rectifiable and unrectifiable oscillations for a class of second order linear differential equations of euler type the main purpose of the paper is to pay attention to a new kind of oscillations so called rectifiable and unrectifiable oscillations which occur in a class of linear second order differential equations including the famous linear euler differential equation it will be shown that this kind of oscillations only depends on a positive real parameter which appears in a singular term of the main equation as well as in a suitable boundary layer condition

bayesian single and double variable sampling plans for the weibull distribution with censoring the sampling inspection problem is one of the main research topics in quality control in this paper we employ bayesian decision theory to study single and double variable sampling plans for the weibull distribution with type ii censoring a general loss function which includes the sampling cost the time consuming cost the salvage value and the after sales cost is proposed to determine the bayes risk and the corresponding optimal sampling plan explicit expressions for the bayes risks for both single and double sampling plans are derived respectively numerical examples are given to illustrate the effectiveness of the proposed method comparisons between single and double sampling plans are made and sensitivity analysis is performed

positive and necklace solitary waves on bounded domains abstract we present new solitary wave solutions of the two dimensional nonlinear schrodinger equation on bounded domains such as rectangles circles and annuli these multi peak necklace solitary waves consist of several identical positive profiles pearls such that adjacent pearls have opposite signs they are stable at low powers but become unstable at powers well below the critical power for collapse p cr this is in contrast with the ground state single pearl solitary waves on bounded domains which are stable at any power below p cr on annular domains the ground state solitary waves are radial at low powers but undergo a symmetry breaking at a threshold power well below p cr as in the case of convex bounded domains necklace solitary waves on the annulus are stable at low powers and become unstable at powers well below p cr unlike on convex bounded domains however necklace solitary waves on the annulus have a second stability regime at powers well above p cr for example when the ratio of the inner to outer radii is 1 2 four pearl necklaces are stable when their power is between 3 1 p cr and 3 7 p cr this finding opens the possibility to propagate localized laser beams with substantially more power than was possible until now the instability of necklace solitary waves is excited by perturbations that break the antisymmetry between adjacent pearls and is manifested by power transfer between pearls in particular necklace instability is unrelated to collapse in order to compute numerically the profile of necklace solitary waves on bounded domains we introduce a non spectral variant of petviashvili s renormalization method

analysis of the linearization around a critical point of an infinite dimensional hamiltonian system partial differential equations that conserve energy can often be written as infinite dimensional hamiltonian systems of the following general form du dt je u where j x x is a symplectic matrix i e jj 1 and e x r is a c 2 functional defined on some hilbert space x

asymptotic behavior of solutions of second order differential equations with integrable coefficients the differential equation x a t f x 0 t 0 is considered under the condition that lim x fl a s ds exists and is finite and necessary and or sufficient conditions are given for this equation to have solutions which behave asymptotically like nontrivial linear functions cl c2t

nonoscillation results for third order nonlinear differential equations abstract criteria are obtained in order that all nontrivial solutions of the third order nonlinear eqs a y q t y sgn y 0 and b y q t y sgn y 0 are nonoscillatory where 0 and q t is positive and continuous on 0 these results extend and complement previous results of kura and also may be considered as third order analogues of results for the second order nonlinear equations

oscillation constants for second order ordinary differential equations related to elliptic equations with p laplacian abstract in this paper we consider the second order nonlinear differential equation t 1 x t 1 p f x 0 x x p 2 x p 1 r with f satisfying x f x 0 x 0 we analyze the difference between the cases p p and p in each case we give a condition on the function f which guarantees that solutions of eq are non oscillatory the principal methods used in this paper are the riccati technique and its modifications the results of our paper complement and extend several previously obtained results on the subject

oscillation theorems for second order nonlinear differential equations abstract optimal in a certain sense conditions are found guaranteeing the oscillation of all proper solutions of the differential equation u f t u u 0

random effects weibull regression model for occupational lifetime abstract with great interest we read the recent publication of sohn et al sohn s y chang i s moon t h 2007 random effects weibull regression model for occupational lifetime european journal of operational research 179 124 131 on a weibull regression model with random effects for modelling occupational lifetime we congratulate sohn and colleagues on their comprehensive and clearly written paper nevertheless we would like to comment on two points the first regarding the moments of the underlying weibull distribution the second regarding the relations of sohn s model to the class of frailty models

on existence of oscillatory solutions of second order emden fowler equations abstract we study the second order emden fowler equation e y t a x y sgn y 0 0 where a x is a positive and absolutely continuous function on 0 let x a x x 3 2 1 and bounded away from zero we prove the following theorem if x l 1 0 where x min x 0 then eq e has oscillatory solutions in particular this result embodies earlier results by jasny kurzweil heidel and hinton chiou and erbe and muldowney

decaying positive solutions of quasilinear elliptic equations in exterior domains in r2 abstract the existence of decaying positive solutions of quasilinear elliptic equations of the form u x u x u x 2 0 is established in an exterior domain r 2 under suitable smoothness and growth conditions the main result is proved by means of a supersolution subsolution method given by noussair and swanson by using phase plane analysis of a system of lienard type a supersolution and a subsolution of the above equation are found out an extension of the main result to more general case is also attempted finally some examples are attached

optimal selling price and lotsize with time varying deterioration and partial backlogging the article deals with an eoq economic order quantity model over an infinite time horizon for perishable items where demand is price dependent and partial backorder is permitted the rate of deterioration is taken to be time proportional and it is assumed that shortage occurs at starting of the inventory cycle based on the partial backlogging and lost sale cases the author develops the criterion for the optimal solution for the replenishment schedule and proves the optimal ordering policy is unique moreover the article suggests to new functions regarding price dependent demand and time varying deterioration rate finally numerical examples are illustrated to test the model in various issues

an economic production lot size model with deteriorating items stock dependent demand inflation and partial backlogging in this paper we present an optimization framework to derive optimal production over a fixed planning horizon for items with a stock dependent demand rate and under inflationary conditions we consider a perishable item that follows a two parameter weibull distribution shortage is allowed and partially backlogged at a fixed rate a numerical example is taken up to illustrate the solution procedure and sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out

finding optimal s s policies is about as simple as evaluating a single policy in this paper a new algorithm for computing optimal s s policies is derived based upon a number of new properties of the infinite horizon cost function c s s as well as a new upper bound for optimal order up to levels s and a new lower bound for optimal reorder levels s the algorithm is simple and easy to understand its computational complexity is only 2 4 times that required to evaluate a specific single s s policy the algorithm applies to both periodic review and continuous review inventory systems

an efficient algorithm for computing optimal s s policies this paper presents an algorithm to compute an optimal s s policy under standard assumptions stationary data well behaved one period costs discrete demand full backlogging and the average cost criterion the method is iterative starting with an arbitrary given s s policy and converging to an optimal policy in a finite number of iterations any of the available approximations can thus be used as an initial solution each iteration requires only modest computations also a lower bound on the true optimal cost can be computed and used in a termination test empirical testing suggests very fast convergence

strict inequality of robin eigenvalues for elliptic differential operators on lipschitz domains abstract on a bounded lipschitz domain we consider two selfadjoint operator realizations of the same second order elliptic differential expression subject to robin boundary conditions where the coefficients in the boundary conditions are functions we prove that inequality between these functions on the boundary implies strict inequality between the eigenvalues of the two operators provided that the inequality of the functions in the boundary conditions is strict on an arbitrarily small nonempty open set

oscillation of solutions of second order nonlinear differential equations of euler type we consider the nonlinear euler differential equation t 2 x g x 0 here g x satisfies xg x 0 for x 0 but is not assumed to be sublinear or superlinear we present implicit necessary and sufficient condition for all nontrivial solutions of this system to be oscillatory or nonoscillatory also we prove that solutions of this system are all oscillatory or all nonoscillatory and cannot be both we derive explicit conditions and improve the results presented in the previous literature we extend our results to the extended

global existence and nonexistence of solutions for second order nonlinear differential equations abstract this paper deals with the global existence and nonexistence of solutions of the second order nonlinear differential equation x x 0 satisfying x 0 x 0 and x 0 x 1 where is a positive parameter and with 0 and 0 is strictly increasing odd bijective and continuous on necessary and sufficient conditions are obtained for the initial value problem to have a unique global solution which is oscillatory and periodic examples are given to illustrate our main result finally a nonexistence result for the equation with a damping term is discussed as an application to our result

oscillation criteria for second order nonlinear differential equations of euler type abstract the purpose of this paper is to solve the oscillation problem for the nonlinear euler differential equation t 2 x g x 0 and the extended equation x a t g x 0 here g x satisfies the sign condition xg x 0 if x 0 but is not assumed to be monotone we give necessary and sufficient conditions for all nontrivial solutions to be oscillatory to this end we use phase plane analysis of the lienard system and the oscillation result on the riemann weber version of the linear euler differential equation t 2 y 1 4 log t 2 y 0 our results are a negative answer to a conjecture which was given by wong finally we illustrate our results by two examples

multi dimensional morse index theorems and a symplectic view of elliptic boundary value problems morse index theorems for elliptic boundary value problems in multi dimensions are proved under various boundary conditions the theorems work for star shaped domains and are based on a new idea of measuring the oscillation of the trace of the set of solutions on a shrinking boundary the oscillation is measured by formulating a maslov index in an appropriate sobolev space of functions on this boundary a fundamental difference between the cases of dirichlet and neumann boundary conditions is exposed through a monotonicity that holds only in the former case

counting eigenvalues via the krein signature in infinite dimensional hamiltonian systems spectra of nonlinear waves in infinite dimensional hamiltonian systems are investigated we establish a connection via the krein signature between the number of negative directions of the second variation of the energy and the number of potentially unstable eigenvalues of the linearization about a nonlinear wave we apply our results to determine the effect of symmetry breaking on the spectral stability of nonlinear waves in weakly coupled nonlinear schrodinger equations

an epq model with partial backorders considering two backordering costs abstract we propose an epq model with partial backorders considering linear and fixed backordering costs time intervals rather than ordering size and backordering level are used as decision variables to derive the closed form optimal solution our approach analyzes different optimal inventory policies and decides whether shortage period should be scheduled in addition a critical backordering rate is derived to determine the feasible optimal solution the numerical example is provided to illustrate the solution procedure

an epq model with inflation in an imperfect production system in this paper a production inventory model is considered for stochastic demand with the effect of inflation generally every manufacturing system wants to produce perfect quality items however due to real life problems labor problems machine breakdown etc a certain percentage of products are of imperfect quality the imperfect items are reworked at a cost the lifetime of a defective item follows a weibull distribution due to the production of imperfect quality items a product shortage occurs the profit function is derived by using both a general distribution of demand and the uniform rectangular distribution of demand computational experiments along with graphical illustrations are presented to discuss the optimality of the probability functions

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

optimization models and a ga based algorithm for stochastic time cost trade off problem in real life projects both the trade off between the project cost and the project completion time and the uncertainty of the environment are considerable aspects for decision makers however the research on the time cost trade off problem seldom concerns stochastic environments besides optimizing the expected value of the objective is the exclusive decision making criterion in the existing models for the stochastic time cost trade off problem in this paper two newly developed alternative stochastic time cost trade off models are proposed in which the philosophies of chance constrained programming and dependent chance programming are adopted for decision making in addition a hybrid intelligent algorithm integrating stochastic simulations and genetic algorithm is designed to search the quasi optimal schedules under different decision making criteria the goal of the paper is to reveal how to obtain the optimal balance of the project completion time and the project cost in stochastic environments

continuous review inventory model in mixed fuzzy and stochastic environment in this paper we consider a continuous review inventory system where fuzziness and randomness appear simultaneously into an optimization setting since demand plays an important role in such type of inventory systems we develop a model in a mixed environment by incorporating fuzzy random variable as customer demand after fuzzifying the random lead time demand we consider the annual average demand as a fuzzy random variable we provide an elegant methodology to determine the optimal order quantity and reorder point such that the total expected annual cost in the fuzzy sense has a minimum value since the expected value of a fuzzy random variable is a fuzzy quantity a method of ranking fuzzy numbers using their possibilistic mean values is adopted to achieve the optimal solution a numerical example is presented to illustrate the proposed model

two storage inventory problem with dynamic demand and interval valued lead time over finite time horizon under inflation and time value of money a finite time horizon inventory problem for a deteriorating item having two separate warehouses one is a own warehouse ow of finite dimension and other a rented warehouse rw is developed with interval valued lead time under inflation and time value of money due to different preserving facilities and storage environment inventory holding cost is considered to be different in different warehouses the demand rate of item is increasing with time at a decreasing rate shortages are allowed in each cycle and backlogged them partially shortages may or may not be allowed in the last cycle and under this circumstance there may be three different types of model here it is assumed that the replenishment cycle lengths are of equal length and the stocks of rw are transported to ow in continuous release pattern for each model different scenarios are depicted depending upon the re order point for the next lot representing the lead time by an interval number and using the interval arithmetic the single objective function for profit is changed to corresponding multi objective functions these functions are maximized and solved by fast and elitist multi objective genetic algorithm femga the models are illustrated numerically and the results are presented in tabular form

oscillation of solutions of second order nonlinear self adjoint differential equations abstract we are concerned with the oscillation problem for the nonlinear self adjoint differential equation a t x b t g x 0 here g x satisfied the signum condition xg x 0 if x 0 but is not imposed such monotonicity as superlinear or sublinear we show that certain growth conditions on g x play an essential role in a decision whether all nontrivial solutions are oscillatory or not our main theorems extend recent results in a serious of papers and are best possible for the oscillation of solutions in a sense to accomplish our results we use sturm s comparison method and phase plane analysis of systems of lienard type we also explain an analogy between our results and an oscillation criterion of kneser hille type for linear differential equations

multi item imperfect production lot size model with hybrid number cost parameters in this study we have developed a multi item finite production lot size model with reworking of imperfect quality items when production stops defected items are assumed to rework at a constant rate the cost parameters in this model are taken here as hybrid numbers i e some of the costs are fuzzy numbers as well as random variables then the model is converted into a multi objective geometric programming gp problem a numerical example is given to support the problem a sensitivity analysis has given to study the nature of the objective functions

the maslov and morse indices for schrodinger operators on 0 1 abstract assuming a symmetric potential and separated self adjoint boundary conditions we relate the maslov and morse indices for schrodinger operators on 0 1 we find that the morse index can be computed in terms of the maslov index and two associated matrix eigenvalue problems this provides an efficient way to compute the morse index for such operators

intersection with the vertical isocline in the generalized lienard equations abstract we consider the generalized lienard system d x d t 1 a x h y f x d y d t a x g x where a f g and h are continuous functions on r and a x 0 for x r under the assumptions that the origin is a unique equilibrium we study the problem whether all trajectories of this system intersect the vertical isocline h y f x which is very important in the global asymptotic stability of the origin oscillation theory and existence of periodic solutions under quite general assumptions we obtain sufficient and necessary conditions which are very sharp our results extend the results of villari and zanolin and hara and sugie for this system with h y y and a x 1 and improve the results presented by sugie et al and gyllenberg and ping

an eoq model with delay in payments and stock dependent demand in the presence of imperfect production abstract in real life situation supplier generally offers a delay period to the retailer to buy more in this connection a mathematical model is considered to investigate the retailer s optimal replenishment policy under permissible delay in payment with stock dependent demand within the eoq economic order quantity framework most of the eoq models are considered with infinite replenishment rate in this article the model is considered with finite replenishment rate under progressive payment scheme with the production of defective items within the cycle time the mathematical models have been derived for obtaining the optimal cycle time so that the annual total relevant cost is minimized numerical examples along with graphical representation and sensitivity analysis are provided to illustrate the model

multi objective fuzzy inventory model with three constraints a geometric programming approach a multi item multi objective inventory model with shortages and demand dependent unit cost has been formulated along with storage space number of orders and production cost restrictions in most of the real world situations the cost parameters the objective functions and constraints of the decision makers are imprecise in nature hence the cost parameters the objective functions and constraints are imposed here in fuzzy environment this model has been solved by geometric programming method the results for the model without shortages are obtained as a particular case the sensitivity analysis has been discussed for the change of the cost parameters the models are illustrated with numerical examples

a nonoscillation theorem for emden fowler equations abstract we study the second order emden fowler equation e y a x y 1 y 0 0 where a x is positive and absolutely continuous on 0 let x x 3 2 where is any positive number theorem let 1 if x satisfies a lim x x k 0 and b x dx then eq e is nonoscillatory

a generalization of olech opial wazeski oscillation criteria to second order nonlinear equations section 1 in this paper we consider the second order nonlinear differential equation y r 40 f y0 09 t e r 0 x n and its prototype the so called generalized emden fowler equation 0 lu r l sgn r r 0 q e c r nj in n we assume yf y 0 y 0 with f c 0 u 0 xc and f y 0 y 0 we shall be interested in establishing sufficient conditions in order that all continuable solutions of n or n are oscillatory in section 4 we shall also discuss the extension of our results to the more general equations y 0 f y0 0 r j and y r ly l sgny r 0 ky where r t 0 t e r is continuous the oscillation nonoscillation problem for n n and its generalizations has been discussed by numerous authors by various techniques cf wong 12 141 for surveys three of the more important oscillation criteria for the linear case ly 1 of n are

a symplectic perspective on constrained eigenvalue problems abstract the maslov index is a powerful tool for computing spectra of selfadjoint elliptic boundary value problems this is done by counting intersections of a fixed lagrangian subspace which designates the boundary conditions with the set of cauchy data for the differential operator we apply this methodology to constrained eigenvalue problems in which the operator is restricted to a not necessarily invariant subspace the maslov index is defined and used to compute the morse index of the constrained operator we then prove a constrained morse index theorem which says that the morse index of the constrained problem equals the number of constrained conjugate points counted with multiplicity and give an application to the nonlinear schrodinger equation

spectra of positive and negative energies in the linearized nls problem we study the spectrum of the linearized nls equation in three dimensions in association with the energy spectrum we prove that unstable eigenvalues of the linearized nls problem are related to negative eigenvalues of the energy spectrum while neutrally stable eigenvalues may have both positive and negative energies the nonsingular part of the neutrally stable essential spectrum is always related to the positive energy spectrum we derive bounds on the number of unstable eigenvalues of the linearized nls problem and study bifurcations of embedded eigenvalues of positive and negative energies we develop the l 2 scattering theory for the linearized nls operators and recover results of grillakis 5 with a fermi golden rule c

intersection with the vertical isocline in the lienard plane abstract in this paper we study the problem of whether all trajectories of the lienard system x y f x and y g x cross the vertical isocline which is very important for the existence of periodic solutions and oscillation theory we solve this problem completely in some sense our results include a proof for an old conjecture of hara and sugie

fuzzy goal programming an additive model abstract an additive model to solve fuzzy goal programming fgp is formulated the method uses arithmetic addition to aggregate the fuzzy goals to construct the relevant decision function cardinal and ordinal weights for nonequivalent fuzzy goals are also incorporated in the method the solution procedure is illustrated with a numerical example

the morse and maslov indices for multidimensional schrodinger operators with matrix valued potentials we study the schrodinger operator l v on a star shaped domain in rd with lipschitz boundary the operator is equipped with quite general dirichletor robin type boundary conditions induced by operators between h1 2 and h 1 2 and the potential takes values in the set of symmetric n n matrices by shrinking the domain and rescaling the operator we obtain a path in the fredholm lagrangian grassmannian of the subspace of h1 2 h 1 2 corresponding to the given boundary condition the path is formed by computing the dirichlet and neumann traces of weak solutions to the rescaled eigenvalue equation we prove a formula relating the number of negative eigenvalues of l the morse index the signed crossings of the path the maslov index the number of negative eigenvalues of the potential matrix evaluated at the center of the domain and the number of negative eigenvalues of a bilinear form related to the boundary operator

inertia law for spectral stability of solitary waves in coupled nonlinear schrodinger equations spectral stability analysis for solitary waves is developed in the context of the hamiltonian system of coupled nonlinear schrodinger equations the linear eigen value problem for a non self adjoint operator is studied with two self adjoint matrix schrodinger operators sharp bounds on the number and type of unstable eigen values in the spectral problem are found from the inertia law for quadratic forms associated with the two self adjoint operators symmetry breaking stability analysis is also developed with the same method

oscillation results for emden fowler type differential equations abstract the third order nonlinear differential equation x a t x b t f x 0 is considered we present oscillation and nonoscillation criteria which extend and improve previous results existing in the literature in particular some results recently stated by m gregus and m gregus jr j math anal appl 181 1994 575 585 in addition contributions to the classification of solutions are given the techniques used are based on a transformation which reduces to a suitable disconjugate form to this aim auxiliary results on the asymptotic behavior of solutions of a second order linear differential equation associated to are stated they are presented in an independent form because they may be applied also to simplify and improve other qualitative problems concerning differential equations with quasiderivatives

nonoscillation criteria for second order nonlinear differential equations abstract a number of known nonoscillation criteria for the second order nonlinear differential equation y q x y 0 0 where q is positive and locally of bounded variation are improved by energy function techniques

linearized instability for nonlinear schrodinger and klein gordon equations in this paper i am introducing a new technique for proving instability of bound states for hamiltonian systems there are already two disparate types of instability results in the literature the approach developed by strauss shatah 20 gave an instability criterion coming from the variational structure of the problem on the other hand jones approach 11 produced a complementary criterion related to the difference between the number of negative eigenvalues of two selfadjoint operators using quite different techniques it turns out that with the methods developed in this paper these two criteria can be derived within a single framework that also leads to a generalization of the previous results finally in order to demonstrate how this method works i apply the instability criterion in some specific examples