neel xxz state overlaps odd particle numbers and lieb liniger scaling limit we specialize a recently proposed determinant formula brockmann de nardis wouters and caux 2014 j phys a math theor 47 145003 for the overlap of the zero momentum n el state with bethe states of the spin 1 2 xxz chain to the case of an odd number of downturned spins showing that it is still of gaudin like form similar to the case of an even number of down spins we generalize this result to the overlap of q raised n el states with parity invariant bethe states lying in a nonzero magnetization sector the generalized determinant expression can then be used to derive the corresponding determinants and their prefactors in the scaling limit to the lieb liniger ll bose gas the odd number of down spins directly translates to an odd number of bosons we furthermore give a proof that the n el state has no overlap with non parity invariant bethe states this is based on a determinant expression for overlaps with general bethe states that was obtained in the context of the xxz chain with open boundary conditions pozsgay 2013 arxiv 1309 4593 kozlowski and pozsgay 2012 j stat mech p05021 tsuchiya 1998 j math phys 39 5946 the statement that overlaps with non parity invariant bethe states vanish is still valid in the scaling limit to ll which means that the bose einstein condensate state de nardis wouters brockmann and caux 2014 phys rev a 89 033601 has zero overlap with non parity invariant ll bethe states

the arctic curve of the domain wall six vertex model the problem of the form of the arctic curve of the six vertex model with domain wall boundary conditions in its disordered regime is addressed it is well known that in the scaling limit the model exhibits phase separation with regions of order and disorder sharply separated by a smooth curve called the arctic curve to find this curve we study a multiple integral representation for the emptiness formation probability a correlation function devised to detect spatial transition from order to disorder we conjecture that the arctic curve for arbitrary choice of the vertex weights can be characterized by the condition of condensation of almost all roots of the corresponding saddle point equations at the same known value in explicit calculations we restrict to the disordered regime for which we have been able to compute the scaling limit of certain generating function entering the saddle point equations the arctic curve is obtained in parametric form and appears to be a non algebraic curve in general it turns into an algebraic one in the so called root of unity cases the arctic curve is also discussed in application to the limit shape of q enumerated with 0 q 4 large alternating sign matrices in particular as q 0 the limit shape tends to a nontrivial limiting curve given by a relatively simple equation

exact formulas for the form factors of local operators in the lieb liniger model we present exact formulas for the form factors of local operators in the repulsive lieb liniger model at finite size these are essential ingredients for both numerical and analytical calculations from the theory of algebraic bethe ansatz it is known that the form factors of local operators satisfy a particular type of recursive relations we show that in some cases these relations can be used directly to derive practical expressions in terms of the determinant of a matrix whose dimension scales linearly with the system size our main results are determinant formulas for the form factors of the operators and r 0 for arbitrary integer r where are the usual field operators from these expressions we also derive the infinite size limit of the form factors of these local operators in the attractive regime

algebraic bethe ansatz for the gl 1 2 generalized model ii the three gradings the algebraic bethe ansatz can be performed rather abstractly for whole classes of models sharing the same r matrix the only prerequisite being the existence of an appropriate pseudo vacuum state here we perform the algebraic bethe ansatz for all models with 9 9 rational gl 1 2 invariant r matrix and all three possibilities of choosing the grading our bethe ansatz solution applies for instance to the supersymmetric t j model the supersymmetric u model and a number of interesting impurity models it may be extended to obtain the quantum transfer matrix spectrum for this class of models the properties of a specific model enter the bethe ansatz solution i e the expression for the transfer matrix eigenvalue and the bethe ansatz equations through the three pseudo vacuum eigenvalues of the diagonal elements of the monodromy matrix which in this context are called the parameters of the model

normal ordering in the theory of correlation functions of exactly solvable models we study models of quantum statistical mechanics which can be solved by the algebraic bethe ansatz the general method of calculating correlation functions is based on the method of determinant representations the auxiliary fock space and auxiliary bose fields are introduced in order to remove the two body scattering and represent correlation functions as a mean value of a determinant of a fredholm integral operator the representation has a simple form for large space and time separations in this paper we explain how to calculate the mean value in the auxiliary fock space of an asymptotic expression of the fredholm determinant it is necessary for the evaluation of the asymptotic form of the physical correlation functions

a kind of logical compilation for knowledge bases the forward chaining algorithm is perhaps the best known algorithm in expert systems however it is not complete because it cannot compute the two valued consequence literals of a propositional knowledge base i e set of rules with negations if the user wants to compute them he must use a particular algorithm which often takes much time we propose a compilation system for knowledge bases which we call logical compilation which allows us to compute the two valued consequence literals of a knowledge base i e set of rules using a forward chaining on the compiled base with any extensional knowledge base i e set of basic facts added we also use this compilation in a wide propositional calculus and solve the or problem in rule conclusion we present several methods with their benefits to make this compilation and we give properties on knowledge bases to avoid this compilation finally we give a theorem which defines incremental compilation

six vertex model with partial domain wall boundary conditions ferroelectric phase we obtain an asymptotic formula for the partition function of the six vertex model with partial domain wall boundary conditions in the ferroelectric phase region the proof is based on a formula for the partition function involving the determinant of a matrix of mixed vandermonde hankel type this determinant can be expressed in terms of a system of discrete orthogonal polynomials which can then be evaluated asymptotically by comparison with the meixner polynomials

inhomogeneous six vertex model with domain wall boundary conditions and bethe ansatz in this note we consider the six vertex model with domain wall boundary conditions defined on an m m lattice in the inhomogeneous case where the partition function depends on 2m inhomogeneities j and k for a particular choice of the set of j we find a new determinant representation for the partition function which allows evaluation of the bulk free energy in the thermodynamic limit this provides a new connection between two types of determinant formulas we also show in a special case that spin correlations on the horizontal line going through the center coincide with the ones for periodic boundary conditions

algebraic arctic curves in the domain wall six vertex model the arctic curve i e the spatial curve separating ordered or frozen and disordered or temperate regions of the six vertex model with domain wall boundary conditions is discussed for the root of unity vertex weights in these cases the curve is described by algebraic equations which can be worked out explicitly from the parametric solution for this curve some interesting examples are discussed in detail the upper bound on the maximal degree of the equation in a generic root of unity case is obtained

on the interaction of the responses at the resonance frequencies of a nonlinear two degrees of freedom system this paper describes the dynamic behaviour of a coupled system which includes a nonlinear hardening system driven harmonically by a shaker the shaker is modelled as a linear single degree of freedom system and the nonlinear system under test is modelled as a hardening duffing oscillator the mass of the nonlinear system is much less than the moving mass of the shaker and thus the nonlinear system has little effect on the shaker dynamics the nonlinearity is due to the geometric configuration consisting of a mass suspended on four springs which incline as they are extended following experimental validation the model is used to explore the dynamic behaviour of the system under a range of different conditions of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the shaker such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the shaker it is found that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur closed detached curves can appear as a part of the overall amplitude frequency response these detached curves can lie outside or inside the main resonance curve and a physical explanation for their occurrence is given

on form factors in nested bethe ansatz systems we investigate form factors of local operators in a multi component quantum nonlinear schrodinger model a prototype theory solvable by the so called nested bethe ansatz we determine the analytic properties of the infinite volume form factors using the coordinate bethe ansatz solution and establish a connection with the finite volume matrix elements in the two component models we derive a set of recursion relations for the magnonic form factors which are the matrix elements on the nested bethe ansatz states in certain simple cases involving states with only one spin impurity we obtain explicit solutions for the recursion relations

an assumption based tms abstract this paper presents a new view of problem solving motivated by a new kind of truth maintenance system unlike previous truth maintenance systems which were based on manipulating justifications this truth maintenance system is in addition based on manipulating assumption sets as a consequence it is possible to work effectively and efficiently with inconsistent information context switching is free and most backtracking and all retraction is avoided these capabilities motivate a different kind of problem solving architecture in which multiple potential solutions are explored simultaneously this architecture is particularly well suited for tasks where a reasonable fraction of the potential solutions must be explored

boundary correlation functions of the six vertex model we consider the six vertex model on an n n square lattice with the domain wall boundary conditions boundary one point correlation functions of the model are expressed as determinants of n n matrices generalizing the known result for the partition function in the free fermion case explicit answers are obtained the introduced correlation functions are closely related to the problem of enumeration of alternating sign matrices and domino tilings

normalization of bethe ansatz states in the chiral invariant gross neveu model the norms of the bethe ansatz eigenstates of the chiral invariant gross neveu hamiltonian are calculated

semi classical analysis of the inner product of bethe states we study the inner product of two bethe states one of which is taken on shell in an inhomogeneous xxx chain in the sutherland limit where the number of magnons is comparable with the length l of the chain and the magnon rapidities arrange in a small number of macroscopically large bethe strings the leading order in the large l limit is known to be expressed through a contour integral of a dilogarithm here we derive the sub leading term our analysis is based on a new contour integral representation of the inner product in terms of a fredholm determinant we give two derivations of the sub leading term besides a direct derivation by solving a riemann hilbert problem we give a less rigorous but more intuitive derivation by field theoretical methods for that we represent the fredholm determinant as an expectation value in a fock space of chiral fermions and then bosonize we construct a collective field for the bosonized theory the short wave length part of which may be evaluated exactly while the long wave length part is amenable to a 1 l expansion our treatment thus results in a systematic 1 l expansion of structure factors within the sutherland limit

boxed skew plane partition and integrable phase model we study the relation between the boxed skew plane partition and the integrable phase model we introduce a generalization of a scalar product of the phase model and calculate it in two ways the first one in terms of the skew schur functions and the other one by use of the commutation relations of operators in both cases a generalized scalar product is expressed as a determinant we show that a special choice of the spectral parameters of a generalized scalar product gives the generating function of the boxed skew plane partition

norms of bethe wave functions for the nonlinear schrodinger model of spin 1 2 particles a formula for scalar products of bethe wave functions in the nonlinear schrodinger model of spin 1 2 particles is proposed it is shown in addition that one can replace conjugate states by dual eigenfunctions to calculate correlation functions for integrable systems

quantum projectors and local operators in lattice integrable models in the framework of the quantum inverse scattering method we consider a problem of constructing local operators for one dimensional quantum integrable models especially for the lattice versions of the nonlinear schrodinger and sine gordon models we show that a certain class of local operators can be constructed from the matrix elements of the monodromy matrix in a simple way they are closely related to the quantum projectors and have nice commutation relations with half of the matrix elements of the elementary monodromy matrix the form factors of these operators can be calculated by using the standard algebraic bethe ansatz techniques

dynamics and energy exchanges between a linear oscillator and a nonlinear absorber with local and global potentials abstract the dynamical behavior of a two degree of freedom system made up of a linear oscillator and a coupled nonlinear energy sink with nonlinear global and local potentials is studied the nonlinear global potential of the energy sink performs direct interactions with the linear oscillator while its local potential depends only on its own behavior during vibratory energy exchanges between two oscillators a time multiple scale method around 1 1 1 resonance is used to detect slow invariant manifold of the system its equilibrium and singular points detected equilibrium points permit us to predict periodic regime s while singular points can lead the system to strongly modulated responses characterized by persistent bifurcations several possible scenarios occurring during these strongly modulated regimes are highlighted all analytical predictions are compared with those which are obtained by direct numerical integration of system equations

combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice we introduce and study several combinatorial properties of a class of symmetric polynomials from the point of view of integrable vertex models in a finite lattice we introduce the l operator related to the uq sl2 r matrix and construct the wavefunctions and their duals we prove the exact correspondence between the wavefunctions and symmetric polynomials which is a quantum group deformation of the grothendieck polynomials this is proved by combining the matrix product method and an analysis on the domain wall boundary partition functions as applications of the correspondence between the wavefunctions and symmetric polynomials we derive several properties of the symmetric polynomials such as the determinant pairing formulas and the branching formulas by analyzing the domain wall boundary partition functions and the matrix elements of the b operators

determinant formula for the field form factor in the anyonic lieb liniger model we derive an exact formula for the field form factor in the anyonic lieb liniger model valid for arbitrary values of the interaction c anyonic parameter kappa and number of particles n analogously to the bosonic case the form factor is expressed in terms of the determinant of a n times n matrix whose elements are rational functions of the bethe quasimomenta but explicitly depend on kappa the formula is efficient to evaluate and provide an essential ingredient for several numerical and analytical calculations its derivation consists of three steps first we show that the anyonic form factor is equal to the bosonic one between two special emph off shell bethe states in the standard lieb liniger model second we characterize its analytic properties and provide a set of conditions that uniquely specify it finally we show that our determinant formula satisfies these conditions

extended trigonometric cherednik algebras and nonstationary schrodinger equations with delta potentials we realize an extended version of the trigonometric cherednik algebra as affine dunkl operators involving heaviside functions we use the quadratic casimir element of the extended trigonometric cherednik algebra to define an explicit nonstationary schrodinger equation with delta potential we use coordinate bethe ansatz methods to construct solutions of the nonstationary schrodinger equation in terms of generalized bethe wave functions it is shown that the generalized bethe wave functions satisfy affine difference knizhnik zamolodchikov equations as functions of the momenta the relation to the vector valued root system analogs of the quantum bose gas on the circle with delta function interactions is indicated

scalar products of bethe vectors in models with mathfrak gl 2 1 symmetry 1 super analog of reshetikhin formula we study scalar products of bethe vectors in integrable models solvable by nested algebraic bethe ansatz and possessing mathfrak gl 2 1 symmetry using explicit formulas of the monodromy matrix entries multiple actions onto bethe vectors we obtain a representation for the scalar product in the most general case this explicit representation appears to be a sum over partitions of the bethe parameters it can be used for the analysis of scalar products involving on shell bethe vectors as a by product we obtain a determinant representation for the scalar products of generic bethe vectors in integrable models with mathfrak gl 1 1 symmetry

fine structure of the asymptotic expansion of cyclic integrals the asymptotic expansion of n dimensional cyclic integrals was expressed as a series of functionals acting on the symmetric function involved in the cyclic integral in this article we give an explicit formula for the action of these functionals on a specific class of symmetric functions these results are necessary for the computation of the o 1 part in the long distance asymptotic behavior of correlation functions in integrable models

determinant representation for dynamical correlation functions of the quantum nonlinear schrodinger equation painleve analysis of correlation functions of the impenetrable bose gas by m jimbo t miwa y mori and m sato 1 was based on the determinant representation of these correlation functions obtained by a lenard 2 the impenetrable bose gas is the free fermionic case of the quantum nonlinear schrodinger equation in this paper we generalize the lenard determinant representation for langle psi 0 0 psi dagger x t rangle to the non free fermionic case we also include time and temeprature dependence in forthcoming publications we shall perform the jmms analysis of this correlationl function this will give us a completely integrable equation and asymptotic for the quantum correlation function of interacting fermions

gaudin hypothesis for the xyz spin chain the xyz spin chain is considered within the framework of the generalized algebraic bethe ansatz developed by takhtajan and faddeev the sum of norms of the bethe vectors is computed and expressed in the form of a jacobian this result corresponds to the gaudin hypothesis for the xyz spin chain

dual field formulation of quantum integrable models equal time correlators are studied in completely integrable models the main example is the quantum non linear schrodinger equation introduction of an auxiliary fock space permits us to represent the generating functional of correlators in the form of a determinant of the integral operator

a simple lattice version of the nonlinear schrodinger equation and its deformation with an exact quantum solution a lattice version of the quantum nonlinear schrodinger nls equation is considered which has a significant simple form and fulfils most of the criteria desirable for such lattice variants of field models unlike most of the known lattice nls equations the present model belongs to a class which does not exhibit the usual symmetry properties however this lack of symmetry itself seems to be responsible for the remarkable simplification of the relevant objects in the theory such as the lax operator the hamiltonian and other commuting conserved quantities as well as their spectra the model allows exact quantum solution through the algebraic bethe ansatz and also a straightforward and natural generalization to the vector case thus giving a new exact lattice version of the vector nls model a deformation representing a new quantum integrable system involving tamm dancoff like q boson operators is constructed

determinant representation of correlation functions for the uq gl 1 1 free fermion model with the help of the factorizing f matrix the scalar products of the uq gl 1 1 free fermion model are represented by determinants by means of these results we obtain the determinant representations of correlation functions of the model

dynamics of multiple degree of freedom oscillators with colliding components abstract an analysis is presented for determining exact steady state response for a class of strongly non linear multiple degree of freedom oscillators these oscillators consist of a linear component with an arbitrary number of degrees of freedom and configuration incorporating a component with a geometric non linearity their behavior is analyzed by generalizing previous work on single and two degree of freedom piecewise linear systems under harmonic excitation first a methodology is developed for locating harmonic and subharmonic response characterized by one abrupt change of the parameters of the non linear element per response cycle then a stability analysis is presented which is appropriate for general piecewise linear systems the present analysis is applicable to a variety of engineering areas here its validity and effectiveness is demonstrated by applying it to two classes of problems with large practical significance and rich dynamics performance of vibration absorbers with elastic stops is investigated first while in the second category of examples the oscillators exhibit 2 1 and 3 1 internal resonance regular and irregular motions are encountered and analyzed the response characteristics are compared with those of systems with continuous non linearities

the riemann hilbert problem associated with the quantum nonlinear schrodinger equation we consider the dynamical correlation functions of the quantum nonlinear schrodinger equation in a previous paper we found that the dynamical correlation functions can be described by the vacuum expectation value of an operator valued fredholm determinant in this paper we show that a riemann hilbert problem can be associated with this fredholm determinant this riemann hilbert problem formulation permits us to write down completely integrable equations for the fredholm determinant and to perform an asymptotic analysis for the correlation function

programming in three valued logic abstract the aim of this paper is to propose a logical and algebraic theory which seems well suited to logic programs with negation and deductive databases this theory has similar properties to those of prolog theory limited to programs with horn clauses and thus can be considered as an extension of the usual theory this parallel with logic programming without negation lies in the introduction of a third truth value indefinite and of a new non monotonic implication connective our proposition is different from the other ways of introducing a third truth value already used in logic programming and databases but it is somehow related to some of them especially to fitting s theory we introduce a consequence operator associated with a logic program with negation which extends the operator of apt and van emden in the case of a consistent program the post fixpoints of this operator are the models of the program as they are usually this operator is related to fitting s one the relation being obtained by completing the program we finally give an operational semantics for a program with negation by the obtention of a three valued interpreter from a bivalued one

arctic curves in path models from the tangent method recently colomo and sportiello introduced a powerful method known as the tangent method for computing the arctic curve in statistical models which have a non or weakly intersecting lattice path formulation we apply the tangent method to compute arctic curves in various models the domino tiling of the aztec diamond for which we recover the celebrated arctic circle a model of dyck paths equivalent to the rhombus tiling of a half hexagon for which we find an arctic half ellipse another rhombus tiling model with an arctic parabola the vertically symmetric alternating sign matrices where we find the same arctic curve as for unconstrained alternating sign matrices the latter case involves lattice paths that are non intersecting but that are allowed to have osculating contact points for which the tangent method was argued to still apply for each problem we estimate the large size asymptotics of a certain one point function using lu decomposition of the corresponding gessel viennot matrices and a reformulation of the result amenable to asymptotic analysis

recursive formulas for the overlaps between bethe states and product states in xxz heisenberg chains we consider the problem of computing the overlaps between the bethe states of the xxz spin 1 2 chain and generic states we derive recursive formulas for the overlaps between some simple product states and off shell bethe states within the framework of the algebraic bethe ansatz these recursive formulas can be used to prove in a simple and straightforward way the recently obtained results for the overlaps of the bethe states with the n el state the dimer state and the q deformed dimer state however these recursive formulas are derived for a broader class of states and represent a concrete starting point for the computation of rather general overlaps our approach can be easily extended to other one dimensional bethe ansatz integrable models

aspects of the inverse problem for the toda chain we generalize babelon s approach to equations in dual variables so as to be able to treat new types of operators which we build out of the sub constituents of the model s monodromy matrix further we also apply sklyanin s recent monodromy matrix identities so as to obtain equations in dual variables for yet other operators the schemes discussed in this paper appear to be universal and thus in principle applicable to many models solvable through the quantum separation of variables

symmetric functions and wavefunctions of xxz type six vertex models and elliptic felderhof models by izergin korepin analysis we present a method to analyze the wavefunctions of six vertex models by extending the izergin korepin analysis originally developed for domain wall boundary partition functions first we apply the method to the case of the basic wavefunctions of the xxz type six vertex model by giving the izergin korepin characterization of the wavefunctions we show that these wavefunctions can be expressed as multiparameter deformations of the quantum group deformed grothendieck polynomials as a second example we show that the izergin korepin analysis is effective for analysis of the wavefunctions for a triangular boundary and present the explicit forms of the symmetric functions representing these wavefunctions as a third example we apply the method to the elliptic felderhof model which is a face type version and an elliptic extension of the trigonometric felderhof model we show that the wavefunctions can be expressed as one parameter deformations of an elliptic analog of the vandermonde determinant and elliptic symmetric functions we present a method to analyze the wavefunctions of six vertex models by extending the izergin korepin analysis originally developed for domain wall boundary partition functions first we apply the method to the case of the basic wavefunctions of the xxz type six vertex model by giving the izergin korepin characterization of the wavefunctions we show that these wavefunctions can be expressed as multiparameter deformations of the quantum group deformed grothendieck polynomials as a second example we show that the izergin korepin analysis is effective for analysis of the wavefunctions for a triangular boundary and present the explicit forms of the symmetric functions representing these wavefunctions as a third example we apply the method to the elliptic felderhof model which is a face type version and an

algebraic bethe ansatze and eigenvalue based determinants for dicke jaynes cummings gaudin quantum integrable models in this work we construct an alternative formulation to the traditional algebraic bethe ans tze for quantum integrable models derived from a generalized rational gaudin algebra realized in terms of a collection of spins 1 2 coupled to a single bosonic mode the ensemble of resulting models which we call dicke jaynes cummings gaudin models are particularly relevant for the description of light matter interaction in the context of quantum optics having two distinct ways to write any eigenstate of these models we then combine them in order to write overlaps and form factors of local operators in terms of partition functions with domain wall boundary conditions we also demonstrate that they can all be written in terms of determinants of matrices whose entries only depend on the eigenvalues of the conserved charges since these eigenvalues obey a much simpler set of quadratic bethe equations the resulting expressions could then offer important simplifications for the numerical treatment of these models

calculation of norms of bethe wave functions a class of two dimensional completely integrable models of statistical mechanics and quantum field theory is considered eigenfunctions of the hamiltonians are known for these models norms of these eigenfunctions in the finite box are calculated in the present paper these models include in particular the quantum nonlinear schrodinger equation and the heisenbergxxz model

norm formulae for the bethe ansatz on root systems of small rank the norms of the bethe ansatz eigenfunctions for the lieb liniger quantum system of n bosonic particles on a ring with pairwise repulsive delta potential interactions are given by a beautiful determinantal formula first conjectured by gaudin in the early seventies and then proven by korepin about a decade later recently e emsiz formulated a similar conjecture generalizing the gaudin korepin norm formula in terms of the root systems of complex simple lie algebras here we confirm the validity of the conjecture in question for small root systems up to rank 3 thus including the important test case of the exceptional root system g2

correlation functions of the higher spin xxx chains using the algebraic bethe ansatz we consider the correlation functions of the integrable higher spin chains we apply a method recently developed for the spin heisenberg chain based on the solution of the quantum inverse problem we construct a representation for the correlation functions on a finite chain for arbitrary spin then we show how the string solutions of the bethe equations can be considered in the framework of this approach in the thermodynamic limit finally a multiple integral representation for the spin 1 zero temperature correlation functions is obtained in the thermodynamic limit

on form factors of the conjugated field in the nonlinear schrodinger model izergin korepin s lattice discretization of the nonlinear schrodinger model along with oota s inverse problem provides one with determinant representations for the form factors of the lattice discretized conjugated field operator we prove that these form factors converge in the zero lattice spacing limit to those of the conjugated field operator in the continuous model we also compute the large volume asymptotic behavior of such form factors in the continuous model these are in particular characterized by fredholm determinants of operators acting on closed contours we provide a way of defining these fredholm determinants in the case of generic parameters

analysis of non linear dynamics of a two degree of freedom vibration system with non linear damping and non linear spring in this paper the non linear dynamics of a two degree of freedom vibration system with non linear damping and non linear spring is studied the analytic results show that the purposes of reducing amplitude and oscillation can be realized by adjusting properly the system parameters and considering the value of exciting frequency the conclusions can provide some available evidences for the design and improvement of the non linear absorber numerical simulations show the system exhibits periodic motions quasiperiodic motions and chaotic motions

the achievement of knowledge bases by cycle search forward chaining is an algorithm that is particularly simple and therefore used in many inference systems it computes the facts that are implied by a set of facts and rules unfortunately this algorithm is not complete with respect to negation to solve this problem it is possible in the context of propositional calculus to automatically add the rules needed to make forward chaining complete this transformation is a logical compilation of knowledge bases this article presents a new method based on a cycle search in a graph associated to the set of rules to compile which allows a precise identification of what is needed for completeness

the intractability of resolution abstract we prove that for infinitely many disjunctive normal form propositional calculus tautologies the length of the shortest resolution proof of cannot be bounded by any polynomial of the length of the tautologies we use were introduced by cook and reckhow 1979 and encode the pigeonhole principle extended resolution can furnish polynomial length proofs of these formulas

refined cauchy littlewood identities and six vertex model partition functions iii deformed bosons abstract we study hall littlewood polynomials using an integrable lattice model of t deformed bosons working with row to row transfer matrices we review the construction of hall littlewood polynomials of the a n root system within the framework of this model introducing appropriate double row transfer matrices we extend this formalism to hall littlewood polynomials based on the b c n root system and obtain a new combinatorial formula for them we then apply our methods to prove a series of refined cauchy and littlewood identities involving hall littlewood polynomials the last two of these identities are new and relate infinite sums over hyperoctahedrally symmetric hall littlewood polynomials with partition functions of the six vertex model on finite domains

diagonally and antidiagonally symmetric alternating sign matrices of odd order we study the enumeration of diagonally and antidiagonally symmetric alternating sign matrices dasasms of fixed odd order by introducing a case of the six vertex model whose configurations are in bijection with such matrices the model involves a grid graph on a triangle with bulk and boundary weights which satisfy the yang baxter and reflection equations we obtain a general expression for the partition function of this model as a sum of two determinantal terms and show that at a certain point each of these terms reduces to a schur function we are then able to prove a conjecture of robbins from the mid 1980 s that the total number of 2n 1 x 2n 1 dasasms is prod i 0 n 3i n i and a conjecture of stroganov from 2008 that the ratio between the numbers of 2n 1 x 2n 1 dasasms with central entry 1 and 1 is n n 1 among the several product formulae for the enumeration of symmetric alternating sign matrices which were conjectured in the 1980 s that for odd order dasasms is the last to have been proved

thermodynamic limit of the six vertex model with domain wall boundary conditions we address the question of the dependence of the bulk free energy on boundary conditions for the six vertex model here we compare the bulk free energy for periodic and domain wall boundary conditions using a determinant representation for the partition function with domain wall boundary conditions we derive toda differential equations and solve them asymptotically in order to extract the bulk free energy we find that it is different and bears no simple relation to the free energy for periodic boundary conditions the six vertex model with domain wall boundary conditions is closely related to algebraic combinatorics alternating sign matrices this implies new results for the weighted counting for large size alternating sign matrices finally we comment on the interpretation of our results in particular in connection with domino tilings dimers on a square lattice

the bcs model and the off shell bethe ansatz for vertex models we study the connection between the bcs pairing model and the inhomogeneous vertex model the two spectral problems coincide in the quasi classical limit of the off shell bethe ansatz of the disordered six vertex model the latter problem is transformed into an auxiliary spectral problem which corresponds to the diagonalization of the integrals of motion of the bcs model a generating functional whose quasi classical expansion leads to the constants of motion of the bcs model and in particular the hamiltonian is identified

the quantum gelfand levitan marchenko equations and form factors in the sine gordon model the quantum gelfand levitan marchenko equation obtained by the author in a previous work see theor math phys vol 60 p 363 75 1984 is used to calculate the form factors in the quantum sine gordon model

linear resolution for consequence finding abstract in this paper we re evaluate the consequence finding problem within first order logic firstly consequence finding is generalized to the problem in which only interesting clauses having a certain property called characteristic clauses should be found the use of characteristic clauses enables characterization of various reasoning problems of interest to ai including abduction nonmonotonic reasoning prime implicates and truth maintenance systems secondly an extension of the model elimination theorem proving procedure sol resolution is presented providing an effective mechanism complete for finding the characteristic clauses an important feature of sol resolution is that it constructs such a subset of consequences directly without testing each generated clause for the required property we also discuss efficient but incomplete variations of sol resolution and their properties which address finding the most specific and the least specific abductive explanations