electrical circuits on mesoscopic sierpinski gaskets a deterministic network of impedances on the sierpinski gasket fractal is considered with particular regard to low generation or mesoscopic systems we study the fractal set of the resonances of the circuit and present calculations on frequency dependent systems the condition of an intermediate size can lead to an oscillatory scaling of the total impedance that disappears in the asymptotic limit several examples are given

nontrivial solutions of kirchhoff type problems via the yang index abstract we obtain nontrivial solutions of a class of nonlocal quasilinear elliptic boundary value problems using the yang index and critical groups

positive solutions of logistic equations with dependence on gradient and nonhomogeneous kirchhoff term abstract consider the equation m x u p u f x u u g x u u in u 0 on the main aim of this paper is to prove existence results for both non degenerate and degenerate cases of the function m our approach relies on the fixed point index and the cone theoretic argument

on the existence of solutions for a class of fourth order differential equations abstract we study the existence of the homoclinic solution of a class of nonlinear fourth order ordinary differential equations which involve particular cases of the extended fisher kolmogorov and swift hohenberg equations we address the case when the source term possesses a nonlinear dependence on the first order derivative of the solution the main result follows from an iterative method using the sequence of solutions obtained through the mountain pass technique in order to illustrate this method some numerical examples are shown

existence of solution for a class of nonvariational kirchhoff type problem via dynamical methods abstract in this paper we use dynamical methods to establish the existence of nontrivial solution for the following class of kirchhoff type problem p 1 b u 2 d x u f u h u u x u 0 x where r n n 2 3 is a smooth bounded domain b 0 f r r and h r r n 0 are c 1 functions that satisfy some technical conditions

modified fgp approach for multi level multi objective linear fractional programming problems in this paper we present a new modified method for solving multi level multi objective linear fractional programming problems ml molfpps based on fuzzy goal programming fgp approach with some modifications in the algorithm suggested by baky 2010 18 which dealt with multi level multi objective linear programming problem ml molpp in proposed modified approach numerator and denominator function of each objective at each level are individually transformed into fuzzy goals and their aspiration levels are determined using individual best solutions different linear membership functions are defined for numerator and denominator function of each objective function then highest degree of each of these membership goals is achieved by minimising the sum of negative deviational variables the proposed algorithm simplifies the ml molfpp by eliminating solution preferences by the decision makers at each level thereby avoiding difficulties associate with multi level programming problems and decision deadlock situations the aim of this paper is to present simple and efficient technique to obtain compromise optimal solution of ml molfp problems numerical examples are illustrated in order to support the proposed modified fgp technique

oscillatory critical amplitudes in hierarchical models we study the oscillatory critical amplitudes of theq states potts model on a diamond hierarchical lattice we consider an example of the generic case finite critical index as well as the degenerate case essential singularity in both cases we compare the magnitude of the oscillations with geometrical characteristics of the julia set of zeroes of the partition function

semilinear elliptic variational inequalities with dependence on the gradient via mountain pass techniques abstract in this paper we consider a semilinear variational inequality with a gradient dependent nonlinear term obviously the nature of this problem is non variational nevertheless we study that problem associating a suitable semilinear variational inequality variational in nature with it and performing an iterative technique used in de figueiredo et al 2004 6 in order to treat semilinear elliptic equations when there is a gradient dependence on the nonlinearity we prove the existence of a non trivial non negative weak solution u for our problem using essentially variational methods a penalization technique and an iterative scheme via lewy stampacchia s estimates and regularity theory for elliptic equation we also show that u is differentiable and its gradient is h lder continuous on for any 0 1

a chance constrained fuzzy goal program abstract a chance constrained goal program in the case of having uncertain aspiration levels is considered however these aspiration levels are random variables with known probability distribution functions the goal constraints considered are probabilistic and fuzzy constraints the equivalent deterministic goal program is developed and an illustrative example is given

fuzzy goal programming approach to multilevel programming problems the purpose of this paper is to propose a procedure for solving multilevel programming problems in a large hierarchical decentralized organization through linear fuzzy goal programming approach here the tolerance membership functions for the fuzzily described objectives of all levels as well as the control vectors of the higher level decision makers are defined by determining individual optimal solution of each of the level decision makers since the objectives are potentially conflicting in nature a possible relaxation of the higher level decision is considered for avoiding decision deadlock then fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables sensitivity analysis with variation of tolerance values on decision vectors is performed to present how the solution is sensitive to the change of tolerance values the efficiency of our concept is ascertained by comparing results with other fuzzy programming approaches

a fuzzy goal programming method with imprecise goal hierarchy two most widely used approaches to treating goals of different importance in goal programming gp are 1 weighted gp where importance of goals is modelled using weights and 2 preemptive priority gp where a goal hierarchy is specified implying infinite trade offs among goals placed in different levels of importance these approaches may be too restrictive in modelling of real life decision making problems in this paper a novel fuzzy goal programming method is proposed where the hierarchical levels of the goals are imprecisely defined the imprecise importance relations among the goals are modelled using fuzzy relations an additive achievement function is defined which takes into consideration both achievement degrees of the goals and degrees of satisfaction of the fuzzy importance relations examples are given to illustrate the proposed method

ac properties of 3d sierpinski gaskets rigorous results the problem of the decimation of a network of impedances on the three dimensional sierpinski gasket is solved the exact map is given and its asymptotic behaviours are studied the most significant invariant subspaces of and the associated submaps are considered this also allows us to address the problem of small size phenomena such as oscillating asymptotic behaviour on this kind of fractal the set of the resonances of the system and the frequency dependence of the total impedance are studied both in the thermodynamic limit and in mesoscopic systems

high energy solutions of systems of kirchhoff type equations in rn in the present paper five new critical point theorems on the product spaces are given and three existence theorems for the sequence of high energy solutions for the systems of kirchhoff type equations are studied

the relationship between goal programming and fuzzy programming abstract goal programming gp and fuzzy programming fp are two approaches for solving the vector optimization problem by reducing it to a single or sequential objective one these two approaches have some similarities and both of them have more than one form to handle the multiobjective problem this paper highlights the similarities between gp and fp and answers the question how each one can lead to the other however we will consider in this paper the min operator to transform the linear fp to a crisp program since this approach is more popular and applied than the others in addition some new forms of fuzzy programs are presented in this paper these new forms use the concept of deviational variables of gp and not the min operator to transform the fp to a crisp one finally a numerical example to illustrate the relationship between the two approaches is given

binary fuzzy goal programming goal programming is an important technique for solving many decision management problems fuzzy goal programming involves applying the fuzzy set theory to goal programming thus allowing the model to take into account the vague aspirations of a decision maker using preference based membership functions we can define the fuzzy problem through natural language terms or vague phenomena in fact decision making involves the achievement of fuzzy goals some of them are met and some not because these goals are subject to the function of environment resource constraints thus binary fuzzy goal programming is employed where the problem cannot be solved by conventional goal programming approaches this paper proposes a new idea of how to program the binary fuzzy goal programming model the binary fuzzy goal programming model can then be solved using the integer programming method finally an illustrative example is included to demonstrate the correctness and usefulness of the proposed model

positive solutions for a quasilinear elliptic equation of kirchhoff type this paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the type m w u 2dx du f x u email protected u 0 email protected email protected where w is a smooth bounded domain of n m is a positive function and f has subcritical growth

renormalisation groups with periodic and aperiodic orbits motivated by recent results for some frustrated hierarchical models the authors analyse the consequences of renormalisation group transformations with periodic and aperiodic orbits they find that the free energy has in general an infinite number of singularities this occurs already when the transformation has a stable periodic orbit they present an idealised example and a new class of hierarchical potts models to which the theory applies

infinitely many radial solutions for kirchhoff type problems in rn abstract in this paper we concern with a class of kirchhoff type problems in r n by using the fountain theorem we obtain three existence results of infinitely many radial solutions for the problem

fuzzy goal programming a parametric approach narasimhan incorporated fuzzy set theory within goal formulation in 1980 since then much research has been performed in this field and various models for solving fuzzy goal programming have been proposed one of the well known models was proposed by tiwari et al in 1987 19 where an additive model was proposed this paper is an extension to the tiwari et al model that deals with the sum of weighted negative deviations between the desirable achievement degree and the common target here properties of the model are proposed a numerical example is also given to illustrate the approach

infinitely many positive solutions for kirchhoff type problems abstract this paper is concerned with the existence of infinitely many positive solutions to a class of kirchhoff type problem a b u 2 d x u f x u in and u 0 on where is a smooth bounded domain of r n a b 0 0 and f r r is a caratheodory function satisfying some further conditions we obtain a sequence of a e positive weak solutions to the above problem tending to zero in l with f being more general than that of k perera z zhang nontrivial solutions of kirchhoff type problems via the yang index j differential equations 221 2006 246 255 z zhang k perera sign changing solutions of kirchhoff type problems via invariant sets of descent flow j math anal appl 317 2006 456 463

study of a nonlinear kirchhoff equation with non homogeneous material abstract in this paper we study a non homogeneous elliptic kirchhoff equation with nonlinear reaction term we analyze the existence and uniqueness of positive solution the main novelty is the inclusion of non homogeneous term making the problem without a variational structure we use mainly bifurcation arguments to get the results

remarks on an elliptic equation of kirchhoff type abstract we present a short survey on the nonlocal elliptic boundary value problem m u 2 d x u f x u in u 0 on where is a smooth bounded domain of r n m is a positive function and f has subcritical growth

fractal structure of zeros in hierarchical models we consider an ising and aq state potts model on a diamond hierarchical lattice we give pictures of the distribution of zeros of the partition function in the complex plane of temperatures for several choices ofq these zeros are just the julia set corresponding to the renormalization group transformation

a fuzzy goal programming approach to multi objective optimization problem with priorities abstract in goal programming problem the general equilibrium and optimization are often two conflicting factors this paper proposes a generalized varying domain optimization method for fuzzy goal programming fgp incorporating multiple priorities according to the three possible styles of the objective function the varying domain optimization method and its generalization are proposed this method can generate the results consistent with the decision maker dm s expectation that the goal with higher priority may have higher level of satisfaction using this new method it is a simple process to balance between the equilibrium and optimization and the result is the consequence of a synthetic decision between them in contrast to the previous method the proposed method can make that the higher priority achieving the higher satisfactory degree to get the global solution of the nonlinear nonconvex programming problem resulting from the original problem and the varying domain optimization method the co evolutionary genetic algorithms gas called genocopiii is used instead of the sqp method in this way the dm can get the optimum of the optimization problem we demonstrate the power of this proposed method by illustrative examples

a goal programming procedure for fuzzy multiobjective linear fractional programming problem abstract this paper presents a goal programming gp procedure for fuzzy multiobjective linear fractional programming fmolfp problems in the proposed approach which is motivated by mohamed fuzzy sets and systems 89 1997 215 gp model for achievement of the highest membership value of each of fuzzy goals defined for the fractional objectives is formulated in the solution process the method of variable change on the under and over deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming lgp methodology the approach is illustrated by two numerical examples

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

existence of multi bump solutions for a class of kirchhoff type problems in r3 using variational methods we establish existence of multi bump solutions for a class of kirchhoff type problems a b r3 u 2dx u v x u f u where f is a continuous function with subcritical growth v x is a critical frequency in the sense that infx r3v x 0 we show that if the zero set of v x has several isolated connected components 1 k such that the interior of i is not empty and i is smooth then for 0 large there exists for any non empty subset j 1 k a bump solution is trapped in a neighborhood of j j j

interactive fuzzy goal programming approach for bilevel programming problem abstract this paper presents an interactive fuzzy goal programming fgp approach for bilevel programming problems with the characteristics of dynamic programming dp in the proposed approach the tolerance membership functions in fuzzy sets for measuring the degree of satisfactions of the objectives of both the decision makers and degree of achievement of the decision vector controlled by the leader is defined first then the dynamic fuzzy goal programming model for achievement of highest degree unity to the extent possible to each of the defined membership functions for the fuzzy goal is developed to solve the decisions of the interrelated stages a satisfactory solution is derived efficiently by updating the satisfactory degrees of the decision makers with the consideration of overall satisfactory balance between both the levels illustrative numerical examples are provided to demonstrate the feasibility of the proposed method

a note on taylor series approach to fuzzy multiple objective linear fractional programming abstract toksari in his paper taylor series approach to fuzzy multiobjective linear fractional programming published in information sciences 178 2008 proposed a new method to solve multiple objective linear fractional programming problems and declared that it is more effective when compare to previous methods he constructed fuzzy goals and then used first order taylor polynomials to approximate the corresponding linear fractional membership functions by linear functions aggregating the linear functions toksari obtained a crisp linear programming problem and claimed that it is equal to the fuzzy fractional one in this paper we indicate the fallacy that arises by using taylor approximation and propose an improved method that guarantees the efficiency of the solution it provides both practical applications from toksari s paper are recalled to show that the improvements we suggest are effective

a note on a nonlinear elliptic problem with a nonlocal coefficient abstract in this paper we investigate a nonlocal and nonlinear elliptic problem p a u 2 d x u u u p in u 0 on where n 3 r n is a bounded domain with smooth boundary a is a nondegenerate continuous function p 1 and r we show several effects of the nonlocal coefficient a on the structure of the solution set of p we first introduce a scaling observation and describe the solution set by using that of an associated semilinear problem this allows us to get unbounded continua of solutions u of p a rich variety of new bifurcation and multiplicity results are observed we also prove that the nonlocal coefficient can induce up to uncountably many solutions in a convenient way lastly we give some remarks from the variational point of view

a sub supersolution approach for a quasilinear kirchhoff equation in this paper we establish an existence result for a quasilinear kirchhoff equation via a sub and supersolution approach by using the minty browder s theorem for pseudomonotone operators theory

positive and negative solutions of a quasi linear elliptic equation by a mountain pass method and truncature techniques abstract the existence of a positive and a negative solution of a problem of the type u f x u u 0 in u 0 on is proved when f has a growth at infinity depending both on u and on u the techniques are based on an iterative scheme of mountain pass approximated solutions and the use of a suitable truncature method

a goal programming procedure for solving problems with multiple fuzzy goals using dynamic programming abstract this paper describes how the preemptive priority based goal programming gp can be used to solve a class of fuzzy programming fp problems with the characteristics of dynamic programming dp in the proposed approach the membership functions of the objective goals of a problem with fuzzy aspiration levels are defined first then under the framework of preemptive priority based gp a multi stage dp model of the problem for achievement of the highest degree unity of each of the membership functions is developed in the decision process the goal satisficing philosophy of gp is used recursively to arrive at the most satisfactory solution two numerical examples are provided to illustrate the approach

on necessary conditions for the comparison principle and the sub and supersolution method for the stationary kirchhoff equation in this paper we propose a counterexample to the validity of the comparison principle and of the sub and supersolution method for nonlocal problems like the stationary kirchhoff equation this counterexample shows that in general smooth bounded domains in any dimension these properties cannot hold true if the nonlinear nonlocal term m u2 is somewhere increasing with respect to the h01 norm of the solution comparing with the existing results this fills a gap between known conditions on m that guarantee or prevent these properties and leads to a condition that is necessary and sufficient for the validity of the comparison principle it is worth noting that equations similar to the one considered here have gained interest recently for appearing in models of thermo convective flows of non newtonian fluids or of electrorheological fluids among others

restoration of macroscopic isotropy on d 1 simplex fractal conductor networks abstract restoration of macroscopic isotropy has been investigated in d 1 simplex fractal conductor networks via exact real space renormalization group transformations using some theorems of fixed point theory it has been shown very rigoroursly that the macroscopic conductivity becomes isotropic for large scales and anisotropy vanishes with a scaling exponent which is computed exactly for arbitrary values of d and decimation numbers b 2 3 4 and 5

complex analytic dynamics on the riemann sphere dichotomie dynamique de fatou et julia points periodiques consequences du theoreme de montel l ensemble de julia est la fermeture de l ensemble des points periodiques repulseurs resultats classiques sur l ensemble de fatou classification de sullivan de l ensemble de fatou une condition pour le developpement sur l ensemble de julia la dynamique des polynomes l ensemble de mandelbrot et le travail de douady et hubbard le theoreme d application de riemann mesurable et la dynamique analytique

fuzzy goal programming algorithm for solving decentralized bi level multi objective programming problems this paper presents fuzzy goal programming fgp algorithm for solving decentralized bi level multi objective programming dbl mop problems with a single decision maker at the upper level and multiple decision makers at the lower level a fgp algorithm for dbl multi objective linear programming dbl molp problems is proposed this algorithm is extended to solve bi level multi objective linear fractional programming dbl molfp problems in the proposed algorithm the membership functions for the defined fuzzy goals of all objective functions at the two levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by uldm are developed in the model formulation of the problem then fgp approach is used to achieve highest degree of each of the membership goals by minimizing their deviational variables and thereby obtaining the most satisfactory solution for all decision makers illustrative numerical examples are given to demonstrate the proposed algorithm

on positive solutions of nonlocal and nonvariational elliptic problems abstract we will study the nonlocal and nonvariational elliptic problem a u q u h x f u in u 0 on by considering in two different results the cases n 1 and n 2 in both cases we will use fixed point theorems