suprema of open and closed formulas and their application to resolution we discuss an algebra of open formulas soaf the algebra is equipped with the operator mgi o which computes suprema of sets of open formulas ordered according to a weak form of instance ordering rules to compute such points are provided these rules supply a computation procedure to unify open formulas next we consider an algebra of closed formulas scaf it has an operator mgi c which computes suprema of set of formulas ordered according to the instance preordering we give rules to compute such points these rules supply a computation procedure to unify closed formulas relations between these operators and unification in open and closed formulas and weak unification in closed formulas are addressed also we consider clausal formulas and apply these considerations to the resolution process this provides a rule alternative to resolution and shows that resolvents can be expressed and effectively obtained as suprema of closed formulas the new rule need not resort to renaming unification and instantiation as first class operations finally applications to resolution in horn clause logic and logic programming are discussed this leads to a more compact theory of logic programming in which for instance the domain of substitutions is eliminated

staggered lattice models some staggered models are studied along three different lines exact solvability yang baxter equations the existence of other exact solutions called disorder solutions their group of symmetries the analysis based on the commutation of row to row transfer matrices of arbitrary size n suggests that the exactly solvable models are either of non staggered type or of free fermion staggered type in contrast disorder solutions can easily be exhibited for staggered models the example of the ashkin teller model is analysed finally the symmetry group of these models is seen to be a straightforward generalisation of the one of homogeneous models

the quantum heisenberg group h 1 q the structure of the quantum heisenberg group is studied in the two different frameworks of the lie algebra deformations and of the quantum matrix pseudogroups the r matrix connecting the two approaches together with its classical limit r are explicitly calculated by using the contraction technique and the problems connected with the limiting procedure discussed some unusual properties of the quantum enveloping heisenberg algebra are shown

the critical z invariant ising model via dimers the periodic case we study a large class of critical two dimensional ising models namely critical z invariant ising models on periodic graphs example of which are the classical mathbb z 2 triangular and honeycomb lattice at the critical temperature fisher j math phys 7 1776 1781 1966 introduced a correspondence between the ising model and the dimer model on a decorated graph thus setting dimer techniques as a powerful tool for understanding the ising model in this paper we give a full description of the dimer model corresponding to the critical z invariant ising model we prove that the dimer characteristic polynomial is equal up to a constant to the critical laplacian characteristic polynomial and defines a harnack curve of genus 0 we prove an explicit expression for the free energy and for the gibbs measure obtained as weak limit of boltzmann measures

duality relations and equilibrium crystal shapes of potts models on triangular and honeycomb lattices abstract we consider the q state potts models on triangular and honeycomb lattices for each lattice it is shown that the anisotropic interfacial tension is related to the anisotropic correlation length on the dual lattice using the star triangle transformation we also find that the anisotropic correlation length on the triangular lattice is the same as that of the honeycomb lattice for q 4 at the first order transition point the anisotropic correlation length is exactly calculated at the first order transition point by a method which introduces auxiliary edges into the models from the calculated anisotropic correlation length the equilibrium droplet shape of one ordered phase embedded inside another is derived via the wulff construction the equilibrium shape is written as a simple algebraic curve which corresponds to the dispersion relation of bound states in the terminology of spin chains

s semantics for logic programming a retrospective look the paper provides an overview of the s semantic approach to the semantics of logic programs which had been developed about twenty years ago the aim of such an approach was that of providing a suitable base for program analysis by means of a semantics which really captures the operational behavior of logic programs and thus offers useful notions of observable program equivalences the semantics is given in terms of extended interpretations which are more expressive than herbrand interpretations extends the standard herbrand semantics and can be obtained as a result of both top down and bottom up constructions the approach has been applied to several extensions of positive logic programs and used to develop semantic based techniques for program analysis verification and transformation

the z invariant ising model via dimers the z invariant ising model baxter in philos trans r soc lond a math phys eng sci 289 1359 315 346 1978 is defined on an isoradial graph and has coupling constants depending on an elliptic parameter k when k 0 the model is critical and as k varies the whole range of temperatures is covered in this paper we study the corresponding dimer model on the fisher graph thus extending our papers boutillier and de tiliere in probab theory relat fields 147 379 413 2010 commun math phys 301 2 473 516 2011 to the fullz invariant case one of our main results is an explicit local formula for the inverse of the kasteleyn operator its most remarkable feature is that it is an elliptic generalization of boutillier and de tiliere 2011 it involves a local function and the massive discrete exponential function introduced in boutillier et al invent math 208 1 109 189 2017 this shows in particular that z invariance and not criticality is at the heart of obtaining local expressions we then compute asymptotics and deduce an explicit local expression for a natural gibbs measure we prove a local formula for the ising model free energy we also prove that this free energy is equal up to constants to that of the z invariant spanning forests of boutillier et al 2017 and deduce that the two models have the same second order phase transition in k next we prove a self duality relation for this model extending a result of baxter to all isoradial graphs in the last part we prove explicit local expressions for the dimer model on a bipartite graph corresponding to the xor version of this z invariant ising model

an r matrix approach to the quantization of the euclidean group e 2 the r matrices for two different deformations of the euclidean group e 2 calculated in a two dimensional representation are used to determine the deformed hopf algebra of the representative functions the duality of the latter with the initial quantum algebras is explicitly proved and the relationship between the two quantum groups is discussed and clarified

unfolding and fixpoint semantics of concurrent constraint logic programs we present a new semantics for a language in the family of concurrent constraint logic languages the semantics can be based on a notion of clause unfolding since the language is closed under this transformation the unfolding semantics is obtained as limit of an infinite unfolding process unfolding is also used to define an immediate consequences operator and therefore a fixpoint semantics in the typical logic programming style the result of both the unfolding and the fixpoint semantics is a set of reactive behaviors which are trees abstractly representing all the possible computations of a program including deadlocks and finite failures the semantics can be made more abstract by defining a suitable notion of equivalence on reactive behaviors in our approach this can be done by reasoning on constraints only thus generalizing the typical behavior of constraint logic programming

hard hexagon model calculation of anisotropic interfacial tension from asymptotic degeneracy of largest eigenvalues of row row transfer matrix to find the directional dependence of the interfacial tension of the hard hexagon model an inhomogeneous system is studied this system is defined on a square lattice with 1 v m columns so that the lhs of the m 1 th column is the hard hexagon model and the rhs of the m 1 th column works as the operator which shifts the particle configuration of a column downward a triplet of the largest eigenvalues of the row row transfer matrix are asymptotically degenerate asm under the conditions that 1 v m 0 mod 3 withv being fixed to be constant the interfacial tension of a tilted interface is calculated from the finite correction terms in this limit

free fermion checkerboard and z invariant lattice models in statistical mechanics it is shown that the two dimensional free fermion model is equivalent to a checkerboard ising model which is a special case of the general z invariant ising model expressions are given for the partition function and local correlations in terms of those of the regular square lattice ising model corresponding results are given for the self dual potts model and the application of the methods to the three dimensional zamolodchikov model is discussed the paper ends with a discussion of the critical and disorder surfaces of the checkerboard potts model

quantum planes and quantum cylinders from poisson homogeneous spaces quantum planes and a new quantum cylinder are obtained as quantization of poisson homogeneous spaces of two different poisson structures on classical euclidean group e 2

symmetry representations in the rigged hilbert space formulation of quantum mechanics we discuss some basic properties of lie group representations in rigged hilbert spaces in particular we show that a differentiable representation in a rigged hilbert space may be obtained as the projective limit of a family of continuous representations in a nested scale of hilbert spaces we also construct a couple of examples illustrative of the key features of group representations in rigged hilbert spaces finally we establish a simple criterion for the integrability of an operator lie algebra in a rigged hilbert space

nondeterminism and infinite computations in constraint programming we investigate the semantics of concurrent constraint programming and of various sublanguages with particular emphasis on nondeterminism and infinite behavior the aim is to find out what is the minimal structure which a domain must have in order to capture these two aspects we show that a notion of observables obtained by the upward closure of the results of computations is relatively easy to model even in presence of synchronization on the contrary modeling the exact set of results is problematic even for the simple sublanguage of constraint logic programming we show that most of the standard topological techniques fail in capturing this more precise notion of observables the analysis of these failed attempts leads us to consider a categorical approach

discrete pluriharmonic functions as solutions of linear pluri lagrangian systems pluri lagrangian systems are variational systems with the multi dimensional consistency property this notion has its roots in the theory of pluriharmonic functions in the z invariant models of statistical mechanics in the theory of variational symmetries going back to noether and in the theory of discrete integrable systems a d dimensional pluri lagrangian problem can be described as follows given a d form l on an m dimensional space m d whose coefficients depend on a function u of m independent variables called field find those fields u which deliver critical points to the action functionals s sigma int sigma l for any d dimensional manifold in the m dimensional space we investigate discrete 2 dimensional linear pluri lagrangian systems i e those with quadratic lagrangians l the action is a discrete analogue of the dirichlet energy and solutions are called discrete pluriharmonic functions we classify linear pluri lagrangian systems with lagrangians depending on diagonals they are described by generalizations of the star triangle map examples of more general quadratic lagrangians are also considered

hard squares with diagonal attractions the authors complete the solution of the square lattice gas with nearest neighbour exclusion and attractive next nearest neighbour diagonal interactions on the special surface corresponding to regimes iii and iv of the generalised hard hexagon model the interfacial tension correlation length and sublattice density difference are calculated throughout these regimes by obtaining the eigenvalues of the row to row and corner transfer matrices the associated critical exponents are found to be mu v 5 4 beta 3 32 in regime iii and mu v 5 2 beta 1 4 in regime iv in particular their results confirm the recent proposal by huse that regime iii is the first order coexistence surface separating the disordered fluid phase from the square ordered solid phases and that the regime iii regime iv boundary is a line of tricritical points

on the susceptibility of the generalised square lattice ising model an exact functional relation is found for the susceptibility of the generalised square lattice ising model this result contains as a particular case a fisher relation between the susceptibilities of the triangular and honeycomb lattices models it is also shown that the closed form expression for the susceptibility of the generalised square lattice proposed by syozi and naya 1960 satisfies the functional relation presented in this letter

hard hexagon model anisotropy of correlation length and interfacial tension the directional dependence of the correlation length of the hard hexagon model is calculated by a new method which introduces the shift operator into the usual transfer matrix method this method is also applied to the calculation of the interfacial tension of the hard hexagon model which is anisotropic in addition the equilibrium droplet shape of one phase embedded inside another is obtained from the analysis of the interfacial tension by the use of wulff s construction

anisotropic correlation length in the eight vertex model we investigate the directional dependence or anisotropy of the correlation length of the eight vertex model by a method which introduces the shift operator into the usual transfer matrix argument for a given x 0 x 1 there are two cases with respect to a parameter q in the case 0 q x3 the anisotropic correlation length acl is independent of q noting that the eight vertex model factors into two ising lattices in the q x4 limit we can directly relate the acl to that of the square lattice ising model when x3 q x2 the acl depends on q using an algebraic curve we show that the acl in this case is connected with that of the ising model on a 4 8 or union jack lattice we suggest that a wide class of models have essentially the same acl as the eight vertex model has

observable behaviors and equivalences of logic programs we first introduce a general semantic scheme for logic programs which provides a uniform framework for defining different compositional semantics parametrically with respect to a given notion of observability the equivalence of the operational top down and fixpoint bottom up construction of the semantics is ensured by the scheme provided a congruence property is verified we then define several observational equivalences on logic programs and investigate how they are related the equivalences are based on various observables successful derivations computed answers partial computed answers and call patterns and on a notion of program composition for each observational equivalence we study the relation with a suitable formal semantics by investigating correctness and full abstraction properties all the semantics we consider are obtained as instances of the general scheme

c expressions a variable free calculus for equational logic programming abstract a relevant drawback between the theory and the current implementations of logic programming languages is represented by the use of metalevel structures like substitutions and mechanisms like mgu and instantiation to deal with the substitution rule substitution rule is highly involved in the formalization of proof procedures including narrowing and resolution we put the substitution rule as an additional operator mgi of the algebra of the language terms and provide them with a variable free abstract representation c expressions a formal definition of the operations of the algebra is given through rules which replacing equal by equal define a calculus having a special class of c expressions as normal forms the calculus provides for a formal construction of reduction machines for unification rewriting and narrowing all having c expressions as programs

complex temperature properties of the 2d ising model with beta h or i pi 2 we study the complex temperature properties of a rare example of a statistical mechanical model which is exactly solvable in an external symmetry breaking field namely the ising model on the square lattice with beta h or i pi 2 this model was solved by lee and yang 1952 we first determine the complex temperature phases and their boundaries from a low temperature high field series expansion of the partition function we extract the low temperature series for the susceptibility chi to o u23 where u e 4k analysing this series we conclude that chi has divergent singularities i at u u3 3 232 with exponent gamma e 5 4 ii at u 1 with exponent gamma 1 5 2 and iii at u us 1 with exponent gamma s 1 we also extract a shorter series for the staggered susceptibility and investigate its singularities using the exact result of lee and yang for the free energy we calculate the specific heat and determine its complex temperature singularities we also carry this out for the uniform and staggered magnetization

unique representation of an inverse kinetic theory for incompressible newtonian fluids abstract fundamental aspects of inverse kinetic theories for the incompressible navier stokes equations m tessarotto m ellero rgd24 italy july 10 16 2004 aip conf proc 762 2005 108 m ellero m tessarotto physica a 355 2005 233 include the possibility of defining uniquely the kinetic equation underlying such models and furthermore the construction of a kinetic theory implying also the energy equation the latter condition is consistent with the requirement that fluid fields result classical solutions of the fluid equations these issues appear of potential relevance both from the mathematical viewpoint and for the physical interpretation of the theory purpose of this work is to prove that under suitable prescriptions the inverse kinetic theory can be determined to satisfy such requirements

the inversion relation method for some two dimensional exactly solved models in lattice statistics the partition functions per site of several two dimensional models notably the eight vertex self dual potts and hard hexagon models can be easily obtained by using an inversion relation for local transfer matrices together with symmetry and analyticity properties this technique is discussed the analyticity properties compared and some equivalences and nonequivalences pointed out in particular the critical hard hexagon model is found to have the same as the self dualq state potts model withq 3 5 2 2 618 the temperley lieb equivalence between the potts and six vertex models is found to fail in certain nonphysical antiferromagnetic cases

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

the critical z invariant ising model via dimers locality property we study a large class of critical two dimensional ising models namely critical z invariant ising models fisher j math phys 7 1776 1781 1966 introduced a correspondence between the ising model and the dimer model on a decorated graph thus setting dimer techniques as a powerful tool for understanding the ising model in this paper we give a full description of the dimer model corresponding to the critical z invariant ising model consisting of explicit expressions which only depend on the local geometry of the underlying isoradial graph our main result is an explicit local formula for the inverse kasteleyn matrix in the spirit of kenyon invent math 150 2 409 439 2002 as a contour integral of the discrete exponential function of mercat discrete period matrices and related topics 2002 and kenyon invent math 150 2 409 439 2002 multiplied by a local function using results of boutillier and de tiliere prob theor rel fields 147 3 4 379 413 2010 and techniques of de tiliere prob th rel fields 137 3 4 487 518 2007 and kenyon invent math 150 2 409 439 2002 this yields an explicit local formula for a natural gibbs measure and a local formula for the free energy as a corollary we recover baxter s formula for the free energy of the critical z invariant ising model baxter in exactly solved models in statistical mechanics academic press london 1982 and thus a new proof of it the latter is equal up to a constant to the logarithm of the normalized determinant of the laplacian obtained in kenyon invent math 150 2 409 439 2002

the early history of the integrable chiral potts model and the odd even problem in the first part of this paper i shall discuss the round about way of how the integrable chiral potts model was discovered about 30 years ago as there should be more higher genus models to be discovered this might be of interest in the second part i shall discuss some quantum group aspects especially issues of odd versus even n related to the serre relations conjecture in our quantum loop subalgebra paper of 5 years ago and how we can make good use of coproducts also borrowing ideas of drinfeld jimbo deguchi fabricius mccoy and nishino

wavevector dependent susceptibility in quasiperiodic ising models using the various functional relations for correlation functions in planar ising models new results are obtained for the correlation functions and the q dependent susceptibility for ising models on a quadratic lattice with quasiperiodic coupling constants the effects are clearest if the interactions are both attractive and repulsive according to a quasiperiodic pattern in particular an exact scaling limit result for the two point correlation function of the z invariant inhomogeneous ising model is presented and the q dependent susceptibility is calculated for some cases where the coupling constants vary according to fibonacci rules it is found that the ferromagnetic case differs drastically from the case with both ferro and antiferromagnetic bonds in the mixed case the peaks of the q dependent susceptibility are everywhere dense for temperature t both above or below the critical temperature tc but due to overlap only a finite number of peaks is visible this number of visible peaks decreases as t moves away from tc in the ferromagnetic case there is typically only one single peak at q 0 in spite of the aperiodicity present in the lattice these results provide evidence that in real systems even if the atoms arrange themselves aperiodically there will be no dramatic difference in the diffraction pattern unless the pair correlation function has clear aperiodic oscillations the number of oscillations per correlation length determines the number of visible peaks

spontaneous magnetisations of the ising model on the bathroom tile lattice the authors evaluate the site spontaneous magnetisations on the general 4 8 or bathroom tile lattice using mappings to checkerboard free fermion and union jack ising models their results verify the conjecture of lin et al 1987 who proposed their formula from twelfth order low temperature series expansions

the three dimensional euclidean quantum group e 3 q and its r matrix a contraction procedure starting from so 4 q is used to determine the quantum analog e 3 q of the three dimensional euclidean group and the structure of its representations a detailed analysis of the contraction of the r matrix is then performed and its explicit expression has been found the classical limit of r is shown to produce an integrable dynamical system by means of the r matrix the pseudogroup of the noncommutative representative functions is considered it will finally be shown that a further contraction made on e 3 q produces the two dimensional galilei quantum group and this in turn can be used to give a new realization of e 3 q and e 2 1 q

the z invariant massive laplacian on isoradial graphs we introduce a one parameter family of massive laplacian operators delta m k k in 0 1 defined on isoradial graphs involving elliptic functions we prove an explicit formula for the inverse of delta m k the massive green function which has the remarkable property of only depending on the local geometry of the graph and compute its asymptotics we study the corresponding statistical mechanics model of random rooted spanning forests we prove an explicit local formula for an infinite volume boltzmann measure and for the free energy of the model we show that the model undergoes a second order phase transition at k 0 thus proving that spanning trees corresponding to the laplacian introduced by kenyon invent math 150 2 409 439 2002 are critical we prove that the massive laplacian operators delta m k k in 0 1 provide a one parameter family of z invariant rooted spanning forest models when the isoradial graph is moreover mathbb z 2 periodic we consider the spectral curve of the massive laplacian we provide an explicit parametrization of the curve and prove that it is harnack and has genus 1 we further show that every harnack curve of genus 1 with z w leftrightarrow z 1 w 1 symmetry arises from such a massive laplacian

sldnf resolution with non safe rule and fixpoint semantics for general logic programs the sldnf resolution sld resolution with negation as failure is often restricted to yield a safe rule that is negation as failure rule is adopted only in the case that the selected negative literal in each goal should be in ground in this paper we investigate extensions of goals in sldnf resolutions with the case of selecting non ground negative literals since shepherdson s proposal is thought of as most general 16 18 we formally show how the success and failure sets by sherpherdson s sldnfs resolution are related with a fixpoint semantics which is generalized to be concerned with atom sets involving the variables

uniform closures the notion of uniform closure operator is introduced and it is shown how this concept surfaces in two different areas of application of abstract interpretation notably in semantics design for logic programs and in the theory of abstract domain refinements in logic programming uniform closures permit generalization from an order theoretic perspective of the standard hierarchy of declarative semantics in particular we show how to reconstruct the model theoretic characterization of the well known s semantics using pure order theoretic concepts only as far as the systematic refinement operators on abstract domains are concerned we show that uniform closures capture precisely the property of a refinement of being invertible namely of admitting a related operator that simplifies as much as possible a given abstract domain of input for that refinement exploiting the same argument used to reconstruct the s semantics of logic programming we yield a precise relationship between refinements and their inverse operators we demonstrate that they form an adjunction with respect to a conveniently modified complete order among abstract domains

declarative modeling of the operational behavior of logic languages abstract the paper defines a new declarative semantics for logic programs which is based on interpretations containing possibly non ground atoms two different interpretations are introduced and the corresponding models are defined and compared the classical results on the herbrand model semantics of logic programs are shown to hold in the new models too i e existence of a minimal model fixpoint characterization etc with the new models we have a stronger soundness and completeness result for sld resolution in particular one of the two models allows the set of computed answer substitutions to be characterized precisely

transfer matrix eigenvectors of the baxter bazhanov stroganov τ2 model for n 2 we find a representation of the row to row transfer matrix of the baxter bazhanov stroganov 2 model for n 2 in terms of an integral over two commuting sets of grassmann variables using this representation we explicitly calculate transfer matrix eigenvectors and normalize them it is also shown how form factors of the model can be expressed in terms of determinants and inverses of certain toeplitz matrices

anisotropic interfacial tension and the equilibrium crystal shape of kagome lattice eight vertex model we exactly calculate the anisotropic interfacial tension of the kagome lattice eight vertex model with the help of two types of square lattice models each square lattice model is inhomogeneous but still possesses a one parameter family of commuting transfer matrices from the anisotropic interfacial tension the equilibrium shape of an inclusion of one ordered phase in an environment of another is obtained by applying the wulff construction calculations are expressed by the use of differential forms on a riemann surface of genus 1 and the equilibrium shape is written as an elliptic curve we suggest the possibility of interpreting critical phenomena in terms of the moduli space of riemann surfaces of genus 1

reply to comment on equilibrium crystal shape of the potts model at the first order transition point the eight vertex model is defined on the square lattice rotated through an arbitrary angle with respect to the coordinate axes we re examine the analysis of the anisotropic correlation length in a previous paper fujimoto m 1996 physica a 233 485 502 we point out that the asymptotic form of the correlation function is expressed by the use of differential forms on a riemann surface of genus 1 combined with the symmetry of the square lattice this fact explains that the anisotropic correlation length is represented in terms of simple algebraic curves the argument is applicable to a wide class of lattice models including unsolvable ones

the gamma poincare quantum group from quantum group contraction we propose a contraction of the de sitter quantum group leading to a poincare quantum group in any dimensions the method relies on the coaction of the de sitter quantum group on a non commutative space and the deformation parameter q is sent to one the bicrossproduct structure of this gamma poincare quantum group is exhibited and shown to be dual to the one of the kappa poincare hopf algebra at least in two dimensions

the spectra of q state vertex models and related antiferromagnetic quantum spin chains some exactly solvable q state vertex models are investigated the author employs inversion relations to determine directly the spectra of the transfer matrices in the thermodynamic limit by avoiding the more cumbersome bethe ansatz the results are applied to related quantum spin chains of which two families are su q and so q invariant respectively various quantities are calculated e g energy momentum excitations and the correlation length for q 3 the su q invariant chain is the pure biquadratic spin 1 hamiltonian which turns out to be non critical the ground state energy the gap and the correlation length are given

equilibrium crystal shape of the potts model at the first order transition point we investigate the q state two dimensional potts model the anisotropic interfacial tension is related by duality to the anisotropic correlation length for q 4 we calculate exactly the anisotropic correlation length at the first order transition point from the calculated anisotropic correlation length the equilibrium crystal shape ecs is derived via the wulff construction the ecs is expressed by means of a simple algebraic curve regarding q as a temperature scale we show that the potts model has the same ecs as the eight vertex model we discuss a connection between the ecs and the q deformed pseudo euclidian algebra

type dependencies for logic programs using aci unification abstract this paper presents a new notion of typing for logic programs which generalizes the notion of directional types the generation of type dependencies for a logic program is fully automatic with respect to a given domain of types the analysis method is based on a novel combination of program abstraction and aci unification which is shown to be correct and optimal type dependencies are obtained by abstracting programs replacing concrete terms by their types and evaluating the meaning of the abstract programs using a standard semantics for logic programs enhanced by aci unification this approach is generic and can be used with any standard semantics the method is both theoretically clean and easy to implement using general purpose tools the proposed domain of types is condensing which means that analyses can be carried out in both top down or bottom up frameworks with no loss of precision for goal independent analyses the proposed method has been fully implemented within a bottom up approach and the experimental results are promising

three dimensional quantum groups from contractions of su 2 q contractions of lie algebras and of their representations are generalized to define new quantum groups an explicit and complete exposition is made for the one dimensional heisenberg h 1 q and the two dimensional euclidean quantum group e 2 q obtained by contracting su 2 q

inversion relations and disorder solutions on potts models the inversion symmetry and the automorphy group generated by the latter when combined with the spatial symmetries are studied for the anisotropic potts models on the triangular and checkerboard lattices the exact expression of the partition function which is known on some particular disorder subvarieties of the triangular model is checked and a generalisation is proposed for the checkerboard lattice the automorphy group is then used to extend the disorder solutions to the infinity of transformed subvarieties

exactly solved models on planar graphs with vertices in z 3 it is shown how exactly solved edge interaction models on the square lattice may be extended onto more general planar graphs with edges connecting a subset of next nearest neighbour vertices of mathbb z 3 this is done by using local deformations of the square lattice that arise through the use of the star triangle relation similar to baxter s z invariance property these local deformations leave the partition function invariant up to some simple factors coming from the star triangle relation the deformations used here extend the usual formulation of z invariance by requiring the introduction of oriented rapidity lines which form directed closed paths in the rapidity graph of the model the quasi classical limit is also considered in which case the deformations imply a classical z invariance property as well as a related local closure relation for the action functional of a system of classical discrete laplace equations

graphical approach to the nonintersecting string model star triangle equation inversion relation and exact solution abstract a general q state nonintersecting string model for q 2 is studied and solved using a graphical approach this model of which special cases were first introduced by strogonov and schultz has recently drawn further attention because of its relation to potts models in its simplest version a uniform separable nonintersecting string model on a quadratic lattice it corresponds to a q2 state potts model with potts spins on every other lattice face we first formulate the related star triangle equation which we solve in terms of a line variable parametrization such a parametrization of a solution of the star triangle equation leads to a simple and direct graphical derivation of an inversion relation for the partition function our graphical analysis also shows that the inversion relation holds if certain boundary effects can be neglected as we shall give a special finite lattice from which the inversion relation can be read off immediately this relation is next solved under appropriate analyticity assumptions again using a simple and direct approach and the result is applied to obtain exact solutions for specific string models

six vertex model with rotated boundary conditions we investigate the six vertex model on a square lattice rotated through an arbitrary angle with respect to the coordinate axes a model recently introduced by litvin and priezzhev auxiliary vertices are used to define an inhomogeneous system which leads to a one parameter family of commuting transfer matrices a product of commuting transfer matrices can be interpreted as a transfer matrix acting on zigzag walls in the rotated system using an equation for commuting transfer matrices we calculate their eigenvalues finite size properties of the model are discussed from the viewpoint of the conformal field theory

an exact result for the kagome lattice ising model with magnetic field an anisotropic ising model with three interaction parameters k1 k2 k3 and a magnetic field h formulated on the kagome lattice is solved exactly for an appropriate relation between ki and h when this relation is satisfied the system becomes equivalent to a free fermion model

zeros of the partition function for the triangular lattice three state potts model the authors obtain the zeros of the partition function for the isotropic triangular lattice three state potts model in a finite lattice the distribution exhibits new points on the real axis which are well fitted by an algebraic equation deduced from the inversion relation and the symmetries of the anisotropic model they identify a symmetry approximately relating all six transition points

orderings for term rewriting systems abstract methods of proving that a term rewriting system terminates are presented they are based on the intuitive notion of simplification orderings orderings in which any term that is syntactically simpler than another is smaller than the other as a consequence of kruskal s tree theorem any nonterminating system must be self embedding in the sense that it allows for the derivation of some term from a simpler one thus termination is guaranteed if every rule in the system is a reduction in some simplification ordering most of the orderings that have been used for proving termination are indeed simplication orderings using this notion often allows for much easier proofs a particularly useful class of simplification orderings the recursive path orderings is defined examples of the use of simplication orderings in termination proofs are given

exact solution of the ising model on a 4 6 lattice we consider an ising model on a lattice of squares and hexagons the 4 6 lattice which does not appear to have been studied previously the critical temperature is obtained as the root of a sixth order equation an exact expression is obtained for the spontaneous magnetization

semantics models for concurrent logic languages abstract in this paper we develop semantic models for a class of concurrent logic languages we give two operational semantics based on a transition system a declarative semantics and a denotational semantics one operational and the declarative semantics model the success set that is the set of computed answer substitutions corresponding to all successfully terminating computations the other operational and the denotational semantics also model deadlock and infinite computations for the declarative and the denotational semantics we extend standard notions such as unification in order to cope with the synchronization mechanism of the class of languages we study the basic mathematical structure for the declarative semantics is the complete lattice of sets of finite streams of substitutions in the denotational semantics we use a complete metric space of tree like structures that are labelled with functions that represent the basic unification step we look at the relations between the different models we relate first the two operational semantics and next the declarative and denotational semantics with their respective operational counterparts

an inverse kinetic theory for the incompressible navier stokes equations abstract an inverse kinetic theory applying specifically to incompressible newtonian fluids which permits us to avoid the n 2 algorithmic complexity of the poisson equation for the fluid pressure is presented the theory is based on the construction of a suitable kinetic equation in phase space which permits us to determine exactly the fluid equations by means of the velocity moments of the kinetic distribution function it is found that the fluid pressure can also be determined as a moment of the distribution function without solving the poisson equation as is usually required in direct solution methods for the incompressible fluid equations finally the dynamical system underlying the incompressible navier stokes equations and advancing in time the fluid fields has been also identified and proven to produce an unique set of fluid equations

phase space lagrangian dynamics of incompressible thermofluids phase space lagrangian dynamics in ideal fluids i e continua is usually related to the so called ideal tracer particles the latter which can in principle be permitted to have arbitrary initial velocities are understood as particles of infinitesimal size which do not produce significant perturbations of the fluid and do not interact among themselves an unsolved theoretical problem is the correct definition of their dynamics in ideal fluids the issue is relevant in order to exhibit the connection between fluid dynamics and the classical dynamical system underlying a prescribed fluid system which uniquely generates its time evolution the goal of this paper is to show that the tracer particle dynamics can be exactly established for an arbitrary incompressible fluid uniquely based on the construction of an inverse kinetic theory ikt m tessarotto m ellero bull am phys soc 45 9 2000 40 m tessarotto m ellero aip conf proc 762 2005 108 rgd24 italy july 10 16 2004 m ellero m tessarotto physica a 355 2005 233 m tessarotto m ellero physica a 373 2007 142 arxiv physics 0602140 m tessarotto m ellero in m s ivanov a k rebrov eds proc 25th rgd international symposium on rarefied gas dynamics st petersburg russia july 21 28 2006 novosibirsk publ house of the siberian branch of the russian academy of sciences 2007 p 1001 arxiv physics 0611113 m tessarotto c cremaschini strong solutions of the incompressible navier stokes equations in external domains local existence and uniqueness arxiv 0809 5164v1 math ph 2008 as an example the case of an incompressible newtonian thermofluid is considered here

from cycle rooted spanning forests to the critical ising model an explicit construction fisher established an explicit correspondence between the 2 dimensional ising model defined on a graph g and the dimer model defined on a decorated version mathcal g of this graph fisher in j math phys 7 1776 1781 1966 in this paper we explicitly relate the dimer model associated to the critical ising model and critical cycle rooted spanning forests crsfs this relation is established through characteristic polynomials whose definition only depends on the respective fundamental domains and which encode the combinatorics of the model we first show a matrix tree type theorem establishing that the dimer characteristic polynomial counts crsfs of the decorated fundamental domain mathcal g 1 our main result consists in explicitly constructing crsfs of mathcal g 1 counted by the dimer characteristic polynomial from crsfs of g1 where edges are assigned kenyon s critical weight function kenyon in invent math 150 2 409 439 2002 thus proving a relation on the level of configurations between two well known 2 dimensional critical models

mathematical properties of the navier stokes dynamical system for incompressible newtonian fluids abstract the connection between fluid dynamics and classical statistical mechanics has motivated in the past mathematical investigations of the incompressible navier stokes ns equations inse by means of an asymptotic kinetic theory this feature has suggested the search for possible alternative exact approaches based on the construction of a suitable inverse kinetic theory ikt which can avoid the asymptotic character and the intrinsic mathematical difficulty of direct kinetic theories in this paper the fundamental mathematical properties of the ns phase space dynamical system underlying inse and determined by ikt are investigated in particular an equivalence theorem with the inse problem and a global existence theorem are proved to hold for the ns dynamical system

a fixpoint semantics of horn sentences based on substitution sets abstract the formal semantics of a given horn sentence is usually defined as a set of ground atoms which is really the minimal herbrand interpretation of the horn sentence by both model theoretic and fixpoint approaches in the present paper we propose another denotational semantics of a horn sentence denoting the set of substitutions with which atoms are derivable by unit deduction from the horn sentence to get a direct correspondence between the semantics of the horn sentence and the answer set concerned with its computation and give denotational semantics even when the horn sentence is unsatisfiable in accordance with the unit deductions from a horn sentence we define a continuous function from a direct product of powersets of a substitution set to itself and regard the least fixpoint of the function as the semantics which can provide the answer set for computations of the horn sentence

remarks on the quantum dilogarithm a quantum analogue of the dilogarithm function has been introduced by faddeev and kashaev 1994 in such a way that a certain identity in the weyl algebra wq plays the role of the five term dilogarithm identity we study this identity in the limit when q approaches a root of unity and show that it then reduces to the restricted star triangle relation which has been used previously by bazhanov and baxter 1992 as a local integrability condition of a class of three dimensional solvable lattice models

bond percolation on isoradial graphs criticality and universality in an investigation of percolation on isoradial graphs we p rove the criti cality of canonical bond percolation on isoradial embeddings of planar graphs thus extending celebrated earlier results for homogeneous and inhomogeneous square tri angular and other lattices this is achieved via the star t riangle transformation by transporting the box crossing property across the family of isoradial graphs as a consequence we obtain the universality of these models at the critical point in the sense that the one arm and 2 j alternating arm critical exponents and therefore also the connectivity and volume exponents are constant across the family of such perco lation processes the isoradial graphs in question are thos e that satisfy certain weak conditions on their embedding and on their track system this class of graphs in cludes for example isoradial embeddings of periodic graphs and graphs derived from rhombic penrose tilings

reactive systems semi saturated semantics and coalgebras on presheaves the semantics of process calculi has traditionally been specified by labelled transition systems ltss but with the development of name calculi it turned out that reaction rules i e unlabelled transition rules are often more natural this leads to the question of how behavioral equivalences bisimilarity trace equivalence etc defined for lts can be transferred to unlabelled transition systems recently in order to answer this question several proposals have been made with the aim of automatically deriving an lts from reaction rules in such a way that the resulting equivalences are congruences furthermore these equivalences should agree with the standard semantics whenever one exists in this paper we propose saturated semantics based on a weaker notion of observation and orthogonal to all the previous proposals and we demonstrate the appropriateness of our semantics by means of two examples logic programming and open petri nets we also show that saturated semantics can be efficiently characterized through the so called semi saturated games finally we provide coalgebraic models relying on presheaves

an abstract interpretation framework to reason on finite failure and other properties of finite and infinite computations we extend the framework of comini et al inform comput 1999 to appear in order to be able to reason on properties of abstractions of possibly infinite sld derivations this issue is relevant since some important operational properties such as finite failure infinite behavior can only be addressed as abstraction of finite and infinite sld derivations the framework allows us to define new fixpoint semantics correctly modelling such properties and address problems such as compositionality w r t various syntactic operators correctness and minimality of the chosen denotations in this paper we also apply the framework in order to obtain a new fixpoint semantics based on a co continuous operator which correctly models finite failure and is compositional w r t the syntactic operators

negation as instantiation we propose a new negation rule for logic programming which derives existentially closed negative literals and we define a version of completion for which this rule is sound and complete the rule is called negation as instantiation nai according to it a negated atom succeeds whenever all the branches of the sld tree for the atom either fail or instantiate the atom the set of the atoms whose negation is inferred by the nai rule is proved equivalent to the complement of tc where tc is the immediate consequence operator extended to non ground atoms m falaschi et al 1989 theoret comput sci 69 3 289 318 the nai rule subsumes negation as failure on ground atoms it excludes floundering and can be efficiently implemented we formalize this way of handling negation in terms of sldni resolution sld resolution with negation as instantiation finally we amalgamate sldni resolution and sldnf resolution thus obtaining a new resolution procedure which is able to treat negative literals with both existentially quantified variables and free variables and we prove its correctness

making abstract interpretations complete completeness is an ideal although uncommon feature of abstract interpretations formalizing the intuition that relatively to the properties encoded by the underlying abstract domains there is no loss of information accumulated in abstract computations thus complete abstract interpretations can be rightly understood as optimal we deal with both pointwise completeness involving generic semantic operations and least fixpoint completeness completeness and fixpoint completeness are shown to be properties that depend on the underlying abstract domains only our primary goal is then to solve the problem of making abstract interpretations complete by minimally extending or restricting the underlying abstract domains under the weak and reasonable hypothesis of dealing with continuous semantic operations we provide constructive characterizations for the least complete extensions and the greatest complete restrictions of abstract domains as far as fixpoint completeness is concerned for merely monotone semantic operators the greatest restrictions of abstract domains are constructively characterized while it is shown that the existence of least extensions of abstract domains cannot be in general guaranteed even under strong hypotheses these methodologies which in finite settings give rise to effective algorithms provide advanced formal tools for manipulating and comparing abstract interpretations useful both in static program analysis and in semantics design a number of examples illustrating these techniques are given

extended z invariance for integrable vector and face models and multi component integrable quad equations in a previous paper kels in j phys a 50 49 495202 2017 the author has established an extension of the z invariance property for integrable edge interaction models of statistical mechanics that satisfy the star triangle relation str form of the yang baxter equation ybe in the present paper an analogous extended z invariance property is shown to also hold for integrable vector models and interaction round a face irf models of statistical mechanics respectively as for the previous case of the str the z invariance property is shown through the use of local cubic type deformations of a 2 dimensional surface associated to the models which allow an extension of the models onto a subset of next nearest neighbour vertices of mathbb z 3 while leaving the partition functions invariant these deformations are permitted as a consequence of the respective ybe s satisfied by the models the quasi classical limit is also considered and it is shown that an analogous z invariance property holds for the variational formulation of classical discrete laplace equations which arise in this limit from this limit new integrable 3d consistent multi component quad equations are proposed which are constructed from a degeneration of the equations of motion for irf boltzmann weights

transforming constraint logic programs abstract we study a la tamaki sato transformations of constraint logic programs we give an operational and fixpoint semantics of our constraint logic programs we extend the tamaki sato transformation system into a transformation system for constraint programs including fold unfold substitution thinning and fattening and constraint simplifications we give a direct proof of its correctness which is simpler than the tamaki sato proof

a theory of observables for logic programs we define a semantic framework to reason about properties of abstractions of sld derivations the framework allows us to address problems such as the relation between the top down operational semantics and the bottom up denotational semantics the existence of a denotation for a set of definite clauses and their properties compositionality w r t various syntactic operators correctness minimality and precision using abstract interpretation techniques to model abstraction allows us to state very simple conditions on the observables which guarantee the validity of several general theorems

the critical ising model via kac ward matrices the kac ward formula allows to compute the ising partition function on any finite graph g from the determinant of 22g matrices where g is the genus of a surface in which g embeds we show that in the case of isoradially embedded graphs with critical weights these determinants have quite remarkable properties first of all they satisfy some generalized kramers wannier duality there is an explicit equality relating the determinants associated to a graph and to its dual graph also they are proportional to the determinants of the discrete critical laplacians on the graph g exactly when the genus g is zero or one finally they share several formal properties with the ray singer overline partial torsions of the riemann surface in which g embeds

the reduced relative power operation on abstract domains abstract in the context of standard abstract interpretation theory a reduced relative power operation for functionally composing abstract domains is introduced and studied the reduced relative power of two abstract domains d 1 the exponent and d 2 the base consists in a suitably defined lattice of monotone functions from d 1 to d 2 called dependencies and it is a generalization of the cousot and cousot reduced cardinal power operation the relationship between reduced relative power and nielson s tensor product of abstract domains is also investigated the case of autodependencies i e base and exponent are the same domain turns out to be particularly interesting under certain hypotheses the domain of autodependencies corresponds to a powerset like completion of the base abstract domain providing a compact set theoretic representation for autodependencies two relevant applications of the reduced relative power operation in the fields of logic program analysis and semantics design are presented notably it is proved that the wellknown abstract domain def for logic program ground dependency analysis can be characterized as the domain of autodependencies of the standard abstract domain representing plain groundness information only on the semantics side it is shown how reduced relative power can be exploited in order to systematically derive compositional semantics for logic programs

bottom up abstract interpretation of logic programs abstract this paper presents a formal framework for the bottom up abstract interpretation of logic programs which can be applied to approximate answer substitutions partial answer substitutions and call patterns for a given program and arbitrary initial goal the framework is based on a tp like semantics defined over a herbrand universe with variables which has previously been shown to determine the answer substitutions for arbitrary initial goals the first part of the paper reconstructs this semantics to provide a more adequate initial goals the first part of the paper reconstructs this semantics to provide a more adequate basis for abstract interpretation a notion of abstract substitution is introduced and shown to determine an abstract semantic function which for a given program can be applied to approximate the answer substitutions for an arbitrary initial goal the second part of the paper extends the bottom up approach to provide approximations of both partial answer substitutions and call patterns this is achieved by applying magic sets and other existing techniques to transform a program in such a way that the answer substitutions of the transformed program correspond to the partial answer substitutions and call patterns of the original program this facilitates the analysis of concurrent logic programs ignoring synchronization and provides a collecting semantics which characterizes both success and call patterns

auxiliary vertices method for kagome lattice eight vertex model we investigate a class of eight vertex models on a kagome lattice with the help of auxiliary vertices the kagome lattice eight vertex model kevm is related to an inhomogeneous system which leads to a one parameter family of commuting transfer matrices using an equation for commuting transfer matrices we determine their eigenvalues from calculated eigenvalues the correlation length of the kevm is derived with its full anisotropy there are two cases in the first case the anisotropic correlation length acl is the same as that of the triangular honeycomb lattice ising model by the use of an algebraic curve it is shown that the kagome lattice ising model the diced lattice ising model and the hard hexagon model also have essentially the same acl as the kevm in the second case we find that the acl displays 12fold rotational symmetry

new solvable lattice models in three dimensions in this paper we establish a remarkable connection between two seemingly unrelated topics in the area of solvable lattice models the first is the zamolodchikov model which is the only nontrivial model on a three dimen sional lattice so far solved the second is the chiral potts model on the square lattice and its generalization associated with theu q sl n algebra which is of current interest due to its connections with high genus algebraic curves and with representations of quantum groups at roots of unity we show that this last sl n generalized chiral potts model can be interpreted as a model on a threedimensional simple cubic lattice consisting ofn square lattice layers with ann valued n 2 spin at each site further in then 2 case this three dimen sional model reduces after a modification of the boundary conditions to the zamolodchikov model we mentioned above

eight vertex model anisotropic interfacial tension and equilibrium crystal shape the anisotropic interfacial tension of the eight vertex model is found by a new method which introduces two inhomogeneous systems as the width of the system becomes large a doublet of the largest eigenvalues of the row row transfer matrix is asymptotically degenerate the anisotropic interfacial tension is calculated from their finite size correction terms in this limit by the use of the anisotropic interfacial tension the equilibrium crystal shape of the eight vertex model is derived via wulff s construction the equilibrium crystal shape is represented as a simple algebraic curve we discuss the close relation between the algebraic curve and the form of an elliptic function appearing in the expression of the interfacial tension

spatial anisotropy and rotational invariance of critical hard squares we develop a new method to analyse solvable models defined on a square lattice rotated through an arbitrary angle phi with respect to the coordinate axes in the method we introduce auxiliary faces into a rotated system to relate it with an inhomogeneous one in the natural orientation phi 0 the inhomogeneous system is investigated by commuting a transfer matrix argument as an application of the method we consider interacting hard squares at the critical point we discuss relations between spatial anisotropy and rotational or conformal invariance of the model in calculations of finite size properties

equilibrium crystal shape of hard squares with diagonal attractions the author exactly calculates the anisotropic interfacial tension of a square lattice gas model with nearest neighbour exclusion and next nearest neighbour attractions this is achieved by a method which introduces the shift operator into the standard transfer matrix argument from the calculated anisotropic interfacial tension the equilibrium crystal shape ecs is derived by the use of the wulff construction the ecs is a closed curve in the x y plane represented as cosh lambda x y kbt a3cosh lambda x y kbt a4 2 0 with a scale factor lambda and constants a3 a4 he argues that this shape is a universal one which appears as the ecss of a wide class of models