extended vikor method in comparison with outranking methods the vikor method was developed to solve mcdm problems with conflicting and noncommensurable different units criteria assuming that compromising is acceptable for conflict resolution the decision maker wants a solution that is the closest to the ideal and the alternatives are evaluated according to all established criteria this method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria and on proposing compromise solution one or more the vikor method is extended with a stability analysis determining the weight stability intervals and with trade offs analysis the extended vikor method is compared with three multicriteria decision making methods topsis promethee and electre a numerical example illustrates an application of the vikor method and the results by all four considered methods are compared

fully supersymmetric hierarchies from an energy dependent super hill operator a super hill operator with energy dependent potentials is proposed and the associated integrable hierarchy is explicitly constructed explicitly it is shown that in the general case the resultant hierarchy is a multi hamiltonian system the miura type transformations and modified hierarchies are also presented

canonical property of the miura maps between the mkp and kp hierarchies continuous and discrete apart from the case of the kp hierarchy all known miura maps between integrable hamiltonian systems had been proven to be canonical the remaining kp case is settled below as a corollary it is shown that the kp hierarchy is a factor hierarchy of the mkp one with the kernel consisting of a single scalar field a discrete mkp hierarchy and the associated miura map are constructed and the latter is shown to be canonical as well as in the continuous case this implies that one can extend the discrete kp hierarchy by a single new field into an extended discrete kp hierarchy in such a way that the extended discrete miura map mkp ekp is a canonical isomorphism

constrained kp hierarchy and bi hamiltonian structures the kakomtsev petviashvili kp hierarchy is considered together with the evolutions of eigenfunctions and adjoint eigenfunctions constraining the kp flows in terms of squared eigenfunctions one obtains 1 1 dimensional integrable equations with scattering problems given by pseudo differential lax operators the bi hamiltonian nature of these systems is shown by a systematic construction of two general poisson brackets on the algebra of associated lax operators gauge transformations provide miura links to modified equations these systems are constrained flows of the modified kp hierarchy for which again a general description of their bi hamiltonian nature is given the gauge transformations are shown to be poisson maps relating the bi hamiltonian structures of the constrained kp hierarchy and the modified kp hierarchy the simplest realization of this scheme yields the akns hierarchy and its miura link to the kaup broer hierarchy

superspaces and supersymmetries a theory of graded banach modules over a banach grassmann algebra is developed and applied to differential geometry of super manifolds the explicit structure of superspaces carrying poincare supersymmetry and extended supersymmetry including central charges is described

structure of basic lie superalgebras and of their affine extensions we generalize to the case of superalgebras several properties of simple lie algebras involving the use of dynkin diagrams if to a simple lie algebra can be associated one dynkin diagram it is a finite set of nonequivalent ones which can be constructed for a basic superalgebra or b s a the knowledge of these diagrams which can be obtained for each b s a in a systematic way allows us to deduce the regular subsuperalgebras of a b s a the symmetries of the dynkin diagrams are related to outer automorphisms of b s a and lead to some singular subsuperalgebras finally we consider the extended dynkin diagrams in order to classify the affine b s a and use their symmetries to construct the twisted basic superalgebras

integration of indifference zone with multi objective computing budget allocation in this paper we consider how to address the issues of having designs with close performance in the multi objective ranking and selection mors problem to resolve this issue we propose integrating the indifference zone iz concept into the multi objective computing budget allocation mocba framework in particular when iz is introduced into the mocba framework we address how to determine the probability of non dominance how to define the pareto set and how to derive allocation rules for the simulation replications empirical results show that the mocba framework with iz can significantly save simulation budget when designs to be compared have close performance

a geometrical formulation of fermionic integrable systems a fermionic hamiltonian system is formulated on a supermanifold it is shown that if the system possesses a bi hamiltonian structure one can naturally define a lax equation associated with a 1 1 tensor on this supermanifold and this allows one to construct a set of conserved quantities furthermore if the corresponding nijenhuis tensor vanishes it is shown that all these conserved quantities would be in involution which is a sufficient condition for integrability of the system the fermionic extension of the kdv equation with a bi hamiltonian structure within this geometrical approach is studied

a fully supersymmetric akns theory we construct a fully supersymmetric bihamiltonian theory in four superfields admitting zero curvature and lax formulation this theory is an extension of the classical akns which can be recovered as a reduction other supersymmetric theories are obtained as reductions of the susy akns namely a nonlinear schrodinger a modified kdv and the manin radul kdv the susy nonlinear schrodinger hierarchy is related to the one of roelofs and kersten we determine its bihamiltonian and lax formulation finally we show that the susy kdv s mentioned before are related through a susy miura map

an experimental comparison of different approaches to determining weights in additive utility models several studies this past decade have examined differences between holistic and decomposed approaches to determining weights in additive utility models some have argued that it matters little which procedure is used whereas others strongly favored particular methods in this paper we address this controversy experimentally by comparing five conceptually different approaches in terms of their weights and predictive ability the five methods are 1 multiple linear and non linear regression analyses of ten and fifteen holistic assessments 2 direct decomposed tradeoffs as proposed by keeney and raiffa keeney r l h raiffa 1977 decisions with multiple objectives wiley new york 3 a recent eigen vector technique of saaty saaty t l 1977 a scaling method for priorities in hierarchical structures j math psych 15 3 234 281 involving redundant pairwise comparisons of attributes 4 a straightforward allocation of hundred importance points and 5 unit weighting i e equal weighting after standardizing the attributes the decision task involved college admissions subjects were asked to evaluate hypothetical college applicants on the basis of verbal sat quantitative sat high school grade point average and a measure of extra curricular activity linear as well as nonlinear attribute utility functions were used in constructing the additive models the nonlinear functions were specified graphically by the subjects through selection from five different shapes i e one per attribute to test the predictive ability of the various models each subject made twenty separate pairwise comparisons of alternatives including direction and strength of preference the prediction criteria were percentage correct predictions as well as correlations using these twenty pairs seventy subjects were tested using an order controlled within subject design in comparing the different methods of weight determination monetary incentives were used to enhance motivation in terms of findings the methods generally differed systematically concerning the weights given to the various attributes as well as the variances of the resulting predictions on average however the methods predicted about equally well except for unit weighting which was clearly inferior the findings differ in this regard from the general literature furthermore nonlinear models were found to be inferior to linear ones finally subjects judged the methods to differ significantly in difficulty and trustworthiness which were found to correlate inversely the overall results raise various applied and theoretical issues which are discussed

the bi hamiltonian structure of fully supersymmetric korteweg de vries systems the bi hamiltonian structure of integrable supersymmetric extensions of the korteweg de vries kdv equation related to then 1 and then 2 superconformal algebras is found it turns out that some of these extensions admit inverse hamiltonian formulations in terms of presymplectic operators rather than in terms of poisson tensors for one extension related to then 2 case additional symmtries are found with bosonic parts that cannot be reduced to symmetries of the classical kdv they can be explained by a factorization of the corresponding lax operator all the bi hamiltonian formulations are derived in a systematic way from the lax operators

a supersymmetric extension of the kadomtsev petviashvili hierarchy an extension of the kadomtsev petviashvili hierarchy by odd variables is given conservation laws and formal integrability are proved

canonical gauge equivalences of the sakns and stb hierarchies we study the gauge transformations between the supersymmetric akns sakns and supersymmetric two boson stb hierarchies the hamiltonian nature of these gauge transformations is investigated which turns out to be canonical we also obtain the darboux backlund transformations for the sakns hierarchy from these gauge transformations

super camassa holm type systems associated to the kuper ramond schwarz superalgebra we describe a class of super integrable systems with a local bi super hamiltonian structure including super camassa holm type systems which can be realized as euler type systems on the dual of the kuper ramond schwarz superalgebra

hamiltonian structures of generalized manin radul super kdv and constrained super kp hierarchies a study of hamiltonian structures associated with supersymmetric lax operators is presented following a constructive approach the hamiltonian structures of inami kanno super kdv hierarchy and constrained modified super kp hierarchy are investigated from the reduced supersymmetric gelfand dickey brackets by applying a gauge transformation on the hamiltonian structures associated with these two nonstandard super lax hierarchies we obtain the hamiltonian structures of generalized manin radul super kdv and constrained super kp hierarchies we also work out a few examples and compare them with the known results

nonstandard drinfeld sokolov reduction subject to some conditions the input data for the drinfeld sokolov construction of kdv type hierarchies is a quadruplet where the are gradations of a loop algebra and is a semisimple element of the nonzero grade a new sufficient condition on the quadruplet under which the construction works is proposed and examples are presented the proposal relies on splitting the grade zero part of into a vector space direct sum of two subalgebras this permits one to interpret certain gelfand dickey type systems associated with a nonstandard splitting of the algebra of pseudodifferential operators in the drinfeld sokolov framework

integrable system constructed out of two interacting superconformal fields we consider an interaction between superconformal fields of the same gradation this entails the construction of a supersymmetric poisson tensor for these fields generating a new class of hamiltonian systems the lax representation is found for one of them by supersymmetrizing the lax operator for the hirota satsuma equation the supersymmetric equation is not reducible to the classical hirota satsuma case we show that our generalized system can be reduced to the the supersymmetric kdv equation a 4 surprisingly the integrals of motion are not reduced to integrals of motion of the supersymmetric kdv equation

on the bihamiltonian structure of the supersymmetric kdv hierarchies a lie superalgebraic approach we give a lie superalgebraic interpretation of the bihamiltonian structure of known supersymmetric kdv equations we show that the loop algebra of a lie superalgebra carries a natural poisson pencil and we subsequently deduce the bihamiltonian structure of the supersymmetric kdv hierarchies by applying to loop superalgebras an appropriate reduction technique this construction can be regarded as a superextension of the drinfeld sokolov method for building a kdv type hierarchy from a simple lie algebra

degree and component size distributions in the generalized uniform recursive tree we propose a generalized model for the famous uniform recursive tree urt by introducing an imperfect growth process which may generate disconnected components clusters the model undergoes an interesting phase transition from a singly connected network to a graph consisting of fully isolated nodes we investigate the distributions of degree and component sizes by both theoretical predictions and numerical simulations for the nontrivial cases we show that the network has an exponential degree distribution while its component size distribution follows a power law both of which are related to the imperfect growth process we also predict the growth dynamics of the individual components all analytical solutions are successfully contrasted with computer simulations

a multiple attribute utility theory approach to ranking and selection managers of large industrial projects often measure performance by multiple attributes for example our paper is motivated by the simulation of a large industrial project called a land seismic survey in which project performance is based on duration cost and resource utilization to address these types of problems we develop a ranking and selection procedure for making comparisons of systems e g project configurations that have multiple performance measures the procedure combines multiple attribute utility theory with statistical ranking and selection to select the best configuration from a set of possible configurations using the indifference zone approach we apply our procedure to results generated by the simulator for a land seismic survey that has six performance measures and describe a particular type of sensitivity analysis that can be used as a robustness check

aggregation of utility based individual preferences for group decision making abstract multi attribute utility theory maut elicits an individual decision maker s preferences for single attributes and develops a utility function by mathematics formulation to add up the preferences of the entire set of attributes when assessing alternatives a common aggregation method of maut for group decisions is the simple additive weighting saw method which does not consider the different preferential levels and preferential ranks for individual decision makers assessments of alternatives in a decision group and thus seems too intuitive in achieving the consensus and commitment for group decision aggregation in this paper the preferential differences denoting the preference degrees among different alternatives and preferential priorities denoting the favorite ranking of the alternatives for each decision maker are both considered and aggregated to construct the utility discriminative values for assessing alternatives in a decision group a comparative analysis is performed to compare the proposed approach to the saw model and a satisfaction index is used to investigate the satisfaction levels of the final two resulting group decisions in addition a feedback interview is conducted to understand the subjective perceptions of decision makers while examining the results obtained from these two approaches for the second practical case both investigation results show that the proposed approach is able to achieve a more satisfying and agreeable group decision than that of the saw method

on the backlund transformation for the gel fand dickey equations we study the backlund transformation of the gel fand dickey equations and in particular how the factorization ofnth order differential operators leads to lax type equations for first order operators generalizing work of adler and moser 1 in a similar fashion we study the toda equations

solving the kp hierarchy by gauge transformations we show that it is convenient to use gauge transformations sometimes called explicit backlund transformations to generate new solutions for the kp hierarchy two particular kinds of gauge transformation operators constructed out of the initial wave functions are of fundamental importance in this approach through such gauge transformations a very simple formula for the tau function is obtained encompassing and unifying all kinds of existing solutions the corresponding free fermion representation and baker functions for the new function can also be constructed

backlund transformations for the kp and mkp hierarchies with self consistent sources using gauge transformations for the corresponding generating pseudo differential operators ln in terms of eigenfunctions and adjoint eigenfunctions we construct several types of auto backlund transformations for the kp hierarchy with self consistent sources kphscs and mkp hierarchy with self consistent sources mkphscs respectively the backlund transformations from kphscs to mkphscs are also constructed in this way

riemann liouville integrals of fractional order and extended kp hierarchy an attempt to formulate the extensions of the kp hierarchy by introducing fractional order pseudo differential operators is given in the case of the extension with the half order pseudo differential operators a system analogous to the supersymmetric extensions of the kp hierarchy is obtained unlike the supersymmetric extensions no grassmannian variable appears in the hierarchy considered here more general hierarchies constructed by the 1 nth order pseudo differential operators their integrability and the reduction procedure are also investigated in addition to finding the new extensions of the kp hierarchy a brief introduction to the riemann liouville integral is provided to yield a candidate for the fractional order pseudo differential operators

a note on the gauge equivalence between the manin radul and laberge mathieu super kdv hierarchies the gauge equivalence between the manin radul and laberge mathieu super kdv hierarchies is revisited apart from the inami kanno transformation we show that there is another gauge transformation which also possesses the canonical property we explore the relationship of these two gauge transformations from the kupershmidt wilson theorem viewpoint and as a by product obtain the darboux backlund transformation for the manin radul super kdv hierarchy the geometrical intepretation of these transformations is also briefly discussed

n extended superelliptic integrable systems a supersymmetric extension for an arbitrary number of odd parameters of the stationary kdv equation is studied we call this an n extended super kdv it is shown that it is related to superelliptic curves and thereafter the complete ring of superdifferential operators commuting with the associated schrodinger operator is constructed

mathematics of dispersive water waves a commuting hierarchy of dispersive water wave equations makes a three hamiltonian system which belongs to a general class of nonstandard integrable systems whose theory is developed the modified water wave hierarchy is a bi hamiltonian system its modification bifurcates the water wave hierarchy and the hierarchies of the korteweg de vries and the modified korteweg de vries equations as well as the classical miura map are given new representations through various specializations of nonstandard systems

darboux theorems and wronskian formulas for integrable systems i constrained kp flows abstract generalizations of the classical darboux theorem are established for pseudo differential scattering operators of the form l i 0 n u i i i 1 m i 1 i i iteration of the darboux transformations leads to a gauge transformed operator with coefficients given by wronskian formulas involving a set of eigenfunctions of l nonlinear integrable partial differential equations are associated with the scattering operator l which arise as a symmetry reduction of the multicomponent kp hierarchy with a suitable linear time evolution for the eigenfunctions the darboux transformation is used to obtain solutions of the integrable equations in terms of wronskian determinants

an operator valued extension of the super korteweg de vries equations an extension of the super korteweg de vries kdv integrable system in terms of operator valued functions is obtained following the ideas of gardner a general algebraic approach for finding the infinitely many conserved quantities of integrable systems is presented the approach is applied to the above described system and infinitely many conserved quantities are constructed in a particular case they reduce to the corresponding conserved quantities of super kdv

supersymmetric drinfeld sokolov reduction the drinfeld sokolov construction of integrable hierarchies as well as its generalizations may be extended to the case of loop superalgebras a sufficient condition on the algebraic data for the resulting hierarchy to be invariant under supersymmetry transformation is given the method used is a construction of the hierarchies in superspace where supersymmetry is manifest several examples are discussed

lie superalgebraic approach to super toda lattice and generalized super kdv equations we propose a super lax type equation based on a certain class of lie superalgebra as a supersymmetric extension of generalized modified kdv hierarchy we are able to construct an infinite set of conservation laws and the consistent time evolution generators for generalized modified super kdv equations thefirst few of the conserved currents the modified super kdv equation and the super miura transformation are worked out explicitly in the case of twisted affine lie superalgebraosp 2 2 2

the extended supersymmetrization of the multicomponent kadomtsev petviashvilli hierarchy we describe three different approaches to the extended n 2 supersymmetrization of the multicomponent kp hierarchy in the first one we utilize only superfermions while in the second only superbosons and in the third superbosons as well as superfermions it is shown that many soliton equations can be embedded in the supersymmetry theory by using the first approach even if we do not change these equations in the bosonic limit of the supersymmetry in the second or third approach we obtain a generalization of the soliton equations in the bosonic limit which remains in the class of the usual commuting functions as a byproduct of our analysis we prove that for the first procedure the bosonic part of the one component supersymmetric kp hierarchy coincides with the usual classical two component kp hierarchy

additional symmetries of supersymmetric kp hierarchies we investigate the additional symmetries of several supersymmetric kp ierarchiess the skp hierarcy of manin and radul the skp2 hierarchy and the jacobian skp hierarchy in all three cases we find that the algebra of symmetries is isomorphic to the algebra of supperdifferential operators or equivalentlysw1 these results seem to suggest that despite their realization depending on the dynamics the additional symmetries are kinematical in nature

ranking and selection for multiple performance measures using incomplete preference information abstract this paper presents two new procedures for ranking and selection r s problems where the best system designs are selected from a set of competing ones based on multiple performance measures evaluated through stochastic simulation in the procedures the performance measures are aggregated with a multi attribute utility function and incomplete preference information regarding the weights that reflect the relative importance of the measures is taken into account a set of feasible weights is determined according to preference statements that are linear constraints on the weights given by a decision maker non dominated designs are selected using two dominance relations referred to as pairwise and absolute dominance based on estimates for the expected utilities of the designs over the feasible weights the procedures allocate a limited number of simulation replications among the designs such that the probabilities of correctly selecting the pairwise and absolutely non dominated designs are maximized the new procedures offer ease of eliciting the weights compared with existing r s procedures that aggregate the performance measures using unique weights moreover computational advantages are provided over existing procedures that identify non dominated designs based on the expected values of the performance measures the new procedures allow to obtain a smaller number of non dominated designs they also identify these designs correctly with a higher probability or require a smaller number of replications for correct selection finally the new procedures allocate a larger number of replications to the non dominated designs that are therefore evaluated with greater accuracy these computational advantages are illustrated through several numerical experiments

symmetries of supersymmetric integrable hierarchies of kp type this article is devoted to the systematic study of additional non isospectral symmetries of constrained reduced supersymmetric integrable hierarchies of kp type the so called skp r mb mf models the latter are supersymmetric extensions of ordinary constrained kp hierarchies which contain as special cases basic integrable systems such as m kdv akns fordy kulish yajima oikawa etc as a first main result it is shown that any skp r mb mf hierarchy possesses two different mutually anti commuting types of superloop superalgebra additional symmetries corresponding to the positive and negative grade parts of certain superloop superalgebras the second main result is the systematic construction of the full algebra of additional virasoro symmetries of skp r mb mf hierarchies which requires nontrivial modifications of the virasoro flows known from the general case of unconstrained manin radul super kp hierarchies the latter flows do not define symmetries for constrained skp r mb mf hierarchies as

solvability of the super kp equation and a generalization of the birkhoff decomposition the unique solvability of the initial value problem for the total hierarchy of the super kadomtsev petviashvili system is established to prove the existence we use a generalization of the birkhoff decomposition which is obtained by replacing the loop variable and loop groups in the original setting by a super derivation operator and groups of infinite order super micro i e pseudo differential operators to show the uniqueness we generalize the fact that every flat connection admits horizontal sections to the case of an infinite dimensional super algebra bundle defined over an infinite dimensional super space the usual kp system with non commutative coefficients is also studied the kp system is obtained from the super kp system by reduction modulo odd variables on the other hand the first modified kp equation can be obtained from the super kp system by elimination of odd variables thus the super kp system is a natural unification of the kp system and the modified kp systems

miura map between lattice kadomtsev petviashvili and its modification is canonical we consider the miura map between the lattice kadomtsev petviashvili hierarchy and the lattice modified kp hierarchy and prove that the map is canonical not only between the first hamiltonian structures but also between the second hamiltonian structures

percolation on hyperbolic lattices the percolation transitions on hyperbolic lattices are investigated numerically using finite size scaling methods the existence of two distinct percolation thresholds is verified at the lower threshold an unbounded cluster appears and reaches from the middle to the boundary this transition is of the same type and has the same finite size scaling properties as the corresponding transition for the cayley tree at the upper threshold on the other hand a single unbounded cluster forms which overwhelms all the others and occupies a finite fraction of the volume as well as of the boundary connections the finite size scaling properties for this upper threshold are different from those of the cayley tree and two of the critical exponents are obtained the results suggest that the percolation transition for the hyperbolic lattices forms a universality class of its own

supersymmetric extension of the korteweg de vries equation it is shown that among a one parameter family of supersymmetric extensions of the korteweg de vries equation there is a special system that has an infinite number of conservation laws which can be formulated in the second hamiltonian structure and which has a nontrivial lax representation its modified version is also discussed

a supertrace identity and its applications to superintegrable systems a supertrace identity on lie superalgebras is established it provides a tool for constructing super hamiltonian structures of zero curvature equations associated with lie superalgebras applications in the case of the lie superalgebra b 0 1 present super hamiltonian structures of a super akns soliton hierarchy and a super dirac soliton hierarchy

the geometry of the super kp flows a supersymmetric generalization of the krichever map is used to construct algebro geometric solutions to the various super kadomtsev petviashvili skp hierarchies the geometric data required consist of a suitable algebraic supercurve of genusg generallynot a super riemann surface with a distinguished point and local coordinates z there and a generic line bundle of degreeg 1 with a local trivialization near the point the resulting solutions to the manin radul skp system describe coupled deformations of the line bundle and the supercurve itself in contrast to the ordinary kp system which deforms line bundles but not curves two new skp systems are introduced an integrable jacobian system whose solutions describe genuine jacobian flows deforming the bundle but not the curve and a nonintegrable maximal system describing independent deformations of bundle and curve the kac van de leur skp system describes the same deformations as the maximal system but in a different parametrization

economic analysis of simulation selection problems ranking and selection procedures are standard methods for selecting the best of a finite number of simulated design alternatives based on a desired level of statistical evidence for correct selection but the link between statistical significance and financial significance is indirect and there has been little or no research into it this paper presents a new approach to the simulation selection problem one that maximizes the expected net present value of decisions made when using stochastic simulation we provide a framework for answering these managerial questions when does a proposed system design whose performance is unknown merit the time and money needed to develop a simulation to infer its performance for how long should the simulation analysis continue before a design is approved or rejected we frame the simulation selection problem as a stoppable version of a bayesian bandit problem that treats the ability to simulate as a real option prior to project implementation for a single proposed system we solve a free boundary problem for a heat equation that approximates the solution to a dynamic program that finds optimal simulation project stopping times and that answers the managerial questions for multiple proposed systems we extend previous bayesian selection procedures to account for discounting and simulation tool development costs

remarks on the complete integrability of dynamical systems with fermionic variables the authors study the role of 1 1 graded tensor field t in the analysis of complete integrability of dynamical systems with fermionic variables they find that such a tensor t can be a recursion operator if and only if t is even as a graded map namely if and only if p t 0 they clarify this fact by constructing an odd tensor for two examples a supersymmetric toda chain and a supersymmetric harmonic oscillator they explicitly show that it cannot be a recursion operator since it does not allow new constants of motion to be built from the first two in contrast to what usually happens with ordinary i e nongraded systems

the zero curvature formulation of the skdv equations the fermionic extensions of the kdv equation are derived from the zero curvature condition associated with the superalgebra osp 2 1 this derivation clarifies why there are only two such extensions possible and why only one of them is supersymmetric a lenard type of derivation of these equations is also presented

computing efforts allocation for ordinal optimization and discrete event simulation ordinal optimization has emerged as an efficient technique for simulation and optimization exponential convergence rates can be achieved in many cases in this paper we present a new approach that can further enhance the efficiency of ordinal optimization our approach intelligently determines the optimal number of simulation replications or samples and significantly reduces the total simulation cost numerical illustrations are included the results indicate that our approach can obtain an additional 74 computation time reduction above and beyond the reduction obtained through the use of ordinal optimization for a 10 design example

bosonic reduction of susy generalized harry dym equation in this paper we construct the two component supersymmetric generalized harry dym equation which is integrable and study various properties of this model in the bosonic limit in particular in the bosonic limit we obtain a new integrable system which under a hodograph transformation reduces to a coupled three component system we show how the hamiltonian structure transforms under a hodograph transformation and study the properties of the model under a further reduction to a two component system we find a third hamiltonian structure for this system which has been shown earlier to be a bi hamiltonian system making this a genuinely tri hamiltonian system the connection of this system to the modified dispersive water wave equation is clarified we also study various properties in the dispersionless limit of our model

classical n 2 w superalgebras from superpseudodifferential operators we study the supersymmetric gelfand dickey algebras associated with the superpseudodifferential operators of positive as well as negative leading order we show that upon the usual constraint these algebras contain the n 2 super virasoro algebra as a subalgebra when the leading order is odd the decompositions of the coefficient functions into n 1 primary fields are then obtained by covariantizing the superpseudodifferential operators we discuss the problem of identifying n 2 supermultiplets and work out a couple of supermultiplets by explicit computations

selecting a selection procedure selection procedures are used in a variety of applications to select the best of a finite set of alternatives best is defined with respect to the largest mean but the mean is inferred with statistical sampling as in simulation optimization there are a wide variety of procedures which begs the question of which selection procedure to select the main contribution of this paper is to identify through extensive experimentation the most effective selection procedures when samples are independent and normally distributed we also a summarize the main structural approaches to deriving selection procedures b formalize new sampling allocations and stopping rules c identify strengths and weaknesses of the procedures d identify some theoretical links between them and e present an innovative empirical test bed with the most extensive numerical comparison of selection procedures to date the most efficient and easiest to control procedures allocate samples with a bayesian model for uncertainty about the means and use new adaptive stopping rules proposed here

on the bi hamiltonian structures of the skdv the first and the second hamiltonian structures of the supersymmetric kdv equation are derived following the conventional approach of gel fand and dickey in particular it is shown that the nonlocal nature of the first bracket is a direct consequence of the constrained nature of the lax operator

percolation transition in a dynamically clustered network we consider a percolationlike phenomenon on a generalization of the barab asi albert model where a modification of the growth dynamics directly allows formation of disconnected clusters the transition is located with high precision by an original numerical technique based on the comparison of the largest and second largest clusters a careful investigation focusing on finite size scaling allows us to highlight properties which would hardly be accessible by an analytical solution of cluster growth equations in the stationary limit our analysis shows that some critical features of the percolation transition are different from those observed in the case of dilution in fully grown networks at variance with other models of percolation on growing networks we also find evidence that the order parameter approaches zero as a power of the field p ensuremath p c driving the transition rather than as a stretched exponential this behavior does not agree with the berezinskii kosterlitz thouless scenario found in other similar models for describing the phase in which a giant cluster develops a key role is played by the crossover number of nodes n x ensuremath sim p ensuremath p c ensuremath ensuremath zeta with ensuremath zeta ensuremath simeq 4 this power law behavior and that of other quantities are conjectured on the basis of scaling arguments and numerical evidence

on the miura map between the dispersionless kp and dispersionless modified kp hierarchies the miura map between the dispersionless kp and dispersionless modified kp hierarchies is investigated it is shown that the miura map is canonical with respect to their bi hamiltonian structures moreover inspired by the works of takasaki and takebe the twistor construction of solution structure for the dispersionless modified kp hierarchy is given

on the equivalence of two super korteweg devries theories a bi hamiltonian viewpoint from a bi hamiltonian viewpoint the equivalence of two supersymmetric korteweg devries theories introduced by manin radul and laberge mathieu is discussed herein it is shown that the transformation connecting the two theories proposed recently in the literature preserves the bi hamiltonian structures moreover another derivation of this transformation stemming from bi hamiltonian reduction theory and strongly emphasizing the geometrical meaning of the above equivalence is presented

canonical miura maps between the modified kp and kp hierarchies we investigate the hamiltonian nature of two miura maps between the modified kp and kp hierarchies we show that they are canonical in the sense that the bi hamiltonian structure of the modified kp hierarchy is mapped to the bi hamiltonian structure of the kp hierarchy