existence of positive solutions for some nonlinear parabolic systems in exteriors domains we prove some existence results of positive continuous solutions to the semilinear parabolic system u u t p x t g v v v t q x t f u in an unbounded domain d with compact boundary subject to some dirichlet conditions where and are nonnegative parameters the functions f g are nonnegative continuous monotone on 0 and the potentials p q are nonnegative and satisfy some hypotheses related to the parabolic kato class j d

global existence of solutions for a weakly coupled system of semilinear damped wave equations abstract in this paper we consider the cauchy problem for a weakly coupled system of semilinear damped wave equations we prove the global existence of solutions for small data in the supercritical case for any space dimension we also give estimates of the weighted energy of solutions and in a special case we prove an almost optimal estimate moreover in the subcritical case we give an almost optimal estimate of the lifespan from both above and below

estimating kappa from binocular data a common error in statistical analysis of ophthalmic data is the lack of accounting for the positive correlation generally present between observations made in fellow eyes the alternative of data analysis from only one eye in each patient may lead to loss of power and unrealistically large confidence intervals this paper discusses a method to estimate kappa a measure of agreement between two graders when both graders rate the same set of pairs of eyes the method assumes that the true left eye and right eye kappa values are equal and makes use of the correlated binocular data to estimate confidence intervals for the common kappa simulations show that the new estimators are better than the estimator based on only one eye new confidence intervals had the correct coverage probability but were usually only about 70 per cent as wide as single eye intervals the general methodology described here applies to analysis of grader agreement in rating other paired body structures

nonexistence of positive weak solutions of elliptic inequalities abstract in this paper we give sufficient conditions for the nonexistence of positive entire weak solutions of coercive and anticoercive elliptic inequalities both of the p laplacian and of the mean curvature type depending also on u and x inside the divergence term while a gradient factor is included on the right hand side in particular to prove our theorems we use a technique developed by mitidieri and pohozaev in e mitidieri s i pohozaev a priori estimates and the absence of solutions of nonlinear partial differential equations and inequalities proc steklov inst math 234 2001 1 362 which relies on the method of test functions without using comparison and maximum principles their approach is essentially based first on a priori estimates and on the derivation of an asymptotics for the a priori estimate finally nonexistence of a solution is proved by contradiction

on entire solutions of degenerate elliptic differential inequalities with nonlinear gradient terms in this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of p laplacian elliptic inequalities with possibly singular weights and gradient terms of the form divfg jxj jduj p 2 dug h jxj f u jxj l jduj under the main request

agreement between two independent groups of raters we propose a coefficient of agreement to assess the degree of concordance between two independent groups of raters classifying items on a nominal scale this coefficient defined on a population based model extends the classical cohen s kappa coefficient for quantifying agreement between two raters weighted and intraclass versions of the coefficient are also given and their sampling variance is determined by the jackknife method the method is illustrated on medical education data which motivated the research

on the existence of multiple positive entire solutions for a quasilinear elliptic systems abstract in this paper our main purpose is to establish the existence of infinitely positive bounded entire solutions of second order quasilinear elliptic systems these extend a work of zuodong yang zuodong yang existence of positive bounded entire solutions of quasilinear elliptic equations appl math comput 156 2004 743 754 which considered the single quasilinear elliptic equation these extend also a work of kawano and kusano n kawano t kusano on positive entire solutions of a class of second order semilinear elliptic systems math zeitschrift 186 3 1984 287 297 which studied the semilinear elliptic equation

nonexistence of global solutions of a nonlinear hyperbolic system consider the initial value problem utt au ivip vtt av u q x e r t t o u x 0 f x v x 0 h x ut x 0 g x vt x 0 x with 1 0 we show that there exists a bound b n oo such that if 1 pq b n all nontrivial solutions with compact support blow up in finite time

asymptotic behavior of entire large solutions to semilinear elliptic equations abstract in this paper by using karamata regular variation theory we study the exact asymptotic behavior of entire large solutions to u b x f u x r n n 3 where b c r n is nonnegative and nontrivial in r n f c 0 is positive and non decreasing on 0 which satisfies keller osserman condition and is rapidly varying or regularly varying at infinity with index 1

complete blow up after tmax for the solution of a semilinear heat equation soit un sous ensemble ouvert borne de r n a frontiere lisse on considere le probleme u t u f u dans o t u 0 sur o t u x o u 0 x x ou f r r est localement de lipschitz non decroissante et f o 0

nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints hamiltoniens sousquadratiques conditions aux limites infinies et donnees d explosion hamiltoniens superquadratiques formulation viscosite des conditions aux limites le probleme ergodique commande stochastique optimale avec contraintes d etat

the role of critical exponents in blow up theorems the sequel abstract in 27 fujita showed that for positive solutions the initial value problem in r n for u t u u p with p 1 exhibited the following behavior if p p c 1 2 n then the initial value problem does not have any nontrivial non negative solution existing on r n 0 a global solution whereas if p p c there exist global small data positive solutions as well as solutions which are non global we call such a result a blow up theorem of fujita type in 50 levine discussed the various theorems of this type that had appeared in the literature prior to 1990 in this paper we revisit the literature since 1990

a note on the kappa statistic for clustered dichotomous data the kappa statistic is widely used to assess the agreement between two raters motivated by a simulation based cluster bootstrap method to calculate the variance of the kappa statistic for clustered physician patients dichotomous data we investigate its special correlation structure and develop a new simple and efficient data generation algorithm for the clustered physician patients dichotomous data based on the delta method and its special covariance structure we propose a semi parametric variance estimator for the kappa statistic an extensive monte carlo simulation study is performed to evaluate the performance of the new proposal and five existing methods with respect to the empirical coverage probability root mean square error and average width of the 95 confidence interval for the kappa statistic the variance estimator ignoring the dependence within a cluster is generally inappropriate and the variance estimators from the new proposal bootstrap based methods and the sampling based delta method perform reasonably well for at least a moderately large number of clusters e g the number of clusters k 50 the new proposal and sampling based delta method provide convenient tools for efficient computations and non simulation based alternatives to the existing bootstrap based methods moreover the new proposal has acceptable performance even when the number of clusters is as small as k 25 to illustrate the practical application of all the methods one psychiatric research data and two simulated clustered physician patients dichotomous data are analyzed

kappa statistic for clustered matched pair data kappa statistic is widely used to assess the agreement between two procedures in the independent matched pair data for matched pair data collected in clusters on the basis of the delta method and sampling techniques we propose a nonparametric variance estimator for the kappa statistic without within cluster correlation structure or distributional assumptions the results of an extensive monte carlo simulation study demonstrate that the proposed kappa statistic provides consistent estimation and the proposed variance estimator behaves reasonably well for at least a moderately large number of clusters e g k 50 compared with the variance estimator ignoring dependence within a cluster the proposed variance estimator performs better in maintaining the nominal coverage probability when the intra cluster correlation is fair 0 3 with more pronounced improvement when is further increased to illustrate the practical application of the proposed estimator we analyze two real data examples of clustered matched pair data copyright 2014 john wiley sons ltd

on the existence of positive solutions for a class of semilinear elliptic equations we prove some existence and nonexistence results for the semilinear elliptic equation u q x f u on rn n 2 where u is required to blow up on the boundary of and f is a nonnegative function which is assumed to be lipschitz continuous and bounded away from zero on each interval e and have at worst linear growth in particular we extend some results already obtained in the case where f u u 0 1

comments on narrow band interference rejection using real time fourier transforms in their paper on narrow band interference excision in ds ss systems d davidovici and e g kanterakis ibid vol 37 p 713 22 1989 concluded that excision need not improve the bit error rate at high interference levels it is argued that while this conclusion follows from the specific cases examined it does not apply to more realistic spread spectrum system designs

large solutions of semilinear elliptic equations under the keller osserman condition abstract we consider the equation u p x f u where p is a nonnegative nontrivial continuous function and f is continuous and nondecreasing on 0 satisfies f 0 0 f s 0 for s 0 and the keller osserman condition 1 f s 1 2 d s where f s 0 s f t d t we establish conditions on the function p that are necessary and sufficient for the existence of positive solutions bounded and unbounded of the given equation

critical exponent for the cauchy problem to the weakly coupled damped wave system abstract in this paper we consider a system of weakly coupled semilinear damped wave equations we determine the critical exponent for any space dimensions our proof of the global existence of solutions for supercritical nonlinearities is based on a weighted energy method whose multiplier is appropriately modified in the case where one of the exponent of the nonlinear term is less than the so called fujita s critical exponent we also give estimates of the lifespan of solutions from above for subcritical nonlinearities

analysis of dft based frequency excision algorithms for direct sequence spread spectrum communications the capacity of direct sequence spread spectrum modulation to reject narrow band interference can be significantly improved by eliminating narrow band energy at the receiver in a process called frequency excision this paper considers several algorithms that operate on the real time discrete fourier transform dft of the received signal to perform frequency excision the case in which only the signal and additive white gaussian noise awgn are present at the receiver is considered as a means of comparing the relative performance of different algorithms that operate without knowledge of the power spectral density of the interference an approach for analysis using the postcorrelation signal to noise ratio snr as the figure of merit is presented that is valid for a broad class of spreading modulations first the algorithm that sets a fixed fraction of the frequency domain record to zero is examined using rank order statistics as an analytical tool this result is then generalized to confirm previous estimates of snr degradation for the algorithm that sets all values that exceed a threshold to zero these results are again generalized to apply to the algorithm that sets a fixed fraction of the band to a fixed amplitude while retaining phase information in an algorithm called fraction clip the relative performances of several clip algorithm options are derived as special cases finally a performance measure of the algorithms in the presence of multiple narrow band interference is provided and illustrated with an example

global existence and finite time blow up for a degenerate reaction diffusion system abstract this paper investigates the blow up and global existence of solutions of the degenerate reaction diffusion system u t u m u v p v t v n u q v x t 0 t with homogeneous dirichlet boundary data where r n is a bounded domain with smooth boundary m n 1 0 and p q 0 it is proved that if m n and pq m n every nonnegative solution is global whereas if m or n or pq m n there exist both global and blow up nonnegative solutions when m n and pq m n we show that there exists 1 which depends on the parameters p q m n such that all positive solutions are global if 1 while if 1 1 all positive solutions blow up in finite time where 1 is the first dirichlet eigenvalue for the laplacian on

the existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term abstract we show the existence and nonexistence of entire positive solutions for semilinear elliptic system with gradient term u u p x f u v v v q x g u v on r n n 3 provided that nonlinearities f and g are positive and continuous the potentials p and q are continuous c positive and satisfy appropriate growth conditions at infinity we find that entire large positive solutions fail to exist if f and g are sublinear and p and q have fast decay at infinity while if f and g satisfy some growth conditions at infinity and p q are of slow decay or fast decay at infinity then the system has infinitely many entire solutions which are large or bounded

performance study of maximum likelihood receivers and transversal filters for the detection of direct sequence spread spectrum signal in narrowband interference linear least squares estimation techniques can be used to enhance suppression of narrowband interference in direct sequence spread spectrum systems nonlinear techniques for this purpose have also been investigated recently the authors derive maximum likelihood receivers for direct sequence signal in gaussian interference with known second order characteristics it is shown that if the receiver uses samples from outside the bit interval then the receiver structure is nonlinear the bit error rate performances of these receivers are compared to those of linear receivers employing one sided and two sided least squares estimation filters for the case of gaussian autoregressive interference the results show that intersymbol interference due to filter taps extending beyond the bit interval cannot be ignored for small processing gains in some cases not accounting for intersymbol interference yields too optimistic error estimates very much away from the true error rates

blow up and global existence of solutions to an inhomogeneous parabolic system abstract we study the critical phenomenon of a weakly coupled inhomogeneous parabolic system which is largely unexplored even though the homogeneous problem has been widely studied the conditions on the powers of the nonlinear terms are new compared with the well known homogeneous case the method appears to be different from the standard ones in the literature an application to the lame emden system is also given

fujita type phenomenon of nonlinear coupled nonlocal diffusion system abstract this paper studies a cauchy problem for a nonlinear coupled nonlocal diffusion system u t j u u v p v t j v v u q we first deal with the critical fujita exponent and then determine the second critical exponent to characterize the critical space decay rate of initial data in the co existence region of global and non global solutions it turns out that the results are coincident with the classical heat system we not only generalize the results in the scalar case obtained by j garcia melian and f quiros 2010 6 to the case of a system but also delete the monotonicity condition on the kernel function j the key techniques are modifying the rescaled test function method with a new test function rather than the eigenfunction of the nonlocal operator to deal with blow up of the solution and selecting a suitable banach space via the estimates obtained by j terra and n wolanski 2011 13 to obtain the global solutions

the form of blow up for nonlinear parabolic equations on considere des equations paraboliques semi lineaires de la forme u t 2 u sf u ou f est positive et 0 ds f s est finie on etudie des problemes a 1 dimension dans la region semi infinie x o et on trouve le temps t

a remark on the radial and nonradial solutions for an elliptic system with a quadratic gradient term recently the authors yang and zhang in y yang x zhang entire blow up solutions of semilinear elliptic system with quadratic gradient term abstract and applied analysis 2012 have been obtained sufficiently conditions for the existence and non existence of radially symmetric solutions for the system of equations du i u i 2 a i x f i u 1 u d on r n n 3 with i 1 d and d 1 2 3 4 our aim in this paper is to give a necessary and a sufficient condition but for the existence of large or explosive solutions for the same class of systems moreover we intend to obtain a non radial solution for the considered problem we also point out that our framework in the obtained results improve and complete some of the results obtained by yang and zhang

some alternatives in transform domain suppression of narrow band interference for signal detection and demodulation conventional detection and demodulation rules are not ideally suited for use with discrete fourier transform dft based narrow band interference suppression if the dft incorporates time weighting to localize the interference spectrally detection rules which are adapted to the time weighting are introduced and shown to offer significant improvements in performance but their implementation is complex it is found that if a spectrally contained orthogonal transform scot is employed in place of the windowed dft however the conventional detection rules have a level of performance comparable to that obtained with dft based suppression and the adapted rules in addition to yielding good interference localization scots benefit from the fact that they provide a karhunen loeve like transform for each component of the observation the primary focus of the paper is the application of interference suppression for the detection of the presence of covert signals however it is also demonstrated that scot based suppression is potentially better suited than dft based suppression for data demodulation in commercial code division multiple access cdma network overlays

a necessary and sufficient condition for the existence of large solutions to sublinear elliptic systems abstract we prove that the elliptic system u p x v v q x u on r n n 3 where 0 1 0 1 and p and q are nonnegative continuous functions has a nonnegative entire radial solution satisfying lim x u x lim x v x if and only if the functions p and q satisfy 0 t p t t 2 n 0 t s n 3 q s d s d t 0 t q t t 2 n 0 t s n 3 p s d s d t with p r 0 r p d and q r 0 r q d this extends previous existence results for both the single equation and systems

a nonlocal in time parabolic system whose fujita critical exponent is not given by scaling abstract we consider the nonlocal coupled parabolic system u t u 0 t t s 1 v p 1 v s d s v t v 0 t t s 2 u q 1 u s d s in 0 t when either r n or r n is a bounded domain with smooth boundary we assume that 0 1 2 1 p q 1 and the initial data u 0 v 0 c 0 we obtain the fujita critical exponent for the system above which is not given by the scaling argument

estimating kappa from binocular data and comparing marginal probabilities suppose that two graders classify all eyes in a sample of patients for the presence or absence of a specified abnormality in the statistical analysis of the data possible correlation between the observations in the right and left eyes should be taken into account recently general methods have been developed to analyse grader agreement in rating paired body structures in the present paper an alternative procedure is proposed that utilizes existing formulae for the computation of weighted kappa and its standard error in addition the mcnemar test is generalized to compare the probabilities of a positive judgement by the two graders

remarks on nonexistence of solutions of mixed sublinear and superlinear elliptic equation in rn abstract in this note we consider the quasilinear elliptic equation p u h x u m h x u n in r n n 3 where 0 m p 1 n we establish conditions sufficient to ensure the nonexistence of nonnegative entire solutions which improves a result of a v lair a v lair large solutions of mixed sublinear superlinear elliptic equations j math anal appl 346 2008 99 106

a generalized concordance correlation coefficient for continuous and categorical data this paper discusses a generalized version of the concordance correlation coefficient for agreement data the concordance correlation coefficient evaluates the accuracy and precision between two measures and is based on the expected value of the squared function of distance we have generalized this coefficient by applying alternative functions of distance to produce more robust versions of the concordance correlation coefficient in this paper we extend the application of this class of estimators to categorical data as well and demonstrate similarities to the kappa and weighted kappa statistics we also introduce a stratified concordance correlation coefficient which adjusts for explanatory factors and an extended concordance correlation coefficient which measures agreement among more than two responses with these extensions the generalized concordance correlation coefficient provides a unifying approach to assessing agreement among two or more measures that are either continuous or categorical in scale

blowup solutions for a reaction diffusion system with exponential nonlinearities abstract we consider the following parabolic system whose nonlinearity has no gradient structure t u u e p v t v v e q u u 0 u 0 v 0 v 0 p q 0 in the whole space r n we show the existence of a stable blowup solution and obtain a complete description of its singularity formation the construction relies on the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to conclude in particular our analysis uses neither the maximum principle nor the classical methods based on energy type estimates which are not supported in this system the stability is a consequence of the existence proof through a geometrical interpretation of the quantities of blowup parameters whose dimension is equal to the dimension of the finite dimensional problem

large solutions of mixed sublinear superlinear elliptic equations abstract we consider the equation u p x u q x u on r n n 3 where p q are nonnegative continuous functions and 0 we establish conditions sufficient to ensure the existence and nonexistence of nonnegative entire large solutions of the equation

global nonexistence for the cauchy problem of some nonlinear reaction diffusion systems we first consider the parabolic equationut 2um a x uq f t x u p w t x t 0 x rn where 2 is the 2 fractional power of the laplacian which for 0 2 stands for impurities and f t x and w t x are given nonnegative functions and find its critical exponent then we consider the criticality for five systems of strongly coupled parabolic equations two of them with nonlinear convective terms our results answer positively some open problems raised recently by bandle deng levine and zhang

narrow band interference rejection using real time fourier transforms an analysis is presented of a bpsk pn binary phase shift keyed with pseudonoise demodulator when present narrowband interference is attenuated using transform domain filtering the signal of interest is a wideband direct sequence spread spectrum signal ds ss the interference is a narrowband signal which may be of high power and which is either intentionally or unintentionally collocated in frequency and interfering with the signal of interest the effect of windowing the input signal by a rectangular or hamming windows as well as the use of an overlap and save scheme is presented it is shown that the hamming window far outperforms the rectangular window and that the interference is for all purposes completely eliminated when the hamming window is used in conjunction with the overlap and save scheme the criterion used to evaluate the effectiveness of the different interference rejection techniques is the bit error rate ber as measured at the output of the demodulator

existence and nonexistence of global solutions for a semilinear reaction diffusion system abstract this paper is concerned with the blow up and global existence of nonnegative solutions to the following cauchy problem u t u v p t 0 x r n v t v a x u q t 0 x r n u x 0 u 0 x v x 0 v 0 x x r n where the constants p q 0 and a x 0 is on the order x m as x m r the fujita critical exponent is determined when m 0 and some results of global existence of solution under some assumptions when m 0 are also obtained the results extend those in escobedo and herrero 1991 9 and indicate that m affects the fujita critical exponent

testing the equality of two dependent kappa statistics procedures are developed and compared for testing the equality of two dependent kappa statistics in the case of two raters and a dichotomous outcome variable such problems may arise when each of a sample of subjects are rated under two distinct settings and it is of interest to compare the observed levels of inter observer and intra observer agreement the procedures compared are extensions of previously developed procedures for comparing kappa statistics computed from independent samples the results of a monte carlo simulation show that adjusting for the dependency between samples tends to be worthwhile only if the between setting correlation is comparable in magnitude to the within setting correlations in this case a goodness of fit procedure that takes into account the dependency between samples is recommended

global blow up of a nonlinear heat equation solutions to semilinear parabolic equations of the form u t u f u x in which blow up at some finite time t are investigated for slowly growing functions f for nonlinearities such as f s 2 s ln 2 s 1 b with 0 u becomes infinite throughout as t t it is alsofound that for marginally more quickly growing functions e g f s 2 s ln 2 s 2 u is unbounded on some subset of which has positive measure and is unbounded throughout if is a small enough region

blow up phenomena for a nonlinear reaction diffusion system with time dependent coefficients abstract we investigate the blow up phenomena for the solution to a nonlinear reaction diffusion system with time dependent coefficients subject to null dirichlet boundary conditions by virtue of kaplan s method method of subsolutions and supersolutions and modified differential inequality technique we establish the blow up criteria for the solution moreover lower and upper bounds for the blow up time are derived

on weak solutions of nonlinear weighted p laplacian elliptic inequalities abstract in this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of class w loc 1 p r n c r n of p laplacian elliptic inequalities with possibly singular weights in order to get the results a new omori yau type principle is used we complement our nonexistence results by establishing existence of infinitely many positive radial solutions each of which blows up at some finite r 0 finally a criterium for the existence of positive entire large radial solutions of class w loc 1 p r n c r n is also established

radial solutions for a quasilinear elliptic system of schrodinger type in this paper we analyze the existence of entire radially symmetric solutions for the schrodinger system d p iu i h i r u i p i 1 a i r f i u 1 u d fori 1 d on r n where p i 1 email protected 1 2 3 h i and a i are nonnegative radial continuous functions and f i are nonnegative non decreasing continuous functions on 0 d in all variables

on the stability of equilibria to weakly coupled parabolic systems in unbounded domains abstract we investigate weakly coupled semilinear parabolic systems in unbounded domains of r 2 or r 3 with general nonlinearities we present several sufficient conditions on the nonlinearities which ensure the stability of the zero solution with respect to h 2 perturbations in addition various examples are discussed to illustrate the scope of application of our results

performance metrics for windows used in real time dft based multiple tone frequency excision the capability of direct sequence spread spectrum receivers to reject narrowband interference can be significantly improved by eliminating narrowband energy in the received signal through a real time discrete fourier transform rt dft process however the loss in received signal strength due to this frequency excision process can be significant in this paper we present a theoretical framework for evaluating the performance of alternative combinations of time weighting functions windows fractions of overlap in overlap and add architectures and frequency domain mapping algorithms the sensitivity loss due to time weighting is presented for variable overlaps and several different windows a set of window metrics is defined that provides a means of calculating distortion losses for an arbitrary number of interfering tones with uniformly distributed center frequencies theoretical results are confirmed by simulation these results can be used to compare sensitivities of alternative rt dft frequency excision direct sequence spread spectrum systems and to calculate the standoff range of a finite number of in band tone emitters

homogeneity score test for the intraclass version of the kappa statistics and sample size determination in multiple or stratified studies quand le coefficient de correlation intra classe ou sa version equivalente du coefficient d agrement kappa ont ete estimes a partir de plusieurs etudes independantes ou d une etude avec stratification nous nous trouvons devant le probleme de la comparaison de statistiques kappa et de la combinaison d information sur ces statistiques en un kappa commun quand leur supposition d homogeneite est satisfaite dans cet article en utilisant la theorie de vraisemblance du score etendue aux parametres de nuisance tarone 1988 nous presentons un test d homogeneite efficace pour comparer plusieurs statistiques kappa independantes et de surcroit nous donnons une methode du score d homogeneite modifiee en employant comme alternative un estimateur non iteratif et consistant nous fournissons la taille d echantillon en employant la methode du score d homogeneite modifiee et nous la comparons a celle de la qualite d ajustement gof donner eliasziw et klar 1996 une etude de simulation pour des tailles d echantillon faibles et moderes a montre que le niveau actuel du test du score d homogeneite employant les estimateurs du maximum de vraisemblance mles des parametres est de maniere satisfaisante proche du nominal et qu il est plus faible que ceux du score d homogeneite mortifiee et des tests de la qualite d ajustement nous etudions les proprietes statistiques de plusieurs estimateurs non iteratifs d un kappa commun l estimateur donner eliasziw et klar 1996 est essentiellement efficace et peut etre employe comme une alternative au mle iteratif nous presentons une estimation par intervalle efficace d un kappa commun en employant la methode de vraisemblance du score

blow up phenomena for a parabolic system with gradient nonlinearity under nonlinear boundary conditions abstract in this paper we consider the following reaction diffusion systems with gradient nonlinearity under nonlinear boundary condition u t u u p v q u x t 0 t v t v v r u s v x t 0 t u g u v h v x t 0 t u x 0 u 0 x v x 0 v 0 x x where r n n 1 is a bounded region with smooth boundary p q r s 0 1 t is a possible blow up time when blow up occurs by constructing an appropriate auxiliary functions and by means of payne weinberger or scott s method a lower bound on blow up time when blow up occurs is derived

a necessary and sufficient condition for existence of large solutions to semilinear elliptic equations we consider the semilinear equation u p x f u on a domain rn n 3 where f is a nonnegative nondecreasing continuous function which vanishes at the origin and p is a nonnegative continuous function with the property that any zero of p is contained in a bounded domain in such that p is positive on its boundary for bounded we show that a nonnegative solution u satisfying u x as x exists if and only if the function s s0 f t dt satisfies 1 s 1 2 ds for unbounded including rn we show that a similar result holds where u x as x within and u x as x if p x decays to zero rapidly as x

existence of large solutions for a class of quasilinear elliptic equations abstract we consider the quasilinear elliptic equation div u p 2 u a x f u u 0 in where p 1 a x 0 a x 0 a x c and f is continuous and non decreasing on 0 satisfies f 0 0 f s 0 for s 0 and the keller osserman condition 1 f s 1 p d s f s 0 s f t d t we establish conditions on the function a that are necessary and sufficient for the existence of positive solutions bounded and unbounded of the given equation

testing the homogeneity of kappa statistics procedures are compared for testing the homogeneity of k or 2 independent kappa statistics in the case of two raters and a dichotomous outcome one of the procedures is based on the estimated large sample variance derived under a model frequently adopted for inferences concerning interobserver agreement the other is based on a goodness of fit approach to this model the results of a monte carlo simulation show that the two approaches have similar properties if the number of subjects in each sample is large 100 and the prevalence of the underlying trait of interest is not extreme while the goodness of fit approach is recommended for comparisons involving smaller numbers of subjects or in which the prevalence of the underlying trait is small 0 3

on the comparison of correlated proportions for clustered data mcnemar s test is often used to compare two proportions estimated from paired observations we propose a method extending this to the case where the observations are sampled in clusters the proposed method is simple to implement and makes no assumptions about the correlation structure we conducted a monte carlo simulation study to compare the size and power of the proposed method with a test developed earlier by eliasziw and donner in the presence of intracluster correlation the size of mcnemar s test can greatly exceed the nominal level the size of eliasziw and donner s test is also inflated for some correlation patterns the proposed method on the other hand is close to the nominal size for a variety of correlation patterns although it is slightly less powerful than eliasziw and donner s procedure the proposed method is a good alternative to eliasziw and donner s test when in practice little is known about the correlation pattern of the data

blow up boundary solutions of semilinear elliptic problems we consider the following semilinear elliptic equation u p x f u in u 0 u 0 in 1 where rn n 3 is a smooth domain bounded or possibly unbounded with compact possibly empty boundary we assume throughout this paper that p is a non negative function such that p c0 if is bounded and p c loc otherwise the nonlinearity f is assumed to ful ll f 1 f c1 0 f 0 f 0 0 and f 0 on 0 and the keller osserman condition see 7 13

the existence and uniqueness of positive monotone solutions for a class of nonlinear schrdinger equations on infinite domains in this paper by constructing a new weighted norm method and analysis technique we establish the conditions for the existence and uniqueness of positive monotone solutions to a class of nonlinear schrdinger equations in planar exterior domains some examples are also given to demonstrate the application of our main results

blow up behaviors for semilinear parabolic systems coupled in equations and boundary conditions abstract this paper concerns with blow up behaviors for semilinear parabolic systems coupled in equations and boundary conditions in half space we establish the rate estimates for blow up solutions and prove that the blow up set is r n under proper conditions on initial data furthermore for n 1 more complete conclusions about such two topics are given

note on critical exponents for a system of heat equations coupled in the boundary conditions this note establishes the blow up estimates near the blow up time for a system of heat equations coupled in the boundary conditions under certain assumptions the exact rate of blow up is established we also prove that the only solution with vanishing initial values whenpq 1 is the trivial one

nonexistence of positive solutions to a quasilinear elliptic system and blow up estimates for a quasilinear reaction diffusion system the prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first then the nonexistence result for radially nonincreasing positive solutions of the system is implied by using this nonexistence result blow up estimates for a class of quasilinear reaction diffusion systems non newtonian filtration systems are established to extend the result for semilinear reaction diffusion systems fujita type

boundedness and blow up for a semilinear reaction diffusion system abstract we consider the semilinear parabolic system s u t u p t u q where x rnn 1 t 0 and p q are positive real numbers at t 0 nonnegative continuous and bounded initial values u0 v0 x are prescribed the corresponding cauchy problem then has a nonnegative classical and bounded solution u t x v t x in some strip st 0 t r n 0 t sup t 0 u v remain bounded in s t we show in this paper that if 0 t so that solutions can be continued for all positive times when pq 1 and 1 pq 1 n 2 with max p q one has t for every nontrivial solution u v t is then called the blow up time of the solution under consideration finally if 1 pq 1 n 2 both situations coexist since some nontrivial solutions remain bounded in any strip s while others exhibit finite blow up times

on the critical exponent for some semilinear reaction diffusion systems on general domains abstract in this study we consider the parabolic systems u t u f t v p v t v f t u q and u t u f t u r v p v t v f t u q v s in 0 t with homogeneous dirichlet boundary condition p q r s 1 and f c 0 the initial data are considered in the space u 0 v 0 c 0 2 u 0 v 0 0 where is a general domain bounded or unbounded with a smooth boundary we find the conditions that guarantee the global existence or the blow up in finite time of nonnegative solutions these conditions are given in terms of the asymptotic behavior of the solution of the homogeneous linear problem u t u 0 in 0

global and nonglobal existence for a strongly coupled parabolic system on a general domain abstract we consider the parabolic system u t u f t u r v s v t v g t u q v s in 0 t where r n is either an unbounded or bounded domain and f g c 0 we find conditions for the global existence or nonglobal existence which are expressed in terms of the behavior of s t u 0 as t where u t s t u 0 is the solution of the linear problem u t u 0 u 0 u 0

a simple method for the analysis of clustered binary data a simple method for comparing independent groups of clustered binary data with group specific covariates is proposed it is based on the concepts of design effect and effective sample size widely used in sample surveys and assumes no specific models for the intracluster correlations it can be implemented using any standard computer program for the analysis of independent binary data after a small amount of preprocessing the method is applied to a variety of problems involving clustered binary data testing homogeneity of proportions estimating dose response models and testing for trend in proportions and performing the mantel haenszel chi squared test for independence in a series of 2 x 2 tables and estimating the common odds ratio and its variance illustrative applications of the method are also presented

existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping abstract this paper concerns with the cauchy problem for the damped nonlinear hyperbolic system u t t u u t v p t x r 1 r n v t t v v t u q t x r 1 r n u 0 x u 0 x u t 0 x u 1 x x r n v 0 x v 0 x v t 0 x v 1 x x r n where p q 1 and satisfy p q 1 we shall prove that if max 1 p p q 1 1 q p q 1 n 2 for n 1 or 3 then the solution with small initial data exists globally in time and satisfies the decay estimates u t c 1 t and v t c 1 t for some positive constants and while if max 1 p p q 1 1 q p q 1 n 2 for n 1 then every solution with initial data having positive average value does not exist globally

a comparison of methods for calculating a stratified kappa investigators use the kappa coefficient to measure chance corrected agreement among observers in the classification of subjects into nominal categories the marginal probability of classification may depend however on one or more confounding variables we consider assessment of interrater agreement with subjects grouped into strata on the basis of these confounders we assume overall agreement across strata is constant and consider a stratified index of agreement or stratified kappa based on weighted summations of the individual kappas we use three weighting schemes 1 equal weighting 2 weighting by the size of the table and 3 weighting by the inverse of the variance in a simulation study we compare these methods under differing probability structures and differing sample sizes for the tables we find weighting by sample size moderately efficient under most conditions we illustrate the techniques by assessing agreement between surgeons and graders of fundus photographs with respect to retinal characteristics with stratification by initial severity of the disease

critical exponents of fujita type for certain evolution equations and systems with spatio temporal fractional derivatives this paper is concerned with establishing necessary or sufficient conditions for the existence of solutions to evolution equations with fractional derivatives in space and time the fujita exponent is determined then these results are extended to systems of reaction diffusion equations our new results shed lights on important practical questions

iterative approximation of solutions for semilinear parabolic equations system in this paper we present the convergence analysis of iterative schemes for solving semilinear systems resulting from multidimensional semilinear second order parabolic partial differential equations pdes defined in a domain n x and subject to cauchy boundary conditions on n using the method of integral successive iterative approximation and the principle of decay estimation we derive the bounded nonnegative local solutions and global solutions blowing up results of the solutions are also presented

global existence and nonexistence of solutions for a system of nonlinear damped wave equations abstract we consider the cauchy problem for the system of semilinear damped wave equations with small initial data t 2 u 1 u 1 t u 1 u k p 1 t 0 x r n t 2 u 2 u 2 t u 2 u 1 p 2 t 0 x r n t 2 u k u k t u k u k 1 p k t 0 x r n u j 0 x a j x t u j 0 x b j x x r n 1 j k we show that a critical exponent which classifies the global existence and the finite time blow up of solutions indeed coincides with the one to a corresponding semilinear heat systems with small data the proof of the global existence is based on the l p l q estimates of fundamental solutions for linear damped wave equations k nishihara l p l q estimates of solutions to the damped wave equation in 3 dimensional space and their application math z 244 2003 631 649 k marcati p nishihara the l p l q estimates of solutions to one dimensional damped wave equations and their application to compressible flow through porous media j differential equations 191 2003 445 469 t hosono t ogawa large time behavior and l p l q estimate of 2 dimensional nonlinear damped wave equations j differential equations 203 2004 82 118 t narazaki l p l q estimates for damped wave equations and their applications to semilinear problem j math soc japan 56 2004 585 626 and the blow up is shown by the fujita kaplan zhang method q zhang a blow up result for a nonlinear wave equation with damping the critical case c r acad sci paris 333 2001 109 114 f sun m wang existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping nonlinear anal 66 12 2007 2889 2910 t ogawa h takeda non existence of weak solutions to nonlinear damped wave equations in exterior domains nonlinear anal 70 10 2009 3696 3701

large time behavior of ode type solutions to a nonlinear parabolic system abstract let u v be a solution to the cauchy problem for a nonlinear parabolic system p t u u v in r n 0 t v v u in r n 0 u x 0 x 0 in r n v x 0 x 0 in r n where 0 with 1 0 and b c r n l r r n with 1 r and inf x r n x inf x r n x then the solution u v to problem p behaves like a positive solution to ode s and in 0 and both of u t l r n and v t l r n diverge as t in this paper we obtain the precise description of the large time behavior of the solution u v

single point blow up for a semilinear initial value problem abstract the initial value problem on r r is considered u t t x u xx t x u t x u t r 0 u 0 x x where 0 and is a fixed large number it is known that for some initial values the solution u t x exists only up to some finite time t and that u t as t t for the specific initial value k where 0 xx 0 r 0 k is sufficiently large it is shown that if x 0 then lim t t u t x and lim t t u x t x exist and are finite in other words blow up occurs only at the point x 0