solutions of the yang baxter equation for isotropic quantum spin chains the author considers solutions of the yang baxter equation such that the logarithmic derivative of the transfer matrix yields a quantum spin hamiltonian which is isotropic in spin space i e su 2 invariant four such solutions are known for each value of the spin s for s 1 2 they degenerate into the same solution and for s 1 they only give three different solutions for s or 6 he shows that these are the only solutions which are su 2 invariant except for s 3 when there is a fifth solution

the method of fundamental solutions for the numerical solution of the biharmonic equation abstract the method of fundamental solutions mfs is a relatively new technique for the numerical solution of certain elliptic boundary value problems it falls in the class of methods generally called boundary methods and like the well known boundary integral equation method is applicable when a fundamental solution of the differential equation is known in the mfs the approximate solution is a linear combination of fundamental solutions with singularities placed outside the domain of the problem the locations of the singularities are either preassigned or determined along with the coefficients of the fundamental solutions so that the approximate solution satisfies the boundary conditions as well as possible in many applications these quantities are determined by a least squares fit of the boundary conditions a nonlinear problem which is solved using standard software in this paper the mfs is formulated for biharmonic problems and is applied to a variety of standard test problems as well as to problems arising in elasticity and fluid flow

some nondifferentiable multiobjective programming under generalized d v type i univexity in this paper we introduce new classes of functions called d v type i univex by extending the definition of d v type i functions and consider a multiobjective optimization problem involving generalized d v type i univex functions a number of karush kuhn tucker type sufficient optimality conditions are obtained for a feasible solution to be a weak pareto efficient solution the mond weir type duality results are also presented the results obtained in this paper generalize and extend the previously known result in this area

variational analysis in nonreflexive spaces and applications to control problems with l 1 perturbations we provide a refined sensitivity analysis for finite and infinite horizon control problems where in both cases the perturbation space is l 1 our underlying technique relies on a recent sequential description of both the generalized gradient of clarke and of the approximate g subdifferential of functions defined on a smooth banach space we also show that the proximal limit formula for the generalized gradient and its l p analogue are direct consequences of these sequential formulas related characterizations of lipschitzness of a function on a smooth space are given

on multiple objective optimization with generalized univexity abstract a multiple objective optimization problem involving generalized univex functions is considered kuhn tucker type sufficient optimality conditions are obtained for a feasible point to be an efficient or properly efficient solution mond weir type duality results are obtained further a vector valued lagrangian is introduced and certain vector saddlepoint results are presented

applicability and applications of the method of fundamental solutions in the present work we investigate the applicability of the method of fundamental solutions for the solution of boundary value problems of elliptic partial differential equations and elliptic systems more specifically we study whether linear combinations of fundamental solutions can approximate the solutions of the boundary value problems under consideration in our study the singularities of the fundamental solutions lie on a prescribed pseudo boundary the boundary of a domain which embraces the domain of the problem under consideration we extend previous density results of kupradze and aleksidze and of bogomolny to more general domains and partial differential operators and with respect to more appropriate norms our domains may possess holes and their boundaries are only required to satisfy a rather weak boundary requirement namely the segment condition our density results are with respect to the norms of the spaces c l analogous density results are obtainable with respect to holder norms we have studied approximation by fundamental solutions of the laplacian biharmonic and m harmonic and modified helmholtz and poly helmholtz operators in the case of elliptic systems we obtain analogous density results for the cauchy navier operator as well as for an operator which arises in the linear theory of thermo elasticity we also study alternative formulations of the method of fundamental solutions in cases when linear combinations of fundamental solutions of the equations under consideration are not dense in the solution space finally we show that linear combinations of fundamental solutions of operators of order m 4 with singularities lying on a prescribed pseudo boundary are not in general dense in the corresponding solution space

optimality and duality in multiobjective fractional programming involving ρ semilocally type i preinvex and related functions abstract optimality conditions are obtained for a nonlinear fractional multiobjective programming problem involving semidifferentiable functions also a general dual is formulated and a duality result is proved using concepts of generalized semilocally type i preinvex functions

nonsmooth multiobjective optimization using limiting subdifferentials in this study using the properties of limiting subdifferentials in nonsmooth analysis and regarding a separation theorem some weak pareto optimality necessary and sufficient conditions for nonsmooth multiobjective optimization problems are proved

diffusion problems using transient discrete source superposition discrete source superposition techniques seek sets of discrete singular source strengths which satisfy the boundary conditions of a particular problem and necessarily the governing differential equation the sum of the fields produced by such sources thus provides an approximation to the required solution in many respects these techniques are a special case of conventional boundary integral equation methods where density distributions of smeared sources are sought in this paper an attempt is made to extend the discrete source superposition technique to transient problems the example addressed is the transient diffusion equation the method developed does seem to have some promise it is found that even coarse spatial discretization can yield quite accurate results and that surprisingly large timesteps can be employed and accuracy maintained further although no direct comparisons are made the absence of spatial integrations indicates that the computational effort per timestep is likely to be less than for conventional bie

some nondifferentiable multiobjective programming problems in this paper it is shown that a relaxation defining the class of generalized d v type i functions leads to a new class of multi objective problems which preserves the sufficient optimality and duality results in the scalar non differentiable case and avoids the major difficulty of verifying that the inequality holds for the same kernel function the results obtained in this paper generalize and extend the previously known results in this area

zn n 1 generalization of the chiral potts model we show that ther matrix which intertwines twon by nn 1 state cyclicl operators related with a generalization ofuq sl n algebra can be considered as a boltzmann weight of four spin box for a lattice model with two spin interaction just as ther matrix of the checkerboard chiral potts model the rapidity variables lie on the algebraic curve of the genusg n2 n 1 n 1 n n 1 defined by 2n 3 independent moduli this curve is a natural generalization of the curve which appeared in the chiral potts model factorization properties of thel operator and its connection to the sos models are also discussed

solutions of the quantum yang baxter equation with extra nonadditive parameters we present a systematic technique to construct solutions to the yang baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters these extra parameters enter the yang baxter equation in a similar way to the spectral parameter but in a non additive form we exploit the fact that quantum non compact algebras such as uq su 1 1 and type i quantum superalgebras such as uq gl 1 mod 1 and uq gl 2 mod 1 are known to admit non trivial one parameter families of infinite dimensional and finite dimensional irreps respectively even for generic q we develop a technique for constructing the corresponding spectral dependent r matrices as examples we work out the the r matrices for the three quantum algebras mentioned above in certain representations

an invariant method of fundamental solutions for two dimensional isotropic linear elasticity abstract in this paper we propose an invariant method of fundamental solutions for solving boundary value problems in two dimensional isotropic linear elasticity the invariant method of fundamental solutions keeps a very basic natural property the so called invariance property under trivial coordinate changes in the problem description e g dilations and or contractions the problems are solved by the tikhonov regularization method in conjunction with morozov s discrepancy principle finally five examples of boundary value problems are investigated to show the efficiency of this method the numerical convergence accuracy and stability of the proposed method with respect to the number of source points the distance between the sources and the boundary and the amount of noise added into the input data respectively are also analyzed

generalized euler identity for subdifferentials of homogeneous functions and applications in this paper we mainly consider subdifferentials and basic subdifferentials of homogeneous functions defined on real banach space and asplund space respectively and obtain the generalized euler identity as applications we consider constrained optimization problems and several geometric properties of banach space

multiobjective programming under generalized type i invexity in this paper we extend a scalarized generalized type i invexity into a vector invexity v type i a number of sufficiency results are established using lagrange multiplier conditions and under various types of generalized v type i requirements weak strong and converse duality theorems are proved in the generalized v invexity type i setting

necessary conditions for constrained optimization problems in smooth banach spaces and applications we derive necessary optimality conditions for constrained minimization problems with lower semicontinuous inequality constraints continuous equality constraints and a set constraint in smooth banach spaces then we apply these necessary optimality conditions to derive subdifferential characterizations of singular normal vectors to the epigraph and the graph of a function subdifferential calculus and necessary optimality conditions for mathematical programs with equilibrium constraints

a new kirchhoff plate model based on a modified couple stress theory in this paper a new kirchhoff plate model is developed for the static analysis of isotropic micro plates with arbitrary shape based on a modified couple stress theory containing only one material length scale parameter which can capture the size effect the proposed model is capable of handling plates with complex geometries and boundary conditions from a detailed variational procedure the governing equilibrium equation of the micro plate and the most general boundary conditions are derived in terms of the deflection using the principle of minimum potential energy the resulting boundary value problem is of the fourth order instead of existing gradient theories which is of the sixth order and it is solved using the method of fundamental solutions mfs which is a boundary type meshless method several plates of various shapes aspect and poisson s ratios are analyzed to illustrate the applicability of the developed micro plate model and to reveal the differences between the current model and the classical plate model moreover useful conclusions are drawn from the micron scale response of this new kirchhoff plate model

the method of fundamental solutions for the solution of steady state free boundary problems abstract the method of fundamental solutions is formulated for the solution of steady state free boundary problems the method is tested on three such problems and the results compared to published results obtained with other numerical methods

the effective condition number applied to error analysis of certain boundary collocation methods abstract the boundary collocation method bcm is widely used in the engineering community for the numerical solution of linear boundary value problems it is commonly stated that the results computed by this method are affected by large rounding errors this conclusion is based on a simple worst case analysis using the conventional condition number for linear systems in this paper we present a refined error analysis for a class of boundary value problems using the concept of effectively well conditioned systems this analysis leads to much smaller a priori bounds for the rounding error in the computed bcm solution these smaller bounds imply that the numerically computed solution expresses much more accurately than previously supposed properties of the ideal bcm solution computed with infinite precision therefore the intrinsic properties of the bcm can be investigated through numerical computations to a far larger extent than previously supposed thus allowing for a numerical diagnostic investigation of the bcm for example when the bcm is applied to problems with certain geometries it is observed that the approximation does not converge using our new smaller error bounds we conclude that the lack of convergence of the bcm solution for these geometries is due to the bcm itself and not to rounding errors

new exact integrable spin 1 quantum chains new exactly integrable quantum spin 1 chains are derived these new quantum hamiltonians like the xxz chain have a free parameter anisotropy and commute with the z component of the total magnetization the eigenvalues and eigenvectors are obtained directly by imposing a generalized coordinate bethe ansatz the derived bethe ansatz equations have an unusual form and the associated r matrix has a dependence with the spectral parameter that is not of difference form like the hubbard quantum chain

nonsmooth multiple objective optimization in separable hilbert spaces abstract this paper provides new necessary and sufficient optimality conditions for nonsmooth multiple objective optimization programs in separable hilbert spaces

necessary and sufficient conditions in constrained optimization additional conditions are attached to the kuhn tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization under appropriate constraint qualifications necessary and sufficient conditions are also given for optimality of the dual problem duality and converse duality are treated accordingly

the trefftz method using fundamental solutions for biharmonic equations in this paper the trefftz method of fundamental solution fs called the method of fundamental solution mfs is used for biharmonic equations the bounds of errors are derived for the mfs with almansi s fundamental solutions denoted as the mafs in bounded simply connected domains the exponential and polynomial convergence rates are obtained from highly and finitely smooth solutions respectively the stability analysis of the mafs is also made for circular domains numerical experiments are carried out for both smooth and singularity problems the numerical results coincide with the theoretical analysis made when the particular solutions satisfying the biharmonic equation can be found the method of particular solutions mps is always superior to the mfs and the mafs based on numerical examples however if such singular particular solutions near the singular points do not exist the local refinement of collocation nodes and the greedy adaptive techniques can be used for seeking better source points based on the computed results the mfs using the greedy adaptive techniques may provide more accurate solutions for singularity problems moreover the numerical solutions by the mafs with almansi s fs are slightly better in accuracy and stability than those by the traditional mfs hence the mafs with the afs is recommended for biharmonic equations due to its simplicity

analysis on the method of fundamental solutions for biharmonic equations abstract in this paper the error and stability analysis of the method of fundamental solution mfs is explored for biharmonic equations the bounds of errors are derived for the fundamental solutions r 2 ln r in bounded simply connected domains and the polynomial convergence rates are obtained for certain smooth solutions the bounds of condition number are also derived to show the exponential growth rates for disk domains numerical experiments are carried out to support the above analysis which is the first time to provide the rigorous analysis of the mfs using r 2 ln r for biharmonic equations

on the equivalence of the trefftz method and method of fundamental solutions for laplace and biharmonic equations in this paper it is proved that the two approaches known in the literature as the method of fundamental solutions mfs and the trefftz method are mathematically equivalent in spite of their essentially minor and apparent differences in formulation in deriving the equivalence of the trefftz method and the mfs for the laplace and biharmonic problems it is interesting to find that the complete set in the trefftz method for the laplace and biharmonic problems are embedded in the degenerate kernels of the mfs the degenerate scale appears using the mfs when the geometrical matrix is singular the occurring mechanism of the degenerate scale in the mfs is also studied by using circulant the comparison of accuracy and efficiency of the two methods was addressed

fundamental solutions method for elliptic boundary value problems we consider a procedure for solving boundary value problems for elliptic homogeneous equations known as the fundamental solutions method we prove its applicability for some second order operators as well as for fourth order ones the boundary conditions of an elliptic problem are approximated by using fundamental solutions of the corresponding operator with singularities located outside the domain of interest in a specific case of the laplacian an estimate shows that the method discussed possesses convergence properties as good as those of any method using harmonic polynomials as trial functions numerical examples are given among which are simple signorini s problems for harmonic and lame operators

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

nondifferentiable multiobjective programming under generalized di invexity abstract in this paper we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints we introduce new concepts of d i invexity and generalized d i invexity in which each component of the objective and constraint functions is directionally differentiable in its own direction d i new fritz john type necessary and karush kuhn tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be weakly efficient efficient or properly efficient moreover we prove weak strong converse and strict duality results for a mond weir type dual under various types of generalized d i invexity assumptions

grid optimization for the boundary element method the quality of solution obtained using the boundary element method bem is dependent on how the boundary is discretized this is particularly true in domains of complex geometry a rule for grid optimization for the bem is derived on the bases of an asymptotic measure of the boundary element error that preserves the number of elements degrees of freedom three example problems are provided to show the advantages of grid optimization in terms of accuracy and cost

yang baxterization of braid group representations for a given braid group representation bgr a process of the yang baxterization is formulated to generate solutions of the yang baxter equation ybe when a bgr admits the birman wenzl bw algebraic structure this process can be explicitly passed through and two types of trigonometric solutions of ybe are generated from such a bgr these two solutions have the essential difference to each other and both of them preserve the crossing symmetry property if the given bgr has by taking certain reduction on the bw algebra the rational solution is also generated a practical condition to judge whether a bgr satisfies the bw algebra is given from which one finds that not only the familiar bgrs of 5 7 9 but also some new ones obtained recently in 12 have the bw structure thus they can be explicitly yang baxterized to solutions of the ybe

cyclic l operator related with a 3 state r matrix we consider the problem of constructing a cyclicl operator associated with a 3 stater matrix related to theuq sl 3 algebra atqn 1 this problem is reduced to the construction of a cyclic i e with no highest weight vector representation of some twelve generating element algebra which generalizes theuq sl 3 algebra we found such representation acting incn cn cn the necessary conditions of the existence of the intertwining operator for two representations are also discussed

representations of the quantum doubles of finite group algebras and spectral parameter dependent solutions of the yang baxter equation quantum doubles of finite group algebras form a class of quasitriangular hopf algebras that algebraically solve the yang baxter equation each representation of the quantum double then gives a matrix solution of the yang baxter equation such solutions do not depend on a spectral parameter and to date there has been little investigation into extending these solutions such that they do depend on a spectral parameter here we first explicitly construct the matrix elements of the generators for all irreducible representations of quantum doubles of the dihedral groups dn these results may be used to determine constant solutions of the yang baxter equation we then discuss baxterization ansatze to obtain solutions of the yang baxter equation with a spectral parameter and give several examples including a new 21 vertex model we also describe this approach in terms of minimal dimensional representations of the quantum doubles of the alternating group a4 and the symmetric group s4

some vector optimization problems in banach spaces with generalized convexity abstract in this paper we consider a vector optimization problem where all functions involved are defined on banach spaces new classes of generalized type i functions are introduced for functions between banach spaces based upon these generalized type i functions we obtain a few sufficient optimality conditions and prove some results on duality

the almansi method of fundamental solutions for solving biharmonic problems a new fundamental solutions method for the numerical solution of two dimensional biharmonic problems is described in this method which is based on the almansi representation of a biharmonic function in the plane the approximate solution is expressed in terms of fundamental solutions of laplace s equation and is determined by a least squares fit of the boundary conditions the results of numerical experiments which demonstrate the efficacy of the method are presented

multiobjective programming under d invexity abstract in this paper a generalization of convexity is considered in the case of nonlinear multiobjective programming problem where the functions involved are nondifferentiable by considering the concept of pareto optimal solution and substituting d invexity for convexity the fritz john type and karush kuhn tucker type necessary optimality conditions and duality in the sense of mond weir and wolfe for nondifferentiable multiobjective programming are given

a novel 15 vertex solution of the sutherland equation the sutherland equation 1970 implying exact integrability of vertex models is studied on a two dimensional square lattice a novel 15 vertex solution commuting with a spin 1 hamiltonian is constructed

comment on solutions of the yang baxter equation for isotropic quantum spin chains we comment on a recent paper by kennedy j phys a math gen 25 1992 2809 in which a systematic search for integrable spin s su 2 invariant quantum chains for s or 6 revealed four spin s families of integrable chains along with an additional integrable chain at s 3 we identify these su 2 invariant chains with known g invariant r matrices where g is a simple lie algebra and give arguments that kennedy s results may well constitute the complete classification of integrable spin s su 2 invariant chains

let s baxterise we recall the concept of baxterisation of an r matrix or of a monodromy matrix which corresponds to build from one point in the r matrix parameter space the algebraic variety where the spectral parameter s live we show that the baxterisation which amounts to studying the iteration of a birational transformation is a win win strategy it enables to discard efficiently the non integrable situations focusing directly on the two interesting cases where the algebraic varieties are of the so called general type finite order iteration or are abelian varieties infinite order iteration we emphasize the heuristic example of the sixteen vertex model and provide a complete description of the finite order iterations situations for the baxter model we show that the baxterisation procedure can be introduced in much larger frameworks where the existence of some underlying yang baxter structure is not used we baxterise l operators local quantum lax matrices and quantum hamiltonians

universal baxterization for z graded hopf algebras we present a method for baxterizing solutions of the constant yang baxter equation associated with z graded hopf algebras to demonstrate the approach we provide examples for the taft algebras and the quantum group u q sl 2

optimality and duality in nondifferentiable multiobjective optimization involvingd type i and related functions abstract in this paper new classes of functions namely d type i d quasitype i and d pseudo type i are defined for a multiobjective nondifferentiable programming problem kuhn tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be a weak minimum for this problem two duals are formulated and various duality results are given by using the above defined classes of functions considering the concept of a weak minimum

dilute birman wenzl murakami algebra and dn 1 2 models a dilute generalization of the birman wenzl murakami algebra is considered it can be baxterized to a solution of the yang baxter algebra the dn 1 2 vertex models constitute a series of solvable lattice models which realize this algebraic structure they can be regarded as a dilute version of the bn 1 vertex models

expressions for subdifferential and optimization problems defined by nonsmooth homogeneous functions abstract in this paper we prove a theoretical expression for subdifferentials of lower semicontinuous and homogeneous functions the theoretical expression is a generalization of the euler formula for differentiable homogeneous functions as applications of the generalized euler formula we consider constrained optimization problems defined by nonsmooth positively homogeneous functions in smooth banach spaces some results concerning karush kuhn tucker points and necessary optimality conditions for the optimization problems are obtained

pre invex functions in multiple objective optimization and called such functions convexlike if s is a convex set and if f is a convex function then clearly f is convexlike elster and nehse obtained a saddlepoint optimality condition for convexlike mathematical programs hayashi and komiya 9 also considered convexlike functions and developed a gordan type theorem of the alternative involving convexlike functions and in addition considered lagrangian duality for convexlike programs hanson 7 considered differentiable functions f s r for which there exists an n dimensional vector function q q u such that for all x u e s

universal spectral parameter dependent lax operators for the drinfeld double of the dihedral group d3 two universal spectral parameter dependent lax operators are presented in terms of the elements of the drinfeld double d d3 of the dihedral group d3 applying representations of d d3 to these yields matrix solutions of the yang baxter equation with a spectral parameter

d invexity and optimality conditions abstract in this paper a generalization of convexity called d invexity is introduced substituting d invex for convex we get some optimality conditions for nondifferentiable multiobjective programming the application is demonstrated by an example

symmetric structure of field algebra of g spin models determined by a normal subgroup let g be a finite group and h a normal subgroup d h g is the crossed product of c h and cg which is only a subalgebra of d g the double algebra of g one can construct a c subalgebra fh of the field algebra f of g spin models so that fh is a d h g module algebra whereas f is not then the observable algebra a h g is obtained as the d h g invariant subalgebra of fh and there exists a unique c representation of d h g such that d h g and a h g are commutants with each other