rectifiable and unrectifiable oscillations for a class of second order linear differential equations of euler type the main purpose of the paper is to pay attention to a new kind of oscillations so called rectifiable and unrectifiable oscillations which occur in a class of linear second order differential equations including the famous linear euler differential equation it will be shown that this kind of oscillations only depends on a positive real parameter which appears in a singular term of the main equation as well as in a suitable boundary layer condition

new kamenev type oscillation criteria for second order neutral nonlinear differential equations abstract in this paper some new oscillation criteria for second order neutral nonlinear differential equation r t y t p t y t i 1 n q i t f i y i t 0 t t 0 are established new oscillation criteria are different from most known ones in the sense that they are based on a class of new functions t s l defined in the sequel our results are sharper than some previous results which can be seen by the example at the end of this paper

parity effect of the initial capital based on parrondo s games and the quantum interpretation abstract in our previous study zhu et al quantum game interpretation for a special case of parrondo s paradox physica a 390 2011 579 the capital dependent parrondo s game where one game depends on the capital modulus m 4 was shown not to have a definite stationary probability distribution and that payoffs of the game depended on the parity of the initial capital this paper presents a generalization of these results to even m greater than 4 an intuitive explanation for producing this phenomenon is that the discrete time markov chain of the game is divided into two completely unrelated inner and outer rings the process taking the inner ring or outer ring of the game is determined by the initial capital of parity and then a win or loss of the game is determined quantum game theory is used to further analyze the phenomenon the results show that the explanation of the game corresponding to a stationary probability distribution is that the probability of the initial capital has reached parity

interval criteria for oscillation of nonlinear second order dynamic equations on time scales interval oscillation criteria are established for a second order nonlinear dynamic equation on time scales by utilizing a generalized riccati technique and an integral averaging technique the theory can be applied to second order dynamic equations regardless of the choice of delta or nabla derivatives

from quantum cellular automata to quantum lattice gases a natural architecture for nanoscale quantum computation is that of a quantum cellular automaton motivated by this observation we begin an investigation of exactly unitary cellular automata after proving that there can be no nontrivial homogeneous local unitary scalar cellular automaton in one dimension we weaken the homogeneity condition and show that there are nontrivial exactly unitary partitioning cellular automata we find a one parameter family of evolution rules which are best interpreted as those for a one particle quantum automaton this model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the dirac equation we describe two generalizations of this automaton the second of which to multiple interacting particles is the correct definition of a quantum lattice gas

history dependent quantum walk on the cycle with an unbalanced coin abstract recently a new model of quantum walk utilizing recycled coins was introduced however little is yet known about its properties in this paper we study its behavior on the cycle graph in particular we will consider its time averaged distribution and how it is affected by the walk s memory parameter a real parameter between zero and eight which affects the walk s coin flip operator despite an infinite number of different parameters our analysis provides evidence that only a few produce non uniform behavior our analysis also shows that the initial state and cycle size modulo four all affect the behavior of this walk we also prove an interesting relationship between the recycled coin model and a different memory based quantum walk recently proposed

second order oscillation of forced functional differential equations with oscillatory potentials new oscillation criteria are established for second order differential equations containing both delay and advanced arguments of the form k t x t p t x t t a 1x t t q t x s t b 1x s t e t t 0 where a 1 and b 1 k p q e t s are continuous real valued functions k t 0 is nondecreasing t and o are nondecreasing t t t s t t and lim t t t the potentials p q and e are allowed to change sign and the information on the whole half line is not required as opposed to the usual case in most articles among others as an application of the results we are able to deduce that every solution of x t m 1sintx t p12 m 2costx t p6 cos2t m 1 m 2 0 is oscillatory provided that either m 1 orm 2 is sufficiently large

forced oscillation of super half linear impulsive differential equations by using a picone type formula in comparison with oscillatory unforced half linear equations we derive new oscillation criteria for second order forced super half linear impulsive differential equations having fixed moments of impulse actions in the superlinear case the effect of a damping term is also considered

oscillation of second order differential equations with mixed argument abstract our aim in this paper is to present a sufficient condition for the oscillation of the second order differential equation with mixed argument formula we compare with the first order advanced equation of the form z t q 2 t z t 0

oscillation criteria for second order quasi linear neutral delay differential equations abstract in this paper some new oscillation criteria for second order neutral nonlinear differential equation r t x t p t x t m 1 x t p t x t q t f x t 0 are established new oscillation criteria are different from most known ones in the sense that they are based on a class of new functions t s l defined in the sequel

correlation effects in a discrete quantum random walk we introduce memory dependent discrete time quantum random walk models by adding uncorrelated memory terms and also by modifying the hamiltonian of the walker to include couplings with memory keeping agents we next study numerically the correlation effects in these models we also propose a correlation exponent as a relevant and promising tool for investigation of correlation or memory hence non markovian effects our analysis can easily be applied to more realistic models in which different regimes may emerge because of competition between different underlying physical mechanisms

oscillation of solutions of second order mixed nonlinear differential equations under impulsive perturbations new oscillation criteria are obtained for second order forced mixed nonlinear impulsive differential equations of the form r t f a x q t f a x k 1nq k t f b k x e t t q ix q i a ix q i x q i b ix q i where f c s s c 1s and b 1 b 2 b m a b m 1 b n 0 if a 1 and the impulses are dropped then the results obtained by sun and wong y g sun j s w wong oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities j math anal appl 334 2007 549 560 are recovered examples are given to illustrate the results

interval oscillation of a general class of second order nonlinear impulsive differential equations with nonlinear damping in this paper a general class of second order nonlinear impulsive differential equations with damping is studied several interval oscillation criteria which generalize and extend some known ones are established moreover examples are given to illustrate the effectiveness and non emptiness of our results

quantum markov chains a new approach to quantum markov chains is presented we first define a transition operation matrix tom as a matrix whose entries are completely positive maps whose column sums form a quantum operation a quantum markov chain is defined to be a pair g e where g is a directed graph and e eij is a tom whose entry eij labels the edge from vertex j to vertex i we think of the vertices of g as sites that a quantum system can occupy and eij is the transition operation from site j to site i in one time step the discrete dynamics of the system is obtained by iterating the tom e we next consider a special type of tom called a transition effect matrix in this case there are two types of dynamics a state dynamics and an operator dynamics although these two types are not identical they are statistically equivalent we next give examples that illustrate various properties of quantum markov chains we conclude by showing that our formalism generalizes the usual framework for quantum random walks

a note on nasr s and wong s papers abstract in the case of oscillatory potentials we give sufficient conditions for the oscillation of the forced nonlinear second order differential equations with delayed argument in the form x t q t x t sgn x t f t in the linear 1 and the superlinear 1 cases

on the positive solutions of the system of rational difference equations xn 1 1 yn k yn 1 yn xn myn m k abstract our aim in this paper is to investigate the periodic nature of solutions of the system of rational difference equations x n 1 1 y n k y n 1 y n x n m y n m k n 0 1 where k is a nonnegative integer m is a positive integer and the initial values x m x m 1 x 0 y m k y m k 1 y 0 are positive real numbers

quantum walks with history dependence we introduce a multi coin discrete quantum walk where the amplitude for a coin flip depends upon previous tosses although the corresponding classical random walk is unbiased a bias can be introduced into the quantum walk by varying the history dependence by mixing the biased walk with an unbiased one the direction of the bias can be reversed leading to a new quantum version of parrondo s paradox

oscillation and nonoscillation of advanced differential equations with variable coefficients the oscillation and nonoscillation of the advanced differential equations x t p t x t 0 t t0 and x t i 1npi t x t i 0 t t0 are investigated where p t pi t c t0 0 and i are positive constants at first a sharp sufficient condition for the oscillation of eq is obtained then the result is generalized to eq these results improve the corresponding conclusions derived by ladas and stavroulakis j differential equations 44 1982 134 152 next two examples are given to illustrate the advantages of our results finally the sufficient conditions for these two equations to be nonoscillatory are also obtained

oscillation criteria for nth order forced functional differential equations in this paper by using the method of general means some new oscillation criteria for forced functional differential equations of the form x n t i 1n 1aix i t q t fxg t e t t0 0 are established where ai are real constants q t f t e t and g t are real continuous functions xf x 0 whenever x 0 and limt g t

oscillations of second order impulses nonlinear fde with forcing term a kind of second order impulses nonlinear fde with forcing term is studied in this paper by means of kartsatos technique we reduce it to a second order nonlinear impulsive homogeneous equation several criteria on the oscillations of solutions are given we find some suitable impulse functions such that all the solutions of the equation are oscillatory under the impulse control at last we give some examples to demonstrate our results

occurrence of complementary processes in parrondo s paradox abstract parrondo s paradox involves two losing processes producing a winning outcome we analyze the paradox with an original and novel method in which we start with one process and seek to construct a complementary process to achieve the paradox we then derive a general condition for the classical parrondo game to have a complementary process numerical simulation predicts that approximately two thirds of such losing games satisfy the required condition this suggests the common occurrence of the paradox indicative of many potentially undiscovered applications in real life scenarios involving stochastic processes

cooperative quantum parrondo s games abstract coordination and cooperation are among the most important issues of game theory recently the attention turned to game theory on graphs and social networks encouraged by interesting results obtained in quantum evolutionary game analysis we study cooperative parrondo s games in a quantum setup the game is modeled using multidimensional quantum random walks with biased coins we use the ghz and w entangled states as the initial state of the coins our analysis shows that an apparent paradox in cooperative quantum games and some interesting phenomena can be observed

interval oscillation theorems for asecond order linear differential equation interval oscillation criteria are given for the forced second order linear differential equation ly t p t y q t y t email protected 0 where p q are locally integrable functions and p t 0 for t 0 no restriction is imposed on t to be the second derivative of an oscillatory function as assumed by kartsatos 1 our results also allow both q and f to change sign in the neighborhood at infinity in particular we show that all solutions of y c sin t y t b cos t with b 0 are oscillatory for c 1 3448 this improves an estimate given by nasr 2 for the linear equation

necessary and sufficient conditions for the oscillation of forced nonlinear second order differential equations with delayed argument abstract for a special class of the external force g t and nonnegative potential a t we give necessary and sufficient conditions for the oscillation of all solutions of a nonlinear second order forced differential equation with delayed argument of emden fowler type in the form x t a t x t sgn x t g t in the superlinear 1 and the sublinear cases

new oscillation criteria for a class of second order nonlinear forced differential equations abstract by using classical variational principle and averaging technique new oscillation criteria are established for second order nonlinear forced differential equations r t x t x t q t f x t e t t t 0 where the functions r q e c t 0 r and f c r r improve and extend some recent results

oscillations caused by several retarded and advanced arguments in this paper we study the oscillatory behavior of equations of the forms y t i 1npiy t i 0 and y t i 1npiy t i 0 where piand i i 1 2 n are positive constants we prove that each one of the following conditions 1 pi i1 e for some i i 1 2 n 2 i 1npi 1 e where min 1 2 n 3 i 1npi 1 n i 1n i 1 e or 4 1 n i 1n pi i 1 2 21 e implies that every solution of and oscillates a generalization in the case where the coefficientspi i 1 2 n are positive and continuous functions is also presented

quantum parrondo s games parrondo s paradox arises when two losing games are combined to produce a winning one a history dependent quantum parrondo game is studied where the rotation operators that represent the toss of a classical biased coin are replaced by general su 2 operators to transform the game into the quantum domain in the initial state a superposition of qubits can be used to couple the games and produce interference leading to quite different payoffs to those in the classical case

oscillation criteria for certain forced second order nonlinear differential equations with delayed argument some new sufficient conditions for the oscillation criteria are given for the forced second order nonlinear differential equations with delayed argument in the form x t q t f x t t e t the results are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our methodology is somewhat different from that of previous authors our results generalize and extend some earlier results of sun 1 furthermore we are able to answer the question in recent paper 1 for the oscillation of bounded solutions of the above equation when f x x lsgn x 0 l 1

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

fredholm realizations of elliptic symbols on manifolds with boundary we show that the existence of a fredholm element of the zero calculus of pseudodifferential operators on a compact manifold with boundary with a given elliptic symbol is determined up to stability by the vanishing of the atiyah bott obstruction it follows that up to small deformations and stability the same symbols have fredholm realizations in the zero calculus in the scattering calculus and in the transmission calculus of boutet de monvel

quantum models of parrondo s games abstract a parrondo s paradox is an effect where two losing games when combined can produce a net winning result we provide a short introduction to quantum versions of parrondo s games and review the current status of the work

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

interval criteria for oscillation of second order differential equations with mixed nonlinearities abstract in this paper we establish interval criteria for oscillation of the second order forced ordinary differential equations with mixed nonlinearities p t x q t x i 1 n q i t x i sgn x e t where p t q t qi t e t are continuous functions defined on 0 p t is positive and differentiable 1 m 1 m 1 n 0 n m 1 no restriction is imposed on the potentials q t qi t and e t to be nonnegative

parrondo games as lattice gas automata parrondo games are coin flipping games with the surprising property that alternating plays of two losing games can produce a winning game we show that this phenomenon can be modelled by probabilistic lattice gas automata furthermore motivated by the recent introduction of quantum coin flipping games we show that quantum lattice gas automata provide an interesting definition for quantum parrondo games

oscillation and nonoscillation of hill s equation with periodic damping we prove new results on the oscillation and nonoscillation of the hill s equation with periodic damping y p t y q t y 0 t 0 where p t and q t are continuous and periodic the results show that the equation y sint y cost y 0 is nonoscillatory whilst the equation y cost y sint y 0 is oscillatory

quantum walks with memory on cycles abstract we study the model of quantum walks on cycles enriched by the addition of 1 step memory we provide a formula for the probability distribution and the time averaged limiting probability distribution of the introduced quantum walk using the obtained results we discuss the properties of the introduced model and the difference in comparison to the memoryless model

interval oscillation criteria for a forced second order nonlinear differential equations with damping abstract in this paper we are concerned with the oscillations in a class of forced second order differential equations with nonlinear damping terms by using classical variational principle and averaging technique several new interval oscillation criteria for the equations are established which improve and extend some known results example is also given to illustrate the results

oscillation criteria for a forced mixed type emden fowler equation with impulses some oscillation criteria for a forced mixed type emden fowler equation with impulses are given when the impulses are dropped our results extend those of sun and meng y g sun f w meng interval criteria for oscillation of second order differential equations with mixed nonlinearities appl math comput 15 2008 375 381 sun and wong y g sun j s w wong oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities j math anal appl 334 2007 549 560 for second order forced ordinary differential equation with mixed nonlinearities nasr a h nasr sufficient conditions for the oscillation of forced superlinear second order differential equations with oscillatory potential proc am math soc 126 1998 123 125 yang q yang interval oscillation criteria for a forced second order nonlinear ordinary differential equations with oscillatory potential appl math comput 135 2003 49 64 for forced superlinear emden fowler equation kong q kong interval criteria for oscillation of second order linear differential equations j math anal appl 229 1999 483 492 for unforced second order linear differential equations and wong j s w wong oscillation criteria for a forced second order linear differential equation j math anal appl 231 1999 235 240 for forced second order linear differential equation

forced oscillations for second order delay differential equations with impulses this paper is devoted to the study of the oscillations for forced second order delay differential equations with impulses the results gained here are based on the information of the forcing term on a sequence of subintervals of t 0 which develops some well known results for the equations without impulses and the equations without delay

winning combinations of history dependent games the parrondo effect describes the seemingly paradoxical situation in which two losing games can when combined become a winning game parrondo harmer and abbott phys rev lett 85 24 2000 here we generalize this analysis to the case where both games are history dependent i e there is an intrinsic memory in the dynamics of each game results are presented for the cases of both random and periodic switching between the two games

a k theoretic proof of boutet de monvel s index theorem for boundary value problems we study the c closure a of the algebra of all operators of order and class zero in boutet de monvel s calculus on a compact connected manifold x with boundary x 6 we find short exact sequences in k theory 0 ki c x ki a k p

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

interval criteria for oscillation of second order nonlinear differential equations by employing the generalized riccati technique and the integral averaging technique new interval oscillation criteria are established for second order nonlinear differential equations

interval oscillation of second order half linear functional differential equations by using an inequality due to hardy littlewood and polya and averaging functions new interval oscillation criteria are established for the half linear functional differential equationr t y t a 1y t q t y t t a 1y t t 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 t 0 rather than on the whole half line our results extend and improve some previous oscillation criteria and handle the cases which are not covered by known results and implies that the delay t t t t does not effect the oscillation where t 0 is a constant in particular several examples that dwell upon the sharp conditions of our results are also included

interval oscillation of second order functional differential equations with oscillatory potentials abstract interval oscillation criteria are established for second order differential equations of the form e k t x t p t x g t q t x g t 1 x g t e t t 0 where 1 k p q e and g are continuous real valued functions k t 0 is nondecreasing g t is nondecreasing lim t g t we consider g t t and g t t separately illustrative examples are included

counterintuitive behaviour in games based on spin models a large class of games based on spin models is analysed for these games the long time gain can be calculated exactly it is shown that the mixing of two losing strategies may lead to a winning one but also that the mixing of two winning ones may lead to a loss also the mixing of a losing and a winning strategy may give unexpected results this behaviour is due to two general features i the class of games is such that mixing the playing of two games is equivalent to playing a third one and ii the break even boundaries for these games are curved

integral averaging technique for the interval oscillation criteria of certain second order nonlinear differential equations abstract we present new interval oscillation criteria related to integral averaging technique for certain classes of second order nonlinear differential equations which are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line they generalize and improve some known results examples are also given to illustrate the importance of our results

on kamenev type oscillation theorems for second order differential equations with damping abstract oscillation criteria for the nonlinear second order ordinary differential equation with damping x p t x f x 0 are given the results are extensions of integral averaging technique of kamenev and include earlier results of yeh yan and chen