eigenvalue bounds for transformations of solvable potentials we study smooth transformations of potentials for which exact bound state solutions of schrodinger s equation are known eigenvalue approximation formulae are obtained which provide lower or upper energy bounds according to whether the transformation function g is convex or concave detailed results are presented for perturbed coulomb potentials of the form and

dimension of the torelli group for out fn let mathcal t n be the kernel of the natural map out fn gln we use combinatorial morse theory to prove that mathcal t n has an eilenberg maclane space which is 2n 4 dimensional and that h 2n 4 mathcal t n mathbb z is not finitely generated n 3 in particular this shows that the cohomological dimension of mathcal t n is equal to 2n 4 and recovers the result of krstic mccool that mathcal t 3 is not finitely presented we also give a new proof of the fact due to magnus that mathcal t n is finitely generated

fuzzy relational equations and the inverse problem abstract the inverse problem concerned with fuzzy relations is investigated the conditions for the existence of a solution are shown and an analytical solution is given a method for the improvement of the solution is proposed

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

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

pt symmetric pseudo perturbation recipe an imaginary cubic oscillator with spikes the pseudo perturbative shifted l expansion technique pslet is shown to be applicable in the non hermitian symmetric context the construction of bound states for several symmetric potentials is presented with special attention paid to v r ir3 ir oscillators

the shifted 1 n expansion and the energy eigenvalues of the hulthen potential for l not 0 the shifted 1 n expansion has been used to obtain the energy values of the hulthen potential for non zero values of the orbital angular momentum the analytic expression for the energies en l yield fairly accurate results for a wide range of values of n l and the screening parameter lambda the energy values obtained by this method have been compared and found to be in excellent agreement with pade approximation calculations

a similarity based bidirectional approximate reasoning method for decision making systems this paper presents a similarity based bidirectional approximate reasoning method which can express the decision maker s disposition for this we shall propose a new type of similarity measure based on the ordered weighted aggregation owa operator the proposed similarity measure has a structure to involve the disposition of a decision maker by choosing a suitable weighting vector of the owa operator from this property we derive a simple and flexible type of similarity based bidirectional approximate reasoning method which can support the making of a decision under more complex situations such as industrial inspection systems for example

a note on unsolvable systems of max min fuzzy equations abstract for unsolvable systems of linear equations of the form a x b over the max min fuzzy algebra r 0 1 max min we propose an efficient method for finding a chebychev best approximation of the matrix a r m n in the set s b d r m n d x b is solvable

eigenvalues of the schrodinger equation with coulomb potentials plus linear and harmonic radial terms analytic approximations for the eigenvalues have been obtained using the two point quasifractional approximants method here we extend and generalize previous work where the method was applied to determine eigenenergies of two dimensional coulomb potentials in the presence of a magnetic field of arbitrary strength we have also shown the advantage of our results with respect to other calculations using the shifted 1 n method or pade approximants

orbits of curves under the johnson kernel this paper has two main goals first we give a complete explicit and computable solution to the problem of when two simple closed curves on a surface are equivalent under the johnson kernel second we show that the johnson filtration and the johnson homomorphism can be defined intrinsically on subsurfaces and prove that both are functorial under inclusions of subsurfaces the key point is that the latter reduces the former to a finite computation which can be carried out by hand in particular this solves the conjugacy problem in the johnson kernel for separating twists using a theorem of putman we compute the first betti number of the torelli group of a subsurface

two interacting electrons in a uniform magnetic field and a parabolic potential the general closed form solution we present an analytical analysis of the two dimensional schrodinger equation for two interacting electrons subjected to a homogeneous magnetic field and confined by a two dimensional external parabolic potential we have found the general closed form expression for the eigenstates of the problem and its corresponding eigenenergies for particular values of magnetic field and spatial confinement length the mathematical framework is just based on a rigorous solution of the three term recursion relation among the coefficients that arises from the series solution of biconfluent heun bhe equation connected with the radial part of the schrodinger equation for the internal motion it is also shown that by vanishing of coulomb repulsion strength the obtained explicit analytical solutions of bhe equation reduces to the well known polynomials satisfying the associated laguerre differential equation furthermore in the presence of this interaction the results are compared with those previously obtained in th

the asymptotic iteration method for the eigenenergies of the schrodinger equation with the potential v r z r gr λr2 the eigenenergies of the schrodinger equation with coulomb potential plus linear and harmonic radial terms are investigated using the perturbation technique within the framework of the asymptotic iteration method the obtained eigenenergies are compared with those obtained from the shifted 1 n expansion method the moment method and also with the exact values obtained from the super symmetric method it is found that asymptotically this method gives accurate results for arbitrary g z and

a basis for variational calculations in d dimensions in this paper we derive expressions for matrix elements i hj for the hamiltonian h qa q rq in d 2 dimensions the basis functions in each angular momentum subspace are of the form the matrix elements are given in terms of the gamma function for all d the significance of the parameters t and p and scale s are discussed applications to a variety of potentials are presented including potentials with singular repulsive terms of the form r 0 perturbed coulomb potentials d r br ar2 and potentials with weak repulsive terms such as r2 r4 0

calculation and application of a minimum fuzzy relational matrix abstract this paper compares the maximum and minimum inverse formulations for fuzzy identification of a relational matrix given a series of non normal input output data baboshin and naryshkin 1990 showed for the case of normal input data that identification of the relational matrix using an estimate of the minimum inverse resulted in a smaller hamming distance between actual and predicted output values than the mamdani identification method this paper extends their work to include unrestricted or non normal input data and confirms that the estimate of the minimum inverse for this case is again better than mamdani s method it is then proven that the relative rank of identification algorithms for minimization of the hamming distance between the actual and predicted output values is the maximum inverse calculation of sanchez 1976 the minimum inverse formulation initial formulation by sanchez 1977 and extended to a series of input output data by sessa 1984 the estimate of the minimum inverse and then the mamdani method however this ranking applies only in the fuzzy domain and not to the discrete or defuzzified domain relevant to many practical applications

a fuzzy inverse model construction method for general monotonic multi input single output miso systems this paper presents a novel method of systematically constructing a fuzzy inverse model for general multi input single output miso systems represented with triangular input membership functions singleton output membership function and fuzzy mean defuzzification the fuzzy inverse model construction method has the ability of uniquely determining the inverse relationship for each input output pair it is derived in a straightforward way and the required input variables can be simultaneously obtained by the fuzzy inferencing calculation to realize the desired output value simulation examples are provided to demonstrate the effectiveness of the proposed method to find the inverse kinematics solutions for complex multiple degree of freedom industrial robot manipulators

diagnosis problem solving using fuzzy relations this paper deals with the restoration and the identification of the causes diagnoses through the observed effects symptoms on the basis of fuzzy relations and zadeh s compositional rule of inference we propose an approach for building fuzzy systems of diagnosis which enables solving fuzzy relational equations together with design and tuning of fuzzy relations on the basis of expert and experimental information the essence of tuning consists of the selection such membership functions for fuzzy causes and effects and also fuzzy relations which minimize the difference between model and experimental results of diagnosis the genetic algorithm is used for solving the optimization problem the proposed approach is illustrated by the computer experiment and the real example of diagnosis

the johnson homomorphism and its kernel we give a new proof of a celebrated theorem of dennis johnson that asserts that the kernel of the johnson homomorphism on the torelli subgroup of the mapping class group is generated by separating twists in fact we prove a more general result that also applies to subsurface torelli groups using this we extend johnson s calculati on of the rational abelianization of the torelli group not only to the subsurface torelli groups but also to finite index subgroups of the torelli group that contain the kernel of the johnson homomorphism

some exact solutions for the potential r 1 2λr 2λ2r2 the authors show how to obtain an infinite number of exact solutions for the excited states of an s wave hydrogen atom with the polynomial perturbation 2 lambda r 2 lambda 2r2 for certain specific values of lambda the energy eigenvalues in such cases satisfy en 1 2 2n 3 mod lambda mod with the corresponding wavefunctions being given by products of exp mod lambda mod r lambda mod lambda mod r2 and polynomials of nth degree in r

stability of the homology of the mapping class groups of orientable surfaces the mapping class group of f fgs r is f rgs wo a where a is the topological group of orientation preserving diffeomorphisms of f which are the identity on df and fix the s punctures when r 0 and 2g s 3 an important feature of f is that it acts properly discontinuously on the teichmiller space us the quotient is the moduli space f of isometry classes of complete hyperbolic metrics of finite area on f since us is homeomorphic to euclidean space and f is virtually torsion free we have

system of fuzzy relation equations with inf composition complete set of solutions the problem of solvability of a system of equations with inf composition is considered on finite universes equations are expressed using operations of a bl algebra we study complete set of solutions of the respective system in the particular case one equation and in the general case in both cases various conditions of solvability are found and proved we characterize all maximal solutions and prove that under certain conditions each solution of the system an equation is less than or equal to a respective maximal one as a result we are able to characterize the complete set of solutions examples of single equations and their systems are considered and complete sets of solutions are found for each

on the set of solutions of composite fuzzy relation equations in this paper we introduce some algorithms which have minimization properties about the fuzziness of solutions in the maxmin fuzzy relation equations

finitary solvability conditions for systems of fuzzy relation equations in this paper we consider the problem of solving systems of fuzzy relation equations two types of these systems with different compositions are considered and processed simultaneously a new sufficient condition and new solvability criteria are proposed for systems of both types all these conditions are finitary and thus can be easily verified the sufficient condition and criteria of solvability characterize a relationship between a skeleton nxn matrix n is a number of equations and a vector of the right hand side

some first excited energy levels for the generalized killingbeck potential with the differential quadratic method the ground energy and some low lying excited energies and the corresponding wavefunctions for the generalized killingbeck potential are investigated within the context of the recently introduced differential quadratic method highly accurate energy eigenvalues and an excellent agreement were found compared with the power series expansion and the supersymmetric perturbation theory

an inference network for bidirectional approximate reasoning based on an equality measure an inference network is proposed as a tool for bidirectional approximate reasoning the inference network can be designed directly from the given fuzzy data knowledge if a fuzzy input is given for the inference network then the network renders a reasonable fuzzy output after performing approximate reasoning based on an equality measure conversely due to the bidirectional structure the network can yield its corresponding reasonable fuzzy input for a given fuzzy output this property makes it possible to perform forward and backward reasoning in the knowledge base system

residuation in fuzzy algebra and some applications abstract the system 0 1 max min has a number of well known applications many of which involve the inversion of linear relations we show the advantage of residuation theory for this process and apply it to the analysis of the problem of chebychev approximation

inverse problem in fuzzy relational equations abstract the paper deals with the problem of handling fuzzy relational equations of the form x r y in the case of an empty solution set with respect to x x r y discussing the essence of the structure of the fuzzy relation r with respect to provided y algorithms have been proposed which enable us to modify the original equation i e the fuzzy set y in a way leading to its genuine solution or at least an approximate one it is explained how these modifications relax a set of constraints needed to be satisfied for any solvable equation a grade of the modification of the original problem is expressed in terms of distortion of the fuzzy set y which forms a cornerstone of the proposed procedures numerical examples are provided some aspects related to the area of diagnostic models in which these equations are studied are also treated

the structure of the torelli group i a finite set of generators for j this is the first of three papers concerning the so called torelli group let m mg be a compact orientable surface of genus g having n boundary components and let 9 xg be its mapping class group that is the group of orientation preserving diffeomorphisms of m which are 1 on the boundary am modulo isotopies which fix 3m pointwise this group is also known to the complex analysts as the teichmuller group or modular group if n 0 or 1 let further 4 jg be the subgroup of d1 which acts trivially on h1 m z the topologists have no traditional name for a but the analysts tell me it was known classically and is called the torelli group several interesting problems and conjectures exist concerning f the principal one can be found in kirby s problem list k and asks if gg is finitely generated in this first paper we shall answer the question affirmatively for both gg 0 and fgg when g 3 and shall give a fairly simple set of generators two other conjectures were made by the author the first involves the subgroup j of f which is generated by twists on nulhomologous simple closed curves ji produces a surjective homomorphism t fgg 1 a3h1 m z which kills c and it is conjectured there that in fact 5y ker t the proof of this is the content of the second paper in the third paper we use the results of the second to compute the abelianization f f explicitly thereby verifying another conjecture in ji the first reasonably simple but infinite set of generators for fg0 was produced by powell in p his generators consist of two types a twists on bounding simple closed curves b opposite twists on a bounding pair of disjoint homologous simple closed curves each of which are nonbounding using his result the author showed in j2 that the maps of the second type which we call bp maps for bounding pair are actually sufficient to generate both kg 0 and fg 1 for g 3 and in fact that we need only those whose two curves bound a genus one subsurface of m note that for g 2 all bp maps are trivial and hence the result fails in this case in the finite set of generators produced in this paper only

on the existence of solutions of systems of fuzzy equations abstract a necessary and sufficient condition for the existence of solutions of a fuzzy equation given by e sanchez is extended to systems of fuzzy equations

interval valued fuzzy backward reasoning the importance and efficiency of backward reasoning in nonfuzzy reasoning has been stressed for a long time especially in the case of expert systems and decision support systems the extension of this reasoning method to fuzzy theory however has never been considered in this paper the authors propose a definition of fuzzy backward reasoning based on the generalized modus ponens and show the necessity of considering interval valued fuzzy backward reasoning then the authors propose solving methods for fuzzy backward reasoning in the case of a rule with one or several conditions as well as in the case of several rules

decentralized fuzzy control of multivariable systems by active decomposition of control laws this paper considers the problem of decentralized fuzzy control of multivariable systems some definitions and theorems with regard to this problem are given decentralized fuzzy control algorithms based on active decomposition of control laws are presented and illustrated by numerical examples the algorithms use local sets of fuzzy relations decoupling the influence of state on control variables when added to the original fuzzy relations it is shown that the number of fuzzy relations is significantly reduced and thus real time control implementation is facilitated

the virtual cohomological dimension of the mapping class group of an orientable surface let f f r be the mapping class group of a surface f of genus g with s punctures and r boundary components the purpose of this paper is to establish cohomology properties of f parallel to those of the arithmetic groups if g is a linear algebraic group defined over q x is the symmetric space associated to g and a is an arithmetic subgroup of g then a is virtually torsion free and acts properly discontinuously on x the rational homology of a is the same as that of x a furthermore there is a bordification of x bs to a manifold with corners 3 and an extension of the action of a to a properly discontinuous action on jf so that the quotient x a is compact the boundary of jf is homotopy equivalent to a wedge of spheres say of dimension d and the virtual cohomological dimension of a is n d 1 where n is the dimension of x in the case of the mapping class group there is no analog for g ivanov unpublished has proven that f is not arithmetic nevertheless f acts properly discontinuously on teichmiiller space r which is homeomorphic to euclidean space of dimension 6 g 6 2 s 3 will play the role of the symmetric space the quotient of 9by f is the moduli space of curves whose rational homology is then identified with that of e harvey har has constructed a borel serre bordification j of 3 by analytic methods in the case where f has punctures we will build g by a different combinatorial method in addition we will explicitly describe inside y a cell complex y of dimension 4 g 4 s onto which j may be f equivariantly retracted thus establishing an analog of the constructions for sl n by serre soul6 sol and ash a this complex will be of the lowest possible dimension because we will use j to prove our main result

extending the contraposition property of propositional logic for fuzzy abduction abduction deals with assumption based reasoning to explain an observation in the context of fuzzy reasoning abduction attempts to determine the membership function of the fuzzy propositions present in the antecedent of a rule when the membership functions for the propositions in the consequent of the rule are given currently available models of fuzzy abduction are capable of inferring the membership function of the antecedent clause accurately when the antecedent includes single fuzzy proposition however when the antecedent clause of a rule contains multiple fuzzy propositions these models fail to determine the independent membership function of the individual propositions present in the antecedent this paper presents a new formulation to handle the above problem by fuzzy extension of the well known contraposition property of propositional logic several interesting properties due to the fuzzy extension of the classical contraposition have been derived an algorithm for automated abduction using the extended contraposition property has been developed to demonstrate the principle of abduction with rules containing one or more fuzzy propositions in the antecedent consequent the time complexity of the proposed fuzzy abduction for a sequence of n chained rules where each rule has m fuzzy propositions is o mn considering a uniform cost for composition operation and t norm computation of the antecedent

shifted 1 n expansion and exact solutions for the potential v r z r gr λr2 the authors have found an infinite number of exact solutions for the hydrogenic atom in the external potential v r gr r2 not only for an s wave state but for higher waves as well from supersymmetric considerations the general schrodinger equation has been treated by the shifted 1 n expansion method the eigenvalues obtained from the shifted 1 n expansion are compared with those obtained by bessis et al 1987 and also with the supersymmetric exact values

neurocomputational approach to solve a convexly combined fuzzy relational equation with generalized connectives abstract in this paper we present a method to solve a convexly combined fuzzy relational equation with generalized connectives for this we propose a neural network whose structure represents the fuzzy relational equation then we derive a learning algorithm by using the concept of back propagation learning since the proposed method can be used for a general form of fuzzy relational equations such fuzzy max min or min max relational equations can be treated as its special cases

oe and w superrigidity results for actions by surface braid groups we show that several important normal subgroups of the mapping class group of a surface satisfy the following property any free ergodic probability measure preserving action y x is stablyoe superrigid these include the central quotients of most surface braid groups and most torelli groups and johnson kernels in addition we show that all these groups satisfy the measure equivalence rigidity and we describe all their lattice embeddings using these results in combination with previous results from cik13 we deduce that any free ergodic probabilitymeasure preserving action of almost any surface braid group is stablyw superrigid i e it can be completely reconstructed from its vonneumann algebra

the dimension of the torelli group we prove that the cohomological dimension of the torelli group for a closed connected orientable surface of genus g 2 is equal to 3g 5 this answers a question of mess who proved the lower bound and settled the case of g 2 we also find the cohomological dimension of the johnson kernel the subgroup of the torelli group generated by dehn twists about separating curves to be 2g 3 for g 2 we prove that the top dimensional homology of the torelli group is infinitely generated finally we give a new proof of the theorem of mess that gives a precise description of the torelli group in genus 2 the main tool is a new contractible complex called the complex of minimizing cycles on which the torelli group acts

hydrogenic atoms in the external potential v r gr λr2 exact solutions and ground state eigenvalue bounds using moment methods an infinite number of exact solutions for the ground and excited states of an s wave hydrogenic atom with the perturbation v r gr lambda r2 are constructed subject to special relations between g lambda and the nuclear charge z a powerful method of stieltjes moments is employed to generate rapidly converging upper and lower bounds to the ground state energy e0 z g lambda for arbitrary g z and positive lambda the accuracies of these bounds are relatively insensitive to the strength of the perturbation the moment method also generates the exact s wave ground state solutions mentioned above

arithmetic group symmetry and finiteness properties of torelli groups we examine groups whose resonance varieties characteristic varieties and sigma invariants have a natural arithmetic group symmetry and we explore implications on various niteness properties of subgroups we compute resonance varieties characteristic varieties and alexander polynomials of torelli groups and we show that all subgroups containing the johnson kernel have nite rst betti number when the genus is at least 4 we also prove that in this range the i adic completion of the alexander invariant is nite dimensional and the kahler property for the torelli group implies the nite generation of the johnson kernel

solvability of fuzzy relational equations and manipulation of fuzzy data abstract the problem of characterization of fuzzy relational equations with respect to their solvability property is studied some aspects of manipulation of fuzzy data with the aid of fuzzy relational equations are considered two stages of manipulation process are indicated combining pieces of evidence and inferring their mutual correspondence both of them are formulated and solved by the use of fuzzy relational equations the role of a solvability index is extensively studied numerical considerations give an illustration of the approach we propose and deal with some real data used for fuzzy controllers

iteration algorithm for solving ax b in max min algebra abstract for solving the linear system a x b we introduce some iteration algorithms where a aij and b bi a given matrix and a column vector with elements from a brouwerian lattice and is a max min composite operation

new class of conditionally exactly solvable potentials in quantum mechanics motivated by an idea of dutra 1993 we obtain a new class of one dimensional conditionally exactly solvable potentials for which the entire spectra can be obtained in an algebraic manner provided one of the potential parameters is assigned a fixed negative value it is shown that using shape invariant potentials as input one may generate different classes of such potentials even in more than one dimension we also illustrate that wkb and supersymmetry inspired wkb methods provide very good approximations for these potentials with the latter doing comparatively better

representation theory and homological stability abstract we introduce the idea of representation stability and several variations for a sequence of representations v n of groups g n a central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability this makes it possible to extend classical theorems of homological stability to a much broader variety of examples representation stability also provides a framework in which to find and to predict patterns from classical representation theory littlewood richardson and murnaghan rules stability of schur functors to cohomology of groups pure braid torelli and congruence groups to lie algebras and their homology to the equivariant cohomology of flag and schubert varieties to combinatorics the n 1 n 1 conjecture the majority of this paper is devoted to exposing this phenomenon through examples in doing this we obtain applications theorems and conjectures beyond the discovery of new phenomena the viewpoint of representation stability can be useful in solving problems outside the theory in addition to the applications given in this paper it is applied by church ellenberg farb in preparation 20 to counting problems in number theory and finite group theory representation stability is also used by church 2012 19 to give broad generalizations and new proofs of classical homological stability theorems for configuration spaces on oriented manifolds

a rule based method to calculate exactly the widest solution sets of a max min fuzzy relational inequality abstract in this paper we propose a rule based method to calculate exactly all the widest solution sets of a fuzzy relational inequality viewed as an extension of fuzzy relational equations fuzzy relational inequalities can be applied to many fields of fuzzy logic yet they provide with more flexibility as they enable to get rid of the sensitivity of fuzzy relational equations to numerical values up to now however fuzzy relational inequalities have received few attention from researchers and few methods have been proposed to solve these inequalities the proposed analytical methods furthermore do not calculate exactly all the widest solutions sets of a fuzzy relational inequality and often lead to redundant solution sets the rule based method we propose in this paper determines easily exactly all the widest solution sets of a fuzzy relational inequality