existence and symmetries of solutions in besov morrey spaces for a semilinear heat wave type equation abstract this paper considers a semilinear integro differential equation of volterra type which interpolates semilinear heat and wave equations global existence of solutions is showed in spaces of besov type based in morrey spaces namely besov morrey spaces our initial data is larger than the previous works and our results provide a maximal existence class for semilinear interpolated heat wave equation some symmetries self similarity and asymptotic behavior of solutions are also investigated in the framework of besov morrey spaces

fuzzy goal programming complementary slackness conditions and computational schemes abstract goal programming gp is an important category in linear programming and multiobjective versions which minimize the deviation among value of each objective function and its goal with satisfying other constraints of problem in this paper we deal with fuzzy goal programming fgp which is a generalized problem in vague nature where parameters relations and goals are given as fuzzy quantities with respect to imprecise data recently inuiguchi et al m inuiguchi j ramik t tanio m vlach satisficing solutions and duality in interval and fuzzy linear programming fuzzy sets and systems 135 2003 151 177 have proved some important dual theorems on fgp which are very close to the same crisp versions in continuation to their works based on fuzzy extensions of relations we get complementary slackness conditions for fgp which have an essential role in many optimization techniques moreover we obtain the most optimistic and pessimistic satisficing solutions employing these conditions and present a convex combination of them which covers the satisficing solutions for a fixed level of certainty our practical schemes implement an efficient interior point algorithm as sub procedure so they are polynomial time algorithms

fuzzy linear programming and applications abstract this paper presents a survey on methods for solving fuzzy linear programs first lp models with soft constraints are discussed then lp problems in which coefficients of constraints and or of the objective function may be fuzzy are outlined pivotal questions are the interpretation of the inequality relation in fuzzy constraints and the meaning of fuzzy objectives in addition to the commonly applied extended addition based on the min operator and used for the aggregation of the left hand sides of fuzzy constraints and fuzzy objectives a more flexible procedure based on yager s parametrized t norm t p is presented finally practical applications of fuzzy linear programs are listed

multiple objective programming problems with possibilistic coefficients abstract we consider the problem of incorporating possibilistic data into a multiple objective linear programming framework a solution concept that is attractive from the standpoints of feasibility and efficiency is specified a necessary and sufficient condition for such a solution is established and ways to single out some satisfying alternative in this context are described a numerical example is also included for the sake of illustration throughout the paper we indicate topics for further research

optimality conditions for linear programming problems with fuzzy coefficients the optimality conditions for linear programming problems with fuzzy coefficients are derived in this paper two solution concepts are proposed by considering the orderings on the set of all fuzzy numbers the solution concepts proposed in this paper will follow from the similar solution concept called the nondominated solution in the multiobjective programming problem under these settings the optimality conditions will be naturally elicited

analyticity of periodic traveling free surface water waves with vorticity we prove that the prole of a periodic traveling wave propagating at the surface of water above a at bed in a ow with a real analytic vorticity must be real analytic provided the wave speed exceeds the horizontal uid velocity throughout the ow the real analyticity of each streamline be

stability of peakons the peakons are peaked solitary wave solutions of a certain nonlinear dispersive equation that is a model in shallow water theory and the theory of hyperelastic rods we give a very simple proof of the orbital stability of the peakons in the h1 norm 2000 john wiley sons inc

the well posedness of the surface quasi geostrophic equations in the besov morrey spaces abstract in this paper we develop the boundedness of riesz transform in morrey spaces which generalize the corresponding result in the usual l p spaces as an application of this boundedness we establish the well posedness and blow up criterion for the surface quasi geostrophic equations in the framework of besov morrey spaces

stability in the energy space of the sum of n peakons for a modified camassa holm equation with higher order nonlinearity considered herein is the orbital stability in the energy space h1 r of a decoupled sum of n peakons for a modified camassa holm equation with higher order nonlinearity the equation studied here admits single peakon and multi peakons based on our obtained result of the stability of a single peakon and then combining modulation argument with monotonicity of the local energy h1 norm we get the stability of the sum of n peakons considered herein is the orbital stability in the energy space h1 r of a decoupled sum of n peakons for a modified camassa holm equation with higher order nonlinearity the equation studied here admits single peakon and multi peakons based on our obtained result of the stability of a single peakon and then combining modulation argument with monotonicity of the local energy h1 norm we get the stability of the sum of n peakons

stability and asymptotic stability in the energy space of the sum of n solitons for subcritical gkdv equations we prove in this paper the stability and asymptotic stability in h1 of a decoupled sum of n solitons for the subcritical generalized kdv equations the proof of the stability result is based on energy arguments and monotonicity of the local l2 norm note that the result is new even for p 2 the kdv equation the asymptotic stability result then follows directly from a rigidity theorem in 16

global solutions of the super critical 2d quasi geostrophic equation in besov spaces abstract in this paper we study the super critical 2d dissipative quasi geostrophic equation we obtain some regularization effects allowing us to prove a global well posedness result for small initial data lying in critical besov spaces constructed over lebesgue spaces l p with p 1 local results for arbitrary initial data are also given

on the cauchy problem for the integrable modified camassa holm equation with cubic nonlinearity abstract considered in this paper is the modified camassa holm equation with cubic nonlinearity which is integrable and admits the single peaked solitons and multi peakon solutions the short wave limit of this equation is known as the short pulse equation the main investigation is the cauchy problem of the modified camassa holm equation with qualitative properties of its solutions it is firstly shown that the equation is locally well posed in a range of the besov spaces the blow up scenario and the lower bound of the maximal time of existence are then determined a blow up mechanism for solutions with certain initial profiles is described in detail and nonexistence of the smooth traveling wave solutions is also demonstrated

dissipative quasi geostrophic equation for large initial data in the critical sobolev space the critical and super critical dissipative quasi geostrophic equations are investigated in mathbb r 2 we prove local existence of a unique regular solution for arbitrary initial data in h2 2 which corresponds to the scaling invariant space of the equation we also consider the behavior of the solution near t 0 in the sobolev space

on the fuzzy multi objective linear programming problem goal programming approach abstract for a fuzzy multi objective linear programming problem we propose a substitute problem the problem is given as the minimization problem the objective function of which is the distance between the l ary restricted optimal values at each optimal solutions kuwano et al 1994 and l ary objective functions with fuzzy parameters

formulation of general possibilistic linear programming problems for complex industrial systems the current models and methods for plp are usually restricted on some special types and usually the same type of possibilistic distribution this paper focuses on linear programming problems with general possibilistic resources grplp and linear programming problems with general possibilistic objective coefficients goplp by introducing some new concepts of the largest most possible point the smallest most possible point the most optimistic point and the most possible decision a new approach for formulating possibilistic constraints through general possibilistic resources and a satisfactory solution method will be discussed in this paper a most possible decision method for grplp and a dual approach for goplp will be proposed for solving complex industrial decision problems

a new possibilistic programming approach for solving fuzzy multiobjective assignment problem in this paper we propose a new possibilistic programming approach to solve a fuzzy multiobjective assignment problem in which the objective function coefficients are characterized by triangular possibility distributions the proposed solution approach simultaneously minimizes the best scenario the likeliest scenario and the worst scenario for the imprecise objective functions using level sets the level sets are used to define the confidence level of the fuzzy judgments of the decision maker additionally we provide a systematic framework in which the decision maker controls the search direction by updating both the membership values and aspiration levels until a set of satisfactory solutions is obtained numerical examples with dataset from realistic situations are provided to demonstrate the effectiveness of the proposed approach

global well posedness for the critical 2d dissipative quasi geostrophic equation we give an elementary proof of the global well posedness for the critical 2d dissipative quasi geostrophic equation the argument is based on a non local maximum principle involving appropriate moduli of continuity

a class of single sampling inspection plans based on possibilistic programming problem abstract the problem of designing the lot tolerance percent defective single sampling inspection plans is considered when the parameters cannot be known precisely the parameters are assumed fuzzy variables so that the problem becomes a possibilistic programming problem a solution procedure is developed to find a compromise plan a numerical example and a sensitivity analysis are included

a new bernstein s inequality and the 2d dissipative quasi geostrophic equation we show a new bernstein s inequality which generalizes the results of cannone planchon danchin and lemarie rieusset as an application of this inequality we prove the global well posedness of the 2d quasi geostrophic equation with the critical and super critical dissipation for the small initial data in the critical besov space and local well posedness for the large initial data

stability in multiobjective possibilistic linear programs abstract this paper continues the authors research in stability analysis in possibilistic programming in that it extends previous results to possibilistic linear programs with multiple objective functions namely we show that multiobjective possibilistic linear programs with continuous fuzzy number coefficients are well posed i e small changes in the membership function of the coefficients may cause only a small deviation in the possibility distribution of the objective function

possibility programming by the comparison of fuzzy numbers abstract a possibility programming approach is proposed based on the use of simple but realistic fuzzy numbers the possibility concept and the comparison of fuzzy numbers the approach appears to be very powerful due to its simplicity and its relatively small requirement of computer time strict exceedance possibility and trapezoidal fuzzy numbers are used to illustrate the approach with numerical examples

global well posedness in the super critical dissipative quasi geostrophic equations we consider the quasi geostrophic equation with the dissipation term in the case constantin cordoba wu 6 proved the global existence of strong solution in h 1 and h 2 under the assumption of small l norm of initial data in this paper we prove the global existence in the scale invariant besov space b 2 2 2 1 for initial data small in the b 2 2 2 1 norm we also prove a global stability result in b 1 2 1

an extension to possibilistic linear programming abstract this paper proposes an extension to the solution of possibilistic linear programming problems with fuzzy number parameters introduced by buckley fuzzy sets and systems31 1989 329 341 the method relies on cuts of the fuzzy number parameters to generate a succession of pairs of classical linear programs the solutions of these linear programs produce a convex possibility distribution of the optimal objective values with the corresponding levels of the decision variables the approach is illustrated with an imprecise water quality management problem

integrable peakon equations with cubic nonlinearity we present a new integrable partial differential equation found by vladimir novikov like the camassa holm and degasperis procesi equations this new equation admits peaked soliton peakon solutions but it has nonlinear terms that are cubic rather than quadratic we give a matrix lax pair for v novikov s equation and show how it is related by a reciprocal transformation to a negative flow in the sawada kotera hierarchy infinitely many conserved quantities are found as well as a bi hamiltonian structure the latter is used to obtain the hamiltonian form of the finite dimensional system for the interaction of n peakons and the two body dynamics n 2 is explicitly integrated finally all of this is compared with some analogous results for another cubic peakon equation derived by zhijun qiao

fuzzy stochastic linear programming survey and future research directions in many real life problems one has to base decision on information which is both fuzzily imprecise and probabilistically uncertain although consistency indexes providing a union nexus between possibilistic and probabilistic representation of uncertainty exist there are no reliable transformations between them this calls for new paradigms for incorporating the two kinds of uncertainty into mathematical models fuzzy stochastic linear programming is an attempt to fulfill this need it deals with modelling and problem solving issues related to situations where randomness and fuzziness co occur in a linear programming framework in this paper we provide a survey of the essential elements methods and algorithms for this class of linear programming problems along with promising research directions being a survey the paper includes many references to both give due credit to results in the field and to help readers obtain more detailed information on issues of interest

a new integrable equation with cuspons and w m shape peaks solitons in this paper we propose a new completely integrable wave equation mt mx u2 ux2 2m2ux 0 m u uxx the equation is derived from the two dimensional euler equation and is proven to have lax pair and bi hamiltonian structures this equation possesses new cusp solitons cuspons instead of regular peakons ce x ct with speed c through investigating the equation we develop a new kind of soliton solutions w m shape peaks solitons there exist no smooth solitons for this integrable water wave equation

tri hamiltonian duality between solitons and solitary wave solutions having compact support a simple scaling argument shows that most integrable evolutionary systems which are known to admit a bi hamiltonian structure are in fact governed by a compatible trio of hamiltonian structures we demonstrate how their recombination leads to integrable hierarchies endowed with nonlinear dispersion that supports compactons solitary wave solutions having compact support or cusped and or peaked solitons a general algorithm for effecting this duality between classical solitons and their nonsmooth counterparts is illustrated by the construction of dual versions of the modified korteweg de vries equation the nonlinear schr odinger equation the integrable boussinesq system used to model the two way propagation of shallow water waves and the ito system of coupled nonlinear wave equations these hierarchies include a remarkable variety of interesting integrable nonlinear differential equations textcopyright 1996 the american physical society

fuzzy optimization an appraisal abstract this paper takes a general look at core ideas that make up the burgeoning body of fuzzy mathematical programming emphasizing the methodological view although fuzzy mathematical programming has enjoyed a rapidly increasing acceptance within the scientific community some technical hurdles exist to hinder a unanimity reasons for this as well as possible ways for improvement are also discussed

global weak solutions for the novikov equation in the paper we mainly study the existence and uniqueness of global weak solutions for the novikov equation we first recall some results and definitions on strong solutions and weak solutions for the equation then we show that the equation has smooth solutions which exist globally in time provided the initial data satisfy certain sign conditions finally we prove the existence and uniqueness of global weak solutions to the equation with the initial data satisfying certain sign conditions

evaluate fuzzy optimization problems based on biobjective programming problems abstract the embedding theorem shows that the set of fuzzy numbers can be embedded into a banach space inspired by this embedding theorem we propose a solution concept of the fuzzy optimization problem by solving a biobjective optimization problem which is transformed from the original fuzzy optimization problem using the embedding theorem we then also consider the fuzzy optimization problem with fuzzy coefficients i e the coefficients are assumed to be fuzzy numbers under a setting of core values of fuzzy numbers we show that the optimal solution of its corresponding crisp optimization problem the usual optimization problem is also an optimal solution of the original fuzzy optimization problem

stability in possibilistic linear programming with continuous fuzzy number parameters abstract we prove that possibilistic linear programming problems introduced by buckley in 2 with continuous fuzzy number parameters are well posed i e small changes of the membership function of the parameters may cause only a small deviation in the possibilistic distribution of the objective function

water quality management with imprecise information abstract the application of fuzzy set and possibility theories for the representation of imprecise information in water quality management problems is investigated imprecision is associated with fuzziness which is non statistical in nature and refers to the absence of sharp boundaries in the information imprecise parameters in water quality decision making can be represented by possibility distributions defining maximum achievable probabilities the corresponding possibilistic programming problem is viewed as an alternative to the stochastic one where the parameters are modeled as fuzzy variables instead of random variables the possibilistic problem can be solved through a succession of classical linear programs the resulting possibility distributions of the objective value provide a possibilistic assessment of the risk based on possibility levels

solving a multiobjective possibilistic problem through compromise programming abstract real decision problems usually consider several objectives that have parameters which are often given by the decision maker in an imprecise way it is possible to handle these kinds of problems through multiple criteria models in terms of possibility theory here we propose a method for solving these kinds of models through a fuzzy compromise programming approach to formulate a fuzzy compromise programming problem from a possibilistic multiobjective linear programming problem the fuzzy ideal solution concept is introduced this concept is based on soft preference and indifference relationships and on canonical representation of fuzzy numbers by means of their cuts the accuracy between the ideal solution and the objective values is evaluated handling the fuzzy parameters through their expected intervals and a definition of discrepancy between intervals is introduced in our analysis

a maximum principle applied to quasi geostrophic equations we study the initial value problem for dissipative 2d quasi geostrophic equations proving local existence global results for small initial data in the super critical case decay of lp norms and asymptotic behavior of viscosity solution in the critical case our proofs are based on a maximum principle valid for more general flows

well posedness global existence and blowup phenomena for a periodic quasi linear hyperbolic equation we establish the local well posedness of a recently derived model for small amplitude shallow water waves for a large class of initial data we prove global existence of the corresponding solution criteria guaranteeing the development of singularities in finite time for strong solutions with smooth initial data are obtained and an existence and uniqueness result for a class of global weak solutions is also given c 1998 john wiley sons inc

orbital stability of the train of peakons for an integrable modified camassa holm equation abstract in this paper we consider the modified camassa holm equation with cubic nonlinearity which is integrable and admits the single peakons and multi peakons using energy argument and combining the method of the orbital stability of a single peakon with monotonicity of the local energy norm we prove that the sum of n sufficiently decoupled peakons is orbitally stable in the energy space

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

drift diffusion equations with fractional diffusion and the quasi geostrophic equation motivated by the critical dissipative quasi geostrophic equation we prove that drift diffusion equations with l 2 initial data and minimal assumptions on the drift are locally holder continuous as an application we show that solutions of the quasi geostrophic equation with initial l 2 data and critical diffusion 1 2 are locally smooth for any space dimension

a new approach to some possibilistic linear programming problems abstract in practice the unit costs profits of new products or new projects the lending and borrowing interest rates and cash flows are always imprecise we provide an auxiliary multiple objective linear programming model to solve a linear programming problem with imprecise objective and or constraint coefficients our strategy is to maximize the most possible value of the imprecise profit at the same time we would like to minimize the risk of obtaining lower profit and maximize the possibility of obtaining higher profit this strategy is equivalent to the practical considerations of financial problems in this paper a numeric investment problem is solved for illustrating the new approach

analysis of critical paths in a project network with fuzzy activity times abstract this paper proposes an approach to critical path analysis for a project network with activity times being fuzzy numbers in that the membership function of the fuzzy total duration time is constructed the basic idea is based on the extension principle and linear programming formulation a pair of linear programs parameterized by possibility level is formulated to calculate the lower and upper bounds of the fuzzy total duration time at by enumerating different values of the membership function of the fuzzy total duration time is constructed and the fuzzy critical paths are identified at the same time moreover by applying the yager ranking method definitions of the most critical path and the relative degree of criticality of paths are developed and these definitions are theoretically sound and easy to use in practice two examples with activity times being fuzzy numbers of l r and l l types discussed in previous studies are solved successfully to demonstrate the validity of the proposed approach since the total duration time is completely expressed by a membership function rather than by a crisp value the fuzziness of activity times is conserved completely and more information is provided for critical path analysis

possibilistic linear programming with triangular fuzzy numbers abstract we consider a mathematical programming problem where all the parameters may be fuzzy variables specified by their possibility distribution and we define the possibility distribution of the objective function the ideas are illustrated on possibilistic linear programming

new method for solving fuzzy transportation problems with lr flat fuzzy numbers transportation problems have various applications in logistics and supply chains for reducing costs in real life situations the parameters of transportation problems may not be known precisely because of uncontrollable factors herein we propose a new method for solving fuzzy transportation problems ftps in which the transportation costs and supply and demand are represented by non negative lr flat fuzzy numbers the ftp is converted into four transportation problems which are solved using standard transportation simplex algorithms the advantages of the proposed method over existing methods are discussed in the context of two application examples the results show that the proposed method is simpler and computationally more efficient than existing methods in the literature

fuzzy multi level minimum cost flow problems both multiple objectives and multiple hierarchies minimum cost flow problems with fuzzy costs and fuzzy capacities in the arcs are investigated to reduce the complexity a possibility programming is used to handle the vagueness in the parameters fuzzy approach can considerably simplify the problem and thus a fairly general multi level problem can be solved reasonably easily in spite of the fact that the multi level problem is np hard and very difficult to solve several numerical examples are considered to illustrate the approach

on possibilistic linear programming abstract the problem of processing and combining possibilistic information in the scope of linear programming is approached as apparatus to cope with this problem we use the concepts of more possible value possibly feasible action and possibly efficient action issues regarding the feasibility of the resulting deterministic programs as well as the characterization of their optimal solutions are also discussed

solving fuzzy transportation problems based on extension principle abstract transportation models play an important role in logistics and supply chain management for reducing cost and improving service this paper develops a procedure to derive the fuzzy objective value of the fuzzy transportation problem in that the cost coefficients and the supply and demand quantities are fuzzy numbers the idea is based on the extension principle a pair of mathematical programs is formulated to calculate the lower and upper bounds of the fuzzy total transportation cost at possibility level from different values of the membership function of the objective value is constructed two different types of the fuzzy transportation problem are discussed one with inequality constraints and the other with equality constraints it is found that the membership function of the objective value of the equality problem is contained in that of the inequality problem since the objective value is expressed by a membership function rather than by a crisp value more information is provided for making decisions

analysis of structure in fuzzy linear programs abstract fuzzy linear programming problems are analyzed within the fuzzy set context to uncover redundancies infeasibilities variables whose values are fixed and implied bounds on rows and columns applications include pre analysis of perturbed constraint matrices and post optimization analysis fuzzy linear programming problems

numerical solutions for systems of qualitative nonlinear algebraic equations by fuzzy logic abstract this paper presents a fuzzy logic approach for determining a numerical solution to a consistent system of algebraic equations f x 0 in which the function f is not explicitly defined and may be underdetermined such systems arise frequently in many engineering design problems where design parameters must be chosen using qualitative information by the designer to meet a set of desired performance constraints the proposed method also can be used for a consistent system of nonlinear equations in which f is explicitly defined and may have fewer independent equations than the number of unknowns however this method is very computationally demanding hence it is not advisable to apply it to problems involving explicit functions that can be solved using other existing numerical methods it is seen that this method works quite well and numerical solutions for such problems can be obtained although it is much slower than newton s method when employed to consistent explicit nonlinear equations

generalizations of the camassa holm equation we classify generalized camassa holm type equations which possess infinite hierarchies of higher symmetries we show that the obtained equations can be treated as negative flows of integrable quasi linear scalar evolution equations of orders 2 3 and 5 we present the corresponding lax representations or linearization transformations for these equations some of the obtained equations seem to be new

linear programming under randomness and fuzziness this paper is concerned with the use of fuzzy sets theory well suited for nuanced human behavior to extend the applicability of linear programming in a way to let both randomness and fuzziness uncertainties be taken into account a fuzzy stochastic linear programming problem is considered and ways to handle it suggested the basic idea behind our approaches is to translate the original problem in deterministic terms via tools provided by fuzzy sets theory to get a classical one some conditions for the resulting problems to be solved without extra computational effort are stressed and illustrative examples given

the trajectories of particles in stokes waves analyzing a free boundary problem for harmonic functions we show that there are no closed particle paths in an irrotational inviscid traveling wave propagating at the surface of water over a flat bed within a period each particle experiences a backward forward motion with a slight forward drift

multiobjective possibilistic linear programming abstract this paper presents two solutions to multiobjective linear programs when all the parameters may be fuzzy variables whose values are restricted by a possibility distribution in the first solution we first find possibility distribution of the objective function and then a solution consists of those values of the decision variables which produce the largest undominated values of the objective function where these values also have maximum possibility in the second solution we first find the possibility distribution of the undominated sets and then a solution consists of those values of the decision variables which are undominated with maximum possibility but also produce the largest undominated values of the objective function for certain multiobjective possibilistic linear programs we show that the two solution concepts are identical

the maximum principle and the global attractor for the dissipative 2d quasi geostrophic equations the long time behavior of the solutions to the two dimensional dissipative quasi geostrophic equations is studied we obtain a new positivity lemma which improves a previous version of a cordoba and d cordoba 10 and 11 as an application of the new positivity lemma we obtain the new maximum principle i e the decay of the solution in l p for any p 2 when f is zero as a second application of the new positivity lemma for the sub critical dissipative case with open image in new window the existence of the global attractor for the solutions in the space h s for any s 2 1 is proved for the case when the time independent f is non zero therefore the global attractor is infinitely smooth if f is this significantly improves the previous result of berselli 2 which proves the existence of an attractor in some weak sense for the case 1 the global attractor exists in h s for any s 0 and the estimate of the hausdorff and fractal dimensions of the global attractor is also available

oscillation induced blow up to the modified camassa holm equation with linear dispersion abstract in this paper we provide a blow up mechanism to the modified camassa holm equation with varying linear dispersion we first consider the case when linear dispersion is absent and derive a finite time blow up result with an initial data having a region of mild oscillation a key feature of the analysis is the development of the burgers type inequalities with focusing property on characteristics which can be deduced from tracing the ratio between solution and its gradient using the continuity and monotonicity of the solutions we then extend this blow up criterion to the case of negative linear dispersion and determine that the finite time blow up can still occur if the initial momentum density is bounded below by the magnitude of the linear dispersion and the initial datum has a local mild oscillation region finally we demonstrate that in the case of non negative linear dispersion the formation of singularities can be induced by an initial datum with a sufficiently steep profile in contrast to the camassa holm equation with linear dispersion the effect of linear dispersion of the modified camassa holm equation on the blow up phenomena is rather delicate

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

existence and uniqueness results for the 2 d dissipative quasi geostrophic equation abstract this paper concerns itself with besov space solutions of the 2 d quasi geostrophic qg equation with dissipation induced by a fractional laplacian the goal is threefold first to extend a previous result on solutions in the inhomogeneous besov space b 2 q r j wu global solutions of the 2d dissipative quasi geostrophic equation in besov spaces siam j math anal 36 2004 2005 1014 1030 to cover the case when r 2 2 second to establish the global existence of solutions in the homogeneous besov space b p q r with general indices p and q and third to determine the uniqueness of solutions in any one of the four spaces b 2 q s b p q r l q 0 t b 2 q s 2 q and l q 0 t b p q r 2 q where s 2 2 and r 1 2 2 p

wave breaking and peakons for a modified camassa holm equation in this paper we investigate the formation of singularities and the existence of peaked traveling wave solutions for a modified camassa holm equation with cubic nonlinearity the equation is known to be integrable and is shown to admit a single peaked soliton and multi peakon solutions of a different character than those of the camassa holm equation singularities of the solutions can occur only in the form of wave breaking and a new wave breaking mechanism for solutions with certain initial profiles is described in detail

local well posedness for the 2d non dissipative quasi geostrophic equation in besov spaces abstract in this paper we prove the local in time well posedness for the 2d non dissipative quasi geostrophic equation and study the blow up criterion in the critical besov spaces these results improve the previous one by constantin et al p constantin a majda e tabak formation of strong fronts in the 2d quasi geostrophic thermal active scalar nonlinearity 7 1994 1495 1533

study on fuzzy optimization methods based on principal operation and inequity degree fuzzy optimization is a well known optimization problem in artificial intelligence manufacturing and management so establishing general and operable fuzzy optimization methods are important in both theory and application in this paper by distinguishing principal indices and secondary indices we give a method for comparing fuzzy information based on synthesizing effect and an operation for achieving fuzzy optimization based on a principal indices transformation further we propose an axiomatic system for fuzzy inequity degree based on the essence of constraint and give an instructive metric method for fuzzy inequity degree then by combining with genetic algorithm we give some fuzzy optimization methods based on principal operation and inequity degree denoted by bpo id fga for short finally we consider the convergence of our algorithm using the theory of markov chains and analyze its performance through two concrete examples all these indicate that bpo id fga can effectively merge decision preferences into the optimization process and that it also possesses better global convergence so it can be applied to many fuzzy optimization problems

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

application of fuzzy sets to aggregate production planning with multiproducts and multitime periods the objective of this study is to develop a fuzzy mathematical programming method to solve aggregate production planning app decision problems that involve multiproducts and multitime periods in a fuzzy environment the fuzzy app model that is developed here attempts to minimize total cost with respect to inventory carrying levels available labor levels machine capacity and warehouse space and the constraint of available budget the proposed app method evaluates monetary interest of related operating cost categories and provides greater computational efficiency and flexibility by adopting triangular fuzzy numbers and piecewise linear membership functions to represent both imprecise data and fuzzy goals the actual performance of an industrial company was used to demonstrate the feasibility of applying the proposed method to real world app decisions the proposed method yields an efficient solution and presents overall decision maker satisfaction with the given goal values this paper also presents several significant management implications that are related to the practical application of the proposed method

fuzzy linear programming using a penalty method in this paper we begin with a standard form of the linear programming problem we replace each constant in the problem with a fuzzy number we then reformat the objective and constraints into an unconstrained fuzzy function by penalizing the objective for possible constraint violations the range of this fuzzy function lies in the space of fuzzy numbers the objective is then redefined as optimizing the expected midpoint of the image of this fuzzy function we show that this objective defines a concave function which therefore can be maximized globally we present an algorithm for finding the optimum

on the 2d critical and supercritical dissipative quasi geostrophic equation in besov spaces abstract we prove the local smoothing effect of the 2d critical and supercritical dissipative quasi geostrophic equations in critical besov spaces as an application a global well posedness result is established by adapting a method in kiselev nazarov and volberg 2007 16 and an idea in dong and du 2008 15 with suitable modifications moreover we show that the unique solution obtained in chen miao and zhang 2007 11 is a classical solution these generalize some previous results in dong 2010 13 dong and du 2008 15 the main ingredients of the proofs are two commutator estimates and the preservation of suitable modulus of continuity of the solutions

modality constrained programming problems a unified approach to fuzzy mathematical programming problems in the setting of possibility theory abstract in this paper fuzzy mathematical programming problems are formulated based on the idea analogous with the chance constrained programming problem the difference in meaning between the ambiguity of the coefficients and that of the decision maker s preference is emphasized the constraints with fuzzy coefficients are treated as the restriction that should be satisfied properly rather than perfectly the objective functions with fuzzy coefficients are treated variously depending on the interpretations i e the optimization of the modalities the optimization of the fractile the minimization of the ambiguity and so forth the deterministic equivalent constraints and the deterministic equivalent problems are shown when the constraints and the objective functions are linear a numerical example is given to illustrate the proposed formulations

some tricks from the symmetry toolbox for nonlinear equations generalizations of the camassa holm equation abstract the main subject of the paper is to give a survey and to present new methods on how integrability results i e results for symmetry groups inverse scattering formulations action angle transformations and the like can be transferred from one equation to others in case the equations are not related by backlund transformations as a main example the so called camassa holm equation is chosen for which the relevant results are obtained by having a look on the korteweg de vries kdv equation the camassa holm equation turns out to be a different factorization equation of the kdv it describes shallow water waves and reconciles the properties which were known for different orders of shallow water wave approximations we follow here an old method already marginally mentioned in fuchssteiner and fokas 1981 and fuchssteiner 1983 and recently applied by others olver and rosenau 1995 the method allows an immediate recovery of the recursion operator for the camassa holm equation from the invariance structure of the kdv although both equations are not related by backlund transformations however in addition and different from other approaches from there by use of the squared eigenfunction relation for the kdv equation the lax pair formulation for the different factorization equation is derived for the example under consideration it is of course the one obtained in camassa and holm 1993 since the methods proposed here can be transferred to any compatible factorization of recursion operators its application even in the special case which was chosen for illustration leads to a large class of integrable equations among which the camassa holm equation can be found as well as a three parameter family of generalizations of the equation the advantage of the general approach to the lax pair presentation is that direct transformations between action and angle variables are obtained so using this lax pair formulation as a novel result a direct transformation between action and angle variables for the camassa holm equation is derived further novel results in the paper are a hodograph link back from a backlund transformation of the camassa holm equation to a particular member of the kdv hierarchy additional symmetries and the construction of the conformal algebra for the hierarchy of the camassa holm equation the methods involved include hereditary operators bi hamiltonian formulations nilpotent flows and scaling symmetries

fuzzy reasoning for solving fuzzy mathematical programming problems abstract we interpret fuzzy linear programming flp problems with fuzzy coefficients and fuzzy inequality relations as multiple fuzzy reasoning schemes mfr where the antecedents of the scheme correspond to the constraints of the flp problem and the fact of the scheme is the objective of the flp problem then the solution process consists of two steps first for every decision variable x r n we compute the fuzzy value of the objective function max x via sup min convolution of the antecedents constraints and the fact objective then an optimal solution to flp problem is any point which produces a maximal element of the set max x x r n in the sense of the given inequality relation we show that our solution process for a classical crisp lp problem results in a solution in the classical sense and under well chosen inequality relations and objective function coincides with those suggested by buckley fuzzy sets and systems 31 1989 329 341 delgado et al control and cybernetics 16 1987 114 121 fuzzy sets and systems 26 1988 49 62 negoita fuzzy sets and systems 6 1981 261 269 ramik and rimanek fuzzy sets and systems 16 1985 123 138 verdegay fuzzy information and decision processes north holland amsterdam 1982 control and cybernetics 13 1984 230 239 and zimmermann int j general systems 2 1976 209 215 furthermore we show how to extend the proposed solution principle to non linear programming problems with fuzzy coefficients we illustrate our approach by some simple examples

fuzzy efficiency measures in data envelopment analysis abstract the existing data envelopment analysis dea models for measuring the relative efficiencies of a set of decision making units dmus using various inputs to produce various outputs are limited to crisp data to deal with imprecise data the notion of fuzziness has been introduced this paper develops a procedure to measure the efficiencies of dmus with fuzzy observations the basic idea is to transform a fuzzy dea model to a family of conventional crisp dea models by applying the cut approach a pair of parametric programs is formulated to describe that family of crisp dea models via which the membership functions of the efficiency measures are derived since the efficiency measures are expressed by membership functions rather than by crisp values more information is provided for management by extending to fuzzy environment the dea approach is made more powerful for applications

time cost trade off analysis of project networks in fuzzy environments abstract this paper proposes a novel approach for time cost trade off analysis of a project network in fuzzy environments different from the results of previous studies in this paper the membership function of the fuzzy minimum total crash cost is constructed based on zadeh s extension principle and fuzzy solutions are provided a pair of two level mathematical programs parameterized by possibility level is formulated to calculate the lower and upper bounds of the fuzzy minimum total crash cost at by enumerating different values of the membership function of the fuzzy minimum total crash cost is constructed and the corresponding optimal activity time for each activity is also obtained at the same time an example of time cost trade off problem with several fuzzy parameters is solved successfully to demonstrate the validity of the proposed approach since the minimum total crash cost is expressed by a membership function rather than by a crisp value the fuzziness of parameters is conserved completely and more information is provided for time cost trade off analysis in project management the proposed approach also can be applied to time cost trade off problems with other characteristics

stability in possibilistic quadratic programming abstract we show that possibilistic quadratic programs with crisp decision variables and continuous fuzzy number coefficients are well posed i e small changes in the membership function of the coefficients may cause only a small deviation in the possibility distribution of the objective function

stability of peakons for an integrable modified camassa holm equation with cubic nonlinearity considered herein is the dynamical stability of the single peaked soliton and periodic peaked soliton for an integrable modified camassa holm equation with cubic nonlinearity the equation is known to admit a single peaked soliton and multi peakon solutions and is shown here to possess a periodic peaked soliton by constructing certain lyapunov functionals it is demonstrated that the shapes of these waves are stable under small perturbations in the energy space

joint solution to fuzzy programming problems we propose a new solution concept for fuzzy programming problems it is based on our new method of solving fuzzy equations 101 for simplicity we discuss in detail only fuzzy linear programming in this paper we define and obtain the basic properties of the joint solution a fuzzy vector in rn and the optimal value of the objective function a fuzzy number three examples are presented illustrating these concepts