difference equations for correlation functions of a 1 n 1 face model with boundary reflection the a 1 n 1 face model with boundary reflection is considered on the basis of the boundary corner transfer matrix bootstrap we construct the fused boundary boltzmann weights to determine the normalization factor we derive difference equations of the quantum knizhnik zamolodchikov type for correlation functions of the boundary model the simplest difference equations are solved in the case of the free boundary condition

compactness of the neumann operator on singular complex spaces let x be a hermitian complex space of pure dimension n we show that the neumann operator on p q forms is compact at isolated singularities of x if p q n 1 n and q 1 the main step is the construction of compact solution operators for the equation on such spaces which is based on a general characterization of compactness in function spaces on singular spaces and that leads also to a criterion for compactness of more general green operators on singular spaces

on the heat kernel of the bergmann metric on algebraic varieties the restriction of the standard fubini study metric of ycpn l to m m is an incomplete kahler metric g called the bergmann metric let us consider the operators d and 3 defined on c1 functions and c1 1 forms on m m respectively we define the domain 9y d of d to be the set of c1 functions 2 f defined on m m such that both f and df are in l similarly we define the domain 92 6 of to be the set of c1 1 forms co such that both co and 2 6 o are in l we then define the laplacian a with respect to the bergmann metric by a d with domain 9 a given by the set of c2 functions f such that f e 9 d and df e 6 the main purpose of this paper is to show that

decision network polynomials and the sensitivity of decision support models abstract decision makers benefit from the utilization of decision support models in several applications obtaining managerial insights is essential to better inform the decision process this work offers an in depth investigation into the structural properties of decision support models we show that the input output mapping in influence diagrams decision trees and decision networks is piecewise multilinear the conditions under which sensitivity information cannot be extracted through differentiation are examined in detail by complementing high order derivatives with finite change sensitivity indices we obtain a systematic approach that allows analysts to gain a wide range of managerial insights a well known case study in the medical sector illustrates the findings

cheeger goreski macpherson s conjecture for the varieties with isolated singularities in 2 cheeger goreski macpherson asked the following question let vclpn ie be a projective variety and let v be the set of regular points of v is the l 2 de rham cohomology group of v with respect to the fubini study metric canonically isomorphic to the intersection cohomology group of v in virtue of the works of cheeger 1 hsian pati 3 and nagase 4 we know that the conjecture is true if dim v 2 our proof will be based on the previous work 5 which complements a result of l saper asserting that there exists a complete kfihler metric ds 2 on v such that the l 2 de rham cohomology group of v with respect to ds 2 is canonically isomorphic to the intersection cohomology group of v to relate saper s l 2 cohomology group to the original one the two metrics ds 2 and say ds 2 shall be connected by a path ds 2 e d s 2 eel0 1 then we shall see that a sharpened version of h6rmanderdonnelly fefferman s l 2 estimate is true for this family cf prop 10 which enables us to compare the space of harmonic forms with respect to ds2v and ds 2 in short it will be shown that the ordinary l 2 cohomology is canonically isomorphic to certain l 2 cohomology which is already known to be isomorphic to the intersection cohomology the manuscript of the present work was written during the author s stay at bergische universitfit gesamthochschule wuppertal on the occasion of aktivitfit in komplex analysis in mpi at bonn he would like to express deep gratitude to the hospitality of these institutions

local geometry of singular real analytic surfaces let v r n be a compact real analytic surface with isolated singularities and assume its smooth part v 0 is equipped with a riemannian metric that is induced from some analytic riemannian metric on r n we prove 1 each point of v has a neighborhood which is quasi isometric naturally and almost isometrically to a union of metric cones and horns glued at their tips 2 a full asymptotic expansion for any p v of the length of v n q dist q p r as r 0 0 3 a gauss bonnet theorem saying that each singular point contributes 1 l 2 where l is the coefficient of the linear term in the expansion of 2 4 the l 2 stokes theorem selfadjointness and discreteness of the laplace beltrami operator on vo an estimate on the heat kernel and a gauss bonnet theorem for the l 2 euler characteristic as a central tool we use resolution of singularities

l 2 serre duality on domains in complex manifolds and applications an l 2 version of the serre duality on domains in complex manifolds involving duality of hilbert space realizations of the operator is established this duality is used to study the solution of the equation with prescribed support applications are given to closed extension of forms as well to bochner hartogs type extension of cr functions comp e with the quotient topology where we endow spaces of compactly supported forms with the natural inductive limit topology in fact condition that the two maps in 1 have closed range is also necessary for the duality theorem to hold see 9 also see 26 27 28 for further results of this type serre s original proof 33 is based on sheaf theory and the theory of topological vector spaces a different approach to this result in the case when is a compact complex manifold was given by kodaira using hodge theory see 23 or 7 in this note we extend kodaira s method to non compact hermitian manifolds to obtain an l 2 analog of the serre duality special cases of serre duality using l 2 methods have appeared before in many contexts see 25 or 11 theorem 5 1 7 and 19 20 for example our treatment aims to streamline and systematize these results with emphasis on non compact manifolds and point out its close relation with the choice of l 2 realizations of the cauchy riemann operator or alternatively choice of boundary conditions for the l 2 realizations of the formal complex laplacian e e e e the l 2 duality can be interpreted in many ways at one level it is a duality between the standard laplacian with neumann boundary conditions and thec laplacian with dual dirichlet boundary conditions using another approach results regarding solution of the equation in l 2 can be converted to statements regarding the solution of the c equation this leads to a solution of the cauchy problem i e solution of the equation with prescribed support at the heart of the matter lies the existence of

pure hodge structure on the l_2 cohomology of varieties with isolated singularities cheeger goresky and macpherson conjectured in cgm an l2 de rham theorem that the intersection cohomology of a projective variety v is naturally isomorphic to the l2 cohomology of the incomplete manifold v singv with metric induced by a projective embedding the early interest in this conjecture was motivated in large part by the hope that one could then put a pure hodge structure on the intersection cohomology of v and even extend the rest of the kahler package cgm to this context saito s1 s2 eventually established the kahler package for intersection cohomology without recourse to l2 cohomology techniques however interest in l2 cohomology did not disappear with this result since among other things l2 cohomology provides intrinsic geometric invariants of an arbitrary complex projective variety which are not apparent from the point of view of d modules for instance l2 coholomology groups depend on boundary conditions ps which as we show here must be treated carefully in order to give the correct hodge components for the l2 cohomology of a singular variety a related fact is that for incomplete manifolds the pure hodge structure and lefschetz decompositions are not direct consequences of the kahler condition as they are in the compact case indeed the primary obstruction to obtaining a hodge structure on the l2 cohomology is the following apparent technicality on an incomplete kahler manifold there are several potentially distinct definitions of a square integrable harmonic form for example a form h might be considered harmonic if dh 0 h or if h 0 h or simply if h 0 moreover there are further domain considerations one imposes boundary conditions which turn out to have no effect on cohomology in the case of d but are crucial for cohomology on a compact or even complete manifold all these definitions of harmonics coincide and one obtains the pure hodge structure by decomposing harmonic forms into their p q components the p q components are harmonic in the weakest sense they are in the kernel of the equality of the different notions of harmonic then allows one to realize these p q components as spaces of both and d cohomology classes the equivalence of the different definitions of harmonic is also required in order to obtain the lefschetz decomposition a local computation shows that interior product with the kahler form preserves the kernel of but one requires the equivalence to see that this also induces an endomorphism on the l2 cohomology

valuation based systems for bayesian decision analysis this paper proposes a new method for representing and solving bayesian decision problems the representation is called a valuation based system and has some similarities to influence diagrams however unlike influence diagrams which emphasize conditional independence among random variables valuation based systems emphasize factorizations of joint probability distributions also whereas influence diagram representation allows only conditional probabilities valuation based system representation allows all probabilities the solution method is a hybrid of local computational methods for the computation of marginals of joint probability distributions and the local computational methods for discrete optimization problems we briefly compare our representation and solution methods to those of influence diagrams

l 2 properties of the overline partial and the overline partial neumann operator on spaces with isolated singularities let x be a hermitian complex space of pure dimension with only isolated singularities and pi m rightarrow x a resolution of singularities let omega subset subset x be a domain with no singularities in the boundary omega omega setminus mathrm sing x and omega pi 1 omega we relate l 2 properties of the overline partial and the overline partial neumann operator on omega to properties of the corresponding operators on omega where the situation is classically well understood outside some middle degrees there are compact solution operators for the overline partial equation on omega exactly if there are such operators on the resolution omega and the overline partial neumann operator is compact on omega exactly if it is compact on omega

sequential valuation networks for asymmetric decision problems abstract this paper deals with representation and solution of asymmetric decision problems we describe a new representation called sequential valuation networks that is a hybrid of covaliu and oliver s sequential decision diagrams and shenoy s valuation networks the solution algorithm is based on the idea of decomposing a large asymmetric problem into smaller sub problems and then using the fusion algorithm of valuation networks to solve the sub problems sequential valuation networks inherit many of the strengths of sequential decision diagrams and valuation networks while overcoming many of their shortcomings we illustrate our technique by representing and solving a modified version of covaliu and oliver s manage sci 41 12 1995 1860 reactor problem in complete detail

the bar partial equation on a non reduced analytic space let x be a possibly non reduced analytic space of pure dimension we introduce a notion of overline partial equation on x and prove a dolbeault grothendieck lemma we obtain fine sheaves mathcal a x q of 0 q currents so that the associated dolbeault complex yields a resolution of the structure sheaf mathscr o x our construction is based on intrinsic semi global koppelman formulas on x

on the determinant of one dimensional elliptic boundary value problems we discuss the regularized determinant of elliptic boundary value problems on a line segment our framework is applicable for separated and non separated boundary conditions

l2 overline partial cohomology groups of some singular complex spaces let x be a pure n dimensional where n 2 complex analytic subset in n with an isolated singularity at 0 in this paper we express the l 2 0 q overline partial cohomology groups for all q with 1 q n of a sufficiently small deleted neighborhood of the singular point in terms of resolution data we also obtain identifications of the l 2 0 q overline partial cohomology groups of the smooth points of x in terms of resolution data when x is either compact or an open relatively compact complex analytic subset of a reduced complex space with finitely many isolated singularities

influence diagrams for bayesian decision analysis abstract influence diagrams for representing bayesian decision problems are redefined in a formal way using conditional independence this makes the graphs somewhat more helpful for exploring the consequences of a clients state beliefs some important results about the manipulation of influence diagrams are extended and reviewed as is an algorithm for computing an optimal policy two new results about the manipulation of influence diagrams are derived a novel influence diagram representing a practical decision problem is used to illustrate the methodologies presented in this paper

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

on the heat operators of normal singular algebraic surfaces soit x une surface algebrique singuliere normale sur c plongee dans l espace projectif p n c l ensemble singularite s de x est un ensemble fini de points isoles en restreignant la metrique de fubini study de p n c a 7b h x s on obtient une variete de riemann incomplete 7b h g on considere le laplacien d agissant sur les fonctions de carre integrable sur 7b h g on demontre que 1 le laplacien est auto adjoint 2 l operateur de la chaleur exp t est de classe trace et il existe une constante k 0 telle que tr exp t kt 2 0 t t 0

degenerating hermitian metrics and spectral geometry of the canonical bundle abstract let x h be a compact and irreducible hermitian complex space of complex dimension m in this paper we are interested in the dolbeault operator acting on the space of l 2 sections of the canonical bundle of reg x the regular part of x more precisely let d m 0 l 2 m 0 reg x h l 2 m 1 reg x h be an arbitrarily fixed closed extension of m 0 l 2 m 0 reg x h l 2 m 1 reg x h where the domain of the latter operator is c m 0 reg x we establish various properties such as closed range of d m 0 compactness of the inclusion d d m 0 l 2 m 0 reg x h where d d m 0 the domain of d m 0 is endowed with the corresponding graph norm and discreteness of the spectrum of the associated hodge kodaira laplacian d m 0 d m 0 with an estimate for the growth of its eigenvalues several corollaries such as trace class property for the heat operator associated to d m 0 d m 0 with an estimate for its trace are derived finally in the last part we provide several applications to the hodge kodaira laplacian in the setting of both compact irreducible hermitian complex spaces with isolated singularities and complex projective surfaces

an algebraic approach to formulating and solving large models for sequential decisions under uncertainty this article presents an algebraic approach to formulating and solving large models for sequential decisions under uncertainty with this approach decision analysis optimization methods can be applied to complex decision problems which are generally analyzed in management science practice using heuristics using the approach a decision problem is formulated in terms of decision variables random variables and functions relating these variables this leads to a compact representation and a simple algorithm can be used to quickly solve algebraic models that would have decision trees with several hundred thousand endpoints an application to research and development planning illustrates the usefulness of such large sequential decision models

some l2 results for overline partial on projective varieties with general singularities let x be an irreducible n dimensional projective variety in bbb c p n with arbitrary singular locus we prove that the l 2 overline partial p 1 cohomology groups with respect to the fubini study metric of the regular part of x are finite dimensional

influence diagrams with super value nodes involving imprecise information the concept of super value nodes was established to allow dynamic programming to be performed within the theory of influence diagrams and to reduce the computational complexity in solving problems by means of influence diagrams this paper is focused on how influence diagrams with super value nodes are affected by the presence of imprecise information we analyze how to reduce the complexity when evaluating an influence diagram in this framework by modelling these kinds of nodes and random magnitudes in terms of fuzzy random variables finally an applied example of the theoretical results is developed

interaction round a face models with fixed boundary conditions the abf fusion hierarchy we use boundary weights and reflection equations to obtain families of commuting double row transfer matrices for interaction round a face models with fixed boundary conditions in particular we consider the fusion hierarchy of the andrews baxter forrester abf models for which we obtain diagonal elliptic solutions to the reflection equations and find that the double row transfer matrices satisfy functional equations with the same form as in the case of periodic boundary conditions

canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant this article contains an elementary constructive proof of resolution of singularities in characteristic zero our proof applies in particular to schemes of finite type and to analytic spaces so we recover the great theorems of hironaka we introduce a discrete local invariant rm inv x a whose maximum locus determines a smooth centre of blowing up leading to desingularization to define rm inv x we need only to work with a category of local ringed spaces x x cal o x satisfying certain natural conditions if a in x then rm inv x a depends only on widehat cal o x a more generally rm inv x is defined inductively after any sequence of blowings up whose centres have only normal crossings with respect to the exceptional divisors and lie in the constant loci of rm inv x cdot the paper is self contained and includes detailed examples one of our goals is that the reader understand the desingularization theorem rather than simply know it is true

asymptotic behavior of two dimensional stochastic magneto hydrodynamics equations with additive noises this paper is devoted to the investigation of the asymptotic behavior of solutions of the stochastic magneto hydrodynamics equations driven by random exterior forced terms both in the velocity and in the magnetic field the nonlinear term is supposed to be time dependent and satisfies certain dissipative conditions the existence of a random attractor for this random dynamical system is obtained

a note on kirkwood s algebraic method for decision problems the main objectives of this note are to point out some strengths and some limitations of kirkwood s algebraic method for decision problems and to propose a modification to address the limitations the modification is based on the valuation network technique and it enables us to better relate kirkwood s method to the graphical techniques of valuation networks and influence diagrams

valuation network representation and solution of asymmetric decision problems abstract this paper deals with asymmetric decision problems we describe a generalization of the valuation network representation and solution technique to enable efficient representation and solution of asymmetric decision problems the generalization includes the concepts of indicator valuations and effective frames we illustrate our technique by solving howard s used car buyer s problem in complete detail we highlight the contribution of this paper over the symmetric valuation network technique

the bar partial operator on algebraic curves for a singular algebraic curve we show that all closed extensions of bar partial are fredholm and we give a general index formula in particular we prove a modified version of a conjecture due to macpherson

poincare duality hilbert complexes and geometric applications abstract let m g be an open oriented and incomplete riemannian manifold the aim of this paper is to study the following two sequences of l 2 cohomology groups 1 h 2 m m i m g defined as the image h 2 min i m g h 2 max i m g 2 h 2 m m i m g defined as the image h 2 min i m g h 2 max i m g we show under suitable hypothesis that the first sequence is the cohomology of a hilbert complex which contains the minimal one and is contained in the maximal one in particular this leads us to prove a hodge theorem for these groups we also show that when the second sequence is finite dimensional then poincare duality holds and that with the same assumptions when dim m 4 n then we can employ h 2 m m 2 n m g in order to define an l 2 signature on m we prove several applications to the intersection cohomology of compact smoothly stratified pseudomanifolds and we get some results about the friedrichs extension i f of i

the dolbeault complex with weights according to normal crossings in the present paper we define a dolbeault complex with weights according to normal crossings which is a useful tool for studying the bar partial equation on singular complex spaces by resolution of singularities where normal crossings appear naturally the major difficulty is to prove that this complex is locally exact we do that by constructing a local bar partial solution operator which involves only cauchy s integral formula in one complex variable and behaves well for lp forms with weights according to normal crossings

koppelman formulas on the a1 singularity in the present paper we study the regularity of the andersson samuelsson koppelman integral operator on the a 1 singularity particularly we prove l p and c 0 estimates as applications we obtain l p homotopy formulas for the dbar equation on the a 1 singularity and we prove that the a forms introduced by andersson samuelsson are continuous on the a 1 singularity

representation and solution of decision problems using sequential decision diagrams in this paper we introduce a new graph the sequential decision diagram to aid in modeling formulation and solution of sequential decision problems under uncertainty while as compact as an influence diagram the sequential diagram captures the asymmetric and sequential aspects of decision problems as effectively as decision trees we show that a unified framework consisting of a sequential diagram an influence diagram and a common formulation table for the problem s data suffices for compact and consistent representation economical formulation and efficient solution of asymmetric decision problems in addition to asymmetry the framework exploits other sources of computational efficiency such as conditional independence and value function decomposition making it also useful in evaluating dynamic programming problems the formulation table and recursive algorithm can be readily implemented in computers for solving large scale problems examples are provided to illustrate the methodology in both

structuring conditional relationships in influence diagrams an influence diagram is a graphical representation of a decision problem that is at once a formal description of a decision problem that can be treated by computers and a representation that is easily understood by decision makers who may be unskilled in the art of complex probabilistic modeling the power of an influence diagram both as an analysis tool and a communication tool lies in its ability to concisely summarize the structure of a decision problem however when confronted with highly asymmetric problems in which particular acts or events lead to very different possibilities many analysts prefer decision trees to influence diagrams in this paper we extend the definition of an influence diagram by introducing a new representation for its conditional probability distributions this extended influence diagram representation combining elements of the decision tree and influence diagram representations allows one to clearly and efficiently represent asymmetric decision problems and provides an attractive alternative to both the decision tree and conventional influence diagram representations

solution of the dual reflection equation for an 1 1 solid on solid model we obtain a diagonal solution of the dual reflection equation for the elliptic an 1 1 solid on solid model the isomorphism between the solutions of the reflection equation and its dual is studied

the equation on a positive current we study the induced equation on a positive current in a complex manifold we extend the l 2 estimates for the equation to harmonic currents of bidimension 1 1 satisfying a frobenius type condition we also show that the l 2 estimates are satisfied for the equation on a positive closed current of bidegree 1 1 on a pseudoconvex domain in n

the equation on homogeneous varieties with an isolated singularity let x be a regular irreducible variety in mathbb cp n 1 y the associated homogeneous variety in mathbb c n and n the restriction of the universal bundle of mathbb cp n 1 to x in the present paper we compute the obstructions to solving the overline partial equation in the lp sense on y for 1 p in terms of cohomology groups h q x mathcal o n mu that allows to identify obstructions explicitly if x is specified more precisely for example if it is equivalent to mathbb cp 1 or an elliptic curve

general solution of reflection equation for eight vertex sos model by using the general solution of the reflection equation for the eight vertex model a general solution of the reflection equation for the eight vertex sos model is obtained we also discuss the solution of the reflection equation for the case of the rsos model