on holder continuity of approximate solutions to parametric equilibrium problems abstract we establish verifiable sufficient conditions for holder continuity of approximate solutions to parametric equilibrium problems when solutions may be not unique many examples are provided to illustrate the need of considering approximate solutions instead of exact solutions and the essentialness of the imposed assumptions as applications we derive this holder continuity for constrained minimization variational inequalities and fixed point problems

a remark on a standard and linear vector network equilibrium problem with capacity constraints in this paper weak vector equilibrium principle with capacity constraints is introduced a necessary condition that a vector minimum cost flow is a vector equilibrium flow with capacity constraints is obtained when the number of paths connecting with each pair of source and sink is less than or equal to 2 a sufficient condition for a vector minimum cost flow to be a vector equilibrium flow is also obtained a generalized weak vector equilibrium principle is also introduced without any additional assumption a necessary and sufficient condition for a weak vector minimum cost flow to be a generalized weak vector equilibrium flow is obtained

on the holder continuity of solutions to parametric multivalued vector equilibrium problems we consider parametric multivalued vector equilibrium problems of both weak and strong types in metric linear spaces sufficient conditions for the local uniqueness and holder continuity of the solutions are established as consequences some new results for variational inequalities are derived and compared with recent papers on the subject

effective sample sizes for confidence intervals for survival probabilities we examine various methods to estimate the effective sample size for construction of confidence intervals for survival probabilities we compare the effective sample sizes of cutler and ederer1 and peto et al 2 as well as a modified cutler ederer effective sample size we investigate the use of these effective sample sizes in the common situation of many censored observations that intervene between the time point of interest and the last death before this time we note that there is no a priori reason to treat upper and lower confidence intervals in a symmetric fashion since censored survival data are by nature asymmetric we recommend the use of the cutler ederer effective sample size in construction of upper confidence intervals and the peto effective sample size in construction of lower confidence intervals two examples with real data demonstrate the differences between confidence intervals formed with different effective sample sizes this study also illustrates the need for caution in the application of simulation studies to real problems

two stage meta analysis of survival data from individual participants using percentile ratios methods for individual participant data meta analysis of survival outcomes commonly focus on the hazard ratio as a measure of treatment effect recently siannis et al 2010 statistics in medicine 29 3030 3045 proposed the use of percentile ratios as an alternative to hazard ratios we describe a novel two stage method for the meta analysis of percentile ratios that avoids distributional assumptions at the study level

localization problem in one dimension mapping and escape a one dimensional schr odinger equation in a discontinuous quasiperiodic potential is reduced to a recursion relation for transfer matrices and then to one for traces of these matrices when the potential is periodic the bandwidth goes to zero as an algebraic function of the period with a critical index which depends upon the potential strength this critical index is also evaluated as the solution to an escape rate problem for the recursion relations

holder continuity and upper estimates of solutions to vector quasiequilibrium problems abstract in this paper we establish the holder continuity of solution mappings to parametric vector quasiequilibrium problems in metric spaces under the case that solution mappings are set valued our main assumptions are weaker than those in the literature and the results extend and improve the recent ones furthermore as an application of holder continuity we derive upper bounds for the distance between an approximate solution and a solution set of a vector quasiequilibrium problem with fixed parameters

perturbations of random matrix products if x1 x2 are identically distributed independent random matrices with a common distribution then with the probability 1 the limit lambda mu mathop lim limits n to infty frac 1 n ln left x n x 1 right exists the paper treats the problem is it true that k if k in the weak sense

a non parametric procedure for evaluating treatment effect in the meta analysis of survival data this paper addresses the problem of combining information from independent clinical trials which compare survival distributions of two treatment groups current meta analytic methods which take censoring into account are often not feasible for meta analyses which synthesize summarized results in published or unpublished references as these methods require information usually not reported the paper presents methodology which uses the log log survival function difference i e log logs2 t log logs1 t as the contrast index to represent the multiplicative treatment effect on survival in independent trials this article shows by the second mean value theorem for integrals that this contrast index denoted as theta is interpretable as a weighted average on a natural logarithmic scale of hazard ratios within the interval 0 t in a trial when the within trial proportional hazards assumption is true theta is the logarithm of the proportionality constant for the common hazard ratio for the interval considered within the trial in this situation an important advantage of using theta as a contrast index in the proposed methodology is that the estimation of theta is not affected by length of follow up time other commonly used indices such as the odds ratio risk ratio and risk differences do not have this invariance property under the proportional hazard model since their estimation may be affected by length of follow up time as a technical artefact thus the proposed methodology obviates problems which often occur in survival meta analysis because trials do not report survival at the same length of follow up time even when the within trial proportional hazards assumption is not realistic the proposed methodology has the capability of testing a global null hypothesis of no multiplicative treatment effect on the survival distributions of two groups for all studies a discussion of weighting schemes for meta analysis is provided in particular a weighting scheme based on effective sample sizes is suggested for the meta analysis of time to event data which involves censoring a medical example illustrating the methodology is given a simulation investigation suggested that the methodology performs well in the presence of moderate censoring

well posedness by perturbations of mixed variational inequalities in banach spaces in this paper we consider an extension of the notion of well posedness by perturbations introduced by zolezzi for a minimization problem to a mixed variational inequality problem in a banach space we establish some metric characterizations of the well posedness by perturbations we also show that under suitable conditions the well posedness by perturbations of a mixed variational inequality problem is equivalent to the well posedness by perturbations of a corresponding inclusion problem and a corresponding fixed point problem also we derive some conditions under which the well posedness by perturbations of a mixed variational inequality is equivalent to the existence and uniqueness of its solution

sensitivity analysis for abstract equilibrium problems we develop the general framework of sensitivity analysis for equilibrium problems in the setting of vector topological normed space our approach does not make any recourse to geometrical properties and the obtained result can be viewed as an extension and generalization of the well known results on variational inequalities in the literature even though we have worked under arbitrary constraints k with holder property that have been decisive in our treatment we have obtained in a similar spirit of domokos j math anal appl 230 1999 382 389 the best lower bound for the continuity modulus despite of the properties of the boundary of k

iterative generalized least squares for meta analysis of survival data at multiple times a method is presented for joint analysis of survival proportions reported at multiple times in published studies to be combined in a meta analysis generalized least squares is used to fit linear models including between trial and within trial covariates using current fitted values iteratively to derive correlations between times within studies multi arm studies and nonrandomized historical controls can be included with no special handling the method is illustrated with data from two previously published meta analyses in one an early treatment difference is detected that was not apparent in the original analysis

franco american meeting on the mathematics of random and almost periodic potentials we present the abstracts of papers given at a conference held at the ecole polytechnique in june 1983 on the mathematics of random and almost periodic potentials

simple robust procedures for combining risk differences in sets of 2 2 tables meta analyses often use a random effects model to incorporate unexplained heterogeneity of study results trimmed versions of meta analytic estimators for the risk difference adapted from procedures designed for a random effects analysis can resist the impact of a few anomalous studies a simulation study compared untrimmed and trimmed versions of four meta analytic procedures that give weighted averages of risk differences an adaptation of winsorized estimates of components of variance gains some resistance to anomalous studies when estimating variability the simulations found that a modified version of the dersimonian laird estimator is attractive when risk differences reveal the added variability described by a random effects model and that a 20 per cent trimmed weighted version of this procedure offers resistance against the impact of highly anomalous results among four trimmed procedures considered the trimmed version of the modified dersimonian laird estimator offers the best performance over a wide range of simulation designs and sample sizes none of the methods whether trimmed or untrimmed is uniformly preferable a published meta analysis of a vaccination against tb provides data that serve to illustrate differences among the eight procedures

meblin transforms associated with julia sets and physical applications we introduce the mellin transform of the balanced invariant measure associated to the julia set generated by a rational transformation we show that its analytic continuation is a meromorphic function the poles of which are on a semi infinite periodic lattice this allows one to have an understanding of the behavior of the measure near a repulsive fixed point trace identities corresponding to the fact that the analytically continued mellin transform vanishes at negative integers are derived for the polynomial case the quadratic map is first analyzed in detail and the analytic properties of the inverse of the green s function are exhibited of interest is the appearance of a dense set of spikes at dyadic points when the julia set is disconnected these results are used to study the residues of the mellin transform a certain number of physically interesting consequences are derived for the spectral dimensionality of quantum mechanical systems the excitation spectrum of which displays unusual oscillations the appearance of complex critical indices for thermodynamical systems is also discussed in the conclusion

kotani theory for one dimensional stochastic jacobi matrices we consider families of operators h on l2 given by h u n u n 1 u n 1 v n u n wherev is a stationary bounded ergodic sequence we prove analogs of kotani s results including that for a e ac h is the essential closure of the set ofe where e the lyaponov index vanishes and the result that ifv is non deterministic then ac is empty

symmetric tests and confidence intervals for survival probabilities and quantiles of censored survival data we describe existing tests and introduce two new tests concerning the value of a survival function these tests may be used to construct a confidence interval for the survival probability at a given time or for a quantile of the survival distribution simulation studies show that error rates can differ substantially from their nominal values particularly at survival probabilities close to zero or one we recommend our new constrained bootstrap test for its good overall performance

log holder continuity of the integrated density of states for stochastic jacobi matrices we consider the integrated density of states k e of a general operator on l2 v of the formh h0 v where h 0 u n sum limits left i right 1 u n i and vu n v n u n wherev is a general bounded ergodic stationary process on v we show that k e k e c log e e 1 when e e 1 2 the key is a thouless formula for the strip

semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems abstract in this paper we establish sufficient conditions for the solution set of parametric multivalued vector quasiequilibrium problems to be semicontinuous all kinds of semicontinuity are considered lower semicontinuity upper semicontinuity hausdorff upper semicontinuity and closedness moreover we investigate both the weak and strong solutions of quasiequilibrium problems

perturbation analysis of error bounds for systems of conic linear inequalities in banach spaces for a general constrained or unconstrained system of conic inequalities we provide sufficient conditions to ensure the existence of a common error bound for each of the systems obtained from the original one when the given data undergoes a small perturbation moreover we also give some dual characterizations on the existence of error bounds for systems of conic inequalities

holder continuity of perturbed solution set for convex optimization problems abstract in this paper we first establish sufficient conditions for the local uniqueness and holder continuity of perturbed solution set for a scalar optimization problem then by using a linear scalarization method we obtain the holder continuity of two classes of perturbed solution sets for a multiobjective programming problem respectively we also give some examples to illustrate that our main results are applicable these examples are also given to illustrate that our main results are new and different from the ones in literature

indexes of contrast and quantitative significance for comparisons of two groups although boundaries for large and small differences are needed to plan research and interpret results the diverse indexes of descriptive contrast for the central indexes a and b of two groups have not received intensive attention for two means the increment of mid r a bmid r reflects the slope of a line showing the effect but is altered by different units of measurement division of mid r a bmid r by the common standard deviation produces the standardized increment si which is sometimes called the effect size despite many advant ages it does not contrast the relative magnitudes of a and b for the latter contrast the relative change or proportionate increment mid r a bmid r b is particularly easy to understand and the relative translocation mid r a bmid r a b produces a bounded range from 1 to 1 nevertheless all indexes of relative magnitude ablate the scales of measurement thereby increasing difficulty in interpretation although seldom applied proportionate reduction in overall system variance can be highly useful its square root leads to eta the analogue of a correlation coefficient which corresponds to a standardized slope for the direct increment the values of eta usually approximate si 2 although arbitrary levels have been proposed for quantitative significance of the si the proportionate reduction in overall system variance is often regarded as ineffectual unless 10 per cent with this belief minimum boundaries for quantitative significance can often be set at eta 0 3 and si 0 6 in indexes of relative magnitude for two proportions or rates p a and p b confusion is produced if q a and q b are alternatively chosen for the denominators the odds ratio p a q b p b q a avoids these choices but is often difficult to interpret for easy understanding and communication the preferred index is nne the number needed to produce one excess effect calculated as the inverse of the direct increment that is 1 mid r p a p b mid r the standardized increment mid r p a p b mid r radical pq where p is the average of p a and p b and q 1 p could offer a single index applicable to both dimensional and binary data but when p becomes quite small that is 0 01 radical pq requires special calculations and also approaches the value of radicalp boundaries of quantitative significance are particularly difficult to establish for comparisons of two rates because of additional consequences in populational extrapolations and clinical implications nevertheless the principles of quantitative significance can aid the ad hoc construction of boundaries that must be set for medical importance when sample sizes are calculated and when results are interpreted for studies of either efficacy or equivalence

on the density of states of schrodinger operators with a random potential using very recent results on ergodic theorems for superadditive processes on rd the authors prove the existence of the density of states for a wide class of random schrodinger operators in particular new non asymptotic estimates on the density of states are obtained and examples are discussed

stability of weak vector variational inequality abstract in this paper a key assumption is introduced by virtue of a parametric gap function then by using the key assumption sufficient conditions of the continuity and hausdorff continuity of a solution set map for a parametric weak vector variational inequality are obtained in banach spaces with the objective space being finite dimensional

schrodinger operators with an electric field and random or deterministic potentials we prove that the schrodinger operatorh d2 dx2 v x f x has purely absolutely continuous spectrum for arbitrary constant external fieldf for a large class of potentials this result applies to many periodic almost periodic and random potentials and in particular to random wells of independent depth for which we prove that whenf 0 the spectrum is almost surely pure point with exponentially decaying eigenfunctions

some jacobi matrices with decaying potential and dense point spectrum we discuss doubly infinite matrices of the formm ij i j 1 i j 1 v i ij as operators on l2 we present for each 0 examples of potentialsv n with v n o n 1 2 and wherem has only point spectrum our discussion should be viewed as a remark on the recent work of delyon kunz and souillard

the holder continuity of solutions to generalized vector equilibrium problems in this paper by using a weaker assumption we discuss the holder continuity of solution maps for two cases of parametric generalized vector equilibrium problems under the case that the solution map is a general set valued one but not a single valued one these results extend the recent ones in the literature several examples are given for the illustration of our results