single variable term semi latticized fuzzy relation geometric programming with max product operator considering the practical application background in peer to peer network system we investigate the single variable term semi latticized fuzzy relation geometric programming with max product operator in this paper based on the characteristics of the objective function and feasible domain we develop a matrix approach to deal with the proposed problem a step by step algorithm is proposed to find an optimal solution without solving all the minimal solutions of the constraint two examples are given to illustrate the feasibility and efficiency of the algorithm

a new algorithm for minimizing a linear objective function with fuzzy relation equation constraints in this paper we study the problem of minimizing a linear objective function subject to a fuzzy system constraint by utilizing the fuzzy system s compact system we define k form chained solutions and spaces of k form chained solutions then we prove that any minimal solution of the fuzzy system is a k form chained solution by using an operation method expressed in tables we sieve out basic solutions from the spaces of k form chained solutions finally we obtain optimal solutions of the studied problem from the obtained basic solutions examples are provided to show that our algorithm is simple and convenient

resolution of a system of fuzzy polynomial equations using the grobner basis the occurrence of imprecision in the real world is inevitable due to some unexpected situations the imprecision is often involved in any engineering design process the imprecision and uncertainty are often interpreted as fuzziness fuzzy systems have an essential role in the uncertainty modelling which can formulate the uncertainty in the actual environment in this paper a new approach is proposed to solve a system of fuzzy polynomial equations based on the grobner basis in this approach first the h cut of a system of fuzzy polynomial equations is computed and a parametric form for the fuzzy system with respect to the parameter of h is obtained then a grobner basis is computed for the ideal generated by the h cuts of the system with respect to the lexicographical order using faugere s algorithm i e f 4 algorithm the grobner basis of the system has an upper triangular structure therefore the system can be solved using the forward substitution hence all the solutions of the system of fuzzy polynomial equations can easily be obtained finally the proposed approach is compared with the current numerical methods some theorems together with some numerical examples and applications are presented to show the efficiency of our method with respect to the other methods

a matrix approach to latticized linear programming with fuzzy relation inequality constraints this paper investigates the latticized linear programming that is subject to the fuzzy relation inequality fri constraints with the max min composition by using the semi tensor product method and proposes a matrix approach to this problem first the resolution of the fri is studied and it is proved that all the minimal solutions and the unique maximum solution are within the finite parameter set solutions based on this and using the semi tensor product solving fris is converted to solving a set of algebraic inequalities and some new results on the resolution of fris are presented second the latticized linear programming that is subject to the fri constraints is solved by taking the following two key steps 1 the optimal value is obtained by calculating the minimum value of the objective function among all the minimal solutions to the fri constraints and 2 the optimal solution set is obtained by solving the fuzzy relation equation that is generated by letting the objective function equal to the optimal value the study of illustrative examples shows that the new results that are obtained in this paper are very effective in solving the latticized linear programming subject to the fri constraints

on the minimal solutions of max min fuzzy relational equations in this paper the minimal solutions of max min fuzzy relational equations are investigated a sufficient and necessary condition for discriminating whether a given solution is minimal or not is shown furthermore we propose a new algorithm for computing all minimal solutions less than or equal to a given one

linear objective function optimization with fuzzy relation equation constraints regarding max av composition in this paper an optimization model with a linear objective function subject to a system of the fuzzy relation equations with max av composition is presented the solution set of such a fuzzy relation equations is a non convex set in this paper firstly we discuss the feasible solution set with two schemes and secondly study relationship between maximum and minimum points and also the feasible points as well furthermore an algorithm and few concrete examples are presented in order to optimize linear objective function

fuzzy linear optimization in the presence of the fuzzy relation inequality constraints with max min composition in this paper we study the new linear objective function optimization with respect to the fuzzy relational inequalities defined by max min composition in which fuzzy inequality replaces ordinary inequality in the constraints fuzzy inequalities enable us to attain the optimal points that are better solutions than those resulting from the resolution of the similar problems with ordinary inequality constraints denoted by x o i in this paper we have presented an algorithm to generate such optimal solutions also two examples are given to illustrate the algorithm presented and some real application of this work

solutions of fuzzy relation equations based on continuous t norms this study is concerned with fuzzy relation equations with continuous t norms in the form atr b where a and b are the fuzzy subsets of x and y respectively email protected xxy is a fuzzy relation and t is a continuous t norm the problem is how to determine a from r and b first an if and only if condition of being solvable is presented novel algorithms are then presented for determining minimal solutions when x and y are finite the proposed algorithms generate all minimal solutions for the equations making them efficient solving procedures

minimization of linear objective functions under the constraints expressed by a system of fuzzy relation equations this paper considers the following optimization problem minimization of linear objective functions under the constraints expressed by a system of fuzzy relation equations using max product composition we first show some properties of minimal solutions of a system of fuzzy relation equations with max product composition and present some rules for reducing the original problem then we derive an algorithm which enables us to find all the optimal solutions for solving the optimization problem and provide some numerical examples to illustrate

mesures et equidistribution sur les espaces de berkovich the proof by ullmo and zhang of bogomolov s conjecture about points of small height in abelian varieties made a crucial use of an equidistribution property for small points in the associated complex abelian variety we study the analogous equidistribution property at p adic places our results can be conveniently stated within the framework of the analytic spaces defined by berkovich the first one is valid in any dimension but is restricted to algebraic metrics the second one is valid for curves but allows for more general metrics in particular to the normalized heights with respect to dynamical systems

an optimization problem on the image set of a max min fuzzy operator abstract the paper deals with the unsolvability of max min linear equation systems with coefficients in the unit interval for fuzzy systems or in an arbitrary real interval general case if the system has no solution then the nearest vector to the right hand side of the system for which the system is solvable is computed a polynomial algorithm for the problem is presented the method is illustrated by numerical examples

equidistribution for torsion points of a drinfeld module we prove an equidistribution result for torsion points of drinfeld modules of generic characteristic we also show that similar equidistribution statements would provide proofs for the manin mumford and the bogomolov conjectures for drinfeld modules

unattainable solutions of a fuzzy relation equation in a fuzzy relation equation the properties of the solution set have been investigated especially when the basic spaces are all finite sets however when the basic spaces are infinite a few properties are known in this paper we use the concepts of attainability and unattainability of a solution to clarify some properties of the solution set and show the condition for existence of a partially attainable solution and an unattainable one

positive line bundles on arithmetic varieties p 5 u integers is defined to count the volume of the lattice i l n of integral sections in the space j7 lon of real sections with supremum norm we want to prove that the leading term of this hilbert function as n f oo is given in terms of the height of x in as 1 this is known as a theorem of gillet and soule gs2 if x has a regular generic fiber beside this known result our proof uses hironaka s theorem on resolutions of singularities and minkowski s theorem on successive minima by hironaka s theorem we may construct

latticized linear programming and fuzzy relation inequalities abstract a logical linear programming problem the latticized linear programming is proposed based on fuzzy lattice and fuzzy relation inequalities the proposed problem is essentially an optimization problem which should be useful under certain logical if then situations to illustrate the proposed approach numerical examples are solved

solving interval valued fuzzy relation equations solving systems of fuzzy relation equations is an important topic in fuzzy set theory this paper studies the composite interval valued fuzzy relation equations after analyzing the properties of its solution set we convert the fuzzy relation equations into a fuzzy relation inequality system and propose an efficient computational procedure to generate the whole solution set examples are included to illustrate the idea and algorithm

minimizing a linear function under a fuzzy max min relational equation constraint in this paper we investigate the problem of minimizing a linear objective function subject to a fuzzy relational equation constraint a necessary condition for optimal solution is proposed based on this necessary condition we propose three rules to simplify the work of computing an optimal solution numerical examples are provided to illustrate the procedure experimental results are reported showing that our new procedure systematically outperforms our previous work

an algorithm for solving optimization problems with fuzzy relational inequality constraints an algorithm for solving a kind of optimization problems with fuzzy relational inequalities was proposed by guo and xia 6 however it is too expensive to verify the optimal condition in this paper some rules for reducing these problems are proposed and the relationship between minimal solutions and fri paths is also given these lead to a new algorithm for solving this kind of problems numerical experiments are presented for illustrating the efficiency of the proposed algorithm

fast solving method of fuzzy relational equation and its application to lossy image compression reconstruction a fast solving method of the solution for max continuous t norm composite fuzzy relational equation of the type g i j r sup t spl square a sub i sup t spl square b sub j i 1 2 i j 1 2 j where a sub i spl isin f x x x sub 1 x sub 2 x sub m bj spl isin f y y y sub 1 y sub 2 y sub n r spl isin f x spl times y and spl square max continuous t norm composition is proposed it decreases the computation time ijmn l t p to jm i n l p where l t and p denote the computation time of min t norm and relative pseudocomplement operations respectively by simplifying the conventional reconstruction equation based on the properties of t norm and relative pseudocomplement the method is applied to a lossy image compression and reconstruction problem where it is confirmed that the computation time of the reconstructed image is decreased to 1 335 6 the compression rate being 0 0351 and it achieves almost equivalent performance for the conventional lossy image compression methods based on discrete cosine transform and vector quantization

preperiodic points and unlikely intersections in this article we combine complex analytic and arithmetic tools to study the preperiodic points of one dimensional complex dynamical systems we show that for any fixed a b c and any integer d 2 the set of c c for which both a and b are preperiodic for z c is infinite if and only if a b this provides an affirmative answer to a question of zannier which itself arose from questions of masser concerning simultaneous torsion sections on families of elliptic curves using similar techniques we prove that if rational functions c z have infinitely many preperiodic points in common then all of their preperiodic points coincide and in particular the maps must have the same julia set this generalizes a theorem of mimar who established the same result assuming that and are defined over q the main arithmetic ingredient in the proofs is an adelic equidistribution theorem for preperiodic points over number fields and function fields with non archimedean berkovich spaces playing an essential role

lagrangian configurations and symplectic cross ratios we consider moduli spaces of cyclic configurations of n lines in a 2n dimensional symplectic vector space such that every set of n consecutive lines generates a lagrangian subspace we study geometric and combinatorial problems related to these moduli spaces and prove that they are isomorphic to quotients of spaces of symmetric linear difference operators with monodromy 1 the symplectic cross ratio is an invariant of two pairs of 1 dimensional subspaces of a symplectic vector space for n 2n 2 the moduli space of lagrangian configurations is parametrized by n 1 symplectic cross ratios these cross ratios satisfy a single remarkable relation related to tridiagonal determinants and continuants given by the pfaffian of a gram matrix

solving fuzzy relation equations with a linear objective function abstract an optimization model with a linear objective function subject to a system of fuzzy relation equations is presented due to the non convexity of its feasible domain defined by fuzzy relation equations designing an efficient solution procedure for solving such problems is not a trivial job in this paper we first characterize the feasible domain and then convert the problem to an equivalent problem involving 0 1 integer programming with a branch and bound solution technique after presenting our solution procedure a concrete example is included for illustration purpose

distribution of rational maps with a preperiodic critical point let f lambda be a family of rational maps of a fixed degree with a marked critical point c lambda under a natural assumption we first prove that the hypersurfaces of parameters for which c lambda is periodic converge as a sequence of positive closed 1 1 currents to the bifurcation current attached to c and defined by demarco we then turn our attention to the parameter space of polynomials of a fixed degree d by intersecting the d 1 currents attached to each critical point of a polynomial bassaneli and berteloot obtained a positive measure mu rm bif of finite mass which is supported on the connectedness locus they showed that its support is included in the closure of the set of parameters admitting d 1 neutral cycles we show that the support of this measure is precisely the closure of the set of strictly critically finite polynomials i e of misiurewicz points

min max programming problem subject to addition min fuzzy relation inequalities a bittorrent like peer to peer file sharing system can be reduced into a system of addition min fuzzy relation inequalities addition min is a new composition and the solution set of addition min fuzzy relation inequalities differs much from that of general max t norm fuzzy relation inequalities or equations in order to avoid network congestion and improve the stability of data transmission a min max programming problem is proposed subject to addition min fuzzy relation inequalities in this paper based on some relevant theorems on resolution a novel algorithm is developed step by step to find an optimal solution of the proposed problem moreover an application example is given to illustrate the feasibility and efficiency of the algorithm finally some further discussions are made concerning the optimal solution of the proposed problem

an algorithm for solving fuzzy relation equations with max t composition operator this paper studies the problem of solving a max t composite finite fuzzy relation equation where t is a special class of pseudo t norms if the equation is solvable then its set of feasible solutions is determined by the greatest solution and a finite number of minimal solutions some necessary conditions are presented for the minimal solutions in terms of the maximum solution and zero value under these conditions some minimal solutions of the system can be obtained easily some procedures are also proposed in order to simplify the original system the simplified system is then decomposed if possible into several subsystems with smaller dimensions which are very easy to solve furthermore a method is presented to solve each subsystem by combining the method and those procedures an efficient algorithm is proposed to obtain the set of feasible solutions of the original system two examples are also given to illustrate the algorithm

another modification from two papers of ghodousian and khorram and khorram et al abstract in this paper we focus on the proposed algorithms to solve a linear programming problem with the convex combination of the max min and the max average composition and the max star composition respectively they have been proposed by ghodousian and khorram a ghodousian e khorram solving a linear programming problem with the convex combination of the max min and the max average fuzzy relation equations appl math comput 180 2006 411 418 and khorram et al e khorram a ghodousian a abbasi molai solving linear optimization problems with max star composition equation constraints appl math comput 179 2006 654 661 respectively firstly we show that the tabular method algorithm in the first paper and the first procedure in the second paper may not lead to the optimal solutions of the two models in some cases secondly we generalize the proposed algorithm by abbasi molai and khorram a abbasi molai e khorram a modified algorithm for solving the proposed models by ghodousian and khorram and khorram and ghodousian appl math comput 190 2007 1161 1167 to solve the two models in fact it modifies the presented algorithms in the two papers finally some numerical examples are given to illustrate the purposes

latticized linear programming subject to max product fuzzy relation inequalities with application in wireless communication in this paper we introduce the latticized linear programming problem subject to max product fuzzy relation inequalities with application in the optimization management model of wireless communication emission base stations resolution of max product fuzzy relation inequalities is studied by comparing with that of the corresponding max product fuzzy relation equations a solution matrix approach is developed for solving the proposed problem without finding all the quasi minimal solutions of the constraint for carrying out the solution matrix approach we provide a step by step algorithm illustrated by a numerical example

on identification in fuzzy systems and its applications in control problems abstract the problem of identification in fuzzy systems described by the use of fuzzy equation is considered the identification method and its performance index is also presented the formal procedure of the identification algorithm is illustrated by means of a numerical example the possibility of using the proposed algorithm for the solution of a control problem is given as well

optimization of fuzzy relational equations with max av composition max min and max product compositions are commonly utilized to optimize a linear objective function subject to fuzzy relational equations both are members in the class of max t norm composition in this study the max av composition is considered for the same optimization model which does not belong to the max t norm composition however max av composition generates some properties of the solution set that are similar to the max product composition thanks to these properties a simple value matrix with rules can be applied to reduce problem size thus this study proposes an efficient procedure for obtaining optimal solutions without decomposing the problem into two sub problems or finding all the potential minimal solutions

fuzzy transforms for compression and decompression of color videos we use fuzzy transforms for coding decoding color frames of videos and we compare the results with the same frames reconstructed with the standard jpeg method we classify all the frames in intra frames and predictive frames by adopting a similarity measure based on the lukasiewicz t norm and a pre processing phase which determines the best similarity threshold value the compression is made on particular frames called d frames obtained from a suitable difference defined on the values of the pixels of an intra frame and a predictive frame under high compression rates we see that the peak signal to noise ratio of the frames obtained with the fuzzy transforms is averagely close to the psnr obtained with the jpeg method we use the videos at url sampl eng ohiostate edu sampl database htm

optimization of linear problems subjected to the intersection of two fuzzy relational inequalities defined by dubois prade family of t norms abstract in this paper optimization of a linear objective function with fuzzy relational inequality constraints is investigated in doing so the feasible region is formed by the intersection of two inequality fuzzy systems and dubois prade family of t norms which are considered as fuzzy composition the most well known continuous t norms are archimedean such as frank yager hamacher sugeno weber and schweizer sklar family an interesting family of t norms that is not archimedean has been introduced by dubois and prade in this paper the resolution of the feasible region of the problem is initialy investigated when it is defined with max duboise prade composition a necessary and sufficient condition along with three other necessary conditions are derived for determining the feasibility of the problem moreover two procedures have also been presented with the aim of simplifying the current linear problems a method is proposed to generate random feasible max dubois prade fuzzy relational inequalities and an algorithm is accordingly presented to solve the problem finally an example is described to illustrate this algorithm

linear fractional multi objective optimization problems subject to fuzzy relational equations with a continuous archimedean triangular norm in this paper linear fractional multi objective optimization problems subject to a system of fuzzy relational equations fres using the max archimedean triangular norm composition are considered first some theorems and results are presented to simplify systems of fuzzy relational equations next the feasible set of the optimization problem is reduced then the linear fractional multi objective optimization problem is converted to a linear one using nykowski and zolkiewski s approach furthermore the efficient solutions are obtained by applying the improved e constraint method in addition we design an algorithm to generate consistent systems of fuzzy relational equations randomly using the covering problem finally the proposed method is effectively tested by solving a randomly generated consistent test problem

geometry of p adic siegel discs abstract we survey recent advances in the study of regular motions over p adic fields show its varied connections with dynamics and number theory and illustrate its significance to an important class of discrete dynamical systems we also show that mappings supporting quasi periodic motions can be naturally interpreted as flows with p adic time

optimization of fuzzy relation equations with max product composition abstract an optimization problem with a linear objective function subject to a system of fuzzy relation equations using max product composition is considered since the feasible domain is non convex traditional linear programming methods cannot be applied we study this problem and capture some special characteristics of its feasible domain and the optimal solutions some procedures for reducing the original problem are presented the problem is transformed into a 0 1 integer program which is then solved by the branch and bound method for illustration purpose an example of the procedures is provided

an accelerated approach for solving fuzzy relation equations with a linear objective function in literature the optimization model with a linear objective function subject to fuzzy relation equations has been converted into a 0 1 integer programming problem by fang and li 1999 they proposed a jump tracking branch and bound method to solve this 0 1 integer programming problem in this paper we propose an upper bound for the optimal objective value based on this upper bound and rearranging the structure of the problem we present a backward jump tracking branch and bound scheme for solving this optimization problem a numerical example is provided to illustrate our scheme furthermore testing examples show that the performance of our scheme is superior to the procedure in the paper by fang and li several testing examples show that our initial upper bound is sharp

preperiodic points of polynomials over global fields given a global field k and a polynomial defined over k of degree at least two morton and silverman conjectured in 1994 that the number of k rational preperiodic points of is bounded in terms of only the degree of k and the degree of in 1997 for quadratic polynomials over k q call and goldstine proved a bound which was exponential in s the number of primes of bad reduction of by careful analysis of the filled julia sets at each prime we present an improved bound on the order of s log s our bound applies to polynomials of any degree at least two over any global field k let k be a field and let k z be a rational function let denote the n iterate of under composition that is is the identity function and for n 1 n 1 we will study the dynamics on the projective line p k in particular we say a point x is preperiodic under if there are integers n m 0 such that x x the point y x satisfies n m y y and is said to be periodic of period n m note that x p k is preperiodic if and only if its orbit x n 0 is finite for example let k q and z z 29 16 then 5 4 1 4 7 4 forms a periodic cycle of period 3 and 5 4 1 4 7 4 and 3 4 each land on this cycle after one or two iterations in addition the point is of course fixed these nine q rational points are all preperiodic under meanwhile it is not difficult to see that no other point in p q is preperiodic by showing that the denominator of a rational preperiodic point must be 4 and that the absolute value must be less than 2 in general for any global field k any dimension n 1 and any morphism p p over k of degree at least two northcott proved in 1950 that the number of k rational preperiodic points of is finite 25 more precisely he showed that the preperiodic points form a set of bounded arithmetic height years later by analogy with the theorems of mazur 19 and merel 20 on k rational torsion of elliptic curves morton and silverman proposed the following conjecture 23 uniform boundedness conjecture morton and silverman 1994 given integers d n 1 and d 2 there is a constant d n d with the following property let k be a number field with k q d and let p p be a morphism of degree d defined over k then has at most preperiodic points in p k the analogy between preperiodic points and torsion comes from the fact that the torsion points of an elliptic curve e are precisely the preperiodic points of the multiplication bytwo map 2 e e in fact taking x coordinates the map 2 induces a rational function known to dynamicists as a lattes map p p of degree 4 whose preperiodic points date june 21 2005 revised december 21 2005 2000 mathematics subject classification primary 11g99 secondary 11d45 37f10

bifurcation measures and quadratic rational maps we study critical orbits and bifurcations in the curves per1 within the moduli space m2 of quadratic rational maps f p 1 p 1 for each 2 c the curve per1 is dened by the condition that the map has a xed point of multiplier we prove that the curve per1 contains innitely many postcritically n ite maps if and only if 0 addressing a special case of bd2 conjecture 1 4 we also show that the two critical points of f dene distinct bifurcation measures along per 1

solving linear optimization problems with max star composition equation constraints in this paper an optimization model with a linear objective function subject to a system of fuzzy relation composition equations is presented since the non empty feasible solution set of the fuzzy relation equations is generally a non convex set the conventional linear programming method will not be suitable for solving such a problem therefore an efficient solution procedure for such problems appears to be necessary in this paper firstly we characterize the feasible solution set and then introduce two efficient procedures for solving the problem finally two concrete examples are included for more details

an algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max prod composition abstract fuzzy sets as the feasible region for optimization problems is an interesting and on going research topic s c fang g li solving fuzzy relations equations with a linear objective function fuzzy sets syst 103 1999 107 113 7 j lu s c fang solving nonlinear optimization problems with fuzzy relation constraints fuzzy sets syst 119 2001 1 20 16 e khorram a ghodpusian linear objective function optimization with fuzzy relation constraints regarding max av composition appl math comput in press doi 10 1016 j amc 2005 04 021 in this paper we focus on these kind problems in which the solutions region is the fuzzy relation equation with max prod composition and the objective function is linear whereas one of the major difficulties in such problems is non convexity of the feasible region it is preferable to study these regions in the first step hence we have primarily investigated two methods and their relationship and then we have determined the feasible region via them after determining the feasible set we have given an algorithm to optimize the linear objective function on such these regions finally we have presented two examples to illustrate the methods and algorithms

addition min fuzzy relation inequalities with application in bittorrent like peer to peer file sharing system abstract the data transmission mechanism in bittorrent like peer to peer p2p file sharing systems may be reduced to some addition min fuzzy relation inequalities the solution set of addition min fuzzy relation inequalities plays an important role in the corresponding optimization problem in this paper we study some properties of the solutions to such system convexity of the solution set and number of minimal solutions are discussed with comparison to those of the classical max t fuzzy relation equations or inequalities besides vertex solution and variable ordering minimal solution are also investigated with application in bittorrent like p2p file sharing system two numerical examples are given to illustrate the feasibility and efficiency of the algorithm for solving the variable ordering solution

łukasiewicz transform and its application to compression and reconstruction of digital images we define the lukasiewicz transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an mv algebra then we describe the lukasiewicz transform based ltb algorithm for image processing demonstrating its applicability

processing in relational structures fuzzy relational equations abstract the paper provides an overview of methodology for processing fuzzy information in relational structures completed in terms of fuzzy relational equations the origin and the central role of relational calculus in general and fuzzy sets in particular is explained with special emphasis paid to its role and representation capabilities it is pointed out that fuzzy relational equations play a significant role as a platform for a uniform development of techniques in fuzzy sets many of the problems and frameworks developed in fuzzy sets so far can be easily translated into the language of fuzzy relational equations which immediately takes a significant advantage of their solid well developed formalisms techniques and clarity of exposition we will study the role of approximate solutions to fuzzy relational equations as a convenient tool to handle probabilistic type of uncertainty moreover those solutions can easily explain the origin and generate a way in which fuzzy sets of higher generality such as for instance type 2 sets interval valued sets can be algorithmically determined finally we study the role of equations in diverse fields of applications making use of an ample framework of general systems theory

sur la compacite des ensembles de julia des polynomes p adiques let r be a rational function of degree 2 with complex coefficients then the julia set of r is a closed subset of 1 and therefore compact if one replace by the field p completion of an algebraic closure of the field p of the p adic numbers then one can define also a julia set for a rational function with p adic coefficients but as p is not locally compact the julia set may or may not be compact in this paper we study the compactness of the julia set of p adic polynomials

a finiteness theorem for canonical heights attached to rational maps over function fields let k be a function field let k t be a rational map of degree d 2 defined over k and suppose that is not isotrivial in this paper we show that a point p p k has canonical height zero if and only if p is preperiodic for this answers affirmatively a question of szpiro and tucker and generalizes a recent result of benedetto from polynomials to rational functions we actually prove the following stronger result which is a variant of the northcott finiteness principle there exists e 0 such that the set of points p p k with canonical height at most e is finite our proof is essentially analytic making use of potential theory on berkovich spaces to study the dynamical green s functions g v x y attached to at each place v of k for example we show that every conjugate of has bad reduction at v if and only if g v x x 0 for all x p1berk v where p 1 berk v denotes the berkovich projective line over the completion of kv in an appendix we use a similar method to give a new proof of the mordell weil theorem for elliptic curves over k

canonical heights transfinite diameters and polynomial dynamics let z be a polynomial of degree at least 2 with coefficients in a number field k iterating gives rise to a dynamical system and a corresponding canonical height function as defined by call and silverman we prove a simple product formula relating the transfinite diameters of the filled julia sets of over various completions of k and we apply this formula to give a generalization of bilu s equidistribution theorem for sequences of points whose canonical heights tend to zero

optimal vector based algorithm for solving min max programming subject to addition min fuzzy relation inequality optimal management model in bittorrent like peer to peer p2p file sharing system can be reduced into a min max programming problem subject to addition min fuzzy relation inequality to deal with such problem we introduce the concept of optimal vector besides a novel optimal vector based ovb algorithm is developed to find a minimal optimal solution based on practical application consideration solution obtained by the ovb algorithm is theoretically demonstrated to be better than or equal to that obtained by the existing method advantage of our proposed ovb algorithm is illustrated by detailed numerical examples

the pu 2 1 configuration space of four points in s 3 and the cross ratio variety the configuration space of four points on the standard cr 3 sphere up to cr automorphisms is a real four dimensional variety we prove the existence of natural complex and cr structures on this space

fuzzy relation equations for coding decoding processes of images and videos we adopt fuzzy relation equations with continuous triangular norms for compression decompression processes of grey images colour images in the rgb space and frames of videos by comparing the results of the reconstructed images with standard methods like jpeg and mpeg 4 any image is subdivided in blocks and each block is coded decoded using arbitrary fuzzy sets as coders in the fuzzy equations we evaluate the peak signal to noise ratio psnr on the decompressed images for several values of the compression rates as measure of the quality of images and frames reconstructed the original frames of a video are classified in intra frames and predictive frames by using a similarity measure based on the well known lukasiewicz t norm

lexicographic optimal solution of the multi objective programming problem subject to max product fuzzy relation inequalities abstract it is shown in this paper that the emission base stations in wireless communication can be reduced into a system of fuzzy relation inequalities with max product composition for optimal management in such system we introduce the fuzzy relation multi objective programming concept of feasible index set fis is defined based on which a novel algorithm named fis algorithm is developed to find the unique lexicographic optimal solution of the proposed problem with polynomial computational complexity applying this method we needn t to find out all the minimal solutions of the constraint a numerical application example is provided to illustrate the feasibility and efficiency of the fis algorithm

a modified algorithm for solving the proposed models by ghodousian and khorram and khorram and ghodousian abstract in this paper we focus on the proposed algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max prod composition that it has been proposed by ghodousian and khorram a ghodousian e khorram an algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max prod composition appl math comput 178 2006 502 509 firstly we show that the algorithm may not lead to the optimal solution in some cases secondly we propose a new algorithm for solving the presented model by ghodousian and khorram 2006 as mentioned above in fact it modifies the presented algorithm in the ghodousian and khorram s paper also this algorithm is extended to the presented model by khorram and ghodousian e khorram a ghodousian linear objective function optimization with fuzzy relation equation constraints regarding max av composition appl math comput 173 2006 872 886 with max av composition finally some numerical examples are given for illustrating the purposes

solving nonlinear optimization problems with fuzzy relation equation constraints abstract an optimization model with a nonlinear objective function subject to a system of fuzzy relation equations is presented since the solution set of the fuzzy relation equations is in general a non convex set when it is not empty conventional nonlinear programming methods are not ideal for solving such a problem in this paper a genetic algorithm ga is proposed this ga is designed to be domain specific by taking advantage of the structure of the solution set of fuzzy relation equations the individuals from the initial population are chosen from the feasible solution set and are kept within the feasible region during the mutation and crossover operations the construction of test problems is also developed to evaluate the performance of the proposed algorithm

a fixed charge model with fuzzy inequality constraints composed by max product operator abstract a fixed charge model subject to a system of fuzzy relation inequalities with max product composite operator is presented the feasible domain of the model is first investiged of which the necessary and sufficient condition is proposed if it is infeasible a minimum calibration procedure is provided to have at least one solution due to the nonconvexity of its feasible domain a solution procedure is designed to have a minimum objective value of which the initial cost is considered an illustrative example is presented

fuzzy relation equations on a finite set abstract the family of all the solutions of a fuzzy relation equation on a finite set is considered it is characterized by the set of all the lower solutions which can be obtained by a combinatorial algorithm

a motion compression reconstruction method based on max t norm composite fuzzy relational equations a motion compression reconstruction method based on max t norm composite fuzzy relational equations mcf is proposed where into intra pictures i pictures and predictive pictures p pictures of the original motion are compressed by uniform and non uniform coders respectively the non uniform coders of the proposed method can preserve edge information of p pictures on the compressed image to perform an effective compression reconstruction of the p pictures a design method of non uniform coders is proposed based on an overlap level of fuzzy sets and a fuzzy equalization an experiment using 10 p pictures confirms that the root mean square error of the reconstructed images obtained by the proposed non uniform coders is decreased to 89 4 of that one of the uniform coders under the condition that compression rate the ratio between the file size of compressed image and original one is 0 0057 two test motions tennis and woman 100 frames are compressed and reconstructed by the proposed mcf

a modified pso algorithm for linear optimization problem subject to the generalized fuzzy relational inequalities with fuzzy constraints fri fc in this paper optimization of a linear objective function subject to a generalized fuzzy relational inequalities is investigated in which an arbitrary continuous t norm is considered as fuzzy composition and fuzzy inequality replaces ordinary inequality in the constraints unlike most optimization algorithms in fuzzy relational inequalities with fuzzy constraints fri fc we find a near feasible solution having a better objective value than those resulting from the resolution of the similar problems with crisp ordinary inequality constraints such solutions are called super optima in this paper subsequently an algorithm is proposed to find a super optimum with pre specified desirable infeasibility for this purpose we firstly study some structural properties of the fri fc problem and present a new formulization that is independent of t norms used in the constraints of the problem this new formulation converts the primary problem into an equivalent problem with simple constraints without considering any penalty parameters however it is proved that the transformed equivalent problem enables our algorithm to distinguish unfavorable points and generate a sequence of solutions converging to a super optimum under a certain sufficient condition finally a modified pso is presented in which the ability of pso to solve unconstrained problems with continuous domain the structure of the transformed problem and some fuzzy structural modifications are combined and form an efficient algorithm to solve the generalized fri fc problems the modified pso algorithm has been applied to the generalized fri fc problem defined with ten well known continuous t norms additionally an idea of the fri fc problems as outer approximators for fri problems with ordinary inequalities is also investigated

posynomial geometric programming problem subject to max min fuzzy relation equations we discuss a class of posynomial geometric programming problem pgpf aimed at minimizing a posynomial subject to fuzzy relational equations with max min composition by introducing auxiliary variables we convert the pgpf into an equivalent programming problem whose objective function is a non decreasing function with an auxiliary variable we show that an optimal solution consists of a maximum feasible solution and one of the minimal feasible solutions by an equivalent programming problem in addition we introduce some rules for simplifying the problem then by using a branch and bound method and fuzzy relational equations fre path we present an algorithm to obtain an optimal solution to the pgpf finally numerical examples are provided to illustrate the steps of the procedure