performance analysis of optimum combining with multiple interferers in flat rayleigh fading this paper is a performance analysis of optimum combining in the presence of multiple equal power interferers and noise when the number of interferers is less than the number of antenna elements desired signal and interferers are subject to flat rayleigh fading and the propagation channels are independent an approximate expression of the probability density function of the output signal to interference plus noise ratio sinr is derived analytically it is then applied to obtain the cumulative distribution function of the sinr and the bit error rate ber of some binary modulations including coherent binary phase shift keying in the case of a single interferer an exact analysis is performed to prove the validity of the approximation in the case of multiple interferers the accuracy of the approximation is assessed through simulations although limited to equipower interferers this analysis is a convenient way of assessing the performance of optimum combining in some typical situations and comparing it with that of maximal ratio combining the final results are remarkably simple and provide a useful complement to previous analyzes especially in the region of reasonably high bers which are of practical interest

the cauchy problem for indefinite improper affine spheres and their hessian equation abstract we give a conformal representation for indefinite improper affine spheres which solve the cauchy problem for their hessian equation as consequences we can characterize their geodesics and obtain a generalized symmetry principle then we classify the helicoidal indefinite improper affine spheres and find a new family with geodesically complete non flat affine metric moreover we present interesting examples with singular curves and isolated singularities

the bernstein problem for affine maximal hypersurfaces in this paper we prove the validity of the chern conjecture in affine geometry 18 namely that an affine maximal graph of a smooth locally uniformly convex function on two dimensional euclidean space r 2 must be a paraboloid more generally we shall consider the n dimensional case r n showing that the corresponding result holds in higher dimensions provided that a uniform strict convexity condition holds we also extend the notion of affine maximal to non smooth convex graphs and produce a counterexample showing that the bernstein result does not hold in this generality for dimension n 10

the monge ampere equation and its link to optimal transportation we survey old and new regularity theory for the monge ampere equation show its connection to optimal transportation and describe the regularity properties of a general class of monge ampere type equations arising in that context

factorization of blaschke products and primary ideals in h let e be a compact subset of g the union set of nontrivial gleason parts and i e be the associate primary ideal of h we give a characterization of the numbering function ord i e x the zero s order of i e at x in e using the geometrical words of e we also give some factorization theorems of blaschke products using these we give some descriptions of the higher order hulls of i e and for a carleson newman blaschke product in i e it is proved that i e is generated by its subproducts as a closed ideal when each ei is separated we also prove that the tensor product i 1ki ei is closed in h

exterior problems for more general parabolic monge ampere equation in more general domain abstract in this paper we consider the exterior problem for more general parabolic monge ampere equation u t logdet d 2 u in more general domain r t 1 2 n 1 d r t 1 2 n 1 r n 1 t 1 t 2 d t 1 t 2 using the perron method we obtain the existence and uniqueness of viscosity solution with asymptotic behavior at infinity the results of exterior problems for the parabolic monge ampere equation u t logdet d 2 u 1 are extended

aspects on single symbol signaling on the frequency flat rayleigh fading channel the optimal single symbol detector on the rayleigh fading channel computes a functional quadratic form in the time continuous received signal a drawback is that closed form solutions of integral equations based on the channel statistics are required this makes simplified discrete receivers attractive a class of suboptimal receivers that transforms the received random process to a set of discrete observables is derived the set of observables constitutes a random vector in a finite dimensional receiver signal space given this vector the maximum likelihood detector computes a quadratic form in the received vector the discretization implies a loss of information therefore such a detector is not in general optimal given the received time continuous signal the purpose is however to achieve close to optimal performance when the number of observables becomes large this class of detectors is analyzed using exact error probability calculations which reveal several interesting properties the length of the observation interval and the number of discrete observables have significant influences on the error probability when the time variations of the fading process are rapid compared with the symbol duration by increasing the number of observables the error floor is lowered and the implicit diversity order is increased this implicit diversity arises as soon as more than one observable per symbol interval is used and is a consequence of the information bearing signal being a random process matched filter receivers use few discrete observables per symbol interval and thus suffer from high error floors and low implicit diversity orders on fast fading channels the error probability is highly dependent on the shapes and durations of the modulator waveforms for instance pulses of long duration give lower error probabilities than shorter pulses and for a certain type of orthogonal waveforms there is no error floor

solutions of some monge ampere equations with isolated and line singularities in this paper we study existence regularity classification and asymptotic behaviors of solutions of some monge ampere equations with isolated and line singularities we classify all solutions of det 2u 1 in r n with one puncture point this can be applied to characterize ellipsoids in the same spirit of serrin s overdetermined problem for the laplace operator in the case of having k non removable singular points for k 1 modulo affine equivalence the set of all generalized solutions can be identified as an explicit orbifold we also establish existence of global solutions with general singular sets regularity properties and optimal estimates of the second order derivatives of generalized solutions near the singularity consisting of a point or a straight line the geometric motivation comes from singular semi flat calabi yau metrics

affine complete locally convex hypersurfaces an open problem in affine geometry is whether an affine complete locally uniformly convex hypersurface in euclidean n 1 space is euclidean complete for n 2 in this paper we give the affirmative answer as an application it follows that an affine complete affine maximal surface in r 3 must be an elliptic paraboloid

ribaucour type transformations for the hessian one equation abstract we extend the classical theory of ribaucour transformations to the family of improper affine maps and use it to obtain new solutions of the hessian one equation we prove that such transformations produce complete embedded ends of parabolic type and curves of singularities which generically are cuspidal edges moreover we show that these ends and curves of singularities do no intersect we apply ribaucour transformations to some helicoidal improper affine maps providing new 3 parameter families with an interesting geometry and a good behavior at infinity in particular we construct improper affine maps periodic in one variable with any even number of complete embedded ends

performance of direct sequence spread spectrum rake receivers with random spreading sequences in this paper we derive error probability expressions for binary phase shift keying bpsk and quaternary phase shift keying qpsk spread direct sequence spread spectrum dsss systems employing random spreading sequences with rake receivers the derived expressions accurately take into account the effect of interpath interference which usually has been neglected in previous analyses selection equal gain and maximal ratio techniques are considered for diversity combining two possible finger assignment strategies one based on the instantaneous amplitudes and another based on the average powers of the multipath components are considered for the assignment of multipath components to the available demodulating fingers in the rake receiver also various simple and in many cases closed form approximations for the error probabilities are derived and their accuracies are assessed

higher order hulls in h ii abstract we give a complete characterization of the closed ideals in h with hull contained in the set g of nontrivial gleason parts and show that these ideals are uniquely determined by their higher order hulls we apply our theorem to finitely generated ideals and obtain an extension of results of j bourgain we also determine generating sets for the class of all ideals with hull contained in g

precise error rate analysis of bandwidth efficient bpsk in nakagami fading and cochannel interference the bit error rate ber of bandlimited binary phase shift keying in a fading and cochannel interference cci environment is derived for the case of perfect coherent detection the fading and interference model assumed is general and of interest for microcellular system studies the model allows both desired signal and interfering signals to experience arbitrary amounts of fading severity a precise ber expression is derived using a characteristic function method using this accurate analytical result the impact of the interfering users fading severity on the desired user error rate is examined the bers obtained under perfect coherent detection are also valid as lower performance bounds for practical realizable receivers where ideal coherent detection is difficult to implement the error rate performance of a novel bandwidth efficient pulse shape is determined for the general fading and cci environment analysis and numerical results show that the new pulse can provide better ber performance than the widely used raised cosine pulse

the exterior dirichlet problem for hessian quotient equations abstract in this paper using a reverse maclaurin inequality we established the existence theorem of the exterior dirichlet problem for hessian quotient equations with a stronger asymptotic behavior at infinity when k n 1 2 we improve the result in l m dai the dirichlet problem for hessian quotient equations in exterior domains j math anal appl 380 2011 87 93 for s k l with k l 3 to the result with any 0 l k

lorentzian affine hyperspheres with constant affine sectional curvature we study ane hyperspheres m with constant sectional curvature with respect to the ane metric h a conjecture by m magid and p ryan states that every such ane hypersphere with nonzero pick invariant is anely equivalent to either where the dimension n satises n 2 m 1o rn 2 m u p to now this conjecture was proved if m is positive denite or if m is a 3 dimensional lorentz space in this paper we give an armative answer to this conjecture for arbitrary dimensional lorentzian ane hyperspheres

the affine plateau problem in this paper we study a second order variational problem for locally convex hypersurfaces which is the affine invariant analogue of the classical plateau problem for minimal surfaces we prove existence regularity and uniqueness results for hypersurfaces maximizing affine area under appropriate boundary conditions

locally strongly convex affine hypersurfaces with parallel cubic form we give a complete classification of locally strongly convex affine hypersurfaces ofr n 1 with parallel cubic form with respect to the levi civita connection of the affine berwald blaschke metric it turns out that all such affine hypersurfaces are quadrics or can be obtained by applying repeatedly the calabi product construction of hyperbolic affine hyperspheres using as building blocks either the hyperboloid or the standard immersion of one of the symmetric spaces sl m r so m sl m c su m su 2m sp m or e6 26 f4

cubic differentials and hyperbolic convex sets we give a parameterization of the moduli space of marked gromov hyperbolic convex domains of rp by the space of bounded holomorphic cubic differentials on the disk

dual connections and affine geometry on etudie des immersions affines de varietes statistiques dans l espace affine plus particulierement on etablit deux resultats sur le rapport entre l existence de telles immersions et le fait que les varietes statistiques connexes en question ont des courbures constantes

on the exterior dirichlet problem for monge ampere equations abstract in this paper we use the perron method to prove the existence of viscosity solutions to a class of monge ampere equations on exterior domains in r n n 2 with prescribed asymptotic behavior at infinity this extends the caffarelli li s result on det d 2 u 1 we also obtain the existence of entire convex viscosity solutions to the monge ampere equations with prescribed asymptotic behavior at infinity

hessian equations on exterior domain abstract in the paper we consider the hessian equation k d 2 u f x where f is a positive function outside a bounded domain of r n n 3 and f x 1 o x for some 2 at infinity using the perron s method we prove the existence and uniqueness for viscosity solutions of exterior dirichlet problem with prescribed asymptotic behavior at infinity there are examples to show that the result is optimal this is an extension of the theorems given by bao li li in 2 for f 1 and bao li zhang in 3 for k n

a bernstein type theorem for parabolic k hessian equations abstract we are concerned with the characterization of entire solutions to the parabolic k hessian equation of the form u t f k d 2 u 1 in r n 0 we prove that for 1 k n any strictly convex monotone solution u u x t c 4 2 r n 0 to u t f k d 2 u 1 in r n 0 must be a linear function of t plus a quadratic polynomial of x under some growth assumptions on u

bit error probabilities mdpsk over the nonselective rayleigh fading channel with diversity reception data transmission using m ary differential phase shift keying mdpsk over the nonselective rayleigh fading channel with diversity reception is considered while previous studies on error probability mostly assume no fading fluctuation the author considers exclusively the case in which the fading process fluctuates from one symbol interval to the next exact bit error probability results for 2 4 and 8 dpsk as well as tight upper bounds are derived some applications of the results are discussed

exterior problems for a parabolic monge ampere equation abstract in this paper we study the exterior problem for a parabolic monge ampere equation u t logdet d 2 u f x t the existence and uniqueness of the viscosity solution with asymptotic behavior at infinity are established by the perron method we generalize the results of exterior problems for the elliptic monge ampere equation

error probability for coherent and differential psk over arbitrary rician fading channels with multiple cochannel interferers this paper discusses the performance of communication systems using binary coherent and differential phase shift keyed psk modulation in correlated rician fading channels with diversity reception the presence of multiple rician faded cochannel users which may have arbitrary and nonidentical parameters is modeled exactly exact bit error probability bep expressions are derived via the moment generating functions mgfs of the relevant decision statistics which are obtained through coherent detection with maximum ratio combining for coherent psk modulation and differential detection with equal gain combining egc for differential modulation evaluating the exact expressions requires a complexity that is exponential in the number of interferers to avoid this potentially time consuming operation we derive two low complexity approximate methods each for coherent and differential modulation formats which are more accurate than the traditional gaussian approximation approach two new and interesting results of this analysis are 1 unlike in the case of rayleigh fading channels increasing correlation between diversity branches may lead to better performance in rician fading channels and 2 the phase distribution of the line of sight or static fading components of the desired user has a significant influence on the bep performance in correlated diversity channels

an extension of a theorem by k jorgens and a maximum principle at infinity for parabolic affine spheres where is a planar domain and f is in the usual holder space c2 without loss of generality we shall consider only locally convex solutions of 1 this equation arises in the context of an affine differential geometric problem as the equation of a parabolic affine sphere in short pa sphere in the unimodular affine real 3 space see c1 c2 cy and lsz contrary to the case of smooth bounded convex domains little is known about solutions of 1 when the domain is unbounded here we recall a famous result by k jorgens which asserts that any solution of 1 on r2 is a quadratic polynomial see j and we also mention a previous paper see fmm where the authors study solutions of 1 on the exterior of a planar domain that are regular at infinity since the underlying almost complex structure of 1 is integrable one expects pa spheres with their canonical conformal structure to be conveniently described in terms of meromorphic functions the reader will find in sect 2 a complex representation of pa spheres and particularly a complex description for the solutions of 1

asymptotic behavior on a kind of parabolic monge ampere equation abstract in this paper we apply level set and nonlinear perturbation methods to obtain the asymptotic behavior of the solution to a kind of parabolic monge ampere equation at infinity the jorgens calabi pogorelov theorem for parabolic and elliptic monge ampere equation can be regarded as special cases of our result

liouville property and regularity of a hessian quotient equation we are concerned with properties of convex solutions to the hessian quotient equation sn c d2 p 1 k n as our first main result we prove some regularity of strong solutions while the second states that for p 1 an entire convex solution with a quadratic growth bound must be a quadratic polynomial

existence for translating solutions of gauss curvature flow on exterior domains abstract in this paper we use the perron method to prove the existence of viscosity solutions to a class of monge ampere equations on exterior domains in r n n 2 with prescribed asymptotic behavior at infinity this problem comes from the study of gauss curvature flow and its generalization the flow by powers of gauss curvature

on the exterior dirichlet problem for the monge ampere equation in dimension two abstract in this paper we consider the dirichlet problem for the monge ampere equation on exterior domains in dimension two and prove a theorem on the existence of solutions with prescribed asymptotic behavior at infinity

the cauchy problem for improper affine spheres and the hessian one equation we give a conformal representation for improper affine spheres which is used to solve the cauchy problem for the hessian one equation with this representation we characterize the geodesics of an improper affine sphere study its symmetries and classify the helicoidal ones finally we obtain the complete classification of the isolated singularities of the hessian one monge ampere equation

the exterior dirichlet problem for fully nonlinear elliptic equations related to the eigenvalues of the hessian in this paper we establish the existence theorem for the exterior dirichlet problems for a class of fully nonlinear elliptic equations which are related to the eigenvalues of the hessian matrix with prescribed asymptotic behavior at infinity this extends the previous results on monge ampere equation and k hessian equation to more general cases in particular including the special lagrangian equation

on the isolation phenomena of locally conformally flat manifolds with constant scalar curvature submanifolds versions abstract in this paper from the viewpoint of submanifold theory we study the isolation phenomena of riemannian manifolds with constant scalar curvature and vanishing weyl conformal curvature tensor firstly for any locally strongly convex affine hyperspheres in an n 1 dimensional equiaffine space r n 1 with constant scalar curvature we prove an inequality involving the traceless ricci tensor the pick invariant and the scalar curvature the inequality is optimal and we can further completely classify the affine hyperspheres which realize the equality case of the inequality secondly and analogously for lagrangian minimal submanifolds of the complex projective space c p n equipped with the fubini study metric under the condition that the weyl conformal curvature tensor vanishes we establish a similar but reverse inequality involving the traceless ricci tensor the scalar curvature and the squared norm of the second fundamental form the inequality is also optimal and we can further completely classify the submanifolds which realize the equality case of the inequality

an interior estimate for convex solutions and a rigidity theorem abstract we establish an interior c 2 estimate for k 1 convex solutions to dirichlet problems of k hessian equations we also use such estimate to obtain a rigidity theorem for k 1 convex entire solutions of k hessian equations in euclidean space

an extension to a theorem of jorgens calabi and pogorelov 1 1 det d2u 1 in rn must be a quadratic polynomial for n 2 a classical solution is either convex or concave the result holds without the convexity hypothesis a simpler and more analytical proof along the lines of affine geometry of the theorem was later given by cheng and yau 9 the first author extended the result for classical solutions to viscosity solutions 4 it was proven by trudinger and wang in 19 that the only open convex subset of rn which admits a convex c2 solution of det d2u 1 in with limx u x is rn in this paper we give the following extension to the theorem of jorgens calabi and pogorelov let u be a convex viscosity solution of det d2u 1 outside a bounded subset of

global smoothness for a singular monge ampere equation abstract the global c n 2 regularity for the graph of solutions to a singular monge ampere equation was established in 7 this equation arises in the study of hyperbolic affine spheres and is singular at the boundary a compatibility condition for higher regularity was found in 7 in this paper we verify the compatibility condition and obtain the global c regularity in the even dimensional case

factorization of blaschke products and ideal theory in h let h be the banach algebra of bounded analytic functions on the open unit disk d let g be the union set of all nontrivial gleason parts in the maximal ideal space of h let e be a nonvoid compact and totally disconnected subset of g and ne be a bounded numbering function on e we characterize ne for which there is a closed ideal i in h such that z i e and ord i x ne x for every x e let i1 i2 ik be closed ideals in h satisfying z ii g for 1 i k we prove that i 1kii i 1kfi fi ii 1 i k is a closed ideal a local ideal theory in h plays an important role to prove our results

optimal boundary regularity for a singular monge ampere equation abstract in this paper we study the optimal global regularity for a singular monge ampere type equation which arises from a few geometric problems we find that the global regularity does not depend on the smoothness of domain but it does depend on the convexity of the domain we introduce a type to describe the convexity as a result we show that the more convex is the domain the better is the regularity of the solution in particular the regularity is the best near angular points

explicit analytical expressions for outage and error rate of diversity cellular systems in the presence of multiple interferers and correlated rayleigh fading the outage probability of maximal ratio combining diversity with an arbitrary number of antennas in the presence of an arbitrary number of cochannel interferers and thermal noise is derived when the branch gains of the desired user signal and interfering signals experience rayleigh fading and have the same correlation matrix two special cases when the correlation matrix is equicorrelated and when the correlation matrix has different eigenvalues are considered for both the equal power cochannel interference case and the unequal power cochannel interference case further the average bit error rate of a coherent binary phase shift keying bpsk modulated cellular system using maximal ratio combining diversity in cochannel interference and correlated rayleigh fading is derived the effects of the average signal to noise ratio snr and the average signal power to interference power ratio on the system performance are examined

affine 3 spheres with constant affine curvature we classify the affine hyperspheres in r 4 which have constant curvature in the affine metric h and whose pick invariant is nonzero in particular the metric h must be flat

existence and regularity of the solutions of some singular monge ampere equations abstract in this paper we investigate the following singular monge ampere equation 0 1 det d 2 u 1 h u n k 2 u k in r n u 0 on where k 0 h 0 are constants and u x u x u x is the legendre transformation of u equation 0 1 is related to proper affine hyperspheres we will show the existence of solutions of 0 1 u c c via regularization method using the technique in 10 12 we also obtain the optimal graph regularity of the solution of 0 1

on the cumulative distribution function of quadratic form receivers over generalized fading channels with tone interference in this paper we develop a general and unified framework for estimating the cumulative distribution function cdf of quadratic form receivers the expression of the cdf that we finally achieve takes on the form of a single integral with finite limits and integrand composed of elementary functions which can be readily integrated using standard techniques in particular the specific contribution of this manuscript is twofold i we present a comprehensive framework for the analysis of multi channel reception systems using either non coherent or differentially coherent detectors diversity systems with practical i e noisy channel estimators and transmitted reference tr receiver architectures working in frequency selective fading channels and ii we show that the framework can be efficiently used for performance assessment of wireless systems over generalized fading channels and under mild assumptions over generalized fading channels further impaired by in band multi tone interference

accurate evaluation for mdpsk with noncoherent diversity the error probability analysis of m ary differential phase shift keying signals with noncoherent diversity combining over general fading channels is not available in the literature except for some simple cases the difficulty lies in the philosophy which attempts to explicitly determine the phase distribution expressions of the received signal and this often leads to a mathematically intractable issue in this paper we take a novel approach by formulating the phase distribution in terms of joint moment generating functions of the real and imaginary parts of the decision variable at the receiver output we further derive fast convergent techniques for two dimensional 2 d inverse laplace transform enabling us to accurately evaluate the phase distribution the error probability formulas thus obtained involve a twofold integral which can be efficiently evaluated by using our algorithms developed on the basis of the 2 d trapezoidal summation and gauss chebyshev quadrature the new technique is very general taking into account the effects of arbitrary diversity order symbol alphabet size m and arbitrary diversity branches correlation numerical results are also presented for illustration

new simple closed form ber expressions for mrc diversity bpsk in correlated rayleigh fading and cci exact closed form expressions are derived for the bit error rate of binary phase shift keying in rayleigh fading channels with maximal ratio combining diversity in the presence of cochannel interference and additive white gaussian noise the desired signal and the interferer signals are subject to correlated rayleigh fading and binary phase shift keying modulation is used by all users

locally strongly convex affine hyperspheres realizing chen s equality abstract in affine differential geometry of hypersurface c scharlach et al found an inequality involving intrinsic and extrinsic curvatures and classified elliptic and hyperbolic affine hyperspheres realizing the equality if an affine invariant 2 dimensional distribution d 2 is integrable in this paper we continue to study affine hyperspheres realizing the equality including parabolic affine hyperspheres as main results firstly we classify parabolic affine hyperspheres realizing the equality if its scalar curvature is constant or d 2 is integrable next by introducing a well defined 3 dimensional distribution d 3 when d 2 is not integrable we complete the classification of locally strongly convex affine hyperspheres realizing the equality if d 3 is integrable finally we pose a conjecture and a problem in order to determine all affine hyperspheres attaining the equality

a unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels we present a unified approach to determine the exact bit error rate ber of noncoherent and differentially coherent modulations with single and multichannel reception over additive white gaussian noise and generalized fading channels the multichannel reception results assume independent fading in the channels and are applicable to systems that employ post detection equal gain combining our approach relies on an alternate form of the marcum q function and leads to expressions of the ber involving a single finite range integral which can be readily evaluated numerically aside from unifying the past results the new approach also allows for a more general solution to the problem in that it includes many situations that in the past defied a simple solution the best example of this occurs for multichannel reception where the fading on each channel need not be identically distributed nor even distributed according to the same family of distributions

complete affine hypersurfaces part i the completeness of affine metrics on etudie les proprietes des hypersurfaces invariantes sous le groupe des transformations affines unimodulaires

ber analysis of bpsk signals in ricean faded cochannel interference the bit error rate of a binary phase shift keying bpsk signal in ricean faded cochannel interference is studied a precise bit error rate expression is derived for a bandlimited bpsk signal corrupted by an arbitrary number of asynchronous ricean faded interfering signals an error rate estimation based on a saddlepoint approximation is also provided it is shown that this approximation is highly accurate for the special case when there is one synchronous ricean faded interfering signal in an interference limited environment an asymptotic error rate analysis based on the saddle point approximation reveals that fading in the cochannel interfering signal can have different impacts on the desired user s error rate performance our study shows that when the signal to interference ratio sir is sufficiently large the error floor of the desired user signal decreases with an increase of the rice factor in the interfering user s fading channel however the opposite phenomenon can happen when the sir is small

singularities of improper affine maps and their hessian equation abstract we study improper affine spheres with some admissible singularities called improper affine maps and associated to the unimodular hessian equation in particular we characterize when a curve of r 3 is the singular curve of some improper affine map with prescribed cuspidal edges and swallowtails also we consider improper affine maps with isolated singularities and show some similarities and differences between the hessian 1 equation and the hessian 1 equation as a consequence we construct global examples with the desired singularities

some new twists to problems involving the gaussian probability integral using an alternate form of the gaussian probability integral discovered a number of years ago it is shown that the solution to a number of previously considered communication problems can be simplified and in some cases made more accurate i e exact rather than bounded these problems include the evaluation of 1 the bit error probability of uncoded phase shift keying psk with costas loop tracking 2 word error probability of antipodal modulation in the presence of fading 3 bit error probability of coded m ary psk mpsk over the memoryless fading channel with given channel state information 4 conditional symbol error probability of mpsk in the presence of carrier synchronization error and 5 the average error probability for the binary additive white gaussian noise awgn intersymbol interference channel also obtained is a generalization of this new alternate form to the case of a two dimensional gaussian probability integral with arbitrary correlation which can be used to evaluate the symbol error probability of mpsk with i q unbalance

calculating error probabilities for intersymbol and cochannel interference the probability of error in a binary symmetric channel with intersymbol interference and additive noise is efficiently calculated by numerical quadrature of a laplace inversion integral along a contour in the complex plane passing through a saddlepoint of the integrand for gaussian noise a bound is set on the truncation error incurred by necessarily restricting the integration to a finite interval the probability of error resulting from cochannel interference is calculated by a similar technique

error rates of dpsk systems with mimo egc diversity reception over rayleigh fading channels this paper analyzes the average bit error probability bep of the differential binary and quaternary phase shift keying dbpsk and dqpsk respectively with multiple input multiple output mimo systems employing postdetection equal gain combining mimo egc diversity reception over rayleigh fading channels finite closed form expressions for the average bep of dbpsk and dqpsk are presented two approaches are introduced to analyze the error rate of dqpsk the proposed structure for the differential phase shift keying dpsk with mimo egc provides a reduced complexity and low cost receiver for mimo systems compared to the coherent phase shift keying system psk with mimo employing maximal ratio combining mimo mrc diversity reception finally a useful procedure for computing the associated legendre functions of the second kind with half odd integer order and arbitrarily degree is presented

boundary regularity for the monge ampere and affine maximal surface equations in this paper we prove global second derivative estimates for solutions of the dirichlet problem for the monge ampere equation when the inhomoge neous term is only assumed to be holder continuous as a consequence of our approach we also establish the existence and uniqueness of globally smooth solutions to the second boundary value problem for the affine maximal surface equation and affine mean curvature equation

quadratic forms in random variables theory and applications textbook for a one semester graduate course for students specializing in mathematical statistics or in multivariate analysis or reference for theoretical as well as applied statisticians confines its discussion to quadratic forms and second degree polynomials in real normal random vectors and matr

rigidity theorems for the entire solutions of 2 hessian equation abstract in this paper we prove some rigidity theorems for the entire 2 convex solutions of 2 hessian equation in euclidean space as an application we obtain a bernstein type theorem for global special lagrangian graphs

a closed form ber expression for bpsk using mrc in correlated cci and rayleigh fading an exact closed form expression for the average bit error rate ber of coherent bpsk using maximal ratio combining mrc with correlated branches in the presence of cochannel interference cci and noise is derived this expression is valid for an arbitrary correlation structure under the assumption that the branch gains of the desired user signal and interfering signals experience correlated rayleigh fading with the same correlation eigenvector matrix

a regularity theorem of the abreu equation abstract in this paper we prove a regularity theorem for the abreu equation under the assumption that the ricci curvature is bounded

classification of complete projective special real surfaces we determine all complete projective special real surfaces by the supergravity r map they give rise to complete projective special kahler manifolds of dimension 6 which are distinguished by the image of their scalar curvature function by the supergravity c map the latter manifolds define in turn complete quaternionic kahler manifolds of dimension 16