on prime factors of determinants of circulant matrices abstract we find the probability that the determinant of an integer circulant n n matrix is divisible by the prime p where p does not divide n

on the number of different permanents of some sparse 0 1 circulant matrices abstract starting from known results about the number of possible values for the permanents of 0 1 circulant matrices with three nonzero entries per row and whose dimension n is prime we prove corresponding results for n power of a prime n product of two distinct primes and n 2 3 h supported by some experimental results we also conjecture that the number of different permanents of n n 0 1 circulant matrices with k nonzero per row is asymptotically equal to n k 2 k o n k 3

the periodicity and solutions of the rational difference equation with periodic coefficients abstract in this paper we give necessary and sufficient conditions for generalized solution and periodicity of the difference equation x n 1 p n x n k x n k 1 q n x n k 1 with k 2 periodic coefficients where k n x k 1 x k x 0 r also we obtain that the generalized solution is periodic with k 1 period

the study of a class of rational difference equations abstract in this paper we study the global behavior of the higher order nonlinear difference equation x n 1 x n k 1 x n 2 k 1 bx n k 1 cx n 2 k 1 n 0 1 where b c and are positive k 1 2 3 and the initial conditions x 2 k 1 x 1 x 0 are positive real numbers we investigate the character of semicycles periodicity global stability and convergence to 2 k cycle solutions of mentioned equation

the qualitative behavior of solutions of a nonlinear difference equation abstract this paper is concerned with the qualitative behavior of solutions to the difference equation x n 1 p qx n k 1 x n n 0 1 2 where the initial conditions x k x 1 x0 are non negative k 1 2 3 and the parameters p q are non negative we start by establishing the periodicity the character of semicycles the global stability and the boundedness of the above mentioned equation we also present solutions that have unbounded behavior it is worth to mention that this difference equation is a special case of an open problem was introduced by m r s kulenovic and g ladas dynamics of second order rational difference equations with open problems and conjectures chapman and hall crc boca raton 2002 several computational examples are given to support our theoretical discussions the presented numerical tests represent different types of qualitative behavior of solutions to our nonlinear difference equation

difference equation modelling of a variable structure system abstract variable structure systems with sliding modes have been widely discussed and used in many different fields of applications the precise behaviour at a switching surface is complicated because there the system is nonanalytic a two dimensional variable structure system is analysed in detail using a special discretisation with a difference equation model which is best in a particular sense this reveals the occurrence and structure of discrete pseudo sliding modes which give insight to the corresponding sliding modes for the continuous system necessary and sufficient conditions are obtained for the occurrence of the pseudo sliding modes and the analysis illustrated with graphs from numerical solutions

global attractivity in a rational recursive sequence our aim in this paper is to investigate the periodic character invariant intervals and the global attractivity of all positive solutions of the nonlinear difference equationx n email protected email protected email protected n 1 n 0 1 where a 0 b c 0 we show that the positive equilibrium of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients

global attractivity in a second order nonlinear difference equation abstract consider the difference equation x n 1 x n x n 1 n 0 1 2 1 where the function satisfies the following conditions 0 0 and is nonincreasing in the equation 1 has a unique positive solution if denotes the unique positive solution of 1 then x x x x x 0 for x x then x is a global attractor of all positive solutions of eq 1

on the higher order rational recursive sequence xn axn k bx n 3k the main purpose of the current paper is to prove that every positive solution of the delay difference equationx n ax n k bx n 3 k where a b 0 the initial conditions x 3 k 1 x 3 k 2 x 0 0 and k 1 2 3 converges eventually to a period k solution we also give the results of computational examples to support our theoretical discussion

global stability of discrete competition model abstract this is a study of global stability of a competition model governed by difference equations it is shown that positive equilibrium of the model is globally stable if the competition matrix is diagonally dominant and the constants defining the intraspecific competition are less than or equal to 1 in the two dimensional case a different type of sufficient conditions for the global stability is established which relaxes the restriction on the constants defining the intraspecific competition

on the global behavior of higher order recursive sequences our basic purpose in this paper is to establish some conditions for the global attractivity and convergence of the kth order recursive sequencex n f x n 1 x n 2 x n k n 1 2 3 we will show that if f is a real valued function with a convex basin w in r k which is differentiable with bounded differential then f has an equilibrium point our final comments are about informative examples

a global convergence result with applications to periodic solutions abstract we establish a global convergence result and then apply it to show that under appropriate hypotheses every positive solution of the difference equation x n 1 i 0 m a i x n 2 i n 0 1 converges to a period two solution

a rational difference equation abstract we investigate the boundedness character the periodic nature and the global asymptotic stability of all positive solutions of the equation in the title with positive parameters and nonnegative initial conditions

some dynamically trivial mappings with applications to the improvement of simple iteration abstract we consider the iteration algorithm defined by x n k g x n x n 1 x n k 1 n 0 1 2 where is a k dimensional means we show that under certain conditions on the function g the algorithm will converge globally to a fixed point of g and that under less stringent conditions it will converge locally even when the corresponding algorithm for simple iteration x n 1 g x n n 0 1 2 does not a corollary of our main theorem answers a related question concerning the dynamic triviality of a class of mappings of r k into itself

dynamics of a higher order rational difference equation abstract our aim in this paper is to investigate the dynamics of difference equation y n 1 p qy n 1 y n k n 0 1 2 where the initial conditions y k y 1 y0 are non negative k 1 2 3 and the parameters p and q are non negative we study characteristics such as the global stability the boundedness of positive solutions and the character of semicycles of the above mentioned difference equation in particular our results solve the open problem introduced by kulenovic and ladas in their monograph m r s kulenovic g ladas dynamics of second order rational difference equations with open problems and conjectures chapman and hall crc boca raton 2002

the dynamics of χn 1 α βχna bχn cxn 1 facts and conjectures abstract we investigate the global character of solutions of the equation in the title with non negative parameters and nonnegative initial conditions

sufficient number of integrals for the pth order lyness equation in this communication we present a sufficient number of first integrals for the lyness equation of arbitrary order we first use the staircase method quispel et al 1991 physica a 173 243 66 to construct integrals of a derivative equation of the lyness equation closed form expressions for the integrals are given based on a non commutative vieta expansion the integrals of the lyness equation then follow directly from these integrals previously found integrals for the lyness equation arise as special cases of our new set of integrals

reduction of order periodicity and boundedness in a class of nonlinear higher order difference equations non autonomous higher order difference equations of type x n email protected i 0ka ix n i g n i 0kb ix n i with real variables and parameters have appeared frequently in the literature we extend some recent results on semiconjugate factorization and reduction of order to cases where characteristic polynomials of the linear expressions i 0 ka iu i and i 0 kb iu i have complex roots this extension yields new results on boundedness and existence of periodic solutions for equations of order 3 or greater

on the global periodicity of discrete dynamical systems and application to rational difference equations a new necessary condition for global periodicity of discrete dynamical systems and of difference equations is obtained here this condition will be applied to contribute to solving the problem of global periodicity for second order rational difference equations

on the periodic cycle of xn 1 an bnxn cnxn 1 the behaviour of solutions of the difference equation x n 1 a n b nx n c nx n 1 n 0 1 2 are investigated where the sequence a n b n and c n are periodic

attractivity and global stability for linearizable difference equations consider the difference equation x n 1 f x n x n k n 0 1 where email protected 0 1 and the initial conditions are real numbers we use the linearization of this equation in the form x n email protected i 1 lkg ix n i n 0 1 where email protected 1 2 and the functions g i r k l r to investigate the asymptotic behavior of the solutions of the considered equation we illustrate our results with various examples

quasi implicit and two level explicit finite difference procedures for solving the one dimensional advection equation a variety of explicit and implicit algorithms has been studied dealing with the solution of the one dimensional advection equation these schemes are based on the weighted finite difference approximations this solution approach proves to be very effective this procedure is carried out in many disciplines including hydrology oceanography and meteorology the main idea behind the finite difference methods for obtaining the solution of a given partial differential equation is to approximate the derivatives appearing in the equation by a set of values of the function at a selected number of points the most usual way to generate these approximations is through the use of taylor series the basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach it is worth noting that from the truncation error of the modified equivalent equation it is possible to eliminate the dominant error terms associated with the finite difference equations that contain weights thus leading to more accurate techniques quasi implicit and two level explicit finite difference techniques are considered in this article to approximately solve the one dimensional advection problem stability of the techniques are investigated using the von neumann stability analysis the results of a numerical experiment are presented and the accuracy and central processor unit cpu time needed are discussed and compared numerical tests show that the new third order or fourth order methods are more accurate than either of the second order techniques

on the recursive sequence yn 1 p yn 1 qyn yn 1 abstract we investigate the periodic character and the global stability of solutions of the equation y n 1 p y n 1 qy n y n 1 with positive parameters and positive initial conditions

an update on minc s survey of open problems involving permanents abstract we summarise the progress which has been made since 1986 on the conjectures and open problems listed in h minc s survey articles on the theory of permanents

on the rational difference equation y n 1 a y n y n k we find conditions for the global asymptotic stability of the unique negative equilibrium y 1 a of the equation yn 1 a yn yn k where y k y k 1 y0 a r and k 1 2 3 4

the oscillatory character of the recursive sequence xn 1 α βxn k 1a bxn 2k 1 abstract the aim of this work is to generalize techniques of difference equations in order to apply them to a wider class we start by establishing the boundedness the oscillatory character and the global stability of the equation x n 1 x n k 1 a bx n 2 k 1 n 0 1 2 with positive parameters k 1 2 and nonnegative initial conditions

oscillation and asymptotic behavior of a class of higher order nonlinear recursive sequences abstract we investigate the global attractivity the periodic behavior and the invariant interval with the semicycles character of solutions of the equation x n 1 x n 2 k 1 bx n k 1 cx n 2 k 1 n 0 1 2 for all admissible non negative values of the parameters b c and the initial conditions x 2 k 1 x 1 x 0 we show that the solutions exhibit a periodic attitude depending on the parameters of the family of the above mentioned difference equation in comparison with each other

on the system of two difference equations xn 1 i 0kai yn ipi yn 1 i 0kbi xn iqi abstract in this paper we study the system of two difference equations of the form x n 1 i 0 k a i y n i p i y n 1 i 0 k b i x n i q i where a i b i i 0 1 k x i y i i k k 1 0 are positive numbers and p i q i i 0 k are positive constants more precisely we investigate the boundedness the persistence of the positive solutions the existence of a unique positive equilibrium and the global asymptotic stability of the positive equilibrium of the above system finally we find solutions of the system which do not oscillate about the positive equilibrium

global attractivity in a nonlinear difference equation abstract we consider the nonlinear difference equation x n a k 1 m b k x n k n 0 1 2 where a and bk k 1 2 m are nonnegative numbers with b mk 1bk 0 and we are interested in whether all positive solutions are attracted by the positive equilibrium l a 2 a 2 2 b

on the recursive sequence xn axn 1 bxn 2c dxn 1xn 2 in this paper we study the invariant intervals the global attractivity of the equilibrium points and the asymptotic behavior of the solutions of the difference equationx n ax n 1 bx n 2c dx n 1x n 2 n 1 2 where a 0 b c d 0

dynamics of a rational difference equation using both theoretical and computational approaches this paper is concerned with the qualitative behavior of solutions to the difference equationx n 1 x n px n qx n k n 0 1 2 where the initial conditions x k x 1 x 0 are non negative email protected 1 2 3 and the parameters p q are non negative our concentration is on invariant intervals the character of semicycles the global stability and the boundedness of the above mentioned equation it is worth to mention that this difference equation was an open problem introduced by kulenovic and ladas in m r s kulenovic and g ladas dynamics of second order rational difference equations with open problems and conjectures chapman and hall crc boca raton 2002 our final comments are about informative examples

global asymptotic stability in a rational recursive sequence in this paper we study the global stability of the difference equationx n a bx n 1 cx n 1 2d x n 2 n 1 2 where a b 0 and c d 0 we show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters and every positive solution of the equation in the basin exponentially converges to the attractor

qualitative analysis of a discrete logistic equation with several delays in this paper we study the qualitative behavior of solutions of the discrete delay logistic equation with several delaysx n 1 x email protected i 1 mr i1 x n k ik n 0 1 2 where r email protected 0 for i 1 m k i i 1 2 m are positive integers and email protected 0 we obtain sufficient conditions for the global attractivity of all positive solutions about the positive equilibrium furthermore we show that such model is uniformly persistent and that all its eventually positive solutions are bounded the oscillation about the positive equilibrium is also discussed

development of a quick speech in noise test for measuring signal to noise ratio loss in normal hearing and hearing impaired listeners this paper describes a shortened and improved version of the speech in noise sin test etymotic research 1993 in the first two of four experiments the level of a female talker relative to that of four talker babble was adjusted sentence by sentence to produce 50 correct scores for normal hearing subjects in the second two experiments those sentences in babble that produced either lack of equivalence or high across subject variability in scores were discarded these experiments produced 12 equivalent lists each containing six sentences with one sentence at each adjusted signal to noise ratio of 25 20 15 10 5 and 0 db six additional lists were also made equivalent when the scores of particular pairs were averaged the final lists comprise the quicksin test that measures the snr a listener requires to understand 50 of key words in sentences in a background of babble the standard deviation of single list scores is 1 4 db snr for hearing impaired subjects based on test retest data a single quicksin list takes approximately one minute to administer and provides an estimate of snr loss accurate to 2 7 db at the 95 confidence level

study of a system of non linear difference equations arising in a deterministic model for hiv infection a deterministic model for hiv infection in the presence of combination therapy is introduced the model is then approximated by an implicit finite difference method a system of difference equations to solve the ivp system we initially purpose the discrete analogue of the continuous model of hiv infection then the boundedness the local and the global asymptotic stability of the equilibria of the system of difference equations the bistability phenomenon and the bifurcation phenomenon are also investigated in addition we will show that the associated approximational method is very robust since the equilibria and the stability conditions are independent on the time step finally numerical simulations of the system are presented when the system has meaningless solutions in view point of biology or our theory is incapable

dynamics of a higher order rational difference equation abstract in this paper we will investigate a nonlinear rational difference equation of higher order our concentration is on invariant intervals periodic character the character of semicycles and global asymptotic stability of all positive solutions of x n 1 x n x n k bx n cx n k n 0 1 it is worth to mention that our results solve the open problem proposed by kulenvic and ladas in their monograph dynamics of second order rational difference equations with open problems and conjectures chapman hall crc boca raton 2002

consonant recognition loss in hearing impaired listeners this paper presents a compact graphical method for comparing the performance of individual hearing impaired hi listeners with that of an average normal hearing nh listener on a consonant by consonant basis this representation named the consonant loss profile clp characterizes the effect of a listener s hearing loss on each consonant over a range of performance the clp shows that the consonant loss which is the signal to noise ratio snr difference at equal nh and hi scores is consonant dependent and varies with the score this variation in the consonant loss reveals that hearing loss renders some consonants unintelligible while it reduces noise robustness of some other consonants the conventional snr loss metric snr50 defined as the snr difference at 50 recognition score is insufficient to capture this variation the snr50 value is on average 12 db lower when measured with sentences using standard clinical procedures than when measured with nonsense syllables a listener with symmetric hearing loss may not have identical clps for both ears some consonant confusions by hi listeners are influenced by the high frequency hearing loss even at a presentation level as high as 85 db sound pressure level

computation of sparse circulant permanents via determinants we consider the problem of computing the permanent of circulant matrices we apply some recent results on the computation of the number of perfect matchings of small genus graphs in order to show that the permanent of a circulant matrix with three nonzero entries per row is the linear combination of just four determinants of circulant matrices with the same structure as the original matrix we also show that the same result holds true for a class of circulant matrices with four nonzero entries per row related to the dimer problem with periodic boundary conditions conversely we give hints at the fact that more general circulants do not share similar properties and thus should be dealt with by means of radically different approaches

global attractivity in a recursive sequence in this paper we study the invariant intervals the globally attractivity of the two equilibrium points and the oscillatory behavior of the solutions of the difference equationx n ax n 1 bx n 2c x n 2 n 1 2 where a b c 0

global attractivity of the difference equation xn 1 α xn k xn in this paper we investigate the global stability of all negative solutions of the difference equationx n email protected x n kx n n 0 1 where a 1 is an integer and the initial conditions x k x 0 are arbitrary real numbers we show that the unique negative equilibrium of the equation is a global attractor with a basin that depends on certain conditions of the coefficient

global stability two conjectures and maple abstract consider the second order difference equation u 1 0 u 0 0 and u n 1 f u n 1 u n for n 0 where either a f u v u p v u q v or b f u v p q v 1 u if 0 q p in case a or p 0 and q 0 in case b it has been conjectured see m r s kulenovic g ladas dynamics of second order rational difference equations chapman and hall crc press 2001 that lim n u n exists and equals l where l 0 and l f l l we prove this conjecture in case a and significantly extend the range of p and q for which it is known in case b in cases a and b these questions are equivalent to global stability of the fixed point l l of the planar map u v v f u v for as in case a we consider natural four dimensional extensions t of 3 and s of 2 for 0 q p we prove that l l l l is a global stable fixed point of t but we also describe precisely a range of parameters 0 q p for which s has at least three distinct fixed points in the positive orthant we describe section 3 some general principles underlying our arguments symbolic calculations using maple play a crucial role in our arguments in section 4

geometric stability conditions for higher order difference equations is a higher order or delay autonomous difference equation if the order m is a fixed positive integer larger than 1 the real valued function f is assumed continuous on r and x x g r are the initial values in 1ym 0 addition to the fact that discretizations of scalar differential equations result in equations of type 1 direct applications of difference equations of order greater than 1 date back to more than half a century ago and nowadays these equations are increasingly encountered in both social and w x w x natural sciences see 4 and 6 for some applications and additional references a solution x of f x x s x is a fixed point or equilibrium of eq 1 like its differential analogs 1 can be and often is translated into a first order vector equation the instability or the asymptotic stability of x may then be determined by linearizing the associated vector function

global attractivity for a class of higher order nonlinear difference equations our aim in this paper is to investigate the global attractivity of all positive solutions of the higher order nonlinear difference equationx n 1 a bx email protected k i 0b ix n i n 0 1 where a b b email protected 0 a b 0 b k email protected 0 email protected 1 2 and the initial conditions x k x 0 are arbitrary real numbers we show that one positive equilibrium of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients

invariant intervals and global behavior of a higher order difference equation in this paper we study the boundedness the invariant intervals the periodic character and the global asymptotic stability of all positive solutions of the higher order nonlinear difference equation y n 1 p qy n k1 y n k ry n k 1 n 0 1 where the parameters p q email protected 0 email protected 0 1 2 and the initial conditions y k 1 y k y email protected 0 we show that the unique positive equilibrium of the above equation is globally asymptotically stable under certain conditions

global asymptotic stability of a second order nonlinear difference equation in this paper the global asymptotic stability of the nonlinear difference equationx n 1 a bx na bx n cx n 1 n 0 1 is investigated where a b a b c 0 are real numbers and the initial conditions x 1 is nonnegative real numbers and x 0 is a positive real number we show that the unique positive equilibrium of the equation is globally asymptotically stable in particular our results solve two conjectures proposed by kulenovic and ladas in their monograph m r s kulenovic g ladas dynamics of second order rational difference equations with open problems and conjectures chapman hall crc boca raton 2002 and by kulenovic et al in their paper m r s kulenovic g ladas l f martins i w rodrigues the dynamics of x n 1 a bx na bx n cx n 1 facts and conjectures comput math appl 45 2003 1087 1099 099

green s function and stability of a linear partial difference scheme abstract this paper is concerned with a linear partial difference equation which arises from discretizing a heat and a first order wave equations a green s function for this equation is derived various representation theorems monotonicity and oscillatory properties of the green s functions are obtained then by means of the representation theorems we derive several stability criteria for arbitrary solutions of this equation

how fast can one compute the permanent of circulant matrices abstract in this paper we address the problem of computing the permanent of 0 1 circulant matrices we investigate structural properties of circulant matrices showing that i if they are dense enough then they contain large arbitrary submatrices and ii if they are very sparse then they are not too far from convertible matrices building upon ii we then develop an efficient algorithm which allows us to compute permanents of very sparse circulants of size up to 200

global asymptotic stability for a higher order nonlinear rational difference equations abstract in this paper we investigate the boundedness periodic character invariant intervals and the global asymptotic stability of all nonnegative solutions of the difference equation x n 1 ax n bx n k a bx n n 0 1 where a b a b are positive real numbers k 1 is a positive integer and the initial conditions x k x 1 x 0 are nonnegative real numbers it is shown that the zero equilibrium of this equation is globally asymptotically stable if b a a and the unique positive equilibrium is globally asymptotically stable if a a b a a the results obtained solve a open problem proposed by kulenovic and ladas m r s kulenovi g ladas dynamics of second order rational difference equations chapman hall crc boca raton fl 2002 p 129

on the difference equation yn 1 a ynyn k with a 0 abstract we find conditions for the global asymptotic stability of the unique negative equilibrium y 1 a of the equation 0 1 y n 1 a y n y n k where y k y k 1 y0 0 a

bounds for solutions of a six point partial difference scheme abstract this paper is concerned with a class of partial difference equations which arise from discretising the one dimensional heat and the first order wave equations explicit bounds are found for their solutions and subexponential solutions are considered using the green s function we derive a stability criteria for arbitrary solutions of this equation

on the parity of permanents of circulant matrices abstract starting from previous results concerning determinants and permanents of 0 1 circulant matrices and using theory on finite fields with characteristic 2 we first see denoting by a the n n 0 1 circulant matrix whose 1 s in the first row are exactly in positions i 1 i 2 i k that per a is even iff gcd x i 1 x i 2 x i k 1 x n 1 in z 2 x we then derive some consequences for specific classes of primes n in particular when n is a prime such that the group z n is generated by the residue class 2 we see that for k n and k odd the value per a is always odd similarly for n 7 and n prime with the group of squares in z n generated by the class 2 we see that for k 3 the value per a is always odd contrary to such cases we find that when n is a mersenne prime greater than 3 there are a significant number of circulants a of the above form with k odd and per a even

normal forms for rational difference equations with applications to the global periodicity problem we propose a classification and derive the associated normal forms for rational difference equations with complex coefficients as an application we study the global periodicity problem for second order rational difference equations with complex coefficients we find new necessary conditions as well as some new examples of globally periodic equations

on the values of permanents of 0 1 circulant matrices with three ones per row abstract starting from previous works concerning permanents of 0 1 circulant matrices with three nonzero entries per row and just using algebraic methods we find some congruences satisfied by the values of such permanents along with simple generalizations to circulants with k ones per row k n k 3 we also give an alternative proof for known relations of fibonacci numbers with some of these values of permanents

determination of nodes in numerical integration rules using difference equation in this paper the difference equations will be employed to produce a polynomial which its roots are the nodes of gauss quadrature rules in this procedure we obtain a system of nonlinear equations according to the concepts of precision degree of integration and the moments of order k hence the resulted polynomials obtained by difference equations have their roots as the nodes finally some examples are given to show the application of the procedure

global asymptotic behavior of a two dimensional difference equation modelling competition we investigate the global asymptotic behavior of solutions of the system of difference equations xn 1 xn a cyn yn 1 yn b dxn n 0 1 where the parameters a and b are in 0 1 c and d are arbitrary positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers we show that the stable manifold of this system separates the positive quadrant into basins of attraction of two types of asymptotic behavior in the case where a b we find an explicit equation for the stable manifold

global attractivity in a nonlinear second order difference equation in this paper we obtain a global attractivity result for the positive equilibrium of a nonlinear second order difference equation of the form xn 1 f xn xn 1 n 0 1 the result applies to the difference equation xn 1 a bxn a n 1 n 0 1 where a b a 0 1996 john wiley sons inc

phoneme recognition in vocoded maskers by normal hearing and aided hearing impaired listeners this study compared modulation benefit for phoneme recognition obtained by normal hearing nh and aided hearing impaired hi listeners consonant and vowel recognition scores were measured using nonsense syllables in the presence of a steady state noise and four vocoded speech maskers vocoded maskers were generated by modulating the steady state noise in either one or six frequency channels with the speech envelope extracted from the speech of either a single talker or a four talker babble aided hi listeners obtained lower consonant recognition scores than nh listeners in all masker conditions vowel recognition scores for aided hi listeners were comparable to nh scores except in the six channel vocoded masker conditions where they were relatively lower analysis using the extended speech intelligibility index developed by rhebergen versfeld and dreschler 2006 j acoust soc am 120 6 3988 3997 suggested that the signal to noise ratio deficit observed in aided hi listeners was largely due to uncompensated audibility loss there was no significant difference between modulation masking release obtained by nh and aided hi listeners for both consonant and vowel recognition

on the recursive sequence xn 1 α βxn γxn 1bxn cxn 1 we investigate the global character of solutions of the equation in the title with nonnegative parameters and positive initial conditions we give a detailed description of the semicycles of solutions and prove that the equilibrium of the equation is globally asymptotically stable

statistical bias in the assessment of binaural benefit relative to the better ear the comparison of measured binaural performance with the better of two monaural measures one from each ear may lead to underestimated binaural benefit due to statistical sampling bias that favors the monaural condition the mathematical basis of such bias is reviewed and applied to speech reception thresholds measured in 32 bilateral cochlear implant ci users for coincident and spatially separated speech and noise it is shown that the bias increases with test retest variation and is maximal for uncorrelated samples of identical underlying performance in each ear when measured differences between ears were assumed to reflect actual underlying performance differences the bias averaged across the ci users was about 0 2 db for coincident target and noise and 0 1 db for spatially separated conditions an upper bound estimate of the bias based on the assumption that both ears have the same underlying performance and observed differences were due to test retest variation was about 0 7 db regardless of noise location to the extent that the test retest variation in these data is comparable to other studies the results indicate that binaural benefits in bilateral cochlear implant users are not substantially underestimated on for average when binaural performance is compared with the better ear in each listening configuration

dynamics of xn 1 xn 2k 1xn 2k 1 αxn 2l abstract we investigate the global stability of all positive solutions of the difference equation x n 1 x n 2 k 1 x n 2 k 1 x n 2 l where is a positive real number k 1 2 l 0 1 and the initial conditions are positive real numbers when x 1 1 is globally asymptotically stable also when 1 we show that this equation possesses solutions that converge to the two cycle 0 1 0 1

on the recursive sequence xn 1 α βxn k 1 γxn 2k 1bxn k 1 cxn 2k 1 abstract our aim in this paper is to investigate the global asymptotic stability of all positive solutions of the higher order nonlinear difference equation x n 1 x n k 1 x n 2 k 1 bx n k 1 cx n 2 k 1 n 0 1 2 where b c and are positive k 1 2 3 and the initial conditions x 2 k 1 x 1 x 0 are positive real numbers we show that the unique positive equilibrium of the equation is globally asymptotically stable and has some basins that depend on certain conditions posed on the coefficients our concentration is on invariant intervals the character of semicycles and the boundedness of the above mentioned equation our final comments are about informative examples

on asymptotic behaviour of the difference equation xn 1 α xn kxn in this paper we investigate the global stability and the periodic character of positive solutions of the difference equationx n email protected x n kx nunder specified conditions

on rational recursive sequences our goal in this chapter is to gain some understanding of the dynamics of rational recursive sequences of the form x n 1 frac a sum limits i 0 k a i x n i b sum limits i 0 k b i x n i n 0 1 3 0 1 where k is a positive integer and the coefficients a b a 0 a k b 0 b k are nonnegative real numbers

on the recursive sequencexn 1 α xn 1 xn abstract we study the global stability the boundedness character and the periodic nature of the positive solutions of the difference equationxn 1 xn 1 xn where 0 and where the initial conditionsx 1andx0are arbitrary positive real numbers

the characteristics of a higher order rational difference equation in this paper we study the global behavior of the higher order nonlinear difference equationx n email protected email protected n k email protected n 2 k 1a bx n k 1 n 0 1 where a b and a b c are positive email protected 1 2 3 and the initial conditions x 2 k 1 x 1 x 0 are positive real numbers we investigate the character of semicycles periodicity global stability and boundedness of above mentioned equation

dynamics of the difference equation xn 1 xn pxn kxn q we study the invariant interval the character of semicycles the global stability and the boundedness of the difference equation x n 1 x n px n kx n q n 0 where the initial conditions x k x 1 x 0 are nonnegative and p q 0

global stability of yn 1 p qyn ryn k1 yn in this paper we investigate the global stability of difference equation y n 1 p qy n ry n k1 y n n 0 1 2 where the initial conditions y k y 1 y 0 are non negative email protected 1 2 3 and the parameters p q and r are non negative we show that when rq 1 and k is odd then this equation possesses unbounded solutions

on the difference equation xn p xn sqxn t xn s abstract we investigate the persistence and global attractivity of the difference equation x n p x n s qx n t x n s n 1 2 3 with positive parameters and positive initial conditions our results not only include some previously known results but apply to some difference equations that have not been investigated so far

on the recursive sequence yn 1 α yn 1β yn yn 1yn abstract we study the global stability the boundedness character and the periodic nature of the positive solutions of the difference equation y n 1 y n 1 y n y n 1 y n n 0 1 2 where 0 2 and the initial conditions y 1 y0 are arbitrary positive real numbers

dynamics of a rational difference equation in this paper we investigate the periodic character invariant intervals oscillation and global stability of all positive solutions of the equationx n 1 px n x n kq x n k n 0 1 where the parameters p and q and the initial conditions x k x 0 are nonnegative real numbers as might be expected the two cases p q give rise to different dynamic behaviors in particular our results solve the open problem proposed by kulenvic and ladas in their monograph dynamics of second order rational difference equations with open problems and conjectures chapman hall crc boca raton 2001

stability criteria for two partial difference equations abstract this paper is concerned with two classes of linear partial difference equations with constant coefficients explicit conditions are derived which are sufficient and or necessary for these equations to have stable solutions

global stability of a higher order rational recursive sequence abstract in this paper we study the qualitative behavior of solutions of the class of delay difference equation x n 1 x n k 1 x n 2 k 1 a bx n k 1 n 0 1 2 where the initial conditions x 2 k 1 x 1 x 0 are positive k 1 2 and the parameters a b are positive our concentration is on invariant intervals and the global stability of the above mentioned equation we obtain sufficient conditions for the global attractivity of all positive solutions about the zero and positive equilibrium points with basins that depend on specific conditions posed on the coefficients furthermore the oscillation and the character of semicycles about the positive equilibrium are thoroughly discussed it is also illustrated that for some special case of parameters the solution will be either a period 2 solution or will converge to the equilibrium point or will have unbounded solutions

on the recursive sequence xn 1 α βxn k 1a bxn k 1 cxn 2k 1 abstract in this paper we study the global asymptotic stability invariant intervals the character of semicycles and the boundedness of all positive solutions of the higher order nonlinear difference equation x n 1 x n k 1 a bx n k 1 cx n 2 k 1 n 0 1 where a b c and are positive k 1 2 3 and the initial conditions x 2k 1 x 1 x0 are positive real numbers we show that the unique positive equilibrium of the equation is globally asymptotically stable finally we present some informative examples

dynamics of a non linear difference equation abstract our aim in this paper is to investigate the dynamics of difference equation y n 1 y n py n k y n q n 0 1 2 where the initial conditions y k y 1 y0 are non negative k 1 2 3 and the parameters p and q are non negative we study characteristics such as periodicity invariant interval the character of semicycles the global stability and the boundedness of positive solutions of the above mentioned difference equation in particular our results solve the open problem introduced by kulenovic and ladas in their monograph dynamics of second order rational difference equations with open problems and conjectures chapman and hall crc boca raton 2002