sun wong type theorems for second order damped elliptic equations abstract the oscillation criteria of sun and wong y g sun j s w wong oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities j math anal appl 334 2007 549 560 are extended to the forced second order damped elliptic differential equation with mixed nonlinearities i j 1 n d i a i j x d j y i 1 n b i x d i y c x y e x when n 1 our results include and improve those of nasr a h nasr sufficient conditions for the forced super linear second order differential equations with oscillatory potential proc amer math soc 126 1998 123 125 for a forced second order superlinear differential equation wong j s w wong oscillation criteria for a forced second order linear differential equations j math anal appl 231 1999 235 240 for a forced second order linear differential equation sun and wong y g sun j s w wong oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities j math anal appl 334 2007 549 560 for a forced second order differential equation with mixed nonlinearities when n 2 our results are more general and improve the oscillation criteria of zhuang r k zhuang annual oscillation criteria for second order nonlinear elliptic differential equations j comput anal math 217 2008 268 276 for a forced second order undamped elliptic differential equation

time independent invariants of motion for the quadratic system a hamiltonian method is developed to obtain first integrals of the form p qmu and p qmu rnu for a general system of two dimensional autonomous ordinary differential equations with quadratic terms where p q and r are linear or quadratic polynomials and mu nu are two real numbers it is found that there is an intimate relationship between the polynomials and the equilibrium points of the system which is useful for determining the existence of periodic orbits and asymptotic behaviour

painleve property and constants of the motion of the complex lorenz model the results of the painleve analysis and of a search for constants of the motion of the complex lorenz model are presented

a possibility measure is not a fuzzy measure abstract in this note we show that a possibility measure is not a particular type of fuzzy measure except in trivial cases

integrals of motion for three dimensional non hamiltonian dynamical systems the problem of finding integrals of motion of three dimensional dynamical systems is analysed the authors introduce a new type of direct method in the search of parameter values for which an integral of motion exists this method consists in proposing an ansatz for the integral that explicitly shows the dependence with respect to one of the phase space coordinates of the system they apply this procedure to the reduced three wave interaction problem and to the rabinovich system for both models new integrals of motion are found

fuzzy set based multiobjective allocation of resources and its applications this paper presents results of research into the use of the bellman zadeh approach to decision making in a fuzzy environment for solving multiobjective optimization problems its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems the use of the bellman zadeh approach has served as a basis for solving a problem of multiobjective allocation of resources or their shortages and developing a corresponding adaptive interactive decision making system aidms1 its calculating kernel permits one to solve maxmin problems using an algorithm based on a nonlocal search modification of the gelfand s and tsetlin s long valley method the aidms1 includes procedures for considering linguistic variables to reflect conditions that are difficult to formalize as well as procedures for constructing and correcting vectors of importance factors for goals the use of these procedures permits one to realize an adaptive approach to processing information of a decision maker to provide successive improving of the solution quality c windows of the aidms1 are presented for input output and special possibilities related to considering linguistic variables and constructing and correcting vectors of importance factors the results of the paper are universally applicable and are already being used to solve power engineering problems

hilbert space description of classical dynamical systems ii abstract it is shown that classical dynamical systems can be described by a hilbert space schrodinger like equation with the hamiltonian a non hermitian one expressed in terms of bose creation and annihilation operators the presented formalism includes the carleman embedding as the special case

a geometrical method towards first integrals for dynamical systems we develop a method based on darboux s and liouville s works to find first integrals and or invariant manifolds for a physically relevant class of dynamical systems without making any assumption on these elements forms we apply it to three dynamical systems lotka volterra lorenz and rikitake

families of invariants of the motion for the lotka volterra equations the linear polynomials family the modified carleman embedding method already introduced by the authors to find first integrals invariants of the motion of polynomial form to the lotka volterra system is described in detail and its efficiency to treat the n dimensional system proved using this method an extensive investigation is performed for polynomials of the first degree which allow a classification of the integrals in three families for some systems possessing one invariant it is possible to find a second invariant using rescaling methods they represent very restrictive solutions implying that there exists a great number of conditions among the equation s coefficients to satisfy a proof is given that the volterra invariants can be deduced as a limit finally the interesting properties of the solutions of these systems are studied in detail

a general time dependent invariant for and integrability of the quadratic system we derive a general time dependent invariant first integral for the quadratic system qs that requires only one condition on the coefficients of the qs the general invariant could yield asymptotic behaviour of phase space trajectories with more conditions imposed on the coefficients the general invariant reduces to polynomial form and is equivalent to polynomial invariants found using a direct method for the special case of a linear polynomial invariant where one of the variables is analytically invertible the solution of the qs is reduced to a quadrature

generalized hamiltonian structures for systems in three dimensions with a rescalable constant of motion the generalized hamiltonian structures of several three dimensional dynamical systems of interest in physical applications are considered in general hamiltonians exist only for systems that possess at least one time independent constant of motion systems with only time dependent constants of motion may sometimes be rescaled and their constant of motion made time independent when this is possible the transformed system may be cast in a generalized hamiltonian formalism with non canonical structure functions

regular ordered semigroups in terms of fuzzy subsets given a set s a fuzzy subset of s or a fuzzy set in s is by definition an arbitrary mapping f s 0 1 where 0 1 is the usual interval of real numbers if the set s bears some structure one may distinguish some fuzzy subsets of s in terms of that additional structure this important concept of a fuzzy set was first introduced by zadeh fuzzy groups have been first considered by rosenfeld fuzzy semigroups by kuroki a theory of fuzzy sets on ordered groupoids and ordered semigroups can be developed some results on ordered groupoids semigroups have been already given by the same authors in n kehayopulu m tsingelis fuzzy sets in ordered groupoids semigroup forum 65 2002 128 132 n kehayopulu m tsingelis the embedding of an ordered groupoid into a poe groupoid in terms of fuzzy sets inform sci 152 2003 231 236 n kehayopulu m tsingelis fuzzy bi ideals in ordered semigroups inform sci 171 2004 13 28 where s has been endowed with the structure of an ordered semigroup and defined fuzzy analogous for several notions that have been proved to be useful in the theory of ordered semigroups the characterization of regular rings in terms of right and left ideals is well known the characterization of regular semigroups and regular ordered semigroups in terms of left and right ideals or in terms of left right ideals and quasi ideals is well known as well the characterization of regular le semigroups that is lattice ordered semigroups having a greatest element in terms of right ideal elements and left ideal elements or right left and quasi ideal elements is also known in the present paper we first give the main theorem which characterizes the regular ordered semigroups by means of fuzzy right and fuzzy left ideals then we characterize the regular ordered semigroups in terms of fuzzy right fuzzy left ideals and fuzzy quasi ideals the paper serves as an example to show that one can pass from the theory of ordered semigroups to the theory of fuzzy ordered semigroups some of our results are true for ordered groupoids in general

poisson structure of dynamical systems with three degrees of freedom it is shown that the poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one form in three dimensions advantage is taken of this fact and the theory of foliations is used in discussing the geometrical structure underlying complete and partial integrability techniques for finding poisson structures are presented and applied to various examples such as the halphen system which has been studied as the two monopole problem by atiyah and hitchin it is shown that the halphen system can be formulated in terms of a flat sl 2 r valued connection and belongs to a nontrivial godbillon vey class on the other hand for the euler top and a special case of three species lotka volterra equations which are contained in the halphen system as limiting cases this structure degenerates into the form of globally integrable bi hamiltonian structures the globally integrable bi hamiltonian case is a linear and the sl 2 r structure is a quadratic unfolding of an integrable one form in 3 1 dimensions it is shown that the existence of a vector field compatible with the flow is a powerful tool in the investigation of poisson structure and some new techniques for incorporating arbitrary constants into the poisson one form are presented herein this leads to some extensions analogous to q extensions of poisson structure the kermack mckendrick model and some of its generalizations describing the spread of epidemics as well as the integrable cases of the lorenz lotka volterra may leonard and maxwell bloch systems admit globally integrable bi hamiltonian structure

ranking function based solutions of fully fuzzified minimal cost flow problem the aim of minimal cost flow problem mcfp is to find the least transportation cost of a single commodity through a capacitated network this paper presents a model to deal with one particular group of such problems in which the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers for easier reference hereafter we refer to this group of problems as fully fuzzified mcfp to represent our model hukuhara s difference and approximated multiplication are used thereafter we sort fuzzy numbers by an order using a ranking function and show that it is a total order i e a reflexive anti symmetric transitive and complete binary relation utilizing the proposed ranking function we transform the fully fuzzified mcfp into three crisp problems solvable in polynomial time from this standpoint combinatorial algorithms are provided to solve the above mentioned problem and find the fuzzy optimal flow furthermore the proposed order is related to the importance weights of the center the left spread and the right spread of each fuzzy number thus this method is capable of handling the decision maker s risk taking by comparing some previous ranking function based works with our method the efficiency of the latter is revealed finally an application of our proposed method to petroleum industry is presented

comments on global dynamics of the generalized lorenz systems having invariant algebraic surfaces abstract in the recent paper global dynamics of the generalized lorenz systems having invariant algebraic surfaces published in physica d the authors study the generalized lorenz system x a y x y b x c y x z z d z x y and consider the subclass of these systems which have an invariant algebraic surface within this subclass they present their global dynamics via the blow up and poincare compactification in this comment we argue that the results presented in the commented paper can be directly obtained from the well known results on global dynamics of the lorenz system having invariant algebraic surfaces to achieve it we use the equivalence existing under generic conditions c 0 between the lorenz system and the generalized lorenz system by means of a linear scaling in time and coordinates on the other hand their study is not complete because a case is missed in the list of six invariant algebraic surfaces in the generalized lorenz system considered by the authors we also analyze here the global dynamics in this seventh situation

necessary and sufficient conditions for finite time singularities in ordinary differential equations abstract this paper gives a theorem which provides necessary and sufficient conditions for the existence of a real finite value of the independent variable at which the general solution of a certain class of ordinary differential equations diverges to infinity this class is a large subset of the set of all autonomous non linear polynomial ordinary differential equation these conditions involve the asymptotic form of the local series representation for the general solutions around the singularities and can be checked algorithmically

invariant algebraic surfaces of the lorenz system in this paper we provide a complete classification of the darboux invariants of the irreducible darboux polynomials of the rational first integrals and of the algebraic integrability for the classical lorenz system s y x rx y xz z bz xy in the proofs we use the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations

dynamics of the lorenz system having an invariant algebraic surface in this paper we characterize all dynamics of the lorenz system x s y x y rx xz y z xy bz having an invariant algebraic surface

coarsening at random in general sample spaces and random censoring in continuous time heitjan and rubin proposed a concept coarsening at random generalizing rubin s theory of missing at random their analysis was done in discrete sample spaces we propose a generalization to general sample spaces among heitjan and rubin s applications was right censoring in survival analysis we discuss the application of the generalized theory to various censoring patterns in continuous time and connect to the modern theory of random censoring

nonlinear dynamical systems and classical orthogonal polynomials it is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract schrodinger equation in hilbert space with boson hamiltonian the fourier coefficients of the expansion of solutions to the schrodinger equation in the particular occupation number representation are expressed by means of the classical orthogonal polynomials the introduced formalism amounts to a generalization of the classical methods for linearization of nonlinear differential equations such as the carleman embedding technique and koopman approach

oscillation theorems for elliptic equations with damping the second order elliptic equation with damping i j 1 dd i a i j x d jy i 1 db i x d iy p x f y 0is considered in an exterior domain w r d where the coefficients b i x i 1 d and p x are not be nonnegative in w by the generalized partial riccati transformation and the integral averaging technique some new oscillation theorems are established

fuzzy and random sets the two distinct concepts of fuzzy and random sets coexist to form the basics for modeling perception based information gathering processes in artificial intelligence these processes viewed as coarsening schemes provide also justifications for various types of uncertainty measures such as belief functions and possibility measures

formal and analytic integrability of the lorenz system the well known lorenz system can be written as and here we study the first integrals of the lorenz system that can be described by formal power series in particular if s 0 and either b is not a negative rational number or b is a negative rational number and k1b k2 1 s 0 for all k1 and k2 non negative integers with k1 k2 0 then the lorenz system has no analytic first integrals in a neighbourhood of the origin

lorenz integrable system moves a la poinsot a transformation is derived which takes the lorenz integrable system into the well known euler equations of a torque free rigid body about a fixed point i e the famous motion a la poinsot the proof is based on lie group analysis applied to two third order ordinary differential equations admitting the same two dimensional lie symmetry algebra lie s classification of two dimensional symmetry algebras in the plane is used if the same transformation is applied to the lorenz system with any values of the parameters then one obtains euler equations of a rigid body about a fixed point subjected to a torsion depending on time and angular velocity the numerical solution of this system yields a three dimensional picture which looks like a tornado the cross section of which has a butterfly shape thus lorenz s butterfly has been transformed into a tornado

some new oscillation theorems for second order nonlinear elliptic equations with damping abstract in this paper some new oscillation criteria are obtained for second order elliptic differential equations with damping of the form a x y b t x y q x f y 0 x where is an exterior domain in r n these criteria are different from most known ones in the sense that they are based on a class of new functions of the form r s l defined in the sequel

a hopfield neural network applied to the fuzzy maximum cut problem under credibility measure this paper deals with maximum cut problem on a graph with fuzzy edges this problem is studied to cluster data under imprecise dependency applying the credibility measure this fuzzy problem is transformed into a nonlinear mixed integer programming problem to solve the problem an adaptive hopfield neural network is proposed with modern simulated annealing cooling schedule which converges into an equilibrium status within few iterations to illustrate the efficiency of this network it is simulated on some benchmark examples also webpage clustering problem is solved to illustrate the application of the studied fuzzy problem and neural network solutions

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

fuzzy preference relations in models of decision making abstract analysis of x r models is considered as part of a general approach to solving optimization problems with fuzzy coefficients this approach involves a modification of traditional optimization methods and is associated with formulating and solving one and the same problem within the framework of mutually interrelated models by constructing equivalent analogs with fuzzy coefficients in objective functions alone the use of the approach allows one to maximally cut off dominated alternatives the subsequent contraction of the decision uncertainty region is based on reducing the problem to multiobjective choice of alternatives in a fuzzy environment three techniques for processing of fuzzy preference relations reflecting criteria of quantitative as well as qualitative character are discussed the results of the paper are universally applicable and are already being used to solve power engineering problems

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

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

integrating the nonintegrable analytic structure of the lorenz system revisited abstract a study of the complex time analytic structure of the lorenz system in nonintegrable parameter regimes reveals the special sets of parameter values for which one time dependent integral of motion exists furthermore the analysis yields the exact form of the part of the integral with the highest homogeneous weight and a method to construct the rest of the integral recursive clustering of singularities in the chaotic regimes of the system is observed in computer studies and explained by a simple analytic argument the analytic techniques used in these studies a systematic resummation of a logarithmic psi series appears to be quite general and can provide explicit representations of a solution even in the chaotic regimes in the neighborhood of a given movable singularity furthermore we suggest that this technique provides a type of renormalization program to study a wide class of nonintegrable systems

exponential factors and darbouxian first integrals of the lorenz system in this article we characterize all the exponential factors and the darbouxian first integrals for the lorenz system s y x rx y xz z bz xy in the proofs we use the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations

connection between the existence of first integrals and the painleve property in two dimensional lotka volterra and quadratic systems taking advantage of the considerable amount of work done in the search for first integrals invariants for the two dimensional lotka volterra system and the quadratic system lvs and qs we compare the relations needed to exhibit invariants one for the lvs at least three for the qs to the two conditions of the painleve test index and compatibility we find that eventually restricting the invariants to those which are analytic all exponents integers and thereby adding new constraints these constraints always coalesce with the two painleve conditions we conclude that straightforward application of the painleve test picks up only these simple analytic invariants and that possession of the painleve property is too strong a condition for the existence of the invariants

a dynamic consensus scheme based on a nonreciprocal fuzzy preference relation modeling in this paper we propose a dynamical consensus scheme which makes use of an index of comparability and of an index of concordance to regulate the information flow in the discussion among the experts in addition to the traditional use of a concordance index to identify the discordant expert who can be invited to review his opinion or to explain his judgment to the other experts here an index of comparability is utilized to identify the experts that have faced difficulties in expressing their preferences with this information at hand a moderator can invite the experts that are confident on their opinions to support the experts that are hesitating in the construction of the fuzzy preference relations

complex singularities and the lorenz attractor the lorenz attractor is one of the best known examples of applied mathematics however much of what is known about it is a result of numerical calculations and not of mathemat ical analysis as a step toward mathematical analysis we allow the time variable in the three dimensional lorenz system to be complex hoping that solutions that have resisted analysis on the real line will give up their secrets in the complex plane knowledge of singularities being fundamental to any investigation in the complex plane we build upon earlier work and give a complete and consistent formal development of complex singular ities of the lorenz system using the psi series the psi series contain two undetermined constants in addition the location of the singularity is undetermined as a consequence of the autonomous nature of the lorenz system we prove that the psi series converge using a technique that is simpler and more powerful than that of hille thus implying a two parameter family of singular solutions of the lorenz system we pose three ques tions answers to which may bring us closer to understanding the connection of complex singularities to lorenz dynamics

integrals of motion for the lorenz system a direct method is proposed for determining the conditions under which the lorenz system is integrable this method uses only leading singular behavior to recover all known integrals of motion together with a few new ones

oscillation criteria for second order linear differential equations abstract some oscillation criteria are given for the second order linear differential equation r t u t c t u t 0 where r t c 1 t 0 0 and c t c t 0 r these results improve oscillation criteria of wintner hartman kamenev yan and philos by using a generalized riccati transformation t a t r t u t u t f t where f c 1 is a given function on t 0 and a t exp 2 t f s ds

integrability partial integrability and nonintegrability for systems of ordinary differential equations the integrability of systems of ordinary differential equations with polynomial vector fields is investigated by using the singularity analysis methods three types of results are obtained first a general relationship between the degrees of first integrals and the so called kowalevskaya exponents is derived second it is shown that all solutions of algebraically integrable systems can be expanded in puiseux series third a new method to study partially integrable systems is studied these different aspects allow us to study algorithmically the integrability partial integrability and nonintegrability of differential systems

lie symmetries of the lorenz model abstract we study the generalized symmetries of the lorenz model to find the parameter values at which one or more time dependent integrals of motion exist in these cases the integrals are found trivially from the symmetries themselves a complete study of the one completely algebraically integrable case shows a the dynamics can be integrated exactly by reducing it first to a lower dimensional system b the symmetry vector field is hamiltonian these facts hold for other dissipative completely integrable dynamical systems as well the analytic study of a natural two form reveals that it is an entire function of time the foliation of phase space induced by the two form for the partially integrable cases has a simple description in terms of the coefficients occurring in the laurent series expansions of the dependent variables

oscillation criteria for second order forced elliptic differential equations with mixed nonlinearities in the case of oscillatory potentials we establish some oscillation criteria for the second order forced elliptic differential equation with mixed nonlinearities div a x y c x y e x when n 1 our results extend those of kong q kong interval criteria for oscillation of second order linear ordinary differential equations j math anal appl 229 1999 258 270 for certain second order linear ordinary differential equations sun and meng y g sun f w meng interval criteria for oscillation of second order differential equations with mixed nonlinearities appl math comput 2007 doi 10 10 1016 j amc 2007 08 042 for certain second order differential equations with mixed nonlinearities yang q yang interval oscillation criteria for a second order nonlinear ordinary differential equations with oscillatory potential appl math comput 135 2003 49 64 for a forced second order superlinear ordinary differential equation when n 2 our theorems are more general and improve the oscillation criteria of zhuang r k zhuang annual oscillation criteria for second order nonlinear elliptic differential equations j comput anal math 2007 doi 10 1016 j cam 2007 06 031 for a forced second order undamped elliptic differential equation

possibility theory is not fully compositional a comment on a short note by h j greenberg abstract a recent short note h j greenberg fuzzy sets and systems 86 1997 249 250 has assumed that a possibility measure is fully compositional with respect to negation conjunction and disjunction up to a trivial exception such a possibility measure does not exist this short note recalls that the calculus of possibility measures on boolean propositions is not compositional except for the disjunction and has little to do with the fully compositional max min calculus of degrees of truth for fuzzy propositions

multiobjective and multiattribute decision making in a fuzzy environment and their power engineering applications two classes of problems requiring the use of a multicriteria approach are defined fuzzy set theory serves for aggregating information arriving from diverse sources combined branches of mathematics of uncertainty serve as a new decision making tool the use of fuzzy set based decision making in power system problems is described benefits of applying fuzzy set theory in problems of power engineering are shown this work presents and generalizes our experience in the use of fuzzy set theory including its combination with another branch of mathematics of uncertainty in developing general approaches and methods for optimization and decision making with considering the uncertainty and multicriteria factors in problems of the design planning operation and control of complex systems two major classes of situations that require the use of a multicriteria approach are identified in accordance with this two general classes of models related to multiobjective x f models and multiattribute x r models problems respectively are considered methods for their analysis based on the use of the bellman zadeh approach to decision making in a fuzzy environment and fuzzy preference modeling techniques respectively are considered although the use of x f and x r models is of an independent character they also serve as parts of a general scheme for multicriteria decision making under conditions of uncertainty this scheme is associated with the use of a generalization of the classic approach to considering the uncertainty of information to multicriteria problems based on analyzing special aggregations of payoff matrices the authors experience in the use of the results indicated above for solving diverse classes of power system planning and operation problems is described this experience convincingly demonstrates diverse advantages of applying fuzzy mathematics in optimization and decision making problems of power engineering

algorithms of discrete optimization and their application to problems with fuzzy coefficients an approach to solving optimization problems with fuzzy coefficients in objective functions and constraints is described it consists in formulating and solving one and the same problem within the framework of mutually related models with constructing equivalent analogs with fuzzy coefficients in objective functions alone it enables one to maximally cut off dominated alternatives from below as well as from above since the approach is applied within the context of fuzzy discrete optimization problems several modified algorithms of discrete optimization are discussed these algorithms are associated with the method of normalized functions are based on a combination of formal and heuristic procedures and allow one to obtain quasi optimal solutions after a small number of steps thus overcoming the computational complexity posed the np completeness of discrete optimization problems the subsequent contraction of the decision uncertainty regions is associated with reduction of the problem to multiobjective decision making in a fuzzy environment with using techniques based on fuzzy preference relations the techniques are also directly applicable to situations in which the decision maker is required to choose alternatives from a set of explicitly available alternatives the results of the paper are of a universal character and can be applied to the design and control of systems and processes of different purposes as well as the enhancement of corresponding cad cam systems and intelligent decision making systems the results of the paper are already being used to solve problems of power engineering

bi hamiltonian structure in frenet serret frame abstract we reduce the problem of constructing bi hamiltonian structure in three dimensions to the solutions of a riccati equation in moving coordinates of frenet serret frame all explicitly constructed examples in the literature are exhausted by constant solutions we conclude that in three dimensions vector fields which are not eigenvectors of the curl operator are locally bi hamiltonian

multicriteria analysis in decision making under information uncertainty abstract this paper presents results of research related to multicriteria decision making under information uncertainty the bellman zadeh approach to decision making in a fuzzy environment is utilized for analyzing multicriteria optimization models x m models under deterministic information its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems this circumstance permits one to generalize the classic approach to considering the uncertainty of quantitative information based on constructing and analyzing payoff matrices reflecting effects which can be obtained for different combinations of solution alternatives and the so called states of nature in monocriteria decision making to multicriteria problems considering that the uncertainty of information can produce considerable decision uncertainty regions the resolving capacity of this generalization does not always permit one to obtain unique solutions taking this into account a proposed general scheme of multicriteria decision making under information uncertainty also includes the construction and analysis of the so called x r models which contain fuzzy preference relations as criteria of optimality as a means for the subsequent contraction of the decision uncertainty regions the paper results are of a universal character and are illustrated by a simple example

invariant hyperplanes and darboux integrability of polynomial vector fields this paper is composed of two parts in the first part we provide an upper bound for the number of invariant hyperplanes of the polynomial vector fields in n variables this result generalizes those given in artes et al 1998 pac j math 184 207 30 and llibre and rodriguez 2000 bull sci math 124 599 619 the second part gives an extension of the darboux theory of integrability to polynomial vector fields on algebraic varieties

fuzzy sets and models of decision making abstract results of research into the use of fuzzy sets for handling various forms of uncertainty in optimization problems related to the design and control of complex systems are presented much attention is given to considering the uncertainty of goals that is associated with a multicriteria character of many optimization problems the application of a multicriteria approach is needed to solve 1 1 problems in which solution consequences cannot be estimated on the basis of a single criterion that involves the necessity of analyzing a vector of criteria and 2 2 problems that may be considered on the basis of a single criterion but their unique solutions are not achieved because the uncertainty of information produces so called decision uncertainty regions and the application of additional criteria can serve as a convincing means to contract these regions according to this two classes of models x m and x r models are considered with applying the bellman zadeh approach and techniques of fuzzy preference relations to their analysis the consideration of x r models is associated with a general approach to solving a wide class of optimization problems with fuzzy coefficients this approach consists in formulating and analyzing one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective functions alone it allows one to maximally cut off dominated alternatives the subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment with its analysis applying one of two techniques based on fuzzy preference relations the results of the paper are of a universal character and are already being used to solve problems of power engineering

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

on multicriteria decision making under conditions of uncertainty this paper deals with multicriteria decision making problems under conditions of uncertainty the main its contribution is the consideration of choice criteria of the classic approach to handle information uncertainty in monocriteria decision making as objective functions within the framework of multiobjective models whose analysis generates harmonious solutions such consideration of choice criteria is of a fundamental character and allows one to modify the generalization originally proposed by ekel martini and palhares 2008 of the classic approach to handle information uncertainty for solving multicriteria problems the modification permits one to overcome limitations of the indicated generalization which can lead to contradictory decisions details of using the modification in a general scheme of multicriteria decision making under uncertainty are presented the general scheme is focused on the use of available quantitative information to the highest degree to reduce decision uncertainty regions however if the problem solving capacity concerning quantitative information processing does not allow one to obtain unique solutions the general scheme assumes the use of qualitative information based on knowledge experience and intuition of experts involved in the decision making process examples are presented to illustrate the modification of generalizing the classic approach as well as the general scheme of multicriteria decision making under information uncertainty

averaging technique and nonlinear second order elliptic oscillation abstract by using the refinement of the standard integral averaging technique we obtain new oscillation criteria for certain nonlinear second order damped elliptic differential equations we do not impose any additional conditions on the damping terms except for the continuity in particular when n 1 our results extend those of rogovchenko and tuncay yu v rogovchenko f tuncay oscillation criteria for second order nonlinear differential equations with damping nonlinear analysis 69 2008 208 221 for second order nonlinear differential equations with damping to damped elliptic differential equations when n 2 our results improve the oscillation criteria of xu jia ma z xu b jia d ma oscillation theorems for elliptic equations with damping appl math comput 156 2004 93 106 for second order elliptic equations with damping four examples are provided to illustrate the relevance of the main results

a general approach to solving a wide class of fuzzy optimization problems results of research into the use of fuzzy sets for handling various forms of uncertainty in the optimal design and control of complex systems are presented a general approach to solving a wide class of optimization problems containing fuzzy coefficients in objective functions and constraints is described it involves a modification of traditional mathematical programming methods and is associated with formulating and solving one and the same problem within the framework of mutually conjugated models this approach allows one to maximally cut off dominated alternatives from below as well as from above the subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment the general approach is applied within the context of a fuzzy discrete optimization model that is based on a modification of discrete optimization algorithms prior to application of these algorithms there is a transition from a model with fuzzy coefficients in objective functions and constraints to an equivalent analog with fuzzy coefficients in objective functions alone the results of the paper are of a universal character and are already being used to solve problems of power engineering

symmetries and first integrals for dissipative systems the connection between symmetries time independent and time dependent first integrals for autonomous systems of first order ordinary differential equations is discussed several new results which have been obtained by applying a reduce package are reported

fuzzy preference modeling and its application to multiobjective decision making this paper reflects results of research into the construction and analysis of models within the framework of a general approach to solving optimization problems with fuzzy coefficients this approach involves a modification of traditional mathematical programming methods and is associated with formulating and solving one and the same problem within the framework of mutually interrelated models the use of the approach allows one to maximally cut off dominated alternatives the subsequent contraction of the decision uncertainty region is based on reducing the problem to models of multiobjective choosing alternatives in a fuzzy environment with the use of fuzzy preference relation techniques for analyzing these models three techniques for fuzzy preference modeling are discussed in the paper the first technique is based on the construction of membership functions of subsets of nondominated alternatives with simultaneous considering of all criteria fuzzy preference relations the second technique is of a lexicographic character and consists of step by step introducing of fuzzy preference relations the third technique is based on aggregating membership functions of subsets of nondominated alternatives corresponding to each preference relation these techniques have served for developing a corresponding system for multiobjective decision making mdms c windows of the mdms are presented for input output and some intermediate procedures the results of the paper are of a universal character and are already being used to solve power engineering naval engineering and management problems

on the scoring approach to admissibility of uncertainty measures in expert systems abstract this paper arose from our need to rigorize clarify and address fully the results of lindley s paper scoring rules and the inevitability of probability internat statist rev 50 1982 1 26 herein we develop a calculus of admissibility in a game theoretic setting in the case of an additive aggregation function it is shown that decomposable measures such as those used in fuzzy logics are admissible also the problem of the admissibility of the dempster shafer belief functions is investigated via the concept of random sets it is shown that the class of admissible measures in a scoring framework depends on the assumptions concerning the aggregation function in use in particular for nonadditive aggregation functions an admissible measure may not be transformable to a finitely additive probability measure

fuzzy set based multiobjective allocation of resources solution algorithms and applications abstract this paper presents results of research in the use of the bellman zadeh approach to decision making in a fuzzy environment for solving multiobjective optimization problems its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems the application of the approach permits one to realize an effective from the computational standpoint as well as rigorous in view of obtaining solutions from the pareto set method of analyzing multiobjective models the use of the bellman zadeh approach has served as a basis for solving problems of multiobjective allocation of resources or their shortages and developing a corresponding adaptive interactive decision making system aidms its calculating kernel permits one to solve maxmin problems using an algorithm based on a non local search modification of gelfand s and tsetlin s long valley method as well as a genetic algorithm the comparison of their computational performance is given on the basis of solving problems of multiobjective power shortage allocation in power systems