the bounds on the solutions of certain two dimensional delay dynamic systems on time scales by means of a new linear gronwall bellman inequality on time scales and an elementary inequality the bounds on the solutions of a class of new nonlinear two dimensional dynamic systems on time scales are obtained

some new nonlinear volterra fredholm type discrete inequalities and their applications some new explicit bounds on solutions to a class of new nonlinear volterra fredholm type discrete inequalities are established which can be used as effective tools in the study of certain sum difference equations application examples are also indicated

oscillation for nonlinear second order dynamic equations on a time scale abstract we obtain some oscillation criteria for solutions to the nonlinear dynamic equation x q t x p t f x 0 on time scales in particular no explicit sign assumptions are made with respect to the coefficients p t q t we illustrate the results by several examples including a superlinear emden fowler dynamic equation

explicit bounds on certain integral inequalities abstract in this paper explicit bounds on retarded gronwall bellman and bihari like integral inequalities and their two independent variable generalizations are established some applications are also given to illustrate the usefulness of one of our results

on the sphere decoding algorithm ii generalizations second order statistics and applications to communications in part i we found a closed form expression for the expected complexity of the sphere decoding algorithm both for the infinite and finite lattice we continue the discussion in this paper by generalizing the results to the complex version of the problem and using the expected complexity expressions to determine situations where sphere decoding is practically feasible in particular we consider applications of sphere decoding to detection in multiantenna systems we show that for a wide range of signal to noise ratios snrs rates and numbers of antennas the expected complexity is polynomial in fact often roughly cubic since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial this suggests that maximum likelihood decoding which was hitherto thought to be computationally intractable can in fact be implemented in real time a result with many practical implications to provide complexity information beyond the mean we derive a closed form expression for the variance of the complexity of sphere decoding algorithm in a finite lattice furthermore we consider the expected complexity of sphere decoding for channels with memory where the lattice generating matrix has a special toeplitz structure results indicate that the expected complexity in this case is too polynomial over a wide range of snrs rates data blocks and channel impulse response lengths

some new generalized volterra fredholm type finite difference inequalities involving four iterated sums in this paper based on some new generalized volterra fredholm type finite difference inequalities involving four iterated sums we derive some new explicit bounds for the unknown functions concerned these inequalities are of more general forms than some existing results in the literature and are generalization of the main results of ma j comput appl math 233 2010 2170 2180 as application of the established results we present a volterra fredholm sum difference equation and research the qualitative as well as quantitative properties for it

explicit bounds on some new nonlinear integral inequalities with delay the purpose of the present note is to establish some new delay integral inequalities which provide explicit bounds on unknown functions and generalize some results of li et al some new delay integral inequalities and their applications j comput appl math 180 2005 191 200 the inequalities given here can be used to investigate the qualitative properties of certain delay differential equations and delay integral equations

some new generalized gronwall bellman type discrete fractional inequalities some new gronwall bellman type discrete fractional inequalities are established explicit bounds for unknown functions in fractional inequalities are derived properties of solutions of one certain fractional difference equation are researched in this paper we present some new generalized gronwall bellman type discrete fractional inequalities including fractional sum inequalities and fractional difference inequalities these inequalities are of new forms compared with the existing results so far in the literature and can be used to provide explicit bounds for unknown functions concerned for illustrating the effectiveness of the presented results we apply them to research qualitative and quantitative properties for the solutions of an ivp with respect to a fractional difference equation

some new delay integral inequalities and their applications the main objective of this paper is to establish some new delay integral inequalities which provide explicit bounds on unknown functions the inequalities given here can be used as tools in the qualitative theory of certain delay differential equations and delay integral equations

initial value problem for first order integro differential equation of volterra type on time scales abstract in this paper we combine the monotone iterative technique with fixed point theory to investigate the extremal solutions of nonlinear integro differential equations on time scales several important lemmas and existence criteria are obtained

generalized gronwall bellman type delay dynamic inequalities on time scales and their applications abstract in this paper we establish some new gronwall bellman type delay dynamic inequalities on time scales which can be used as a handy tool in the investigation of qualitative as well as quantitative analysis of solutions of delay dynamic equations on time scales our results generalize the main results of ou iang l ou iang the boundedness of solutions of linear differential equations y a t y 0 shuxue jinzhan 3 1957 409 415 jiang f c jiang f w meng explicit bounds on some new nonlinear integral inequality with delay j comput appl math 205 2007 479 486 and yuan z l yuan x w yuan f w meng some new delay integral inequalities and their applications appl math comput 208 2009 231 237

approximation of the zakai equation for nonlinear filtering in this paper we consider numerical approximations of solutions to the zakai equation time discretization based on the implicit milshtein and euler methods and galerkin approximation in the spatial coordinates are investigated convergence and rate of convergence of approximation methods are established

the inequalities for some types of q integrals using the restriction of the q integral over a b to a finite sum and q integral of riemann type we establish new integral inequalities of q chebyshev type q gruss type q hermite hadamard type and cauchy buniakowsky type some inequalities which include the boundaries of functions are also indicated

integer parameter estimation in linear models with applications to gps we consider parameter estimation in linear models when some of the parameters are known to be integers such problems arise for example in positioning using carrier phase measurements in the global positioning system gps where the unknown integers enter the equations as the number of carrier signal cycles between the receiver and the satellites when the carrier signal is initially phase locked given a linear model we address two problems 1 the problem of estimating the parameters and 2 the problem of verifying the parameter estimates we show that with additive gaussian measurement noise the maximum likelihood estimates of the parameters are given by solving an integer least squares problem theoretically this problem is very difficult computationally np hard verifying the parameter estimates computing the probability of estimating the integer parameters correctly requires computing the integral of a gaussian probability density function over the voronoi cell of a lattice this problem is also very difficult computationally however by using a polynomial time algorithm due to lenstra lenstra and lovasz 1982 the lll algorithm the integer least squares problem associated with estimating the parameters can be solved efficiently in practice sharp upper and lower bounds can be found on the probability of correct integer parameter estimation we conclude the paper with simulation results that are based on a synthetic gps setup

improvement of some ostrowski gruss type inequalities abstract in this paper we improve and further generalize some ostrowski gruss type inequalities involving bounded once and twice differentiable mappings

integral inequalities for retarded volterra equations integral inequalities are very useful in the qualitative analysis of differential and integral equations starting with o lipovan a retarded gronwall like inequality and its applications j math anal appl 252 2000 389 401 several recent investigations see o lipovan a retarded integral inequality and its applications j math anal appl 285 2003 436 443 b g pachpatte explicit bounds on certain integral inequalities j math anal appl 267 2002 48 61 b g pachpatte on some retarded integral inequalities and applications j inequal pure appl math 3 2002 article 18 b g pachpatte on a certain retarded integral inequality and its applications j inequal pure appl math 5 2004 article 19 b g pachpatte on some new nonlinear retarded integral inequalities j inequal pure appl math 5 2004 article 80 were devoted to retarded integral inequalities in this paper we consider the case of retarded volterra integral equations we establish bounds on the solutions and by means of examples we show the usefulness of our results in investigating the asymptotic behaviour of the solutions

estimates on some power nonlinear volterra fredholm type discrete inequalities and their applications some explicit bounds on solutions to a class of new power nonlinear volterra fredholm type discrete inequalities are established which can be used as effective tools in the study of certain sum difference equations application examples are also given

remez type inequalities and their applications abstract the remez inequality gives a sharp uniform bound on 1 1 for real algebraic polynomials p of degree at most n if the lebesgue measure of the subset of 1 1 where p is at most 1 is known remez type inequalities give bounds for classes of functions on a line segment on a curve or on a region of the complex plane given that the modulus of the functions is bounded by 1 on some subset of prescribed measure this paper offers a survey of the extensive recent research on remez type inequalities for polynomials generalized nonnegative polynomials exponentials of logarithmic potentials and muntz polynomials remez type inequalities play a central role in proving other important inequalities for the above classes the paper illustrates the power of remez type inequalities by giving a number of applications

some inequalities via probabilistic method in this paper we obtain some new inequalities by means of the mean inequalities of random variables which include generalizations of the greub rheinboldt inequality

some delay integral inequalities on time scales in this paper using gronwall s inequality we investigate some delay integral inequalities on time scales which provide explicit bounds on unknown functions our results unify and extend some delay integral inequalities and their corresponding discrete analogues the inequalities given here can be used as tools in the qualitative theory of certain classes of delay dynamic equations on time scales

dynamic equations on time scales a survey the study of dynamic equations on time scales which goes back to its founder stefan hilger 1988 is an area of mathematics that has recently received a lot of attention it has been created in order to unify the study of differential and difference equations in this paper we give an introduction to the time scales calculus we also present various properties of the exponential function on an arbitrary time scale and use it to solve linear dynamic equations of first order several examples and applications among them an insect population model are considered we then use the exponential function to define hyperbolic and trigonometric functions and use those to solve linear dynamic equations of second order with constant coefficients finally we consider self adjoint equations and more generally so called symplectic systems and present several results on the positivity of quadratic functionals

on retarded integral inequalities and their applications abstract the main results of j math anal appl 285 2003 436 443 are here generalized to the following retarded integral inequalities u m t c m m n m m n 0 t f s u n s w u s g s u n s d s and u m t c m m n m m n 0 t f s u n s w u s d s m m n 0 t g s u n s w u s d s where m n 0 are constants and t r 0 the results given here can be applied to the global existence of solutions to differential equations with time delay

some generalized integral inequalities and their applications in this paper we generalize some integral inequalities to more general situations we establish bounds on the solutions and by means of examples we show the usefulness of our results in investigating the global existence of the solutions of integral equations and differential equations

discrete non linear inequalities and applications to boundary value problems in this paper we generalize some existing discrete gronwall bellman ou iang type inequalities to more general situations these are in turn applied to study the boundedness uniqueness and continuous dependence of solutions of certain discrete boundary value problem for difference equations

some new delay integral inequalities and their applications the aim of the present paper is to establish some new delay integral inequalities which provide explicit bounds on unknown functions the inequalities given here can be used as tools in the qualitative theory of certain delay differential equations and delay integral equations

on retarded integral inequalities in two independent variables and their applications the object of this paper is to establish some nonlinear retarded integral inequalities in two independent variables which can be used as handy tools in the theory of partial differential and integral equations with time delays

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

maximum likelihood sequence estimation from the lattice viewpoint considers the problem of data detection in multilevel lattice type modulation systems in the presence of intersymbol interference and additive white gaussian noise the conventional maximum likelihood sequence estimator using the viterbi algorithm has a time complexity of o m sup spl nu 1 operations per symbol and a space complexity of o spl delta m sup spl nu storage elements where m is the size of input alphabet spl nu is the length of channel memory and spl delta is the truncation depth by revising the truncation scheme and viewing the channel as a linear transform the authors identify the problem of maximum likelihood sequence estimation with that of finding the nearest lattice point from this lattice viewpoint the lattice sequence estimator for pam systems is developed which has the following desired properties 1 its expected time complexity grows as spl delta sup 2 as snr spl rarr spl infin 2 its space complexity grow as spl delta and 3 its error performance is effectively optimal for sufficiently large m a tight upper bound on the symbol error probability of the new estimator is derived and is confirmed by the simulation results of an example channel it turns out that the estimator is effectively optimal for m spl ges 4 and the loss in signal to noise ratio is less than 0 5 db even for m 2 finally limitations of the proposed estimator are also discussed

a retarded integral inequality and its applications we prove a retarded nonlinear integral inequality and present some applications of it to the global existence of solutions to differential equations with time delay