a survey on oscillation of impulsive delay differential equations this paper presents a systematic development of the oscillatory results for the linear and nonlinear impulsive delay differential equations we also discuss linearized oscillation theory and give some applications to mathematical biology

fixed points and stability of neutral stochastic delay differential equations in this paper we consider a linear scalar neutral stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions an asymptotic mean square stability theorem with a necessary and sufficient condition is proved some well known results are improved and generalized

two classes of asymptotically different positive solutions of the equation y t f t yt abstract the equation y t f t y t is considered for t the existence of two classes of positive solutions which are asymptotically different is proved using two different techniques the method of monotone sequences and the retract method combined with razumikhin s technique with the aid of linear estimates of the right hand side of the equation considered inequalities for both types of positive solutions are given as well the results are illustrated by an example

first order variance of travel time in nonstationary formations 1 evaluating uncertainty in solute transport under nonstationary flow conditions is a computationally demanding task this is particularly true for cases with a two point covariance function of log conductivity depending on the actual positions of the points rather than their distance vector these may occur when the geological formation exhibits a trend nonstationarity can also be the result of uncertainty in the trend parameters of the mean log conductivity value or it may originate from conditioning of the log conductivity field to measurements of for example head or conductivity we present an efficient numerical method for evaluating the variance of travel time in such formations we cover cases in which the nonstationary covariance functions are constructed from stationary counterparts either by scaling functions or by summation with nonstationary functions resulting from marginalization or conditioning we apply a matrix based first order second moment fosm method for uncertainty propagation using the continuous adjoint state method for coupled systems to evaluate the sensitivity matrix the resulting matrix matrix multiplications are accelerated by fast fourier transformation fft techniques after periodic embedding of the covariance matrices referring to the stationary counterparts the combination of these methods makes it possible to compute the travel time uncertainty in domains discretized by several hundred thousand log conductivity values on standard personal computers within a reasonable time frame for demonstration we apply the method to a binary medium and a medium exhibiting a continuous trend in the covariance function in the latter application we also demonstrate the effects of marginalization and conditioning

perron type theorems for functional differential equations with infinite delay in a banach space for functional differential equations in a banach space we obtain some results on the asymptotic behavior of solutions which correspond to perron type theorems for differential equations without delay or with finite delay

h asymptotic stability by fixed point in neutral nonlinear differential equations with delay abstract we use fixed point theory to obtain h asymptotic stability results about the zero solution of nonlinear differential equations with functional delay neither boundedness of the deviations nor a fixed sign on the coefficients functions are asked an explicit estimation of the solutions is obtained and a necessary and sufficient condition is determined classical results are improved and generalized

travel time moments for sorbing solutes in heterogeneous domains under nonuniform flow conditions 1 a methodology for evaluating the unconditional and conditional moments of travel time for a sorbing solute is presented the approach is applicable for any flow configuration and for a wide range of mass transfer rate limited linear processes the methodology is applicable to the general case of spatially variable hydrological and chemical parameters the sorption model used to derive the temporal moments is that of a continuous distribution of mass rate coefficients haggerty and gorelick 1998 models such as instantaneous equilibrium first order and two site sorption kinetics among others can be considered as particular cases of this general model using a deterministic approach the low order moments of the breakthrough curves for reactive solutes can be obtained as a function of those for conservative tracers using a stochastic approach the unconditional low order statistics of the travel time moments can be obtained these moments depend on the statistics of two lagrangian functions the travel time for a conservative solute and an integral of the variations of the chemical parameters weighted by the inverse local velocity along the trajectory finally conditional temporal moments are derived moments can be conditioned to any type of information hard or soft hydraulic or geochemical conditioning is found to reduce uncertainty characterized by a reduction in the variance of the travel time the general results are particularized for both uniform in the mean and convergent flow conditions and for simple sorption models such as linear instantaneous equilibrium and first order kinetics in all such cases close form results based on small perturbations expansions are presented for the travel time moments

asymptotic stability of impulsive stochastic partial differential equations with infinite delays in this paper we study the existence and asymptotic stability in pth moment of mild solutions to nonlinear impulsive stochastic partial differential equations with infinite delay by employing a fixed point approach sufficient conditions are derived for achieving the required result these conditions do not require the monotone decreasing behaviour of the delays

variable order fractional discrete time recurrent neural networks abstract discrete fractional calculus is suggested to describe neural networks with memory effects fractional discrete time recurrent neural network is proposed on an isolated time scale stability results are investigated via banach fixed point technique the attractive solution space is constructed and stability conditions are provided furthermore short memory and variable order fractional neural networks are given according to the stability conditions two and three dimensional numerical examples are used to demonstrate the theoretical results

the stability of neutral stochastic delay differential equations with poisson jumps by fixed points in the paper the asymptotic mean square stability of the zero solution for neutral stochastic delay differential equations with poisson jumps is studied by fixed points theory without lyapunov functions the coefficient functions have not been asked for a fixed sign and the sufficient condition for mean square stability has been obtained therefore some well known results are improved and generalized

explicit exponential stability conditions for linear differential equations with several delays abstract new explicit conditions of exponential stability are obtained for the nonautonomous linear equation x t k 1 m a k t x h k t 0 where k 1 m a k t 0 h k t t by comparing this equation with a nonoscillatory exponentially stable equation of the form x t k i a k t x g k t 0 where i 1 m g k t t every comparison result gives 2 m 1 different stability conditions due to the a priori choice of a subset i

fixed points and stability in linear neutral differential equations with variable delays in this paper we consider the asymptotic stability of a generalized linear neutral differential equation with variable delays by using the fixed point theory an asymptotic stability theorem with a necessary and sufficient condition is proved which improves and generalizes some results due to burton 2003 3 zhang 2005 14 raffoul 2004 13 and jin and luo 2008 12 two examples are also given to illustrate our results

three dimensional steady state flow to a well in a randomly heterogeneous bounded aquifer 1 we consider flow in a confined aquifer of uniform thickness due to a well of zero radius that fully penetrates the aquifer and discharges at a constant rate if the lateral extent of the aquifer is infinite a steady state flow regime never develops it is however well known that if the aquifer is additionally uniform a quasi steady state region extends from the well out to a cylindrical surface whose radius expands as the square root of time on the expanding surface head is uniform and time invariant inside this surface head at any time is described by a steady state solution a rigorous analysis of the analogous situation in a randomly heterogeneous aquifer would require the solution of a three dimensional transient stochastic flow problem in an aquifer of infinite lateral extent here we take a different approach by developing a three dimensional steady solution for mean flow to a well in a randomly heterogeneous aquifer with a cylindrical prescribed head boundary in analogy to the uniform case we expect our solution to approximate a quasi steady state region whose radius is initially small in comparison to the horizontal correlation scale of log conductivity but grows with time to become eventually much larger we treat log conductivity as a statistically homogeneous random field characterized by a gaussian spatial covariance function that may have different horizontal and vertical correlation scales our solution consists of analytical expressions for the ensemble mean and variance of head in the aquifer to second order in the standard deviation of log conductivity it is based on recursive approximations of exact nonlocal moment equations that are free of distributional assumptions and so apply to both gaussian and non gaussian log conductivity fields the analytical solution is supported by numerical monte carlo simulations it clarifies the manner in which relationships between the horizontal and vertical scales of the quasi steady state region and those of statistical anisotropy impact the statistical moments of drawdown and the equivalent and apparent hydraulic conductivities of the aquifer both conductivities are shown to exhibit a scale effect by growing with distance from the well within a radius of one to two horizontal integral scales from it

on asymptotic convergence and boundedness of stochastic systems with time delay analyzing the long term behavior of a nonlinear dynamical system is an important but challenging task especially in the presence of noise and delays this paper investigates asymptotic convergence and boundedness properties of stochastic systems with time delay we are particularly interested in asymptotic convergence that may not be exponential as observed in many practical applications general criteria for checking both moment and almost sure asymptotic convergence and boundedness are established such criteria are mainly motivated by stochastic systems with time varying coefficients and multiple delays and or different orders of nonlinearities as shown by several examples the existing results cannot be applied to analyze such systems thus we generalize the existing theory by allowing the diffusion operator associated with a lyapunov function to satisfy a weaker assumption which involves time varying coefficients and several auxiliary functions to cope with possible multiple delays and or different orders of nonlinearities the results presented in this paper provide an effective tool for checking asymptotic convergence and boundedness properties of general stochastic nonlinear systems with time delay

flow to partially penetrating wells in unconfined heterogeneous aquifers mean head and interpretation of pumping tests 1 a partially penetrating well of length lw and radius rw starts to pump at constant discharge qw at t 0 from an unconfined aquifer of thickness d the aquifer is of random and stationary conductivity characterized by kg geometric mean y2 log conductivity variance and i and iv the horizontal and vertical integral scales the flow problem is solved under a few simplifying assumptions commonly adopted in the literature for homogeneous media rw lw 1 linearization of the free surface condition and constant drainable porosity n additionally it is assumed that rw i 1 and lw iv 1 to simplify the well boundary conditions and that a first order approximation in y2 extended to finite y2 on a conjectural basis is adopted the solution is obtained for the mean head field h r z t and the associated water table equation the main result of the analysis is that the flow domain can be divided into three zones for h 1 the neighborhood of the well r i where h qw lwka h0 r z tkefuv nd with h0 being the zero order solution pertaining to a homogeneous and isotropic aquifer ka being the conductivity arithmetic mean and kefuv being the effective vertical conductivity in mean uniform flow 2 an exterior zone r i in which h qw lwkefuh h0 r z tkefuv nd with kefuh being the horizontal effective conductivity and 3 an intermediate zone in which the solution requires a few numerical quadratures not carried out here the application to pumping tests reveals that identification of the aquifer parameters for homogeneous and anisotropic aquifers by commonly used methods can be applied for the drawdown measured in an observation well of length lowiv to ensure exchange of space and ensemble head averages in the second zone in order to identify kefuh kefuv and n in contrast the use of the drawdown in the well first zone leads to an overestimation of kefuh by the factor ka kefuh

the extended thiem s solution including the impact of heterogeneity 1 in this study we present a formula for the hydraulic head describing the mean drawdown of a three dimensional steady state pumping test in heterogeneous anisotropic porous media effectively by modeling the hydraulic conductivity k x as spatial random function and using the upscaling method coarse graining we succeed in deriving a closed form solution hefw r which we understand as an extension of thiem s formula to heterogeneous media the solution hefw r does not only depend on the radial distance r but accounts also for the statistics of k x namely geometric mean kg variance 2 horizontal correlation length l and anisotropy ratio e we perform a sensitivity analysis on the parameters of hefw r and implement an inverse estimation strategy using numerical pumping tests we show the applicability of hefw r on the interpretation of drawdown data this will be done for both an ensemble of as well as for single pumping tests making use of the inverse estimation method we find excellent agreement of estimated parameters with initial values in particular for the horizontal correlation length

three dimensional stochastic analysis of macrodispersion in aquifers the dispersive mixing resulting from complex flow in three dimensionally heterogeneous porous media is analyzed using stochastic continuum theory stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three dimensional statistically anisotropic input covariance describing the hydraulic conductivity with a statistically isotropic input covariance the longitudinal macrodispersivity is convectively controlled but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term with an arbitrarily oriented anisotropic conductivity covariance all components of the macrodispersivity tensor are convectively controlled and the ratio of transverse to longitudinal dispersivity is of the order of 10 1 in this case the off diagonal components of the dispersivity tensor are significant being numerically larger than the diagonal transverse terms and the transverse dispersion process can be highly anisotropic dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and monte carlo simulations the theory which treats the asymptotic condition of large displacement indicates that a classical gradient transport fickian relationship is valid for large scale displacements

study of the stability in nonlinear neutral differential equations with functional delay using krasnoselskii burton s fixed point in this paper we use a modification of krasnoselskii s fixed point theorem introduced by burton 2002 see 6 theorem 3 to obtain stability results of the zero solution of the totally nonlinear neutral differential equations with functional delayx email protected ddtqt email protected gt xt email protected stability of the zero solution of this equation provided that h0 qt 0 gt 0 0 0 the caratheodory condition is used for the functions q and g

fixed points stability and exact linearization abstract we study the scalar equation x f t x x x b t g x t l 0 by means of contraction mappings conditions are obtained to ensure that each solution x t x t 0 0 as t the conditions allow f to grow as large as t but not as large as t 2 this is parallel to the classical result of smith quart j math oxford ser 12 2 1961 123 for the linear equation without a delay

stochastic analysis of well type flows in randomly heterogeneous porous formations 1 well type flow takes place in a heterogeneous porous formation where the transmissivity is modeled as a stationary random space function rsf general expressions for the covariances of the head and flux are obtained and analyzed the second order approximation of the mean radial flux is represented as the product between the solution valid in a homogeneous domain and a distortion term which adjusts according to the medium heterogeneity the spatial dependence of the function is studied in view of the formation identification problem the equivalent t eq and apparent t ap transmissivity are computed the important result is the relationship may be either eq or ap where th and tg represent the harmonic and the geometric means of the transmissivity respectively the position dependent weight is explicitly calculated indeed close to the well it yields which is understandable in view of the fact that the limit is equivalent to i which is the heterogeneity structure of a stratified formation nevertheless the effective transmissivity of a stratified formation is precisely th in contrast far from the well one has with the flow being slowly varying in the mean there it is shown that grows with increasing in the case of t eq the rate of growing is found similar to dagan and lessoff 2007 to be strongly dependent upon the position in the flow domain whereas t ap is a more robust property finally it is shown how the general results can be used for practical applications

a note on well boundary condition for flow through heterogeneous formations 1 in modeling flow toward wells it is mathematically convenient to replace the well by a singularity line along its axis in the case of homogeneous aquifers confined flow and fully penetrating wells the strength of the sources is constant and the common condition of constant head on the well is satisfied exactly it also leads to constant flux on the well envelope in the case of aquifers of spatially variable conductivity the constant head boundary condition can be satisfied accurately if the well radius is much smaller than the log conductivity horizontal integral scale by selecting a variable source strength that is proportional to the local conductivity along the well indelman et al 1996 fiori et al 1998 indelman 2003a 2003b in this case the equivalent conductivity tends to the arithmetic mean near the well it changes with distance approaching from above the effective conductivity in uniform horizontal mean flow far from the well selecting inadvertently a constant source strength violates the condition of constant well head the equivalent conductivity tends to the harmonic mean near the well and approaches from below the effective one in uniform mean flow the equivalent conductivity is derived for both types of sources for stratified formations as well as for aquifers of a three dimensional heterogeneous structure the implications on interpretation of head measurements by the two models is illustrated by a few examples

preservation of stability in delay equations under delay perturbations we consider a class of linear delay equations with perturbed time lags and present conditions which guarantee that the asymptotic stability of the trivial solution of the equation at hand is preserved under these perturbations as an example we show how our results can be used to obtain an estimate on the maximum allowable sampling interval in the stabilization of a hybrid system with feedback delays we also present applications of our perturbation theorem to obtain stability conditions for delay equations with multiple delays

stochastic analysis of unsaturated steady flows above the water table steady flowtakes place into a three dimensional partially saturated porous medium where due to their spatial variability the saturated conductivity ks and the relative conductivity kr are modeled as random space functions rsf s as a consequence the flow variables fvs i e pressure head and specific flux are also rsfs the focus of the present paper consists into quantifying the uncertainty of the fvs above the water table the simple expressions most of which in closed form of the second order moments pertaining to the fvs allow one to follow the transitional behavior from the zone close to the water table where the fvs are non stationary till to their far field limit where the fvs become stationary rsfs in particular it is shown how the stationary limits and the distance from the water table at which stationarity is attained depend upon the statistical structure of the rsfs ks kr and the infiltrating rate the mean pressure head k l has been also computed and it is expressed as k l 0 1 being a characteristic heterogeneity function which modifies the zero order approximation 0 of the pressure head valid for a vadose zone of uniform soil properties to account for the spatial variability of ks and kr two asymptotic limits i e close near field and away far field from the water table are derived into a very general manner whereas the transitional behavior of between the near far field can be determined after specifying the shape of the various input soil properties besides the theoretical interest results of the present paper are useful for practical purposes as well indeed the model is tested against to real data and in particular it is shown how it is possible for the specific case study to grasp the behavior of the fvs within an environment i e the vadose zone close to the water table which is generally very difficult to access by direct inspection

mackey glass model of hematopoiesis with non monotone feedback stability oscillation and control for the blood cell production model with a unimodal hump feedback email protected t email protected q ny email protected q n y n email protected we review the known results and investigate generalizations of this equation permanence oscillation and stability of the positive equilibrium are studied for non autonomous equations including equations with a distributed delay in addition a linear control is introduced and possibilities to stabilize an otherwise unstable positive equilibrium are explored

a new approach to stability of impulsive functional differential equations in this work a new approach to stability theory of impulsive functional differential equations is proposed instead of putting all components of the state variable x in one liapunov function several functions of partial components of x which can be much easier constructed are used so that the conditions ensuring that stability are simpler and less restrictive also an example is given to illustrate the advantages of the obtained results

fixed point theorems for the sum of two weakly sequentially continuous mappings abstract in the present paper we prove some krasnosel skii leray schauder type fixed point theorems for weak topology some fixed point theorems for the sum of two weakly sequentially continuous mappings are also presented our results extend and improve on ones from several earlier works

nonlocal properties of nonuniform averaged flows in heterogeneous media the properties of nonuniform average potential flows in media of stationary random conductivity are studied the mathematical model of average flow is derived as a system of governing equations to be satisfied by mean velocity and mean head the averaged darcy s law determines the effective conductivity as an integral operator of the convolution type relating the mean velocity to the mean head gradient in a nonlocal way in fourier domain the mean velocity is proportional to the mean head gradient the coefficient of proportionality is referred to as the effective conductivity tensor and is derived by perturbation methods in terms of functionals of the conductivity spatial moments it is shown that the effective conductivity cannot be defined uniquely for potential flows however this nonuniqueness does not affect the spatial distribution of the mean head and velocity analytical expressions of the effective conductivity tensor are derived for two and three dimensional flows and for exponential and gaussian correlations of isotropic conductivity the fundamental solution of the governing equations in effective media mean green function is calculated for the same cases two new asymptotic models of the averaged darcy s law are developed to be applicable to large and small scales of heterogeneity several asymptotic expansions of tue two dimensional and three dimensional mean green functions are derived for exponential and gaussian correlations

effective groundwater model parameter values influence of spatial variability of hydraulic conductivity leakance and recharge a stochastic simulation approach was used to inspect the influence of spatial variability in aquifer and recharge properties on effective averaged groundwater model parameters a two dimensional unconfined aquifer model was set up for an area similar to that near livermore california monte carlo simulations were generated for different sets of spatial correlation structures assuming stationarity and an exponential semivariogram for each monte carlo realization groundwater flow was simulated and estimates of the means and standard deviations of the hydraulic head were obtained nine different cases were studied involving different correlation lengths of hydraulic conductivity conditional simulations parameter zonation and spatial recharge distributions results indicate that there is no single uniform value of the hydraulic conductivity that reproduces the expected head values spatial averaging to obtain effective values was based on the p norm power norm which ranges from 1 for the arithmetic mean to 1 for the harmonic mean with 0 representing the geometric mean for the unconditional case the 0 4 p norm seems to best reproduce the expected values the 0 2 p norm gave the best result for the conditional simulation case if the geometric mean were used instead the heads would deviate from the expected heads by about 2 m near the wells some value between the arithmetic and the geometric means of riverbed leakance will give results close to the expected head values the arithmetic mean of aerially distributed recharge produced results with small deviations from the expected head values these particular results may only apply to this modeled system as the pumping pattern and magnitudes exhibited strong influences on zones of maximum head deviation the implication of this work is that if an effective hydraulic conductivity is used in a simulation model it must be selected for a particular set of wells and pumping rates in an aquifer with significant pumping centers the best effective value for a two dimensional unconfined flow model is most likely between the geometric and harmonic mean if the wells are turned off the effective hydraulic conductivity for that flow model reverts to the geometric mean

remark on krasnoselskii s fixed point theorem abstract a well known result due to krasnoselskii ensures the existence of a fixed point for an operator k a b which is defined on a non empty bounded closed convex subset s of a banach space x where i a is a contraction ii b is a compact operator and iii a s b s s in the present note an easy sufficient condition for fulfilling iii in the case of a locally convex space is given an application to the existence of solutions of a nonlinear integral equation illustrates this result

stabilities in fdes by schauder s theorem abstract in a series of papers burton and furumochi dyn syst appl 10 2001 89 116 funkcial ekvac 44 2001 71 82 nonlinear anal 49 2002 445 454 dyn syst appl 11 2002 499 521 nonlinear stud to appear burton nonlinear stud 9 2002 181 190 furumochi qualitative theor differential equations to appear stability properties of solutions of fdes have been investigated by means of fixed point theory here we obtain new stability results for super linear fdes by using schauder s first theorem and a weighted norm and show some examples

correlation structure of flow variables for steady flow toward a well with application to highly anisotropic heterogeneous formations the study a continuation of that of indelman et al 1996 aims at deriving the second order moments of flow variables such as hydraulic head its gradient and the specific discharge for steady flow toward a fully penetrating well in a confined heterogeneous aquifer the log conductivity y ln k is modeled as a three dimensional stationary function of gaussian correlation of anisotropy ratio e by using first order approximations in 2y and e we derive the variance and the vertical integral scale of the piezometric head h of its radial gradient er and of the radial component of the specific discharge qr owing to the nonuniformity of the average flow these quantities are functions of the distance from the well it is shown that the variances of the head 2h and of its gradient 2er as well as the crossvariance e y between er and y vanish at the well whereas the discharge variance 2qr tends to the product between the log conductivity variance 2y and the squared mean discharge qr 2 this behavior pertains to a stratified formation surrounding the well far from the well 75 horizontal y integral scales i the head variance approaches a constant value for r 10i the moments 2er 2qr and ery tend to the corresponding values for uniform flow but with the local mean head gradient replacing the constant one the head vertical integral scale grows indefinitely with r whereas the vertical integral scale of the flux is larger by one log conductivity vertical scale than the one prevailing in uniform flow this latter property is explained by the presence of the source line which increases the correlations in the vertical direction the present results may be used in identifying the log conductivity statistical parameters from flowmeter velocity measurements in piezometers surrounding pumping or injecting wells

transmissivity upscaling in numerical aquifer models of steady well flow unconditional statistics 1 numerical solution of regional scale aquifer flow requires discretizing the transmissivity t typically the numerical element scale r and the transmissivity integral scale i are both of the order of hundreds of meters then the upscaled block transmissivity is random and its statistical moments depend on those of t on flow conditions and on r i modeling y ln t as a two dimensional normally distributed stationary random field we derive unconditional statistics of the upscaled ln accurate to the first order in y2 for strongly nonuniform flow in a circular block of radius r centered on a well of radius rw in an unbounded domain after a proper definition it was found that the ensemble mean is approximately but not exactly equal to ln tg the geometric mean and that the variance ratio 2 y2 which depends on rw i and the shape of the correlation drops slowly from unity for r i 0 to approximately 0 6 for r i 10 hence the variance of the upscaled transmissivity in radial flow is larger than that determined previously for uniform flow additionally defining the equivalent teq as a deterministic value for which the solution of the flow problem renders directly the mean upscaled head drop and specific discharge we find that in radial flow teq th the harmonic mean and grows slowly with increasing r i whereas for mean uniform flow teq tg application of the procedure is illustrated for an example of aquifer with selected values of parameters

krasnoselskii s fixed point theorem for weakly continuous maps abstract we consider the sum a b m x where m is a weakly compact and convex subset of a banach space x a m x is weakly continuous and b l x with bp 1 p 1 an alternative condition is given in order to guarantee the existence of fixed points in m for a b some illustrative applications are given

global asymptotic stability of a class of nonautonomous integro differential systems and applications abstract in this paper we study the global asymptotic stability of a class of nonautonomous integro differential systems by constructing suitable lyapunov functionals we establish new and explicit criteria for the global asymptotic stability in the sense of definition 2 1 in the autonomous case we discuss the global asymptotic stability of a unique equilibrium of the system and in the case of periodic system we establish sufficient criteria for existence uniqueness and global asymptotic stability of a periodic solution also explored are applications of our main results to some biological and neural network models the examples show that our criteria are more general and easily applicable and improve and generalize some existing results

a note on stability of mackey glass equations with two delays abstract if the mackey glass equation x t r t a x h t 1 x g t x t with a 1 and 0 incorporates not one but two variable delays some new phenomena arise there may exist non oscillatory about the positive equilibrium unstable solutions the effect of possible absolute stability for certain a and disappears we obtain sufficient conditions for local and global stability of the positive equilibrium and illustrate the stability tests as well as new effects of two different delays with examples

stability results for stochastic delayed recurrent neural networks with discrete and distributed delays we present new conditions for asymptotic stability and exponential stability of a class of stochastic recurrent neural networks with discrete and distributed time varying delays our approach is based on the method using fixed point theory which do not resort to any liapunov function or liapunov functional our results neither require the boundedness monotonicity and differentiability of the activation functions nor differentiability of the time varying delays in particular a class of neural networks without stochastic perturbations is also considered examples are given to illustrate our main results

perron type stability theorems for neutral equations abstract in this paper we present two perron type asymptotic stability results for a neutral functional differential equation of the form x t sx t px t r d d t q t x t g t x t when the linear part x t sx t px t r is asymptotically stable in particular q and g are allowed to be unbounded functions of t and q need not be differentiable the results are based on krasnoselskii s fixed point theorem it is to be emphasized that unlike perron we obtain only asymptotic stability because of the unboundedness of q and g

stability in functional differential equations established using fixed point theory abstract in this paper we consider a nonlinear scalar delay differential equation with variable delays and give some new conditions for the boundedness and stability by means of krasnoselskii s fixed point theory a stability theorem with a necessary and sufficient condition is proved the results in t a burton stability by fixed point theory or liapunov s theory a comparison fixed point theory 4 2003 15 32 t a burton t furumochi asymptotic behavior of solutions of functional differential equations by fixed point theorems dynamic systems and applications 11 2002 499 519 b zhang fixed points and stability in differential equations with variable delays nonlinear analysis 63 2005 e233 e242 are improved and generalized some examples are given to illustrate our theory

asymptotic behavior of recursions via fixed point theory in this paper we provide a formulation of initial value problems for explicit and implicit difference equations in terms of abstract equations in sequence spaces they will be solved using appropriate fixed point theorems and we obtain quantitative attractivity properties

boundedness and persistence of delay differential equations with mixed nonlinearity for a nonlinear equation with several variable delays x t k 1 m f k t x h 1 t x h l t g t x t where the functions fk increase in some variables and decrease in the others we obtain conditions when a positive solution exists on 0 as well as explore boundedness and persistence of solutions finally we present sufficient conditions when a solution is unbounded examples include the mackey glass equation with non monotone feedback and two variable delays its solutions can be neither persistent nor bounded unlike the well studied case when these two delays coincide

nonstationary flow and nonergodic transport in random porous media 1 transport processes taking place in natural formations are often characterized by the spatial nonstationarity of flow field and the nonergodic condition of solute spreading the former may originate from statistical inhomogeneity of porous media properties or from the influence of boundary conditions as well as from conditioning procedures on measured data while the latter is generally due to the finite size of the solute source in real world applications these aspects sometimes dominate the transport phenomena and known literature results based on statistical homogeneity and ergodicity assumptions cannot be properly applied in this paper a method is proposed to handle different and concurrent causes of the flow field nonstationarity and to describe nonergodic transport of inert solutes by spatial moments in a domain of finite size the goal is reached by expanding the steady state flow equation in taylor series limited to the first order and by the recursive application of finite element fe method the unknowns are the piezometric head mean values and its derivatives in respect to the fluctuating porous media hydraulic conductivity from the latter the velocity statistics are derived on the basis of darcy s law according to the first order approximation by neglecting the pore scale dispersion the spatial moments of a solute plume are a posteriori obtained by a consistent lagrangian analysis starting from the knowledge of the velocity field covariance matrices without any restriction regarding the statistical homogeneity of flow and or ergodicity conditions the proposed method is here applied to investigate the influence of boundary conditions on the solute transport developing in a limited domain the results obtained from different test cases give a velocity field behavior in agreement with literature findings and allow us to define the nonergodic transport in bounded domains the comparison of the results with some ad hoc developed monte carlo simulations ensures the applicability of the proposed approach at least to the small heterogeneity cases here considered

analysis of the spatial structure of properties of selected aquifers data from 31 regional aquifers are analyzed to identify the horizontal spatial correlation structure of transmissivity hydraulic conductivity and storage coefficient three parameters are estimated the variance of small scale variability or nugget and the variance and integral scale range of an exponential covariance function the assumption of normality of the aforementioned geohydrologic parameters and their logarithmic transformations is also examined results are obtained which indicate that the logarithms of these properties generally pass normality tests

oscillation and stability of linear impulsive delay differential equations the main results of this paper are that the oscillation and the stability of a linear impulsive delay differential equation are equivalent respectively to the oscillation and the stability of a corresponding linear delay differential equation without impulses the results of this paper can be used to improve and derive some of the known results in the literature

fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays the fixed point theory is first used to consider the stability for stochastic partial differential equations with delays some conditions for the exponential stability in pth mean as well as in sample path of mild solutions are given these conditions do not require the monotone decreasing behavior of the delays which is necessary in t caraballo k liu exponential stability of mild solutions of stochastic partial differential equations with delays stoch anal appl 17 1999 743 763 ruhollan jahanipur stability of stochastic delay evolution equations with monotone nonlinearity stoch anal appl 21 2003 161 181 even in this special case our results also improve the results in t caraballo k liu exponential stability of mild solutions of stochastic partial differential equations with delays stoch anal appl 17 1999 743 763

steady flow toward wells in heterogeneous formations mean head and equivalent conductivity we consider steady flow of water in a confined aquifer toward a fully penetrating well of radius rw figure 1 the hydraulic conductivity k is modeled as a three dimensional stationary random space function the two point covariance of y in k kg is of axisymmetric anisotropy with i and i the horizontal and vertical integral scales respectively and kg the geometric mean of k unlike previous studies which assumed constant flux the well boundary condition is of given constant head figure 1 the aim of the study is to derive the mean head h and the mean specific discharge q as functions of the radial coordinate r and of the parameters y2 e i i and rw i an approximate solution is obtained at first order in y2 by replacing the well by a line source of strength proportional to k and by assuming ergodicity i e equivalence between space averages over the vertical and h q ensemble means an equivalent conductivity keq is defined as the fictitious one of a homogeneous aquifer which conveys the same discharge q as the actual one for the given head hw in the well and a given head in a piezometer at distance r from the well this definition corresponds to the transmissivity determined in a pumping test by an observer that measures hw andq the main result of the study is the relationship 19 keq ka 1 kefu where ka is the conductivity arithmetic mean and kefu is the effective conductivity for mean uniform flow in the horizontal direction in the same aquifer the weight coefficient 10 has the simple approximate expression ln r i in r rw near the well 0 and keq ka which is easily understood since for rw i 1 the formation behaves locally like a stratified one in contrast far from the well 1 and keq kefu the flow being slowly varying there since ka kefu our result indicates that the transmissivity is overestimated in a pumping test in a steady state and it decreases with the distance from the well however the difference between ka and kefu is small for highly anisotropic formations for which e 1 a nonlocal effective conductivity which depends only on the heterogeneous structure is derived in appendix a along the lines of indelman and abramovich 1994

generalizations of the krasnoselskii fixed point theorem abstract we obtain new generalized forms of the krasnoselskii theorem on fixed points for a sum of two operators and show that our new results encompass a number of previously known generalizations of the theorem

fixed points and stability in differential equations with variable delays abstract in this paper we consider a linear scalar differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically stable by means of fixed point theory these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions an asymptotic stability theorem with a necessary and sufficient condition is proved

macrodispersion in a radially diverging flow field with finite peclet numbers 1 perturbation theory approach we study the transport behavior of a tracer in a radially diverging heterogeneous velocity field making use of homogenization theory we derive effective transport equations these effective transport equations are very similar to those defined on the local scale however the local transport parameters such as local dispersion coefficients are replaced by effective dispersion coefficients for smoothly varying heterogeneous media explicit results for effective radial dispersion coefficients are derived starting with the purely advective transport behavior infinite peclet numbers we extend our calculations to transport with finite peclet numbers we find that the impact of molecular diffusion on the effective dispersivity differs from the impact of local dispersion including local dispersion leads to effective dispersivities which are constant and equivalent to the effective dispersivities found in uniform flow configurations in contrast effective dispersivities including diffusion are not constant but depend on the radial distance we compare the results found by homogenization theory with those derived by neuweiler et al this issue by standard method of moments

exponential stability of the split step θ method for neutral stochastic delay differential equations with jumps abstract the exponential mean square stability of the split step method for neutral stochastic delay differential equations nsddes with jumps is considered new conditions for jumps are proposed to ensure the exponential mean square stability of the trivial solution if the drift coefficient satisfies the linear growth condition it is shown that the split step method can reproduce the exponential mean square stability of the trivial solution for the constrained stepsize then by applying the chebyshev inequality and the borel cantelli lemma the almost sure exponential stability of both the trivial solution and the numerical solution can be obtained since split step method covers euler maruyama em method and split step backward euler ssbe method the conclusions are valid for these two methods moreover they can adapt to the nsddes and the sddes with jumps finally a numerical example illustrates the effectiveness of the theoretical results

on stability of some linear and nonlinear delay differential equations abstract new explicit conditions of exponential stability are obtained for the nonautonomous equation with several delays y t k 1 l a k t y h k t 0 by the following method several delays in the left hand side are chosen and the solution is estimated using an auxiliary ordinary differential equation y t k i a k t y t 0 where i 1 2 l is the chosen set of indices these results are applied to analyze the stability of the nonlinear equation x t k 1 l a k t x h k t f t x t x g 1 t x g m t by the first approximation it is to be noted that coefficients and delays are not assumed to be continuous functions

existence results for a generalized nonlinear hammerstein equation on l1 spaces abstract in this paper we are concerned with existence results for a nonlinear hammerstein integral equation acting on l 1 vector valued functions making use of the de blasi measure of weak noncompactness we establish a variant of the topological fixed point theorem of krasnosel skii for the sum of two operators without requiring weak compactness or weak continuity assumptions such a result provides an adequate tool for deriving an existence theory for problem 1 1

on oscillation of a second order impulsive linear delay differential equation abstract for the delay differential equation x t k 1 m a k t x g k t 0 g k t t with impulsive conditions x j a j x j 0 x j b j x j 0 a connection between the following properties is established nonoscillation of the differential equation and the corresponding differential inequality positiveness of the fundamental function and the existence of a solution of a generalized riccati inequality explicit conditions for nonoscillation and oscillation and comparison theorems are presented

fixed points and exponential stability for stochastic volterra levin equations in this paper we study a stochastic volterra levin equation by using fixed point theory we give some conditions for ensuring that this equation is exponentially stable in mean square and is also almost surely exponentially stable our result generalizes and improves on the results in 14 1 30

asymptotic integration of a system resulting from the perturbation of an h system z systems were introduced in lo with the intention of obtaining results about stability for a weakly stable system at least weaker than those given by exponential stability under some perturbations in this paper we get asymptotic formulae for these systems which state new results about asymptotic integration for nonlinear systems under general hypotheses moreover the corresponding results for linear systems give new insight about levinson s theorem on asymptotic integration in this way using the h systems we get a uniform treatment for the concept of stability and we verify that several classical theorems of stability take a precise form by the asymptotic formulae in section 2 we recall the definition and some properties of an h system and we state two new theorems about asymptotic behavior of solutions of perturbed h systems in section 3 some general results about asymptotic integration are given these results extend those given in lo in section 4 we apply the technique to the linear case finally in section 5 we show examples and applications and we study the emden fowler equation which originally does not satisfy the general hypothesis but can be transformed into one where they are satisfied 2 h systems let us consider the differential system

pth moment asymptotic stability of stochastic delayed hybrid systems with levy noise the problem of pth moment asymptotic stability analysis is considered for stochastic delayed hybrid systems with levy noise by virtue of ito s formula and m matrix theories we propose some sufficient conditions to guarantee the asymptotic stability and exponential stability of the system the criterion of mean square asymptotic stability is derived as well for delayed neural networks with levy noise a numerical example is provided to show the usefulness of the proposed asymptotic stability criterion

convergence of numerical solutions to stochastic delay differential equations with jumps this paper studies a class of stochastic delay differential equations with jumps sddejs explicit solutions can hardly be obtained for the sddejs appropriate numerical approximation schemes such as the euler scheme are needed to apply sddejs in practice or to study their properties in this paper it is proved that the euler approximation solutions converge to the analytic solution for sddejs under weaker conditions than the linear growth condition and global lipschitz condition an example is given for illustration

three dimensional numerical analysis of steady state pumping tests in heterogeneous confined aquifers 1 we study three dimensional steady state flow field generated by a fully penetrating well extracting a constant water discharge from a confined aquifer of constant thickness the hydraulic conductivity k is modeled as an axisymmetric stationary random space function and the flow equation is solved by using the seven node finite volume numerical scheme in view of application in aquifer characterization we analyze how the equivalent conductivity keq varies as a function of the distance from the extraction well the numerical simulations showed that the boundary condition at the well exerts a large impact on keq and that the first order solution in y2 obtained by indelman et al 1996 is valid up to y2 0 5 for higher values of y2 the first order solution overestimates keq with differences that for a given y2 reduce progressively as the formation becomes more anisotropic a simple inverse procedure based on keq obtained through cross well interference is finally proposed and tested with the objective of estimating the parameters of the geostatistical model of variability of the hydraulic conductivity a few parametric examples showed that a suitable interpretation of pumping tests can be used to safely estimate parameters such as the geometric mean of the hydraulic conductivity its variance and although with larger uncertainty the horizontal integral scale while the inference of the anisotropy ratio is highly uncertain and error prone

the boundedness and stability of neutral delay differential equations with damped stochastic perturbations via fixed point theory in this paper a class of neutral stochastic differential equation is studied by using the fixed point method some conditions are established for ensuring the equation is bounded asymptotically stable and j c stable in mean square then with borel cantelli lemma several sufficient conditions for almost surely asymptotic stability and j c stability are given the conditions do not require the boundedness of delays nor do they ask for the continuousness on the coefficient functions the results of this paper are new and they extend and improve previously known results

mackey glass equation with variable coefficients the mackey glass equation dndt r t n g t 1 n g t c b t n t is considered with variable coefficients and a nonconstant delay under rather natural assumptions all solutions are positive and bounded persistence and extinction conditions are presented for this equation in the case when there exists a constant positive equilibrium local asymptotic stability of the constant solution and oscillation about this equilibrium are analyzed the results are illustrated by numerical examples in particular it is demonstrated that with delay in both terms a solution with positive initial conditions may become negative

explicit stability conditions for multivariable nonautonomous retarded systems we consider retarded systems governed by the vector equation where r 0 is a matrix valued function defined on a real segment 0 and r 1 t is a matrix valued function defined on sharp explicit conditions for the exponential stability are derived

the stability of imitation dynamics with discrete distributed delays abstract this paper investigates the stability in a new model of imitation dynamics with discrete distributed delays some sufficient conditions of the asymptotical stability for the interior nash equilibrium of the imitation dynamics with multiple delay are obtained finally numerical experiments are displayed which support the theoretical results through the snowdrift game

prediction of steady state flow in nonuniform geologic media by conditional moments exact nonlocal formalism effective conductivities and weak approximation we consider the effect of measuring randomly varying local hydraulic conductivities k x on one s ability to predict steady state flow within a bounded domain driven by random source and boundary functions more precisely we consider the prediction of local hydraulic head h x and darcy flux q x by means of their unbiased ensemble moments h x and q x conditioned on measurements of k x these predictors satisfy a deterministic flow equation in which q x x h x r x where x is a relatively smooth unbiased estimate of k x and r x is a residual flux we derive a compact integral expression for r x which is rigorously valid for a broad class of k x fields including fractals it demonstrates that q x is nonlocal and non darcian so that an effective hydraulic conductivity does not generally exist we show analytically that under uniform mean flow the effective conductivity may be a scalar a symmetric or a nonsymmetric tensor or a set of directional scalars which do not form a tensor we demonstrate numerically that in two dimensional mean radial flow it may increase from the harmonic mean of k x near interior and boundary sources to the geometric mean far from such sources for cases where r x can neither be expressed nor approximated by a local expression we propose a weak integral approximation closure which appears to work well in media with pronounced heterogeneity and improves as the quantity and quality of k x measurements increase the nonlocal deterministic flow equation can be solved numerically by standard methods our theory shows clearly how the scale of grid discretization should relate to the scale quantity and quality of available data after providing explicit approximations for the second moments of head and flux prediction errors we conclude by discussing practical methods to compute x from noisy measurements of k x and to calculate required second moments of the associated estimation errors when k x is lognormal

spatial averaging of transmissivity in heterogeneous fields with flow toward a well steady state nonuniform flow in a heterogeneous medium is investigated using a combined numerical empirical approach the objective of the study is to determine the effective transmissivity of a square field with a constant head external boundary and a constant rate well at its center transmissivity at the point scale is modeled as an isotropic and multivariate lognormal spatial random function block transmissivities are defined using an empirical scaling up of point support values within the field the scaling process is a weighted spatial geometric averaging where log transmissivities are weighted by the inverse square of their distance from the well block transmissivities thus obtained and true effective values calculated using a numerical flow model are compared for realizations a finely discretized transmissivity field the principal finding of this study is that effective transmissivities obtained from the numerical flow model and block values obtained by spatial averaging are in excellent agreement for low to moderate variances of log transmissivity and moderately eccentric field geometries the geostatistical model for point scale transmissivity and the deterministic spatial averaging law are combined in order to create a geostatistical model for transmissivity at the block scale exact expressions are derived for the ensemble moments of block averaged transmissivities and well drawdowns in both the nonconditional case and the conditional case when transmissivity at the well bore is known the ensemble mean of block averaged transmissivity is found to decrease from the ensemble arithmetic mean toward the ensemble geometric mean as the field size becomes large compared to the integral range of spatial correlation this result contradicts earlier published work numerical results presented in this study also disagree with the analytical results of a recent stochastic analysis of specific discharge in radial systems

beyond thiem a new method for interpreting large scale pumping tests in heterogeneous aquifers 1 the heterogeneous character of aquifers prevents a consistent interpretation of pumping tests based on thiem s formula which has been developed for homogeneous aquifers we present a new mathematical method for interpreting an ensemble and single large scale pumping tests in heterogeneous confined isotropic aquifers by combining a multiscale technique called coarse graining with renormalization group analysis we derive an explicit formula for the coarse grained aquifer transmissivity the coarse grained transmissivity is dependent on the radial distance from the well close to the well it equals the local transmissivity in single pumping tests and the harmonic mean of the heterogeneous transmissivity field in ensemble pumping tests in the far field of the well the coarse grained transmissivity approaches the geometric mean the transition between both regimes is mainly determined by the transmissivities correlation length this relation is used for an inversely estimate of the statistical properties of the transmissivity such as its geometric mean in addition this method allows for determining aquifer structures characterized by a correlation length from a single pumping test while the variance can be estimated from pumping tests with ensemble averaged hydraulic heads

stability conditions for scalar delay differential equations with a non delay term abstract the problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non autonomous equations which include a non delay term and one or more delayed terms first we demonstrate that introducing a non delay term with a non negative coefficient can destroy stability of the delay equation next sufficient exponential stability conditions for linear equations with concentrated or distributed delays and global attractivity conditions for nonlinear equations are obtained the nonlinear results are applied to the mackey glass model of respiratory dynamics

stability results for neutral stochastic functional differential equations via fixed point methods in this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential systems with variable delays by using a contraction mapping principle name

a stochastic analysis of pumping tests in laterally nonuniform media conventional pumping test analysis methodology assumes that aquifer transmissivity is invariant in space the ramifications of this assumption are examined for hypothetical units whose variations in transmissivity are considered to be reasonable representations of variations possible in natural systems the dependence of pumping test transmissivity on spatial angular and radial and temporal location of observations and the method of drawdown analysis is assessed the dependence on the angular position of an observation well appears of little significance dependence on radial position however can be strong the dependence on the interval of time used in the pumping test analysis is only important in highly variable systems methods of drawdown analysis that yield identical estimates in uniform units yield differing estimates in nonuniform ones as a result of a difference in data fitting procedures a reasonable estimate of transmissivity at a regional scale can be obtained from a cooper jacob analysis applied at a large duration of pumpage in general conventional approaches for pumping test analysis should be viable in the nonuniform aquifers of the type considered here

on continuous solutions of a generalized cauchy riemann system with more than one singularity abstract we study the solvability of the riemann hilbert problem for a generalized cauchy riemann system with several singularities and reveal several new phenomenon for the number of continuous solutions we shall show that it depends not only on the index but also on the location and type of the singularities moreover it does not depend continuously on the coefficients of the equation

stochastic modeling of groundwater flow by unconditional and conditional probabilities 1 conditional simulation and the direct problem mathematical modeling of groundwater flow in heterogeneous porous formations of large extent is investigated the formation properties hydraulic conductivity transmissivity as well as flow variables head specific discharge solute concentration are regarded as random variables subjected to uncertainty the main aim of the study is to analyze the influence of conditional probability of input variables upon the statistical structure of the dependent variables the unconditional probability density functions are supposed to be stationary multivariate normal while conditioning accounts for the measured values at a few points of the formation two problems of groundwater flow are discussed in part 1 conditional simulation and the direct problem for steady flow analytical results are obtained by using perturbation approximations average uniform head gradient flows as well as recharge and flow to wells are discussed in unconditional modeling the input variable the conductivity or transmissivity log is regarded as stationary and is represented by its constant mean and variogram the ensemble of formations on which statistical calculations are carried out represents all aquifers with same probability density distributions in conditional modeling the measured values at a few points are kept fixed and uncertainty prevails only at other points consequently statistical computations are performed for the subensemble of aquifers which preserve the measured values and as a result both input and output variables are nonstationary the main effect of conditioning is to reduce the variance i e the uncertainty of these variables this effect is particularly important in the case of flow toward wells application of the modeling method to field problems is outlined

stability of linear neutral differential equations with delays and impulses established by the fixed points method abstract in this paper we consider the impulsive effects on the stability of the zero solution of the linear neutral differential equations with variable delays by transforming the equations into ones without impulses and using fixed point theory some sufficient conditions for asymptotic stability and exponential stability of the zero solution are obtained the paper extends and improves results on sufficient conditions obtained by jin and luo 2008 17 and ardjouni and djoudi 2011 18 which is shown clearly in example 1 this paper also shows that the impulse intensity and the impulse time both influence the decay rate of the convergence to zero of the solutions finally two examples are given to show applications of some results obtained

asymptotic stability of second order neutral stochastic differential equations in this paper we study the existence and asymptotic stability in pth moment of mild solutions to second order nonlinear neutral stochastic differential equations further this result is extended to establish stability criterion for stochastic equations with impulsive effects with the help of fixed point strategy stochastic analysis technique and semigroup theory a set of novel sufficient conditions are derived for achieving the required result finally an example is provided to illustrate the obtained result

comparison principle and stability of ito stochastic differential delay equations with poisson jump and markovian switching abstract in this paper the comparison principle for the nonlinear ito stochastic differential delay equations with poisson jump and markovian switching is established later using this comparison principle we obtain some stability criteria including stability in probability asymptotic stability in probability stability in the p th mean asymptotic stability in the p th mean and the p th moment exponential stability of such equations some known results are generalized and improved