sufficiency and duality in nonsmooth multiobjective optimization involving generalized f α π d type i functions in this paper new classes of generalized f a p d type i functions are introduced for a nonsmooth multiobjective programming problem based upon these generalized functions sufficient optimality conditions are established weak strong and strict converse duality theorems are also derived for wolfe and mond weir type multiobjective dual programs in order to relate the efficient and weak efficient solutions of primal and dual problems

nonclassical symmetry reductions of the three dimensional incompressible navier stokes equations the nonclassical reduction method as pioneered by bluman and cole j meth mech 18 1025 42 is used to examine symmetries of the full three dimensional unsteady incompressible navier stokes equations of fluid mechanics the procedure when applied to a system of partial differential equations yields reduced sets of equations with one fewer independent variables we find eight possibilities for reducing the navier stokes equations in the three spatial and one temporal dimensions to sets of partial differential equations in three independent variables some of these reductions are derivable using the lie group method of classical symmetries but the remainder are genuinely nonclassical further investigations of one of our eight forms shows how it is possible to derive novel exact solutions of the navier stokes equations by the nonclassical method

symmetry reduction for nonlinear relativistically invariant equations symmetry reduction is studied for the relativistically invariant scalar partial differential equation h u u 2 u 0 in n 1 dimensional minkowski space m n 1 the introduction of k symmetry variables 1 k as invariants of a subgroup g of the poincare group p n 1 having generic orbits of codimension k n in m n 1 reduces the equation to a pde in k variables all codimension 1 symmetry variables in m n 1 n arbitrary reducing the equation studied to an ode are found as well as all codimension 2 and 3 variables for the low dimensional cases n 2 3 the type of equation studied includes many cases of physical interest in particular nonlinear klein gordon equations such as the sine gordon equation and hamilton jacobi equations

the exotic conformal galilei algebra and nonlinear partial differential equations abstract the conformal galilei algebra cga and the exotic conformal galilei algebra ecga are applied to construct partial differential equations pdes and systems of pdes which admit these algebras we show that there are no single second order pdes invariant under the cga but systems of pdes can admit this algebra moreover a wide class of nonlinear pdes exists which are conditionally invariant under cga it is further shown that there are systems of nonlinear pdes admitting ecga with the realisation obtained very recently in d martelli y tachikawa comments on galilei conformal field theories and their geometric realisation preprint arxiv 0903 5184v2 hep th 2009 moreover wide classes of nonlinear systems invariant under two different 10 dimensional subalgebras of ecga are explicitly constructed and an example with possible physical interpretation is presented

continuous subgroups of the generalized schrodinger groups some general results on the subalgebras of the lie algebra asch n of the generalized schrodinger group sch n and on the subalgebras of the lie algebra asch n of the generalized extended schrodinger group sch n have been obtained the subalgebra structure of the algebras asch n and asch n are studied with respect to inner automorphisms of the groups sch n and sch n respectively the maximal abelian subalgebras and the one dimensional subalgebras of the algebras asch n and asch n have been explicitly found the full classification of the subalgebras of the algebras asch 3 asch 3 which are nonconjugate to the subalgebras of asch 2 asch 2 respectively has been carried out

υ preinvexity and υ invexity in mathematical programming in the paper we introduce and characterize a new class of nonconvex functions in mathematical programming named c preinvex functions which are called c invex functions in the case of differentiability the class of c reinvex functions is wider than that of preinvex functions and thus in the case of differentiability than the class of invex functions some optimality results are obtained under c preinvexity assumption for a constrained optimization problem with not necessarily differentiable functions further a number of sufficiency conditions and wolfe duality theorems are established under c invexity assumption an alternative approach with a modified c invexity notion to optimality conditions and duality results is also considered

p r invex sets and functions abstract notions of invexity of a function and of a set are generalized the notion of an invex function with respect to can be further extended with the aid of p invex sets slight generalization of the notion of p invex sets with respect to leads to a new class of functions a family of real functions called in general p r pre invex functions with respect to without differentiability or p r invex functions with respect to in the differentiable case is introduced some geometric properties of these classes of functions are derived sufficient optimality conditions are obtained for a nonlinear programming problem involving p r invex functions with respect to

new optimality conditions and duality results of g type in differentiable mathematical programming abstract in this paper a new class of differentiable functions called g invex functions with respect to is introduced by extending the definition of invex functions new necessary optimality conditions of g f john and g karush kuhn tucker type are obtained for differentiable constrained mathematical programming problems the g invexity concept introduced is used to prove the sufficiency of these necessary optimality conditions further a so called g mond weir type dual is formulated and various duality results are also established by assuming the functions involved to be g invex with respect to the same function

on the relationships between g preinvex functions and semistrictly g preinvex functions a new class of functions termed semistrictly g preinvex functions is introduced in this paper the relationships between semistrictly g preinvex functions and g preinvex functions are investigated under mild assumptions our results improve and extend the existing ones in the literature

non classical symmetry reduction example of the boussinesq equation a symmetry of an equation will leave the set of all solutions invariant a conditional symmetry will leave only a subset of solutions defined by some differential condition invariant the authors show how a specific class of conditional symmetries can be used to reduce a partial differential equation to an ordinary one in particular for the boussinesq equation these conditional symmetries together with the ordinary ones provide all possible reductions to ordinary differential equations a group theoretical explanation of the recently obtained new reductions is provided

the galilean relativistic principle and nonlinear partial differential equations the second order partial differential equations invariant under transformations of galilei rotation scale and projection are described

new non lie ansatze and exact solutions of nonlinear reaction diffusion convection equations a constructive method for obtaining new exact solutions of nonlinear evolution equations is further developed the method is based on the consideration of a fixed nonlinear partial differential equation together with an additional generating condition in the form of a linear high order ordinary differential equation using this method new non lie ansatze and exact solutions are obtained for two classes of diffusion equations with power and exponential nonlinearities which describe real processes in physics chemistry and biology the analysis of the found solutions and the relation of the proposed method to some approaches which have been suggested in several recently published papers are presented

arcsine test for publication bias in meta analyses with binary outcomes in meta analyses it sometimes happens that smaller trials show different often larger treatment effects one possible reason for such small study effects is publication bias this is said to occur when the chance of a smaller study being published is increased if it shows a stronger effect assuming no other small study effects under the null hypothesis of no publication bias there should be no association between effect size and effect precision e g inverse standard error among the trials in a meta analysis a number of tests for small study effects publication bias have been developed these use either a non parametric test or a regression test for association between effect size and precision however when the outcome is binary the effect is summarized by the log risk ratio or log odds ratio log or unfortunately these measures are not independent of their estimated standard error consequently established tests reject the null hypothesis too frequently we propose new tests based on the arcsine transformation which stabilizes the variance of binomial random variables we report results of a simulation study under the copas model on the log or scale for publication bias which evaluates tests so far proposed in the literature this shows that i the size of one of the new tests is comparable to those of the best existing tests including those recently published and ii among such tests it has slightly greater power especially when the effect size is small and heterogeneity is present arcsine tests have additional advantages that they can include trials with zero events in both arms and that they can be very easily performed using the existing software for regression tests

relationships between pre invex concepts abstract it is well known that some properties of convex optimization problems especially sufficient conditions for optimality and duality conditions are preserved when convexity is weakened to pre invexity however there are several distinct pre invex concepts b vex b pre invex pre univex p r pre invex and these are not equivalent the pre invexity concepts mentioned above have also some properties which are characteristic and invariant for functions belonging to these classes of functions

reduction and exact solutions of the navier stokes equations the authors construct a complete set of g 1 3 inequivalent ansatze of codimension 1 for the navier stokes ns field which reduce the ns equations to systems of ordinary differential equations ode having solved these odes they thereby obtain solutions of the ns equations formulae of group multiplication of solutions are given several non lie ansatze are discussed

on the classification of subalgebras of the conformal algebra with respect to inner automorphisms we give a complete justification of the classification of inequivalent subalgebras of the conformal algebra with respect to the inner automorphisms of the conformal group and we perform the classification of the subalgebras of the conformal algebra ac 1 3

optimality and duality for nonsmooth multiobjective programming using g type i functions abstract in this paper generalized g type i functions are defined for a nonlinear multiobjective programming problem where the functions involved are assumed to be locally lipschitz this new class of functions is a generalization of g invex functions defined in kang et al 2012 20 examples are given to show the existence of these functions g type kuhn tucker necessary conditions are established for a nondifferentiable multiobjective programming problem gmp by using suitable g type i functions sufficient optimality conditions are derived for the problem gmp further a mond weir type dual gmwd is formulated and using these newly defined functions various duality results are established

a note on invex problems with nonnegative variable we provide sufficient optimality conditions involving invexity for mathematical programming problems with nonnegative variable we also show that upon certain assumptions on the scaling function these problems are convex transformable hence certain associated convex problems should be solved some applications are shown

operating characteristics of a rank correlation test for publication bias an adjusted rank correlation test is proposed as a technique for identifying publication bias in a meta analysis and its operating characteristics are evaluated via simulations the test statistic is a direct statistical analogue of the popular funnel graph the number of component studies in the meta analysis the nature of the selection mechanism the range of variances of the effect size estimates and the true underlying effect size are all observed to be influential in determining the power of the test the test is fairly powerful for large meta analyses with 75 component studies but has only moderate power for meta analyses with 25 component studies however in many of the configurations in which there is low power there is also relatively little bias in the summary effect size estimate nonetheless the test must be interpreted with caution in small meta analyses in particular bias cannot be ruled out if the test is not significant the proposed technique has potential utility as an exploratory tool for meta analysts as a formal procedure to complement the funnel graph

vortices and invariant surfaces generated by symmetries for the 3d navier stokes equations abstract we show that certain infinitesimal operators of the lie point symmetries of the incompressible 3d navier stokes equations give rise to vortex solutions with different characteristics this approach allows an algebraic classification of vortices and throws light on the alignment mechanism between the vorticity and the vortex stretching vector s where s is the strain matrix the symmetry algebra associated with the navier stokes equations turns out to be infinite dimensional new vortical structures generalizing in some cases well known configurations such as for example the burgers and lundgren solutions are obtained and discussed in relation to the value of the dynamic angle arctan s s a systematic treatment of the boundary conditions invariant under the symmetry group of the equations under study is also performed and the corresponding invariant surfaces are recognized

a comparison of methods to detect publication bias in meta analysis meta analyses are subject to bias for many of reasons including publication bias asymmetry in a funnel plot of study size against treatment effect is often used to identify such bias we compare the performance of three simple methods of testing for bias the rank correlation method a simple linear regression of the standardized estimate of treatment effect on the precision of the estimate and a regression of the treatment effect on sample size the tests are applied to simulated meta analyses in the presence and absence of publication bias both one sided and two sided censoring of studies based on statistical significance was used the results indicate that none of the tests performs consistently well test performance varied with the magnitude of the true treatment effect distribution of study size and whether a one or two tailed significance test was employed overall the power of the tests was low when the number of studies per meta analysis was close to that often observed in practice tests that showed the highest power also had type i error rates higher than the nominal level based on the empirical type i error rates a regression of treatment effect on sample size weighted by the inverse of the variance of the logit of the pooled proportion using the marginal total is the preferred method

on subalgebras of the lie algebra of the extended poincare group p 1 n some general results on the subalgebras of the lie algebra ap 1 n of the extended poincare group p 1 n n 2 with respect to p 1 n conjugation have been obtained all subalgebras of ap 1 4 that are nonconjugate to the subalgebras of ap 1 4 are classified with respect to p 1 4 conjugation the list of representatives of each conjugacy class is presented

improved kinetic renormalisation group approach to diffusion limited aggregation an improved kinetic renormalisation group approach to diffusion limited aggregation is presented this approach is based on the growth process itself and accounts for the dispersity in the growth probabilities it yields the multifractal spectrum d q with better values at smaller q on the 2d square lattice the authors find df 1 694 for the fractal dimensions of the cluster and that of its interface and d 1 1 01 for the information dimension the former agrees with the simulation results df approximately 1 70 and the latter compares very well with the exact value d 1 1

g pre invex functions in mathematical programming in the present paper we introduce the concept of g pre invex functions with respect to h defined on an invex set with respect to h these function unify the concepts of nondifferentiable convexity pre invexity and r pre invexity furthermore relationships of g pre invex functions to various introduced earlier pre invexity concepts are also discussed some geometric properties of this class of functions are also derived finally optimality results are established for optimization problems under appropriate g pre invexity conditions

explaining heterogeneity in meta analysis a comparison of methods exploring the possible reasons for heterogeneity between studies is an important aspect of conducting a meta analysis this paper compares a number of methods which can be used to investigate whether a particular covariate with a value defined for each study in the meta analysis explains any heterogeneity the main example is from a meta analysis of randomized trials of serum cholesterol reduction in which the log odds ratio for coronary events is related to the average extent of cholesterol reduction achieved in each trial different forms of weighted normal errors regression and random effects logistic regression are compared these analyses quantify the extent to which heterogeneity is explained as well as the effect of cholesterol reduction on the risk of coronary events in a second example the relationship between treatment effect estimates and their precision is examined in order to assess the evidence for publication bias we conclude that methods which allow for an additive component of residual heterogeneity should be used in weighted regression a restricted maximum likelihood estimator is appropriate although a number of other estimators are also available methods which use the original form of the data explicitly for example the binomial model for observed proportions rather than assuming normality of the log odds ratios are now computationally feasible although such methods are preferable in principle they often give similar results in practice

necessary and sufficient conditions in constrained optimization additional conditions are attached to the kuhn tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization under appropriate constraint qualifications necessary and sufficient conditions are also given for optimality of the dual problem duality and converse duality are treated accordingly

continuous subgroups of the poincare group p 1 4 an exhaustive description of the nonsplitting subalgebras of the lp 1 4 algebra with respect to p 1 4 conjugation is presented

sufficiency and duality in nondifferentiable multiobjective programming involving generalized type i functions abstract recently hachimi and aghezzaf defined generalized f d type i functions a new class of functions that unifies several concepts of generalized type i functions in this paper the generalized f d type i functions are extended to nondifferentiable functions by utilizing the new concepts we obtain several sufficient optimality conditions and prove mixed type and mond weir type duality results for the nondifferentiable multiobjective programming problem

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

nonlinear galilei invariant pdes with infinite dimensional lie symmetry a class of nonlinear galilei invariant generalizations of the heat equation admitting infinite dimensional lie symmetry is presented lie symmetries and examples of exact solutions are found for some nonlinear equations generalizing the heat equation full sets of the absolute differential invariants for two non equivalent representations of the galilei algebra are constructed

continuous symmetries of difference equations lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations in this article we review the results of a much more recent program the use of lie groups to study difference equations we show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners one is to use generalized symmetries acting on solutions of difference equations but leaving the lattice invariant the other is to restrict them to point symmetries but to allow them to also transform the lattice

issues in the selection of a summary statistic for meta analysis of clinical trials with binary outcomes meta analysis of binary data involves the computation of a weighted average of summary statistics calculated for each trial the selection of the appropriate summary statistic is a subject of debate due to conflicts in the relative importance of mathematical properties and the ability to intuitively interpret results this paper explores the process of identifying a summary statistic most likely to be consistent across trials when there is variation in control group event rates four summary statistics are considered odds ratios or risk differences rd and risk ratios of beneficial rr b and harmful outcomes rr h each summary statistic corresponds to a different pattern of predicted absolute benefit of treatment with variation in baseline risk the greatest difference in patterns of prediction being between rr b and rr h selection of a summary statistic solely based on identification of the best fitting model by comparing tests of heterogeneity is problematic principally due to low numbers of trials it is proposed that choice of a summary statistic should be guided by both empirical evidence and clinically informed debate as to which model is likely to be closest to the expected pattern of treatment benefit across baseline risks empirical investigations comparing the four summary statistics on a sample of 551 systematic reviews provide evidence that the rr and or models are on average more consistent than rd there being no difference on average between rr and or from a second sample of 114 meta analyses evidence indicates that for interventions aimed at preventing an undesirable event greatest absolute benefits are observed in trials with the highest baseline event rates corresponding to the model of constant rr h the appropriate selection for a particular meta analysis may depend on understanding reasons for variation in control group event rates in some situations uncertainty about the choice of summary statistic will remain

optimality and duality for generalized fractional programming involving nonsmooth f ρ convex functions using a parametric approach we establish necessary and sufficient conditions and derive duality theorems for a class of nonsmooth generalized minimax fractional programming problems containing f r convex functions

on integrable doebner goldin equations we integrate sub families of a family of nonlinear schrodinger equations proposed by doebner and goldin in the 1 1 dimensional case which have exceptional lie symmetries since the method of integration involves non local transformations of dependent and independent variables general solutions obtained include implicitly determined functions by properly specifying one of the arbitrary functions contained in these solutions we obtain broad classes of explicit square integrable solutions the physical significance and some analytical properties of the solutions obtained are briefly discussed

group invariant solutions without transversality we present a generalization of lie s method for finding the group invariant solutions to a system of partial differential equations our generalization relaxes the standard transversality assumption and encompasses the common situation where the reduced differential equations for the group invariant solutions involve both fewer dependent and independent variables the theoretical basis for our method is provided by a general existence theorem for the invariant sections both local and global of a bundle on which a finite dimensional lie group acts a simple and natural extension of our characterization of invariant sections leads to an intrinsic characterization of the reduced equations for the group invariant solutions for a system of differential equations the characterization of both the invariant sections and the reduced equations are summarized schematically by the kinematic and dynamic reduction diagrams and are illustrated by a number of examples from fluid mechanics harmonic maps and general relativity this work also provides the theoretical foundations for a further detailed study of the reduced equations for group invariant solutions

nonsmooth minimax programming under locally lipschitz φ ρ invexity abstract minimax programming problems involving locally lipschitz invex functions are considered the parametric and non parametric necessary and sufficient optimality conditions for a class of nonsmooth minimax programming problems are obtained under nondifferentiable invexity assumption imposed on objective and constraint functions when the sufficient conditions are utilized parametric and non parametric dual problems in the sense of mond weir and wolfe may be formulated and duality results are derived for the considered nonsmooth minimax programming problem with the reference to the said functions we extend some results of optimality and duality for a larger class of nonsmooth minimax programming problems

bias of estimates of the number needed to treat there are several commonly used measures of association between treatment and control event rates in the population pit and pic respectively one such measure the number needed to treat nnt indicates the number of patients on average who must be treated in order to prevent one additional adverse event and is equal to 1 pic pit because the population values pic and pit are unknown the sample proportions rates pc and pt are used as estimates the precision of a sample based estimator is usually exhibited in terms of confidence intervals however the accuracy of the estimator i e its bias is often ignored the purpose of the present study is to examine the degree of bias using exact calculations based on the binomial theorem we determined the bias of an estimate of nnt conditional on pc not equal pt and the bias of an adjusted estimator of the nnt for various sample sizes n 10 20 30 40 50 100 and population parameters 0 01 or pic or 0 9 0 01 or pic pit or 0 8 the magnitude and non monotonic nature of the bias are due to the nnt scale the bias of the adjusted estimator can be approximated for some studies using the tabular results in this analysis

on non linear partial differential equations with an infinite dimensional conditional symmetry abstract the invariance of non linear partial differential equations under a certain infinite dimensional lie algebra a n z in n spatial dimensions is studied the special case a 1 2 was introduced in j stat phys 75 1994 1023 and contains the schrodinger lie algebra sch 1 as a lie subalgebra it is shown that there is no second order equation which is invariant under the massless realizations of a n z however a large class of strongly non linear partial differential equations is found which are conditionally invariant with respect to the massless realization of a n z such that the well known monge ampere equation is the required additional condition new exact solutions are found for some representatives of this class

galilei invariant nonlinear systems of evolution equations all systems of n 1 dimensional quasilinear second order evolution equations invariant under chain of algebras ag 1 n contained in implied by ag1 1 n contained in implied by ag2 1 n are described the results obtained are illustrated by the examples of the nonlinear schrodinger equations hamilton jacobi type systems and reaction diffusion equations

on invex sets and preinvex functions abstract in this paper we consider the class of the invex function introduced by hanson we show that under certain condition an invex function defined on an invex set a is preinvex on a similarly a quasiinvex function defined on an invex set a is pre quasiinvex

intertwining operators for l conformal galilei algebras and hierarchy of invariant equations the l conformal galilei algebra denoted by is a non semisimple lie algebra specified by a pair of parameters d l the algebra is regarded as a nonrelativistic analogue of the conformal algebra we derive hierarchies of partial differential equations which have invariance of the group generated by with a central extension as kinematical symmetry this is done by developing a representation theory such as verma modules singular vectors of and vector field representations for d 1 2

a group analysis of the 2d navier stokes fourier equations abstract we study a 2 1 dimensional model of an incompressible thermoconducting fluid named navier stokes fourier system we apply a group theoretical analysis in correspondence of the generators of the symmetry group allowed by this model exact solutions are found some of them show possible interesting physical interpretations in our first exploration this feature is illustrated by dealing with simple special cases

bayesian approaches to random effects meta analysis a comparative study current methods for meta analysis still leave a number of unresolved issues such as the choice between fixed and random effects models the choice of population distribution in a random effects analysis the treatment of small studies and extreme results and incorporation of study specific covariates we describe how a full bayesian analysis can deal with these and other issues in a natural way illustrated by a recent published example that displays a number of problems such analyses are now generally available using the bugs implementation of markov chain monte carlo numerical integration techniques appropriate proper prior distributions are derived and sensitivity analysis to a variety of prior assumptions carried out current methods are briefly summarized and compared to the full bayes analysis

the symmetry and some exact solutions of the nonlinear many dimensional liouville d alembert and eikonal equations multiparametrical exact solutions of the many dimensional nonlinear d alembert liouville sine gordon and eikonal equations are obtained the maximally extensive local invariance groups of the equations are determined and invariants of the extended poincare group are found

pre invex functions in multiple objective optimization and called such functions convexlike if s is a convex set and if f is a convex function then clearly f is convexlike elster and nehse obtained a saddlepoint optimality condition for convexlike mathematical programs hayashi and komiya 9 also considered convexlike functions and developed a gordan type theorem of the alternative involving convexlike functions and in addition considered lagrangian duality for convexlike programs hanson 7 considered differentiable functions f s r for which there exists an n dimensional vector function q q u such that for all x u e s

why add anything to nothing the arcsine difference as a measure of treatment effect in meta analysis with zero cells for clinical trials with binary endpoints there are a variety of effect measures for example risk difference risk ratio and odds ratio or the choice of metric is not always straightforward and should reflect the clinical question additional issues arise if the event of interest is rare in systematic reviews trials with zero events in both arms are encountered and often excluded from the meta analysis the arcsine difference as is a measure which is rarely considered in the medical literature it appears to have considerable promise because it handles zeros naturally and its asymptotic variance does not depend on the event probability this paper investigates the pros and cons of using the as as a measure of intervention effect we give a pictorial representation of its meaning and explore its properties in relation to other measures based on analytical calculation of the variance of the arcsine transformation a more conservative variance estimate for the rare event setting is proposed motivated by a published meta analysis in cardiac surgery we examine the statistical properties of the various metrics in the rare event setting we find the variance estimate of the as to be more stable than that of the log or even if events are rare however parameter estimation is biased if the groups are markedly unbalanced though from a theoretical viewpoint the as is a natural choice its practical use is likely to continue to be limited by its less direct interpretation