on oscillation of nonlinear second order differential equation with damping term we present new oscillation criteria for the second order nonlinear differential equation with damping our theorems are stated in general form they complement and extend related results known in the literature the relevance of our results is illustrated with a number of examples to facilitate computations in these examples we use mathematica r a symbolic computer language

oscillation results for a second order damped differential equation with nonmonotonous nonlinearity abstract we present new oscillation criteria for a nonlinear second order differential equation with a damping term an essential feature of our results is that we do not require the nonlinearity to be nondecreasing furthermore as opposed to the recent results by s r grace 1989 math nachr 141 117 127 1992 j math anal appl 171 220 241 and s r grace and b s lalli 1990 j math anal appl 149 277 311 we do not impose any additional condition on the damping term p t consequently our theorems apply to new classes of equations which are not covered by the known criteria the relevance of the results obtained is illustrated with a number of carefully selected examples

averaged lagrangians and the mean effects of fluctuations in ideal fluid dynamics we begin by placing the generalized lagrangian mean glm equations for a compressible adiabatic fluid into the euler poincare ep variational framework of fluid dynamics for an averaged lagrangian we then state the ep averag ing result that glm equations arise from glm hamilton s principles in the ep framework next we derive a new set of approximate small amplitude glm equations gm equations at second order in the fluctuating displacement of a lagrangian trajectory from its mean position these equations express the linear and nonlinear back reaction effects on the eulerian mean fluid quantities by the fluctuating displacements of the lagrangian trajectories in terms of their eulerian second moments the derivation of the gm equations uses the linearized relations between eulerian and lagrangian fluctuations in the tradition of lagrangian stability analysis for fluids the gm derivation also uses the method of averaged lagrangians in the tradition of wave mean flow interaction wmfi the gm ep motion equations for compressible and incompressible ideal fluids are compared with the euler alpha turbulence closure equations an alpha model is a glm or gm fluid theory with a taylor hypothesis closure thc such closures are based on the linearized fluctuation relations that determine the dynamics of the lagrangian statistical quantities in the euler alpha closure equations we use the ep averaging result to bridge between the glm equations and the euler alpha closure equations hence combining the small amplitude approximation with thc yields in new gm turbulence closure equations for compressible fluids in the ep variational framework 2002 elsevier science b v all rights reserved

length scale estimates for the lans α equations in terms of the reynolds number abstract foias holm and titi c foias d d holm e s titi the three dimensional viscous camassa holm equations and their relation to the navier stokes equations and turbulence theory j dynam differential equations 14 2002 1 35 have settled the problem of existence and uniqueness for the 3d lans equations on periodic box 0 l 3 there still remains the problem first introduced by doering and foias c r doering c foias energy dissipation in body forced turbulence j fluid mech 467 2002 289 306 for the navier stokes equations of obtaining estimates in terms of the reynolds number r e whose character depends on the fluid response as opposed to the grashof number whose character depends on the forcing r e is defined as r e u l where u is a bounded spatio temporally averaged navier stokes velocity field and l the characteristic scale of the forcing it is found that the inverse kolmogorov length is estimated by l k 1 c l 1 4 r e 5 8 moreover the estimate of foias holm and titi for the fractal dimension of the global attractor in terms of r e comes out to be d f a c v v l 1 2 l 2 1 9 8 r e 9 4 where v l l 1 2 3 and v l l l 3 it is also shown that there exists a series of time averaged inverse squared length scales whose members n 0 2 are estimated as n 1 l 2 n 0 2 c n v n 1 n r e 11 4 7 4 n ln r e 1 n c 1 r e ln r e the upper bound on the first member of the hierarchy 1 0 2 coincides with the inverse squared taylor micro scale to within log corrections

time space trade offs for reversible computation a reversible turing machine is one whose transition function is 1 1 so that no instantaneous description id has more than one predecessor using a pebbling argument this paper shows that for any varepsilon 0 ordinary multitape turing machines using time t and space s can be simulated by reversible ones using time o t 1 varepsilon and space o s log t or in linear time and space o st varepsilon the former result implies in particular that reversible machines can simulate ordinary ones in quadratic space these results refer to reversible machines that save their input thereby insuring a global 1 1 relation between initial and final ids even when the function being computed is many to one reversible machines that instead erase their input can of course compute only 1 1 partial recursive functions and indeed provide a godel numbering of such functions the time space cost of computing a 1 1 function on such a machine is equal within a small polynomial to the cost of co

oscillation criteria for second order nonlinear damped differential equations abstract this paper discusses a class of second order nonlinear damped differential equations by using the generalized riccati technique and the integral averaging technique new oscillation criteria are obtained

oscillation criteria for even order half linear distributed delay differential equations with damping by using the generalized riccati technique and an inequality due to hardy littlewood and polya several new oscillation criteria are established for a class of even order half linear distributed for a differential equation with damping the results obtained extend and improve earlier results in existing literature

interval criteria for oscillation of second order half linear differential equations by employing a generalized riccati technique and an integral averaging method interval oscillation criteria are established for the second order half linear differential equation r t x t 1x t q t x t 1x t 0 these criteria are different from most known ones in the sense that they are based on information only on a sequence of subintervals of t0 rather than on the whole half line they also extend improve and complement a number of existing results and can be applied to extreme cases such as t0 q s ds in particular several interesting examples that illustrate the importance of our results are included

oscillation criteria for certain nonlinear differential equations we present new oscillation criteria for certain classes of second order nonlinear differential equations and delay differential equations obtained by using an integral averaging technique our theorems complement a number of existing results and handle the cases which are not covered by known criteria

oscillation criteria for second order nonlinear delay dynamic equations on time scales by employing the generalized riccati transformation we establish some new oscillation criteria for second order delay dynamic equations on time scales the obtained results essentially improve the well know oscillation results for half linear dynamic equations such as kamenev type and philos type oscillation criteria some interesting examples are given to illustrate the versatility of our results

asymptotic behavior of solutions of second order nonlinear delay differential equations with impulses this paper is concerned with second order nonlinear delay differential equations with impulses of the form r t x t p t x t f t x email protected 0 t t k x t k i k x t k x t k j k x t k t t k k 1 2 t t 0 by impulsive differential inequality and riccati transformation sufficient conditions of asymptotic behavior of all solutions of second order nonlinear delay differential equations with impulses are obtained some examples are also inserted to illustrate the impulsive effect

rush hour is psapce complete or why you should generously tip parking lot attendants rush hour is a children s game that consists of a grid board several cars that are restricted to move either vertically or horizontally but not both a special target car and a single exit on the perimeter of the grid the goal of the game is to find a sequence of legal moves that allows the target car to exit the grid we consider a slightly generalized version of the game that uses an nn grid and assume that we can place the single exit and target car at any location we choose on initialization of the game in this work we show that deciding if the target car can legally exit the grid is pspace complete our constructive proof uses a lazy form of dual rail reversible logic such that movement of output cars can only occur if logical combinations of input cars can also move emulating this logic only requires three types of devices two switches and one crossover thus our proof technique can be easily generalized to other games and planning problems in which the same three primitive devices can be constructed

oscillation criteria for nonlinear differential equations with damping oscillation criteria are established for the nonlinear second order damped differential equation rx px qf x 0 which are different from most known results

the distance between zeros of an oscillatory solution to a half linear differential equation consider the oscillatory equation u t 1u t q t u t 1u t 0 where q t a r is locally integrable for some a 0 we prove some results on the distance between consecutive zeros of a solution of we apply also the results to the following equations r t u t 1u t q t u t 1u t 0 and i 1ndi du n 2diu c x u n 2u 0 a where i r c 0 0 and ar t 1 ii di xi d d1 dn a x rn x a is an exterior domain and c c a 0 iii 0 n 1 and n 2

oscillation of certain second order nonlinear differential equations abstract in this paper we consider the second order nonlinear differential equation formula where 0 is any quotient of odd integers a c 1 r 0 q c r r f c r r xf x 0 f x 0 for x 0 some new sufficient conditions for the oscillation of all solutions of are obtained several examples that dwell upon the importance of our results are also included

reversible simulation of irreversible computation abstract computer computations are generally irreversible while the laws of physics are reversible this mismatch is penalized by among other things generating excess thermic entropy in the computation computing performance has improved to the extent that efficiency degrades unless all algorithms are executed reversibly for example by a universal reversible simulation of irreversible computations all known reversible simulations are either space hungry or time hungry the leanest method was proposed by bennett and can be analyzed using a simple reversible pebble game the reachable reversible simulation instantaneous descriptions pebble configurations of such pebble games are characterized completely as a corollary we obtain the reversible simulation by bennett and moreover show that it is a space optimal pebble game we also introduce irreversible steps and give a theorem on the tradeoff between the number of allowed irreversible steps and the memory gain in the pebble game in this resource bounded setting the limited erasing needs to be performed at precise instants during the simulation the reversible simulation can be modified so that it is applicable also when the simulated computation time is unknown

sturmian comparison theorem for half linear second order differential equations let be defined by s s p 2 s with p 1 a fixed number we extend sturm comparison theorem of the linear differential equation to the nonlinear differential equation by using the wirtinger inequality a lyapunov inequality and some oscillation criteria of e are also given

oscillation theorems for certain nonlinear differential equations of second order abstract we present new oscillation criteria for the second order nonlinear differential equations these criteria involve the use of averaging functions our theorems are stated in general form they complement and extend related results known in the literature also the relevance of our results is to show that some of manojlovic s results contain the superfluous condition

asymptotic behavior of solutions of second order nonlinear impulsive differential equations in this work the asymptotic behavior of all solutions of second order nonlinear ordinary differential equations with impulses is investigated by impulsive differential inequality and riccati transformation sufficient conditions of asymptotic behavior of all solutions of second order nonlinear ordinary differential equations with impulses are obtained an example is also inserted to illustrate the impulsive effect

interval criteria for oscillation of second order functional differential equations by using averaging functions new interval oscillation criteria are established for the second order functional differential equation r t x t a 1x t f t x t x t t x t x t t 0 t t 0that are different from most known ones in the sense that they are based on information only on a sequence of subintervals of t 0 rather than on the whole half line our results can be applied to three cases ordinary delay and advance differential equations in the case of half linear functional differential equations our criteria implies that the t t t delay and gt t t advance cases do not affect the oscillation in particular several examples are given to illustrate the importance of our results

oscillation criteria for second order nonlinear neutral variable delay dynamic equations abstract this paper is concerned with oscillation of second order nonlinear neutral dynamic equations on time scales with a variable delay by using the generalized riccati technique and integral averaging technique new oscillation criteria are obtained for all solutions of the equation some results extend known results for difference equations when the time scale is the set z of positive integers and for differential equations when the time scale is r several examples are given to illustrate the results of the paper

scaling property of turbulent flows we discuss a possible theoretical interpretation of the self scaling property of turbulent flows extended self similarity ess our interpretation predicts that even in cases when ess is not observed a generalized self scaling must be observed this prediction is checked on a number of laboratory experiments and direct numerical simulations

the local structure of turbulence in incompressible viscous fluid for very large reynolds numbers 1 we shall denote by u p u x 1 x 2 x 3 t 1 2 3 the components of velocity at the moment t at the point with rectangular cartesian coordinates x 1 x 2 x 3 in considering the turbulence it is natural to assume the components of the velocity u p at every point p x 1 x 2 x 3 t of the considered domain g of the four dimensional space x 1 x 2 x 3 t are random variables in the sense of the theory of probabilities cf for this approach to the problem millionshtchikov 1939 denoting by the mathematical expectation of the random variable a we suppose that 2 and d u d x 2 are finite and bounded in every bounded subdomain of the domain g

on a leray α model of turbulence in this paper we introduce and study a new model for three dimensional turbulence the leray model this model is inspired by the lagrangian averaged navier stokes model of turbulence also known navier stokes model or the viscous camassa holm equations as in the case of the lagrangian averaged navier stokes model the leray model compares successfully with empirical data from turbulent channel and pipe flows for a wide range of reynolds numbers we establish here an upper bound for the dimension of the global attractor the number of degrees of freedom of the leray model of the order of l l d 12 7 where l is the size of the domain and l d is the dissipation length scale this upper bound is much smaller than what one would expect for three dimensional models i e l l d 3 this remarkable result suggests that the leray model has a great potential to become a good sub grid scale large eddy simulation model of turbulence we support this observation by studying analytically and computationally the energy spectrum and show that in addition to the usual k 5 3 kolmogorov power law the inertial range has a steeper power law spectrum for wavenumbers larger than 1 finally we propose a prandtl like boundary layer model induced by the leray model and show a very good agreement of this model with empirical data for turbulent boundary layers

design of 1 tape 2 symbol reversible turing machines based on reversible logic elements this paper proposes a novel scheme for constructing reversible turing machines rtms via various reversible logic elements a reversible logic element is similar to a conventional reversible logic gate except that the element also carries a 1 bit memory that can store binary states the usage of internal states allows much more efficient and straightforward constructions of rtms based on reversible elements than based on reversible logic gates in particular a remarkable feature of our constructions is that they can operate asynchronously whereby the clock signal which is indispensable for synchronizing all elements as in a reversible logic circuit can possibly be removed from the construction

the camassa holm equations and turbulence abstract in this paper we will survey our results on the camassa holm equations and their relation to turbulence as discussed in s chen c foias d d holm e olson e s titi s wynne the camassa holm equations as a closure model for turbulent channel and pipe flow phys rev lett 81 1998 5338 s chen c foias d d holm e olson e s titi s wynne a connection between the camassa holm equations and turbulent flows in channels and pipes phys fluids in press in particular we will provide a more detailed mathematical treatment of those equations for pipe flows which yield accurate predictions of turbulent flow profiles for very large reynolds numbers there are many facts connecting the camassa holm equations to turbulent fluid flows the dimension of the attractor agrees with the heuristic argument based on the kolmogorov statistical theory of turbulence the statistical properties of the energy spectrum agree in numerical simulation with the kolmogorov power law furthermore comparison of mean flow profiles for turbulent flow in channels and pipes given by experimental and numerical data show acceptable agreement with the profile of the corresponding solution of the camassa holm equations

time and space bounds for reversible simulation we prove a general upper bound on the trade off between time and space that suffices for the reversible simulation of irreversible computation previously only simulations using exponential time or quadratic space were known the trade off shows for the first time that we can simultaneously achieve subexponential time and subquadratic space the boundary values are the exponential time with hardly any extra space required by the lange mckenzie tapp method and the log 3 th power time with square space required by the bennett method we also give the first general lower bound on the extra storage space required by general reversible simulation this lower bound is optimal in that it is achieved by some reversible simulations

oscillation theorems for nonlinear differential equations of second order abstract in this paper we present some new criteria for the oscillation of the differential equation a t x t x t p t x t q t f x t 0 the obtained results extend improve and correlate a number of existing criteria

oscillation of even order half linear functional differential equations with damping in this paper a class of even order half linear functional differential equations with damping are studied by using the generalized riccati transformation and the integral averaging technique the new oscillation criteria which generalize and improve some known results are obtained for all solutions of the equations

oscillation theorems for nonlinear second order differential equations in this paper some new oscillation criteria are given for the second order nonlinear differential equation r t x t x t c t x t 0 t t0 where r c t0 0 c c t0 r c r r and r r is defined by s s p 2s with p 1 a fixed real number these criteria involve the use of averaging functions

integral averages and oscillation criteria for half linear partial differential equation the technique of weighted integral averages known in the oscillation theory of ordinary differential equations is extended to the half linear partial differential equation e div email protected email protected p email protected u c x u p 2u 0 p 1 this technique is used to obtain new oscillation criteria for e on the unbounded domains

oscillation criteria for second order sublinear differential equation abstract the basic purpose of this paper is to present a new oscillation criteria for second order sublinear differential equation a t x t x t q t t 0 t t 0 0 where a a c 1 t 0 is positive function q c t 0 has no restriction on its sign c 1 r are such that x 0 x x 0 for x 0

interval oscillation criteria for second order nonlinear differential equations with damping new oscillation criteria are established for the nonlinear damped differential equation ry py qf y 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are sharper than some previous results and extend and improve the recent interval criteria of kong and huang and can be applied to extreme cases such as t0 q s ds in particular several examples that dwell upon the sharp conditions of our results are also included

oscillation criteria of second order nonlinear matrix differential systems in this paper the second order nonlinear matrix differential systems p t y t f t y t y t 0 t t 0is considered where p t y t and f t y t y t are nxn real continuous matrix functions and p t 0 are positive definite and symmetric one some new oscillation criteria for the systems are established and some known results in the literature are improved and generalized

note on wong s paper using the method of interval integral average we establish some new oscillation criteria which improve the oscillation criteria due to james s w wong

oscillation criteria for second order nonlinear perturbed differential equations abstract we present new oscillation criteria for the second order nonlinear perturbed differential equations these criteria are of a high degree of generality and they extend and unify a number of existing results

oscillation criteria for half linear dynamic equations on time scales this paper is concerned with oscillation of the second order half linear delay dynamic equation r t x p t x t 0 on a time scale t where 1 is the quotient of odd positive integers p t and t t are positive rd continuous functions on t r t is positive and delta differentiable t t and limt t we establish some new sufficient conditions which ensure that every solution oscillates or converges to zero our results in the special cases when t r and t n involve and improve some oscillation results for second order differential and difference equations and when t hn t q n 0 and t n 2 our oscillation results are essentially new some examples illustrating the importance of our results are also included

oscillation and asymptotics for second order half linear differential equations this paper discusses a class of second order half linear differential equations by using the generalized riccati technique and the averaging technique new oscillation criteria are obtained for all solutions of the equations to be oscillatory asymptotic behavior for forced equations is also discussed

oscillation criteria related to integral averaging technique for linear matrix hamiltonian systems by employing a generalized riccati technique and an integral averaging technique new oscillation criteria are established for the linear matrix hamiltonian system u a x u b x v v c x u a x v under the assumption that all a x b x b x 0 and c x c x are n n matrices of real valued continuous functions on the interval i x0 x0 these criteria extend improve and unify a number of existing results and also handle cases not covered by known criteria several interesting examples that illustrate the importance of our results are included

kamenev type oscillation criteria for second order nonlinear dynamic equations on time scales the purpose of this paper to establish oscillation criteria for second order nonlinear dynamic equation r t x t f t x g t 0 on an arbitrary time scale t where is a quotient of odd positive integers and r is a positive rd continuous function on t the function g t t satisfies g t t and limt g t and f c t r r we establish some new sufficient conditions such that the above equation is oscillatory by using generalized riccati transformation our results in the special cases when t r and t n involve and improve some oscillation results for second order differential and difference equations and when t hn t qn0 and t n2 our oscillation results are essentially new some examples illustrating the importance of our results are included

ordinary differential equations in the oscillation theory of partial half linear differential equation abstract in the paper we study the damped half linear partial differential equation div a x u p 2 u b x u p 2 u c x u p 2 u 0 using radialization method we derive general oscillation results which allow to deduce new oscillation criteria for this equation from oscillation criteria for ordinary differential equations using careful radialization we improve several known oscillation criteria

extended self similarity in turbulent flows we report on the existence of a hitherto undetected form of self similarity which we call extended self similarity ess ess holds at high as well as at low reynolds number and it is characterized by the same scaling exponents of the velocity differences of fully developed turbulence

oscillation and asymptotics for nonlinear second order differential equations this paper discusses a class of second order nonlinear differential equations by using the generalized riccati technique and the averaging technique new oscillation criteria are obtained for all solutions of the equation to be oscillatory asymptotic behavior for forced equations is also discussed

oscillation criteria for second order nonlinear perturbed differential equations abstract some criteria are obtained which guarantee that all solutions of the second order nonlinear perturbed differential equations r t y t p t y t q t y t h t y t y t are oscillatory

oscillation of nonlinear dynamic equations on time scales by means of riccati transformation techniques we establish some new oscillation criteria for the second order nonlinear dynamic equation p t x d t d q t f x s t 0 email protected a b on time scales in terms of the coefficients and the graininess function we illustrate our results with a nontrivial example

oscillation criteria for second order nonlinear differential equations with nonlinear damping this paper is concerned with the oscillation of a class of general type second order differential equations with nonlinear damping several new oscillation criteria are established under quite general assumptions which improve and extend the known results in the literature

oscillation criteria for second order linear differential equations abstract some oscillation criteria are given for the second order linear differential equation r t u t c t u t 0 where r t c 1 t 0 0 and c t c t 0 r these results improve oscillation criteria of wintner hartman kamenev yan and philos by using a generalized riccati transformation t a t r t u t u t f t where f c 1 is a given function on t 0 and a t exp 2 t f s ds

interval oscillation of a general class of second order nonlinear differential equations with nonlinear damping abstract the paper is concerned with the oscillation of a class of general type second order differential equations with nonlinear damping terms several new interval oscillation criteria are established for such a class of differential equations under quite general assumptions examples are also given to illustrate the results in particular it is shown that under some very mild conditions on k 1 k 2 and f the equation k 1 x x cos tk 2 x x x sin tf x 0 is oscillatory which extends the result obtained by kwong and wong j math anal appl 288 2003 15

integral averaging techniques for the oscillation of second order nonlinear differential equations abstract in this paper we enlist some known and establish some new oscillation criteria for the second order nonlinear differential equations of the form if a t x t t su p t t q t f x t 0 where the coefficients p t and q t are not assumed to be nonnegative for all large values of t these criteria are obtained by using integral averaging techniques and can be applied to some special cases where other classical oscillation results are not applicable a systematic study is attempted to extend improve and correlate a number of existing results

highly turbulent solutions of the lagrangian averaged navier stokes alpha model and their large eddy simulation potential we compute solutions of the lagrangian averaged navier stokes alpha lans alpha model for significantly higher reynolds numbers up to re approximately 8300 than have previously been accomplished this allows sufficient separation of scales to observe a navier stokes inertial range followed by a second inertial range specific to the lans alpha model both fully helical and nonhelical flows are examined up to reynolds numbers of approximately 1300 analysis of the third order structure function scaling supports the predicted l3 scaling it corresponds to a k 1 scaling of the energy spectrum for scales smaller than alpha the energy spectrum itself shows a different scaling which goes as k1 this latter spectrum is consistent with the absence of stretching in the subfilter scales due to the taylor frozen in hypothesis employed as a closure in the derivation of the lans alpha model these two scalings are conjectured to coexist in different spatial portions of the flow the l3 e k approximately k 1 scaling is subdominant to k1 in the energy spectrum but the l3 scaling is responsible for the direct energy cascade as no cascade can result from motions with no internal degrees of freedom we demonstrate verification of the prediction for the size of the lans alpha attractor resulting from this scaling from this we give a methodology either for arriving at grid independent solutions for the lans alpha model or for obtaining a formulation of the large eddy simulation optimal in the context of the alpha models the fully converged grid independent lans alpha model may not be the best approximation to a direct numerical simulation of the navier stokes equations since the minimum error is a balance between truncation errors and the approximation error due to using the lans alpha instead of the primitive equations furthermore the small scale behavior of the lans alpha model contributes to a reduction of flux at constant energy leading to a shallower energy spectrum for large alpha these small scale features however do not preclude the lans alpha model from reproducing correctly the intermittency properties of the high reynolds number flow

kamenev type and interval oscillation criteria for second order linear differential equations on a measure chain abstract we establish kamenev type criteria and interval criteria for oscillation of the second order scalar differential equation p t x t q t x t 0 on a measure chain our results cover those for differential equations and provide new oscillation criteria for difference equations several examples are given to show the significance of the results

sub grid effects of the voigt viscoelastic regularization of a singular dyadic model of turbulence in this work we investigate the spectral signature of navier stokes voigt nsv viscoelastic fluid flows by employing numerical simulations of a singular dyadic shell model our results clearly show that as the relaxation time is increased above a threshold the inertial range is reduced conserving part of the large scale statistics these results differ drastically from the two power law scenarios observed in a previous work where the nsv model was studied via sabra shell model simulations instead we also show that the additional elastic term regularizes the singular dyadic model which is the main reason behind this reduction of degrees of freedom the results of this work aim at proposing the nsv regularization as a sub grid model

oscillatory behavior of solutions of certain second order nonlinear differential equations abstract in this paper some simple inequalities are used to offer sufficient conditions for the oscillation of all solutions of the differential equation formula where 0 p q with p q odd integers or p even and q odd integers several examples which dwell upon the importance of our results are also included

wave turbulence in shallow water models we study wave turbulence in shallow water flows in numerical simulations using two different approximations the shallow water model and the boussinesq model with weak dispersion the equations for both models were solved using periodic grids with up to 2048 2 points in all simulations the froude number varies between 0 015 and 0 05 while the reynolds number and level of dispersion are varied in a broader range to span different regimes in all cases most of the energy in the system remains in the waves even after integrating the system for very long times for shallow flows nonlinear waves are nondispersive and the spectrum of potential energy is compatible with ensuremath sim k ensuremath 2 scaling for deeper boussinesq flows the nonlinear dispersion relation as directly measured from the wave and frequency spectrum calculated independently shows signatures of dispersion and the spectrum of potential energy is compatible with predictions of weak turbulence theory ensuremath sim k ensuremath 4 3 in this latter case the nonlinear dispersion relation differs from the linear one and has two branches which we explain with a simple qualitative argument finally we study probability density functions of the surface height and find that in all cases the distributions are asymmetric the probability density function can be approximated by a skewed normal distribution as well as by a tayfun distribution

quantum theory the church turing principle and the universal quantum computer it is argued that underlying the church turing hypothesis there is an implicit physical assertion here this assertion is presented explicitly as a physical principle every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means classical physics and the universal turing machine because the former is continuous and the latter discrete do not obey the principle at least in the strong form above a class of model computing machines that is the quantum generalization of the class of turing machines is described and it is shown that quantum theory and the universal quantum computer are compatible with the principle computing machines resembling the universal quantum computer could in principle be built and would have many remarkable properties not reproducible by any turing machine these do not include the computation of non recursive functions but they do include quantum parallelism a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it the intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than everett s some of the numerous connections between the quantum theory of computation and the rest of physics are explored quantum complexity theory allows a physically more reasonable definition of the complexity or knowledge in a physical system than does classical complexity theory

interval criteria for oscillation of certain matrix differential systems by employing a generalized riccati technique and an averaging technique interval oscillation criteria are established for the second order matrix differential system of the form p t y q t y 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are presented in the form of a high degree of generality handle the cases which are not covered by known criteria and can be applied to extreme cases such as limt 1 t0tq s ds in particular several interesting examples that dwell upon the importance of our results are included

a note on bennett s time space tradeoff for reversible computation given any irreversible program with running time t and space complexity s and given any varepsilon 0 bennett shows how to construct an equivalent reversible program with running time o t 1 varepsilon and space complexity o s ln t although these loose upper bounds are formally correct they are misleading due to a hidden constant factor in the space bound it is shown that this constant factor is approximately varepsilon 2 1 varepsilon which diverges exponentially as varepsilon approaches 0 bennett s analysis is simplified using recurrence equations and it is proven that the reversible program actually runs in time theta t 1 varepsilon s varepsilon and space theta s 1 ln t s bennett claims that for any varepsilon 0 the reversible program can be made to run in time o t and space o st varepsilon this claim is corrected and tightened as follows whenever t geqq 2s and for any varepsilon geqq 1 0 58 lg t s

linear programs in a simple reversible language very simple reversible programming languages can be useful for the study of reversible transformations for this purpose we define simple reversible language srl a very simple reversible language and analyse its properties the language srl is similar to the loop languages that have been used by several authors to characterise the set of primitive recursive functions there are however important differences srl has domain z instead of n and only reversible programs can be written in srl the reversibility of linear homogeneous srl programs is related to the fact that the corresponding set of matrices has the algebraic structure of a group we show that such programs implement exactly the linear transformations corresponding to the group of integer positive modular matrices while in esrl an extended version of srl the set of transformations that can be implemented by linear homogeneous programs corresponds exactly to the group of integer modular matrices