oscillation theorems for differential equations with a nonlinear damping term in this paper we are concerned with a class of nonlinear second order differential equations with a nonlinear damping term passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity and as a consequence our results apply to wider classes of nonlinear differential equations two illustrative examples are considered

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

philos type oscillation criteria for linear differential equations with impulsive effects abstract the present paper deals with the problem of oscillation for a second order linear differential equation in which an impulsive effect is considered this equation can be regarded as an equation of motion in which the moving speed of a mass point changes sharply by some influence it is proved that there is a case that the mass point may oscillate due to the influence of the impulsive effect even if the mass point does not oscillate in the model removing the impulsive effect it is also shown that the obtained results extend some previous ones through the use of an example

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

new refinements of the jensen inequalities based on samples with repetitions abstract in this paper we give a refinement of the jensen inequality for any mid convex function f by arithmetic means of f evaluated at arithmetic means of samples with repetitions the case of samples without repetitions was treated by j e pecaric and v volenec osterreich akad wiss math natur kl sonderdruck sitzungsber 197 1988 463 467

mixed mean inequalities for several positive definite matrices on basis of the geometric mean proposed recently by t ando chi kwong li and roy mathias in this paper we present several kinds of mixed means for three or more positive definite matrices and prove some related mixed mean inequalities

on weighted hermite hadamard inequalities abstract in this paper we give a weighted form of the hermite hadamard inequalities some applications of them are also derived the results presented here would provide extensions of those given in earlier works finally we pose two interesting problems

oscillation of second order nonlinear ode with damping we are concerned with a class of general type second order differential equations with a nonlinear damping term new oscillation criteria are established which 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

on the loss of information in conditional maximum likelihood estimation of item parameters in item response models of the rasch type fischer molenaar 1995 item parameters are often estimated by the conditional maximum likelihood cml method this paper addresses the loss of information in cml estimation by using the information concept of f information liang 1983 this concept makes it possible to specify the conditions for no loss of information and to define a quantification of information loss for the dichotomous rasch model the derivations will be given in detail to show the use of the f information concept for making comparisons for different estimation methods it is shown that by using cml for item parameter estimation some information is almost always lost but compared to jml joint maximum likelihood as well as to mml marginal maximum likelihood the loss is very small the reported efficiency in the use of information of cml to jml and to mml in several comparisons is always larger than 93 and in tests with a length of 20 items or more larger than 99

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

a rasch model for partial credit scoring a unidimensional latent trait model for responses scored in two or more ordered categories is developed this partial credit model is a member of the family of latent trait models which share the property of parameter separability and so permit specifically objective comparisons of persons and items the model can be viewed as an extension of andrich s rating scale model to situations in which ordered response alternatives are free to vary in number and structure from item to item the difference between the parameters in this model and the category boundaries in samejima s graded response model is demonstrated an unconditional maximum likelihood procedure for estimating the model parameters is developed

oscillation criteria for second order nonlinear differential equations involving general means consider the second order nonlinear differential equation e y a t f y 0 where a t c 0 f y c1 f y 0 and yf y 0 for y 0 furthermore f y also satisfies either a superlinear or a sublinear condition which covers the nonlinear function f y y y 1 with 1 and 0 1 respectively commonly known as the emden fowler case here the coefficient function a t is allowed to be negative for arbitrarily large values of t kamenev type oscillation criteria involving integral averages for the linear equations l y a t y 0 are extended to the nonlinear equation e by using more general means the results extend similar results on general means by philos for the linear equation l and also results based upon kamenev s integral averaging method concerning the nonlinear equation e

on oscillation of nonlinear second order differential equations with damping term the paper is concerned with oscillation of a novel class of nonlinear differential equations with a damping term first it is demonstrated how known oscillation results for another intensively studied class of equations can be translated to the one in question and vice versa advantages and drawbacks of such translation are carefully examined then an oscillation criterion for the new class of equations is established the principal result of the paper is compared to those reported in the literature and an illustrative example to which known oscillation criteria fail to apply is provided

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

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 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

on the construction of all factors of the model for factor analysis a construction method is given for all factors that satisfy the assumptions of the model for factor analysis including partially determined factors where certain error variances are zero various criteria for the seriousness of indeterminacy are related it is shown that green s 1976 conjecture holds for a linear factor predictor the mean squared error of prediction is constant over all possible factors a simple and general geometric interpretation of factor indeterminacy is given on the basis of the distance between multiple factors it is illustrated that variable elimination can have a large effect on the seriousness of factor indeterminacy a simulation study reveals that if the mean square error of factor prediction equals 5 then two thirds of the persons are correctly selected by the best linear factor predictor

oscillation criteria for second order nonlinear differential equations with damping abstract for a second order nonlinear differential equation with a damping term we obtain new oscillation criteria without an assumption that has been required for related results reported in the literature over the last two decades two approaches refining the standard integral averaging technique suggested in the paper can be used to derive a variety of simpler oscillation theorems for different classes of nonlinear differential equations and both sets of oscillation criteria established in the paper are of independent interest several examples are provided to illustrate the relevance of the new theorems

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

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

some inequalities involving means and their converses using an idea of j sandor and v e s szabo an inequality of ky fan and its generalizations are proved we also establish some converses of these inequalities as consequences some well known inequalities are obtained

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

some results on mean square error for factor score prediction for the confirmatory factor model a series of inequalities is given with respect to the mean square error mse of three main factor score predictors the eigenvalues of these mse matrices are a monotonic function of the eigenvalues of the matrix p 1 2 p p 1 p 1 2 this matrix increases with the number of observable variables p a necessary and sufficient condition for mean square convergence of predictors is divergence of the smallest eigenvalue of p or equivalently divergence of signal to noise schneeweiss mathes 1995 the same condition is necessary and sufficient for convergence to zero of the positive definite mse differences of factor predictors convergence to zero of the distance between factor predictors and convergence to the unit value of the relative efficiencies of predictors various illustrations and examples of the convergence are given as well as explicit recommendations on the problem of choosing between the three main factor score predictors