the total energy which includes contributions from both matter and gravitation is positive this assertion was demonstrated in our previous paper in the important case when the space time admits a maximal slice here this assumption is removed and the general theorem is demonstrated abstracts of the results of this paper appeared in 11 and 13

yamabe flow and adm mass on asymptotically flat manifolds in this paper we investigate the behavior of adm mass and einstein hilbert functional under the yamabe flow through studying the yamabe flow by weighted spaces for parabolic operators we show that the asymptotically flat property is preserved under the yamabe flow we also obtain that adm mass is invariant under the yamabe flow and yamabe flow is the gradient flow of einstein hilbert functional on n dimensional n 3 asymptotically flat manifolds with order n 22 for n 3 4 or n 3 for n 4 moreover we show that adm mass and einstein hilbert functional are non increasing under the yamabe flow on n dimensional asymptotically flat manifolds if we only assume the order n 22 for n 4

gaussian codes and weighted nearest neighbor decoding in fading multiple antenna channels we investigate the fading multiple antenna channel the decoder is assumed to possess imperfect channel fading information a modified nearest neighbor decoder with an innovative weighting factor is introduced and an expression for the generalized mutual information gmi the achievable rate is obtained we show that under certain conditions the achievable rate is equivalent to that of a fading multiple antenna gaussian channel where fading is known to the receiver and is equal to the channel estimation and where noise is due to both the channel noise and the channel estimation error we show that for our communication scheme the minimum mean square error mmse channel estimator is optimal in the sense that it achieves the highest value of gmi and hence the highest communication rate additionally a training based multiple input multiple output mimo scheme in a block fading channel is investigated and it is shown that the number of degrees of freedom depends on the signal to noise ratio snr

a property of the brown york mass in schwarzschild manifolds abstract we will extend partially our previous results about the limit of the brown york mass of a family of convex revolution surfaces in the schwarzschild manifold such that these surfaces may have unbounded ratios of their radii

proof of the riemannian penrose inequality with charge for multiple black holes we present a proof of the riemannian penrose inequality with charge in the context of asymptotically flat initial data sets for the einstein maxwell equations having possibly multiple black holes with no charged matter outside the horizon and satisfying the relevant dominant energy condition the proof is based on a generalization of hubert bray s conformal flow of metrics adapted to this setting

isometric embeddings into the minkowski space and new quasi local mass the definition of quasi local mass for a bounded space like region in space time is essential in several major unsettled problems in general relativity the quasi local mass is expected to be a type of flux integral on the boundary two surface sigma partial omega and should be independent of whichever space like region sigma bounds an important idea which is related to the hamiltonian formulation of general relativity is to consider a reference surface in a flat ambient space with the same first fundamental form and derive the quasi local mass from the difference of the extrinsic geometries this approach has been taken by brown york 4 5 and liu yau 16 17 see also related works 3 6 9 12 14 15 28 32 to define such notions using the isometric embedding theorem into the euclidean three space however there exist surfaces in the minkowski space whose quasilocal mass is strictly positive 19 it appears that the momentum information needs to be accounted for to reconcile the difference in order to fully capture this information we use isometric embeddings into the minkowski space as references in this article we first prove an existence and uniqueness theorem for such isometric embeddings we then solve the boundary value problem for jang s 13 equation as a procedure to recognize such a surface in the minkowski space in doing so we discover a new expression of quasi local mass for a large class of admissible surfaces see theorem a and remark 1 1 the new mass is positive when the ambient space time satisfies the dominant energy condition and vanishes on surfaces in the minkowski space it also has the nice asymptotic behavior at spatial infinity and null infinity some of these results were announced in 29

scalar curvature rigidity of geodesic balls in sn in this paper we prove a scalar curvature rigidity result for geodesic balls in s n this result contrasts sharply with the counterexamples to min oo s conjecture constructed in deformations of the hemisphere that increase scalar curvature invent math 185 2011 175 197

a polyhedron comparison theorem for 3 manifolds with positive scalar curvature the study of comparison theorems in geometry has a rich history in this paper we establish a comparison theorem for polyhedra in 3 manifolds with nonnegative scalar curvature answering affirmatively a dihedral rigidity conjecture by gromov for a large collections of polyhedra with interior non negative scalar curvature and mean convex faces we prove the dihedral angles along its edges cannot be everywhere less or equal than those of the corresponding euclidean model unless it is isometric to a flat polyhedron

well posedness results for differential and integral equations containing henstock kurzweil integrable vector valued functions abstract in this paper we prove existence uniqueness and comparison results for solutions of differential and integral equations in banach spaces containing henstock kurzweil integrable functions from a compact real interval to an ordered banach space

the gbc mass for asymptotically hyperbolic manifolds the paper consists of two parts in the first part by using the gauss bonnet curvature which is a natural generalization of the scalar curvature we introduce a higher order mass the gauss bonnet chern mass m mathbb h k for asymptotically hyperbolic manifolds and show that it is a geometric invariant moreover we prove a positive mass theorem for this new mass for asymptotically hyperbolic graphs and establish a relationship between the corresponding penrose type inequality for this mass and weighted alexandrov fenchel inequalities in the hyperbolic space mathbb h n in the second part we establish these weighted alexandrov fenchel inequalities in mathbb h n for any horospherical convex hypersurface sigma begin aligned int sigma v sigma 2k 1 d mu ge c n 1 2k 1 omega n 1 left left frac sigma omega n 1 right frac n k n 1 left frac sigma omega n 1 right frac n 2k k n 1 right k end aligned where sigma j is the j th mean curvature of sigma subset mathbb h n v cosh r and sigma is the area of sigma as an application we obtain an optimal penrose type inequality for the new mass defined in the first part begin aligned m k mathbb h ge frac 1 2 k left left frac sigma omega n 1 right frac n k n 1 left frac sigma omega n 1 right frac n 2k k n 1 right k end aligned for asymptotically hyperbolic graphs with a horizon type boundary sigma provided that a dominant energy type condition tilde l k ge 0 holds both inequalities are optimal

the positive mass theorem for manifolds with distributional curvature we formulate and prove a positive mass theorem for n dimensional spin manifolds whose metrics have only the sobolev regularity c 0 cap w rm loc 1 n at this level of regularity the curvature of the metric is defined in the distributional sense only and we propose here a generalized notion of adm mass for such a metric our main theorem establishes that if the manifold is asymptotically flat and has non negative scalar curvature distribution then its generalized adm mass is well defined and non negative and vanishes only if the manifold is isometric to euclidian space prior applications of witten s spinor method by lee and parker and by bartnik required the much stronger regularity w rm loc 2 p with p n our proof is a generalization of witten s arguments in which we must treat the dirac operator and its associated lichnerowicz weitzenbock identity in the distributional sense and cope with certain averages of first order derivatives of the metric over annuli that approach infinity finally we observe that our arguments are not specific to scalar curvature and also allow us to establish a universal positive mass theorem

monotone convergence theorems for henstock kurzweil integrable functions and applications abstract in this paper we prove monotone convergence theorems for henstock kurzweil integrable functions from a compact real interval to an ordered banach space these theorems are then applied to prove existence results for solutions of a discontinuous functional integral equation containing henstock kurzweil integrable functions

deformation of scalar curvature and volume the stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the einstein metrics one may consider the modified problem of finding stationary points for the volume functional on the space of metrics whose scalar curvature is equal to a given constant in this paper we localize a condition satisfied by such stationary points to smooth bounded domains the condition involves a generalization of the static equations and we interpret solutions and their boundary values of this equation variationally on domains carrying a metric that does not satisfy the condition we establish a local deformation theorem that allows one to achieve simultaneously small prescribed changes of the scalar curvature and of the volume by a compactly supported variation of the metric we apply this result to obtain a localized gluing theorem for constant scalar curvature metrics in which the total volume is preserved finally we note that starting from a counterexample of min oo s conjecture such as that of brendle marques neves counterexamples of arbitrarily large volume and different topological types can be constructed

complex optimal sequences with constant magnitude for fast channel estimation initialization optimal sounding sequences which satisfy a certain autocorrelation property are useful for fast channel estimation techniques which are based on noniterative channel sounding methods we study optimal sequences consisting of complex symbols with constant magnitude an indirect sequence construction method is derived by considering the phase difference between sequence symbols our construction method includes periodic and nonperiodic optimal sequences and provides insight into the nature and properties of optimal sequences that are based on consecutive roots of unity phase difference sequences

leveraging coherent space time codes for noncoherent communication via training training codes are introduced for the multiple antenna noncoherent multiple block rayleigh fading channel in which the fading coefficients which are constant over a fixed number of dimensions coherence interval for each block and then change independently to a new realization are known neither at the transmitter nor at the receiver each codeword of a training code consists of a part known to the receiver used to form a minimum mean squared error mmse estimate of the channel and a part that contains codeword s of a space time block or trellis code designed for the coherent channel in which the receiver has perfect knowledge of the channel the channel estimate is used as if it were error free for decoding the information bearing part of the training codeword training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have high rate and to be efficiently decodable conditions for which the estimator detector e d receiver is equivalent to the optimal noncoherent receiver are established a key performance analysis result of this paper is that the training codes when decoded with the e d receiver achieve a diversity order of the error probability that is equal to the diversity order of the underlying coherent code in some cases the performance of training codes can be measured relative to coherent reception via training efficiency which is then optimized over the energy allocation between the training and data phases in the limit of increasing block lengths training codes always achieve the performance of coherent reception the examples of training codes provided in this work have polynomial complexity in rate but an error rate comparable to the best performing unitary designs available even though the latter require exponential decoding complexity

on scalar curvature rigidity of vacuum static spaces in this paper we extend the local scalar curvature rigidity result in brendle and marques j differ geom 88 379 394 2011 to a small domain on general vacuum static spaces which confirms the interesting dichotomy of local surjectivity and local rigidity about the scalar curvature in general in the light of the paper corvino commun math phys 214 137 189 2000 we obtain the local scalar curvature rigidity of bounded domains in hyperbolic spaces we also obtain the global scalar curvature rigidity for conformal deformations of metrics in the domains where the lapse functions are positive on vacuum static spaces with positive scalar curvature and show such domains are maximal which generalizes the work in hang and wang commun anal geom 14 91 106 2006

on the positive mass theorem for manifolds with corners we study the positive mass theorem for certain non smooth metrics following p miao s work our approach is to smooth the metric using the ricci flow as well as improving some previous results on the behaviour of the adm mass under the ricci flow we extend the analysis of the zero mass case to higher dimensions

curvature estimates for immersed hypersurfaces in riemannian manifolds we establish mean curvature estimate for immersed hypersurface with nonnegative extrinsic scalar curvature in riemannian manifold n n 1 bar g through regularity study of a degenerate fully nonlinear curvature equation in general riemannian manifold the estimate has a direct consequence for the weyl isometric embedding problem of mathbb s 2 g in 3 dimensional warped product space n 3 bar g we also discuss isometric embedding problem in spaces with horizon in general relativity like the anti de sitter schwarzschild manifolds and the reissner nordstrom manifolds

optimal design and placement of pilot symbols for channel estimation the problem of designing and placing pilot symbols for the estimation of frequency selective random channels is considered the channel is assumed to be a block fading model with finite impulse response fir for both single input single output siso and multiple input multiple output mimo channels under the assumption of independent and identical distributed channel taps the cramer rao bound crb on the mean square error mse of semi blind channel estimators is derived and minimized with respect to pilot symbols and their placement it is shown that the optimal strategy is to place pilot symbols satisfying certain orthogonality condition in such a way that data and pilot symbols with higher power are in the middle of the packet the results also indicate that the optimal pilot placements are independent of channel probability distribution for constant modulus symbols we show that the quasi periodic placement and its generalization in the multiuser case turn out to be optimal we further consider estimating channels with correlated taps and show that the previous placement strategy is also optimal among orthogonal pilot sequences

optimal placement of training for frequency selective block fading channels the problem of placing training symbols optimally for orthogonal frequency division multiplexing ofdm and single carrier systems is considered the channel is assumed to be quasi static with a finite impulse response of length l 1 samples under the assumptions that neither the transmitter nor the receiver knows the channel and that the receiver forms a minimum mean square error mmse channel estimate based on training symbols only training is optimized by maximizing a tight lower bound on the ergodic training based independent and identically distributed i i d capacity for ofdm systems it is shown that the lower bound is maximized by placing the known symbols periodically in frequency for single carrier systems under the assumption that the training symbols are placed in clusters of length spl alpha spl ges 2l 1 it is shown that the lower bound is maximized by a family of placement schemes called qpp spl alpha where qpp stands for quasi periodic placement these placement schemes are formed by grouping the known symbols into as many clusters as possible and then placing these clusters periodically in the packet for both ofdm and single carrier systems the optimum energy tradeoff between training and data is also obtained

geometric inequalities for quasi local masses in this paper lower bounds are obtained for quasi local masses in terms of charge angular momentum and horizon area in particular we treat three quasi local masses based on a hamiltonian approach namely the brown york liu yau and wang yau masses the geometric inequalities are motivated by analogous results for the adm mass they may be interpreted as localized versions of these inequalities and are also closely tied to the conjectured bekenstein bounds for entropy of macroscopic bodies in addition we give a new proof of the positivity property for the wang yau mass which is used to remove the spin condition in higher dimensions furthermore we generalize a recent result of lu and miao to obtain a localized version of the penrose inequality for the static wang yau mass

comment on positivity of quasilocal mass liu and yau phys rev lett 90 231102 2003 propose a definition of quasi local mass for any space like topological 2 sphere with positive gauss curvature and subject to a second convexity condition they are able to show it is positive using a result of shi and tam j diff geom 62 79 2002 however as we show here their definition can give a strictly positive mass for a sphere in flat space

on the effect of receiver estimation error upon channel mutual information our goal in this paper is to study the effect of the receiver structure upon the achievable data rates we consider transmission of linearly precoded data symbols over a frequency selective block fading multiple input multiple output mimo wireless channel to encompass a number of transmission schemes we study this problem utilizing affine precoding which is a unified model of linearly precoded data symbols with superimposed training we focus on bayesian receivers that estimate both the unknown fading coefficients and the data symbols the receiver may adopt either of the following strategies to retrieve the data symbols strategy i the receiver obtains joint bayesian channel and symbol estimates strategy ii the receiver obtains a bayesian channel estimate initially and the channel measurement is utilized to estimate the data symbols for both strategies we provide lower bounds on the mutual information between the data symbols and their corresponding estimates and we relate these bounds to the symbol cramer rao bound crb matrices in contrast to strategy ii for strategy i the lower bound does not depend on either the channel estimate or the covariance of the channel estimation error for strategy ii we show that asymptotically as the size of the transmission block grows there is no loss of information after the maximum a posteriori map estimate of gaussian symbols we also provide guidelines to design affine precoders that maximize the derived lower bounds under the total average transmit power constraint

positive scalar curvature with skeleton singularities we study positive scalar curvature on the regular part of riemannian manifolds with singular uniformly euclidean l infty metrics that consolidate gromov s scalar curvature polyhedral comparison theory and edge metrics that appear in the study of einstein manifolds we show that in all dimensions edge singularities with cone angles le 2 pi along codimension 2 submanifolds do not affect the yamabe type in three dimensions we prove the same for more general singular sets which are allowed to stratify along 1 skeletons exhibiting edge singularities angles le 2 pi and arbitrary l infty isolated point singularities we derive as an application of our techniques positive mass theorems for asymptotically flat manifolds with analogous singularities

on the sensitivity of a suboptimal precoding scheme for frequency selective block based channels with respect to channel inaccuracies water filling is the precoding scheme that achieves capacity in gaussian parallel or block based channels a suboptimal precoding scheme which has been observed to perform quite close to water filling in some cases of great interest is when all active eigenvectors of the input data covariance matrix receive the same power both techniques require perfect channel knowledge at the transmitter in this work we consider the sensitivity of the suboptimal scheme when a channel estimate is used at the transmitter as if it were the true channel using tools from matrix perturbation theory we derive closed form expressions and bounds relating the channel estimation error covariance matrix with the mean mutual information decrease we thus uncover the factors that determine the behavior of the suboptimal precoding scheme under channel uncertainties simulations are in agreement with our theoretical results