the smooth cohomology of n 2 supersymmetric landau ginzburg field theories we compute the smooth cohomology both unrestricted and compactly supported of the supercharge of an ultraviolet cutoffn 2 supersymmetric landau ginzburg field theory

microwave tomography using topology optimization techniques microwave tomography is a technique in which microwaves illuminate a specimen and measurements of the scattered electrical field are used to determine and depict the specimen s dielectric and conductive properties this article presents a new method to perform the reconstruction the reconstruction method is illustrated by assuming time harmonic scattering in two space dimensions in a setup tailored for medical applications we prove that the resulting constrained nonlinear least squares problem admits a solution the governing helmholtz equation is discretized by using the finite element method and the dielectric properties are allowed to attain different values at each element within a given region the reconstruction algorithm uses methodologies borrowed from topology optimization of linearly elastic structures numerical examples illustrate the reconstruction method in a parameter range typical for human tissue and for the challenging case where the size of the object is in the same order as the wavelength a reasonable estimate of the dielectric properties is obtained by using one observation per 20 unknowns when the permittivity is allowed to vary continuously within a given interval using a priori information that the permittivity attains only certain values results in a good estimate and a sharp image as opposed to topology optimization for structures there is no indication of mesh dependency and checkerboarding when forcing the permittivity to attain discrete values

topology optimization of metallic antennas we introduce an approach to carry out layout optimization of metallic antenna parts an optimization technique first developed for the optimization of load bearing elastic structures is adapted for the purpose of metallic antenna design the local conductivity values in a given region are used as design variables and are iteratively updated by a gradient based optimization algorithm given a set of time domain signals from exterior sources the design objective is here to maximize the energy received by the antenna and transmitted to a coaxial cable the optimization proceeds through a sequence of coarsely defined lossy designs with successively increasing details and less losses as the iterations proceed the objective function gradient is derived based on the fdtd discretization of maxwell s equations and is expressed in terms of field solutions of the original antenna problem and an adjoint field problem the same fdtd code but with different wave sources is used for both the original antenna problem and the adjoint problem for any number of design variables the gradient is evaluated on the basis of only two fdtd simulations one for the original antenna problem and another for the adjoint field problem we demonstrate the capability of the method by optimizing the radiating patch of both uwb monopole and microstrip antennas the uwb monopole is designed to radiate over a wide frequency band 1 10 ghz while the microstrip patch is designed for single and dual frequency band operation in these examples there are more than 20 000 design variables and the algorithm typically converges in less than 150 iterations the optimization results show a promising use of the proposed approach as a general method for conceptual design of near resonance metallic antennas

on classification of n 2 supersymmetric theories we find a relation between the spectrum of solitons of massiven 2 quantum field theories ind 2 and the scaling dimensions of chiral fields at the conformal point the condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetricn 2 conformal theories and their massive deformations in terms of a suitable generalization of dynkin diagrams which coincides with the a d e dynkin diagrams for minimal models the landau ginzburg theories are a proper subset of this classification in the particular case of lg theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of picard lefschetz theory

on the complete classification of unitary n 2 minimal superconformal field theories aiming at a complete classification of unitary n 2 minimal models where the assumption of space time supersymmetry has been dropped it is shown that each modular invariant candidate partition function of such a theory is indeed the partition function of a fully fledged unitary n 2 minimal model subject to the assumptions that orbifolding is a physical process and that the space time supersymmetric mathcal a mathcal d mathcal e models are physical a family of models constructed via orbifoldings of either the diagonal model or of the space time supersymmetric exceptional models then demonstrates that there exists a unitary n 2 minimal model for every one of the allowed partition functions in the list obtained from gannon s work gannon in nucl phys b 491 659 688 1997

some constraints on frobenius manifolds with a tt structure the article gives a necessary and sufficient condition for a frobenius manifold to be a cdv structure we show that there exists a positive definite cdv structure on any semi simple frobenius manifold we also compare three natural connections on a cdv structure and conclude that the underlying hermitian manifold of a non trivial cdv structure is not a kahler manifold finally we compute the harmonic potential of a harmonic frobenius manifold

topology optimization of an acoustic horn we present a method for topology optimization of an acoustic horn with the aim of radiating sound as efficiently as possible using a strategy commonly employed for topology optimization of elastic structures we optimize over a scalar function indicating presence of material the helmholtz equation modeling the wave propagation is solved using the finite element method and the associated adjoint equation provides the required gradients numerical experiments validates that the result of the optimization provides horns with the desired acoustical properties the resulting horns are very efficient in the frequency span subject to optimization

dualities in integrable systems and n 2 susy theories we discuss dualities in the integrable dynamics behind the exact solution to the n 2 susy yang mills theory it is shown that t duality in the string theory is related to the separation of variables procedure in the dynamical system we argue that there are analogues of s duality as well as three dimensional mirror symmetry in the many body systems of hitchin type governing the low energy effective actions

graphs and reflection groups it is shown that graphs that generalize the ade dynkin diagrams and have appeared in various contexts of two dimensional field theory may be regarded in a natural way as encoding the geometry of a root system after recalling what are the conditions satisfied by these graphs we define a bilinear form on a root system in terms of the adjacency matrices of these graphs and undertake the study of the group generated by the reflections in the hyperplanes orthogonal to these roots some non integrally laced graphs are shown to be associated with subgroups of these reflection groups the empirical relevance of these graphs in the classification of conformal field theories or in the construction of integrable lattice models is recalled and the connections with recent developments in the context of mathcal n 2 supersymmetric theories and topological field theories are discussed a claude

f manifolds with flat structure and dubrovin s duality this work continues the study of f manifolds m first defined in hema int math res notices 6 1999 277 286 preprint math qa 9810132 and investigated in he frobenius manifolds and moduli spaces for singularities cambridge university press cambridge 2002 the notion of a compatible flat structure is introduced and it is shown that many constructions known for frobenius manifolds do not in fact require invariant metrics and can be developed for all such triples m in particular we extend and generalize recent dubrovin s duality du2 on almost duality for frobenius manifolds preprint math dg 0307374

electromagnetic theorems for complex anisotropic media complex anisotropic media can generally be described by a 6 times 6 macroscopic constitutive tensor hat c using hat c properties a reaction integral formula is derived from which an anisotropic reaction theorem modified reciprocity theorem is developed reduction of the hat c medium into a reciprocal medium is discussed including tensor symmetry attributes and limiting cases the anisotropic reaction theorem is utilized to derive a zero reaction theorem and then treated in relation to the moment method mutual and self impedance elements of a network are also derived in terms of reaction integrals symmetry covered using the anisotropic reaction theorem and impedance elements related to moment calculations use of spectral domain analysis is also covered

kodaira spencer theory of gravity and exact results for quantum string amplitudes we develop techniques to compute higher loop string amplitudes for twistedn 2 theories with 3 i e the critical case an important ingredient is the discovery of an anomaly at every genus in decoupling of brst trivial states captured to all orders by a master anomaly equation in a particular realization of then 2 theories the resulting string field theory is equivalent to a topological theory in six dimensions the kodaira spencer theory which may be viewed as the closed string analog of the chern simons theory using the mirror map this leads to computation of the number of holomorphic curves of higher genus curves in calabi yau manifolds it is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the correspondingn 2 theory relations withc 1 strings are also pointed out

spectral electromagnetic modeling of a planar integrated structure with a general grounded anisotropic slab a formulation for the solution of the electromagnetic field in vertically stratified structures with a general anisotropic grounded slab under planar electric excitation conditions is presented the development of the solution is obtained by using the two dimensional fourier transform applied to the partial differential equations describing the electromagnetic field which can be expressed in terms of dyadic electric green s functions moreover a spectral equivalent circuit representation of the solution separated into its spectral transverse electric te and transverse magnetic tm components with respect to the vertical direction is given it is demonstrated that such a spectral circuit representation is always possible when the constitutive epsilon and mu tensors are reduced to their diagonal form the transmission line representation for an unbounded gyrotropic medium with vertical preferred axis is presented this theory is applied to a planar structure with an anisotropic biaxial grounded slab and an electric horizontal point source embedded in it numerical examples of evaluation of the radiated pattern and noteworthy information about the radiation on the horizon plane are given

infinite hierarchies of nonlocal symmetries of the chen kontsevich schwarz type for the oriented associativity equations we construct infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using solutions of associated vector and scalar spectral problems the symmetries in question generalize those found by chen kontsevich and schwarz nucl phys b 730 352 63 for the wdvv equations as a byproduct we obtain a darboux type transformation and a conditional backlund transformation for the oriented associativity equations

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

superstrings and topological strings at large n we embed the large n chern simons topological string duality in ordinary superstrings this corresponds to a large n duality between generalized gauge systems with n 1 supersymmetry in four dimensions and superstrings propagating on noncompact calabi yau manifolds with certain fluxes turned on we also show that in a particular limit of the n 1 gauge theory system certain superpotential terms in the n 1 system including deformations if spacetime is noncommutative are captured to all orders in 1 n by the amplitudes of noncritical bosonic strings propagating on a circle with self dual radius we also consider d brane anti d brane system wrapped over vanishing cycles of compact calabi yau manifolds and argue that at large n they induce a shift in the background to a topologically distinct calabi yau which we identify as the ground state system of the brane anti brane system

curves of marginal stability in two dimensional cp n 1 models with zn symmetric twisted masses we consider curves of marginal models in two dimensions with supersymmetry in these theories one can introduce twisted mass terms the bps spectrum has different numbers of states in the weak and strong coupling regimes this spectral restructuring can be explained by the fact that two regimes are separated by cms on which some bps states decay we focus on a special case of zn symmetric twisted masses in this case the general solution due to dorey greatly simplifies and cms can be found explicitly for small n values numerical results are presented in the large n limit we find cms analytically up to ln n n corrections

mirror symmetry in two steps a i b we suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories the first theory is the twisted sigma model of a toric variety in the infinite volume limit the a model the second theory is an intermediate model which we call the i model the equivalence between the a model and the i model is achieved by realizing the former as a deformation of a linear sigma model with a complex torus as the target and then applying to it a version of the t duality on the other hand the i model is closely related to the twisted landau ginzburg model the b model that is mirror dual to the a model thus the mirror symmetry is realized in two steps via the i model in particular we obtain a natural interpretation of the superpotential of the landau ginzburg model as the sum of terms corresponding to the components of a divisor in the toric variety we also relate the cohomology of the supercharges of the i model to the chiral de rham complex and the quantum cohomology of the underlying toric variety

fusion rings and geometry the algebraic structure of fusion rings in rational conformal field theories is analyzed in detail in this paper a formalism which closely parallels classical tools in the study of the cohomology of homogeneous spaces is developed for fusion rings in general and for current algebra theories in particular it is shown that fusion rings lead to a natural orthogonal polynomial structure the rings are expressed through generators and relations the relations are then derived from some potentials leading to an identification of the fusion rings with deformations of affine varieties in general the fusion algebras are mapped to affine varieties which are the locus of the relations the connection with modular transformations is investigated in this picture it is explained how chiral algebras arising in n 2 superconformal field theory can be derived from fusion rings in particular it is argued that theories of the type su n k su n 1 are the n 2 counterparts of grassmann manifolds and that there is a natural identification of the chiral fields with schubert varieties which is a graded algebra isomorphism

geometry and integrability of topological antitopological fusion integrability of equations of topological antitopological fusion being proposed by cecotti and vafa describing the ground state metric on a given 2d topological field theory tft model is proved for massive tft models these equations are reduced to a universal form being independent on the given tft model by gauge transformations for massive perturbations of topological conformal field theory models the separatrix solutions of the equations bounded at infinity are found by the isomonodromy deformations method also it is shown that the ground state metric together with some part of the underlined tft structure can be parametrized by pluriharmonic maps of the coupling space to the symmetric space of real positive definite quadratic forms

kink manifolds in a three component scalar field theory in this work we identify the manifold of solitary waves arising in a three component scalar field model using the bogomol nyi arrangement of the energy functional a rich structure of topological and non topological kinks exists in the different sub models contained in the theory

limits of families of brieskorn lattices and compactified classifying spaces we investigate variations of brieskorn lattices over non compact parameter spaces and discuss the corresponding limit objects on the boundary divisor we study the associated variation of twistors and the corresponding limit mixed twistor structures we construct a compact classifying space for regular singular brieskorn lattices and prove that its pure polarized part carries a natural hermitian structure and that the induced distance makes it into a complete metric space

harmonic maps into lie groups classical solutions of the chiral model on considere deux aspects de la structure algebrique de 7b m l espace des applications harmoniques d un domaine a 2 dimensions simplement connexe dans un groupe de lie reel g r la forme reelle d un groupe complexe g on construit une representation du groupe boucle 7b a s 1 g r sur 7b m correspondant a l algebre de lie de kacmoody des deformations infinitesimales on decrit l action sur 7b m et l action d un sous groupe sur l espace des applications harmoniques dans des gaussmanniens dans une seconde partie on se restreint a une theorie qui s applique seulement quand est un domaine riemannien a 2 dimensions simplement connexe et le groupe est g r u n

dubrovin s duality for f manifolds with eventual identities abstract a vector field e on an f manifold m e is an eventual identity if it is invertible and the multiplication x y x y e 1 defines a new f manifold structure on m we give a characterization of such eventual identities this being a problem raised by manin 2005 12 we develop a duality between f manifolds with eventual identities and we show that this duality is compatible with the local irreducible decomposition of f manifolds and preserves the class of riemannian f manifolds we find necessary and sufficient conditions on the eventual identity which ensure that the classes of harmonic higgs bundles d c h k structures and weak cv structures are preserved by our duality examples of such structures are given in the case of a semi simple multiplication we use eventual identities to construct compatible pairs of metrics

polarized mixed hodge structures and the local monodromy of a variation of hodge structure a variation of polarized hodge structures on the complement of a divisor with normal crossings gives rise locally on the divisor to a commuting set ni of nilpotent endomorphisms of the vector space underlying the variation the logarithms of the unipotent parts of the various picard lefschetz transformations these reflect properties of the singularities of the period map associated to the variation cf 5 7 9 and sect 3 for example a variation depending on a single parameter defines asymptotically a mixed hodge structure whose weight filtration is the monodromy weight filtration of the corresponding endomorphism n 9 11 this paper is mainly concerned with the properties of the set n arising in the several parameters case in particular theorem 3 3 asserts that all the elements in the open polyhedral cone c spanned over r by the n s determine the same monodromy weight filtration it also describes the relationship between this common filtration and those associated to the faces of the cone this statement was conjectured by deligne based on his analogous result 4 1 9 2 for the q cone associated to those variations which arise from families of polarized non singular algebraic varieties in w 1 we discuss some general properties of commuting sets of nilpotent endomorphisms and their associated filtrations section2 focuses on the case when each element in such set defines in the sense of 2 4 a polarized mixed hodge structure with a fixed hodge filtration f as is the case for the monodromy cone c of a variation these conditions imply cf 2 16 a generic uniqueness for the monodromy weight filtration we also consider those pola

an integral structure in quantum cohomology and mirror symmetry for toric orbifolds abstract we introduce an integral structure in orbifold quantum cohomology associated to the k group and the class in the case of compact toric orbifolds we show that this integral structure matches with the natural integral structure for the landau ginzburg model under mirror symmetry by assuming the existence of an integral structure we give a natural explanation for the specialization to a root of unity in y ruan s crepant resolution conjecture yongbin ruan the cohomology ring of crepant resolutions of orbifolds in contemp math vol 403 amer math soc providence ri 2006 pp 117 126

integrable hierarchies and the mirror model of local cp1 abstract we study structural aspects of the ablowitz ladik al hierarchy in the light of its realization as a two component reduction of the two dimensional toda hierarchy and establish new results on its connection to the gromov witten theory of local c p 1 we first of all elaborate on the relation to the toeplitz lattice and obtain a neat description of the lax formulation of the al system we then study the dispersionless limit and rephrase it in terms of a conformal semisimple frobenius manifold with non constant unit whose properties we thoroughly analyze we build on this connection along two main strands first of all we exhibit a manifestly local bi hamiltonian structure of the ablowitz ladik system in the zero dispersion limit second we make precise the relation between this canonical frobenius structure and the one that underlies the gromov witten theory of the resolved conifold in the equivariantly calabi yau case a key role is played by dubrovin s notion of almost duality of frobenius manifolds as a consequence we obtain a derivation of genus zero mirror symmetry for local c p 1 in terms of a dual logarithmic landau ginzburg model

further results on light propagation in helicoidal bianisotropic mediums oblique propagation the recent fabrication of thin film helicoidal bianisotropic mediums hbms has created an impetus for understanding their electromagnetic response using the oseen transformation we have derived a 4 4 matrix ordinary differential equation for oblique i e non axial propagation in general linear hbms a perturbational technique is presented for almost axial propagation and two other techniques one semi analytic and the other analytic are presented for general oblique propagation all three techniques yield exact closed form results for axial propagation our use of the oseen transformation amounts to viewing oblique propagation not by itself but as a graft on axial propagation and is thus responsible for the stability of all three techniques

gpu acceleration of stiffness matrix calculation and efficient initialization of efg meshless methods abstract meshless methods have a number of virtues in problems concerning crack growth and propagation large displacements strain localization and complex geometries among other despite the fact that they do not rely on a mesh meshless methods require a preliminary step for the identification of the correlation between nodes and gauss points before building the stiffness matrix this is implicitly performed with the mesh generation in fem but must be explicitly done in efg methods and can be time consuming furthermore the resulting matrices are more densely populated and the computational cost for the formulation and solution of the problem is much higher than the conventional fem this is mainly attributed to the vast increase in interactions between nodes and integration points due to their extended domains of influence for these reasons computing the stiffness matrix in efg meshless methods is a very computationally demanding task which needs special attention in order to be affordable in real world applications in this paper we address the pre processing phase dealing with the problem of defining the necessary correlations between nodes and gauss points and between interacting nodes as well as the computation of the stiffness matrix a novel approach is proposed for the formulation of the stiffness matrix which exhibits several computational merits one of which is its amenability to parallelization which allows the utilization of graphics processing units gpus to accelerate computations

ising field theory quadratic difference equations for the n point green s functions on the lattice for the two dimensional ising model at arbitrary temperature a system of quadratic difference equations is presented involving the correlations of n order variables and that of n ensuremath 2 order and two disorder variables with suitable boundary conditions these equations specify the correlations

f manifold algebras and deformation quantization via pre lie algebras abstract the notion of an f manifold algebra is the underlying algebraic structure of an f manifold we introduce the notion of pre lie formal deformations of commutative associative algebras and show that f manifold algebras are the corresponding semi classical limits we study pre lie infinitesimal deformations and extension of pre lie n deformation to pre lie n 1 deformation of a commutative associative algebra through the cohomology groups of pre lie algebras we introduce the notions of pre f manifold algebras and dual pre f manifold algebras and show that a pre f manifold algebra gives rise to an f manifold algebra through the sub adjacent associative algebra and the sub adjacent lie algebra we use rota baxter operators more generally o operators and average operators on f manifold algebras to construct pre f manifold algebras and dual pre f manifold algebras

finiteness of ricci flat supersymmetric non linear σ models combining the constraints of kahler differential geometry with the universality of the normal coordinate expansion in the background field method we study the ultraviolet behavior of 2 dimensional supersymmetric non linear models with target space an arbitrary riemannian manifoldm we show that the constraint ofn 2 supersymmetry requires that all counterterms to the metric beyond one loop order be cohomologically trivial it follows that such supersymmetric non linear models defined on locally symmetric spaces are super renormalizable and thatn 4 models are on shell ultraviolet finite to all orders of perturbation theory

the vortex filament in the minkowski 3 space and generalized bi schrodinger maps by extending the concept of generalized bi schrodinger maps to the case that the target manifold is a para kahler manifold we show that the third order timelike and spacelike correction models of the vortex filament in the minkowski 3 space are equivalent to the generalized bi schrodinger maps from to the hyperbolic 2 space and the de sitter 2 space respectively as a consequence all three typical second to fourth order integrable systems of the akns hierarchy are interpreted in a unified way in terms of generalized bi schrodinger maps based on this exploitation and a general discussion of the generalized bi schodinger maps from into an arbitrary riemannian surface we reveal a property of generalized bi schrodinger maps that is not admitted for schrodinger maps

on the signature of certain intersection forms we prove a conjecture of zuber on the signature of intersection forms associated with affine algebras of type a which is based on connections between n 2 integrable models in two dimensions and certain class of graphs

a class of globally convergent optimization methods based on conservative convex separable approximations this paper deals with a certain class of optimization methods based on conservative convex separable approximations ccsa for solving inequality constrained nonlinear programming problems each generated iteration point is a feasible solution with lower objective value than the previous one and it is proved that the sequence of iteration points converges toward the set of karush kuhn tucker points a major advantage of ccsa methods is that they can be applied to problems with a very large number of variables say 104 105 even if the hessian matrices of the objective and constraint functions are dense

a canonical frobenius structure we show that it makes sense to speak of the frobenius manifold attached to a convenient and nondegenerate laurent polynomial

gpu accelerated computation of the isogeometric analysis stiffness matrix abstract due to high regularity across mesh elements isogeometric analysis achieves higher accuracy per degree of freedom and improved spectrum properties among others compared with finite element analysis however this inherent feature of isogeometric analysis increases the density of the stiffness matrix and requires more elaborate numerical integration schemes for its computation for these reasons the assembly of the stiffness matrix in isogeometric analysis is a computationally demanding task which needs special attention in order to be affordable for real world applications in this paper we address the computational efficiency of assembling the stiffness matrix using the standard element wise gaussian quadrature a novel approach is proposed for the formulation of the stiffness matrix which exhibits several computational merits among them its amenability to parallelization and the efficient utilization of the graphics processing units to drastically accelerate computations

the self duality equations on a riemann surface in this paper we shall study a special class of solutions of the self dual yang mills equations the original self duality equations which arose in mathematical physics were defined on euclidean 4 space the physically relevant solutions were the ones with finite action the so called instantons the same equations may be dimensionally reduced to euclidean 3 space by imposing invariance under translation in one direction these equations also have physical relevance the solutions which have finite action in three dimensions are the magnetic monopoles if we take the reduction process one step further and consider solutions which are invariant under two translations we obtain a set of equations in the plane here however there is no clear physical meaning and indeed attempts to find finite action solutions have failed nevertheless these are the equations we shall consider despite the lack of interesting solutions in r2 the equations have the important property conformal invariance which allows them to be defined on manifolds modelled on r2 by conformal maps namely riemann surfaces we shall consider here solutions of the self duality equations defined on a compact riemann surface there are in fact solutions as we shall show and the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure which will be the focus of our study it brings together in a harmonious way the subjects of riemannian geometry topology algebraic geometry and symplectic geometry illuminating all these facets of the same object accounts for the length of this paper the self duality equations are equations from gauge theory geometrically they are defined in terms of connections on principal bundles while the group of the principal bundle may be chosen arbitrarily for the equations to make sense we restrict attention here to the simplest case of su 2 or so 3 there are two reasons for this the first and most obvious is that it simplifies calculations and avoids the use of inductive processes which are inherent in the consideration of a general lie group of higher rank the second reason is that solutions for su 2 have an intimate relationship with the internal structure of the riemann surface as a consequence of results we shall prove about solutions to the self duality equations we learn something about the moduli space of complex structures on the surface itself namely teichmuller space

ising model and n 2 supersymmetric theories we establish a direct link between massive ising model and arbitrary massiven 2 supersymmetric qft s in two dimensions this explains why the equations which appear in the computation of spin correlations in the non critical ising model are the same as those describing the geometry of vacua inn 2 theories the tau function appearing in the ising model i e the spin correlation function is reinterpreted in then 2 context as a new index in special cases this new index is related to the ray singer analytic torsion and can be viewed as a generalization of that to the loop space of kahler manifolds

vertex operator representation of the soliton tau functions in the an 1 toda models by dressing transformations we study the relation between the group algebraic approach and the dressing symmetry one to the soliton solutions of the an 1 toda field theory in 1 1 dimensions originally solitons in the affine toda models were found by olive turok and underwood single solitons are created by exponentials of elements which ad diagonalize the principal heisenberg subalgebra alternatively babelon and bernard exploited the dressing symmetry to reproduce the known expressions for the fundamental tau functions in the sine gordon model in this paper we show the equivalence between these two methods to construct solitons in the an 1 toda models

ends of the moduli space of higgs bundles we associate to each stable higgs pair a 0 phi 0 on a compact riemann surface x a singular limiting configuration a infinity phi infinity assuming that det phi has only simple zeroes we then prove a desingularization theorem by constructing a family of solutions a t t phi t to hitchin s equations which converge to this limiting configuration as t infinity this provides a new proof via gluing methods for elements in the ends of the higgs bundle moduli space and identifies a dense open subset of the boundary of the compactification of this moduli space

third order implementation and convergence of the strong property fluctuation theory in electromagnetic homogenization the strong property fluctuation theory spft has been widely applied under the second order approximation also known as the bilocal approximation to estimate the constitutive properties of effectively homogeneous composite mediums a third order mass operator approximation is developed here the convergence of the long wavelength bilocally approximated spft is demonstrated for isotropic chiral composite mediums as well as for chiroferrite composite mediums

wall crossing holomorphic anomaly and mock modularity of multiple m5 branes using wall crossing formulae and the theory of mock modular forms we derive a holomorphic anomaly equation for the modified elliptic genus of two m5 branes wrapping a rigid divisor inside a calabi yau manifold the anomaly originates from restoring modularity of an indefinite theta function capturing the wall crossing of bps invariants associated to d4 d2 d0 brane systems we show the compatibility of this equation with anomaly equations previously observed in the context of mathcal n 4 topological yang mills theory on mathbbm p 2 and e strings obtained from wrapping m5 branes on a del pezzo surface the non holomorphic part is related to the contribution originating from bound states of singly wrapped m5 branes on the divisor we show in examples that the information provided by the anomaly is enough to compute the bps degeneracies for certain charges we further speculate on a natural extension of the anomaly to higher d4 brane charge

riccati type equations generalised wznw equations and multidimensional toda systems we associate to an arbitrary gradation of the lie algebra of a lie group a system of riccati type first order differential equations the particular cases under consideration are the ordinary riccati and the matrix riccati equations the multidimensional extension of these equations is given the generalisation of the associated redheffer reid differential systems appears in a natural way the connection between the toda systems and the riccati type equations in lower and higher dimensions is established within this context the integrability problem for those equations is studied as an illustration some examples of the integrable multidimensional riccati type equations related to the maximally nonabelian toda systems are given

on the equivalence of optimality criterion and sequential approximate optimization methods in the classical topology layout problem we study the classical topology optimization problem in which minimum compliance is sought subject to linear constraints using a dual statement we propose two separable and strictly convex subproblems for use in sequential approximate optimization sao algorithms respectively the subproblems use reciprocal and exponential intermediate variables in approximating the non linear compliance objective function any number of linear constraints or linearly approximated constraints are provided for the relationships between the primal variables and the dual variables are found in analytical form for the special case when only a single linear constraint on volume is present we note that application of the ever popular optimality criterion oc method to the topology optimization problem combined with arbitrary values for the heuristic numerical damping factor proposed by bendsoe results in an updating scheme for the design variables that is identical to the application of a rudimentary dual sao algorithm in which the subproblems are based on exponential intermediate variables what is more we show that the popular choice for the damping factor 0 5 is identical to the use of sao with reciprocal intervening variables finally computational experiments reveal that subproblems based on exponential intervening variables result in improved efficiency and accuracy when compared to sao subproblems based on reciprocal intermediate variables and hence the heuristic topology oc method hitherto used this is attributed to the fact that a different exponent is computed for each design variable in the two point exponential approximation we have used using gradient information at the previously visited point copyright 2007 john wiley sons ltd

topology optimization of non linear elastic structures and compliant mechanisms abstract a linear elastic response is assumed in most structural topology optimization problems while this assumption is valid for a wide variety of problems it is not valid for structures undergoing large displacements the elastic structural analysis used here accommodates geometric and material non linearities the material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities the filtering scheme is embedded in the structural analysis to resolve the non existent solution to the solid void topology problem in this way we know precisely what optimization problem is being solved the structural topology optimization formulation is also used to design compliant mechanisms

lattice and q difference darboux zakharov manakov systems via delta dressing method a general scheme is proposed for the introduction of lattice and q difference variables to integrable hierarchies in the frame of the delta dressing method using this scheme lattice and q difference darboux zakharov manakov systems of equations are derived darboux backlund and combescure transformations and exact solutions for these systems are studied

stokes matrices and monodromy of the quantum cohomology of projective spaces in this paper we compute stokes matrices and monodromy of the quantum cohomology of projective spaces this problem can be formulated in a classical framework as the problem of computation of stokes matrices and monodromy of differential equations with regular and irregular singularities we prove that the stokes matrix of the quantum cohomology coincides with the gram matrix in the theory of derived categories of coherent sheaves we also study the monodromy group of the quantum cohomology and we show that it is related to hyperbolic triangular groups

analysis of fictitious domain approximations of hard scatterers consider the helmholtz equation nabla cdot alpha nabla p k 2 alpha p 0 in a domain that contains a so called hard scatterer the scatterer is represented by the value alpha epsilon fo

the connection between factorization properties and closed form solutions of certain linear dyadic differential operators representation of the electromagnetic field in terms of dyadic green functions leads to the requirement to solve dyadic partial differential equations for the dyadic green functions while a formal solution for the infinite medium problem can be given in a straightforward manner for even the most general linear medium the extraction of closed form expressions is a complicated issue the existence of such expressions for the dyadic green functions is closely linked to the factorization properties of the determinant operator which is associated with the dyadic differential operator of the dyadic green functions this connection is investigated for a special type of homogeneous anisotropic dielectric medium

nilpotent orbits of a generalization of hodge structures we study a generalization of hodge structures which first appeared in the work of cecotti and vafa it consists of twistors that is holomorphic vector bundles on p 1 with additional structure a flat connection on c a real subbundle and a pairing we call these objects terp structures we generalize to terpstructures a correspondence of cattani kaplan and schmid between nilpotent orbits of hodge structures and polarized mixed hodge structures the proofs use work of simpson and mochizuki on variations of twistor structures and a control of the stokes structures of the poles at zero and infinity the results are applied to terp structures which arise via oscillating integrals from holomorphic functions with isolated singularities

temperature correlators of the impenetrable bose gas as an integrable system it is shown that the temperature equal time correlators of impenetrable bosons in one space dimension are described by a classical integrable system partial differential equations for two point as well as for multipoint correlators are obtained the short distance and low density expansions are constructed

geometry and braiding of stokes data fission and wild character varieties a family of new algebraic poisson varieties will be constructed generalising the complex character varieties of riemann surfaces then the well known poisson mapping class group actions on the character varieties will be generalised

stability conditions on a non compact calabi yau threefold we study the space of stability conditions stab x on the non compact calabi yau threefold x which is the total space of the canonical bundle of mathbb p 2 we give a combinatorial description of an open subset of stab x and state a conjecture relating stab x to the frobenius manifold obtained from the quantum cohomology of mathbb p 2 we give some evidence from mirror symmetry for this conjecture

megapixel topology optimization on a graphics processing unit we show how the computational power and programmability of modern graphics processing units gpus can be used to efficiently solve large scale pixel based material distribution problems using a gradient based optimality criterion method to illustrate the principle a so called topology optimization problem that results in a constrained nonlinear programming problem with over 4 million decision variables is solved on a commodity gpu

a construction of frobenius manifolds with logarithmic poles and applications a construction theorem for frobenius manifolds with logarithmic poles is established this is a generalization of a theorem of hertling and manin as an application we prove a partial generalization of the reconstruction theorem of kontsevich and manin for projective smooth varieties with convergent gromov witten potential a second application is a construction of frobenius manifolds out of a variation of polarized hodge structures which degenerates along a normal crossing divisor when certain generation conditions are fulfilled

isomonodromy aspects of the tt equations of cecotti and vafa ii riemann hilbert problem in guest et al arxiv 1209 2045 part i we computed the stokes data for the smooth solutions of the tt toda equations whose existence we had previously established by p d e methods here we formulate the existence problem as a riemann hilbert problem based on this stokes data and solve it under certain conditions theorem 5 4 in the process we compute the connection matrix for all smooth solutions thus completing the computation of the monodromy data theorem 5 5 we also give connection formulae relating the asymptotics at zero and infinity of all smooth solutions theorem 4 1 clarifying the region of validity of the formulae established earlier by tracy and widom finally we resolve some conjectures of cecotti and vafa concerning the positivity of s st where s is the stokes matrix and the unimodularity of the eigenvalues of the monodromy matrix theorem 5 6 in particular we show that unitarity implies regularity for the tt toda equations

special kahler manifolds we give an intrinsic definition of the special geometry which arises in global n 2 supersymmetry in four dimensions the base of an algebraic integrable system exhibits this geometry and with an integrality hypothesis any special kahler manifold is so related to an integrable system the cotangent bundle of a special kahler manifold carries a hyperkahler metric we also define special geometry in supergravity in terms of the special geometry in global supersymmetry

the witten equation mirror symmetry and quantum singularity theory for any nondegenerate quasi homogeneous hypersurface singularity we describe a family of moduli spaces a virtual cycle and a corresponding cohomological eld theory associated to the singularity this theory is analogous to gromov witten theory and generalizes the theory of r spin curves which corresponds to the simple singularity ar 1 we also resolve two outstanding conjectures of witten the rst conjecture is that ade singularities are self dual and the second conjecture is that the total potential functions of ade singularities satisfy corresponding ade integrable hierarchies other cases of integrable hierarchies are also discussed

the method of moving asymptotes a new method for structural optimization a new method for non linear programming in general and structural optimization in particular is presented in each step of the iterative process a strictly convex approximating subproblem is generated and solved the generation of these subproblems is controlled by so called moving asymptotes which may both stabilize and speed up the convergence of the general process

distributed parameter optimization and topology design for non linear thermoelasticity abstract topology optimization has been the focus of considerable attention in the shape optimization community in recent years since significant performance improvements can be obtained if the topology is allowed to vary in shape optimization problems attention has mainly focussed on the topology design of an elastic continuum for minimum compliance subject to a volume constraint the macroscopic version of this problem is not well posed if no restrictions are placed on the structure topology the most widely used method for making the problem has been the so called homogenization method which introduces microstructure to the design space though there are a number of advantages to this method it also suffers from some drawbacks optimal designs generated using an optimal microstructure are difficult to manufacture while using sub optimal microstructures reverts the problem back to the original ill posed problem in addition extension of the homogenization method to problems involving non linear material behavior is quite difficult to address some of these issues a new method for making the compliance optimization problem well posed has recently been proposed this method introduces an additional constraint on the perimeter of the solid regions in the design to make the problem well posed since microstructure is not introduced the designs are easily manufacturable preliminary results for topology design using the perimeter method for problems where the material behavior is linear elastic have already been reported in the literature we show that the perimeter method can be used even when the material behavior involves material and geometric non linearities we formulate the distributed parameter optimization and topology design problems using the perimeter method for non linear thermoelasticity finite element optimization procedures based on this formulation are developed and numerical solutions for the distributed parameter optimization problem are presented though we use the compliance as the objective function one could optimize any objective function by making minor modifications in the method outlined here

topological orbifold models and quantum cohomology rings we discuss the topological sigma model on an orbifold target space we describe the moduli space of classical minima for computing correlation functions involving twisted operators and show through a detailed computation of an orbifold ofcp1 by the dihedral groupd4 how to compute the complete ring of observables through this procedure we compute all the rings of dihedralcp1 orbifolds we then considercp2 d4 and show how the techniques of topologicalanti topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds