closed subsets in duals of commutative table algebras a lower bound on the number of elements outside a closed subset of a c basis of a commutative c algebra with dual a table algebra is derived as is an equivalent condition for when the lower bound is met as corollaries lower bounds are obtained on the number of primitive idempotent matrices of rank greater than 1 in the adjacency algebra of a commutative imprimitive association scheme and for a given normal subgroup n of a finite group g on the number of irreducible characters of g whose kernels do not contain n and on the number of conjugacy classes of g not contained in n also found are equivalent conditions for when these lower bounds are met

on association schemes with thin thin residue abstract let s be a scheme of finite valency and assume that o s o s it is known that s is schurian which means that s arises from a finite group if the normal closed subsets normal subgroups of o s are linearly ordered with respect to set theoretic inclusion cf m hirasaka p h zieschang sufficient conditions for a scheme to originate from a group j combin theory ser a 104 2003 17 27 in this note it is shown that s is schurian if o s is direct product of two simple closed subsets finite simple groups of different order

a random euler scheme for caratheodory differential equations we study a random euler scheme for the approximation of caratheodory differential equations and give a precise error analysis in particular we show that under weak assumptions this approximation scheme obtains the same rate of convergence as the classical monte carlo method for integration problems

permutation modules over table algebras and applications to association schemes abstract inspired by the notion of an action of a finite hypergroup on a finite set we introduce the more general concept of a permutation module over a table algebra it is easy to see that each permutation module over a table algebra is a direct sum of transitive permutation modules among the transitive permutation modules the w maximal and the maximal permutation modules are the most interesting ones we give various characterizations of these modules and we shall see that a standard table algebra admits a maximal transitive permutation module if and only if it arises from a finite association scheme we also show that the regular module of a standard table algebra is isomorphic to a direct summand of each w maximal transitive permutation module as a consequence one obtains 1 m for any irreducible character of the bose mesner algebra of a finite association scheme and its multiplicity m

on wreath products of c algebras table algebras and association schemes abstract in this paper we will first present characterizations of wreath products of c algebras and show that the dual of the wreath product of c algebras is isomorphic to the wreath product of the duals of those c algebras in the reverse order then we prove the krull schmidt type theorems for the wreath products of table algebras as well as for the wreath products of association schemes

new code upper bounds from the terwilliger algebra and semidefinite programming we give a new upper bound on the maximum size a n d of a binary code of word length n and minimum distance at least d it is based on block diagonalizing the terwilliger algebra of the hamming cube the bound strengthens the delsarte bound and can be calculated with semidefinite programming in time bounded by a polynomial in n we show that it improves a number of known upper bounds for concrete values of n and d from this we also derive a new upper bound on the maximum size a n d w of a binary code of word length n minimum distance at least d and constant weight w again strengthening the delsarte bound and yielding several improved upper bounds for concrete values of n d and w

reality based algebras with a two dimensional representation abstract it is shown that a two dimensional irreducible representation of a reality based algebra with a standard degree map is determined by the other irreducible representations of the algebra and the action of its given anti automorphism on the distinguished basis this generalizes known results for algebras of dimensions 5 6 7 and 8 explicit conclusions equivalent to those for dimensions 5 and 6 are recovered here by specializing the procedure of proof of the main theorem

complex symplectomorphisms and pseudo kahler islands in the quantization of toric manifolds let p be a delzant polytope we show that the quantization of the corresponding toric manifold x p in toric kahler polarizations and in the toric real polarization are related by analytic continuation of hamiltonian flows evaluated at time t sqrt 1 s we relate the quantization of x p in two different toric kahler polarizations by taking the time sqrt 1 s hamiltonian flow of strongly convex functions on the moment polytope p by taking s to infinity we obtain the quantization of x p in the singular real toric polarization recall that x p has an open dense subset which is biholomorphic to mathbb c n the quantization of x p in a toric kahler polarization can also be described by applying the complexified hamiltonian flow of the abreu guillemin symplectic potential g at time t sqrt 1 to an appropriate finite dimensional subspace of quantum states in the quantization of t mathbb t n in the vertical polarization by taking other imaginary times t k sqrt 1 k in mathbb r we describe toric kahler metrics with cone singularities along the toric divisors in x p for convex hamiltonian functions and sufficiently negative imaginary part of the complex time we obtain degenerate kahler structures which are negative definite in some regions of x p we show that the pointwise and l 2 norms of quantum states are asymptotically vanishing on negative definite regions

toric surfaces k stability and calabi flow let x be a toric surface and u be a normalized symplectic potential on the corresponding polygon p suppose that the riemannian curvature is bounded by a constant c 1 and int partial p u d sigma 0 depending only on c 1 c 2 and p such that donaldson s m condition holds for u as an application we show that if x p is analytic relative k stable then the modified calabi flow converges to an extremal metric exponentially fast by assuming that the calabi flow exists for all time and the riemannian curvature is uniformly bounded along the calabi flow

ricci flat kahler metrics on crepant resolutions of kahler cones we prove that a crepant resolution y x of a ricci flat kahler cone x admits a complete ricci flat kahler metric asymptotic to the cone metric in every kahler class in h 2 c y mathbb r a kahler cone x bar g is a metric cone over a sasaki manifold s g i e x c s s times mathbb r 0 with bar g dr 2 r 2 g and x bar g is ricci flat precisely when s g einstein of positive scalar curvature this result contains as a subset the existence of ale ricci flat kahler metrics on crepant resolutions pi y rightarrow x mathbb c n gamma with gamma subset sl n mathbb c due to p kronheimer n 2 and d joyce n 2 we then consider the case when x c s is toric it is a result of a futaki h ono and g wang that any gorenstein toric kahler cone admits a ricci flat kahler cone metric it follows that if a toric kahler cone x c s admits a crepant resolution y x then y admits a tn invariant ricci flat kahler metric asymptotic to the cone metric x bar g in every kahler class in h 2 c y mathbb r a crepant resolution in this context is a simplicial fan refining the convex polyhedral cone defining x we then list some examples which are easy to construct using toric geometry

noncommutative standard table algebras with at most one nontrivial multiplicity abstract standard table algebras that have an irreducible character of degree two and with all other irreducible characters of multiplicity one are classified to exact isomorphism

tropical counting from asymptotic analysis on maurer cartan equations let be a toric surface and let be its landau ginzburg lg mirror where is the hori vafa potential as shown in their preprint we apply asymptotic analysis to study the extended deformation theory of the lg model and prove that semi classical limits of fourier modes of a specific class of maurer cartan solutions naturally give rise to tropical disks in with maslov index 0 or 2 the latter of which produces a universal unfolding of for our construction reproduces gross perturbed potential adv math 224 2010 pp 169 245 which was proven to be the universal unfolding of written in canonical coordinates we also explain how the extended deformation theory can be used to reinterpret the jumping phenomenon of across walls of the scattering diagram formed by maslov index 0 tropical disks originally observed by gross in the same work in the case of

the generalized terwilliger algebra and its finite dimensional modules when d 2 terwilliger j algebraic combin 1 1992 363 388 considered the c algebra generated by a given bose mesner algebra m and the associated dual bose mesner algebra m this algebra is now known as the terwilliger algebra and is usually denoted by t terwilliger showed that each vanishing intersection number and krein parameter of m gives rise to a relation on certain generators of t these relations are often called the triple product relations they determine much of the structure of t though not all of it in general to illuminate the role these relations play the current author introduced j algebra233 2000 213 252 a generalization t of t to go from t to t we replace m and m with a pair of dual character algebras c and c the dimensions of c and c are equal let d 1 denote this common dimension intuitively t is the associative c algebra with identity generated by c and c subject to the analogues of terwilliger s triple product relations t is infinite dimensional and noncommutative in general in this paper we study t and its finite dimensional modules when d 2 and t has no extra vanishing intersection numbers or dual intersection numbers in this case we show t is c algebra isomorphic to m3 c a where m3 c denotes the c algebra consisting of all 3 by 3 matrices with entries in c and a denotes the associative c algebra with identity generated by the symbols e and f subject to the relations e2 e and f2 f we find a basis for a and we determine the center of a we classify the finite dimensional indecomposable a modules up to isomorphism there are four such a modules in every odd dimension and in every even dimension these modules are parameterized by a single complex number we also classify the finite dimensional irreducible a modules up to isomorphism using our results concerning a we find a basis for t we describe the center of t and we classify both the finite dimensional indecomposable and the finite dimensional irreducible t modules up to isomorphism

lagrangian floer theory on compact toric manifolds i we introduced the notion of weakly unobstructed lagrangian submanifolds and constructed their potential function po purely in terms of a model data in fooo3 in this article we carry out explicit calculations involving po on toric manifolds and study the relationship between this class of lagrangian submanifolds with the earlier work of givental g1 which advocates that the quantum cohomology ring is isomorphic to the jacobian ring of a certain function called the landau ginzburg superpotential combining this study with the results from fooo3 we also apply the study to various examples to illustrate its implications to symplectic topology of lagrangian fibers of toric manifolds in particular we relate it to the hamiltonian displacement property of lagrangian fibers and to entov polterovich s symplectic quasi states

scalar curvature and stability of toric varieties we define a stability condition for a polarised algebraic variety and state a conjecture relating this to the existence of a kahler metric of constant scalar curvature the main result of the paper goes some way towards verifying this conjecture in the case of toric surfaces we prove that under the stability hypothesis the mabuchi functional is bounded below on invariant metrics and that minimising sequences have a certain convergence property in the reverse direction we give new examples of polarised surfaces which do not admit metrics of constant scalar curvature the proofs use a general framework developed by guillemin and abreu in which invariant kahler metrics correspond to convex functions on the moment polytope of a toric variety this paper is a step towards the solution of the general problem of finding conditions under which a complex projective variety admits a kahler metric of constant scalar curvature the pattern of the answer one expects is that this differential geometric condition should be equivalent to some notion of stability in the sense of geometric invariant theory this expectation is probably now an item of folklore going back to suggestions put forward by yau in the case of kahlereinstein metrics and the many results of tian and others in this case reinforced by a detailed formal picture which makes clear the analogy with the well established relation between the stability of vector bundles and yang mills connections 5 here we begin the investigation of

character products of association schemes since group algebras of finite groups are hopf algebras products of characters of finite groups are characters too in the present paper we prove that products of characters of finite schemes g are characters if one of the two factors contains the thin residue of g in its kernel we also give details in this situation

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

a momentum construction for circle invariant kahler metrics examples of kahler metrics of constant scalar curvature are relatively scarce over the past two decades several workers in geometry and physics have used symmetry reduction to construct complete kahler metrics of constant scalar curvature by ode methods one fruitful idea the calabi ansatz is to begin with an hermitian line bundle p l h m g m over a kahler manifold and to search for kahler forms p m dd c f t in some disk subbundle where t is the logarithm of the norm function and f is a function of one variable our main technical result theorem a is the calculation of the scalar curvature for an arbitrary kahler metric g arising from the calabi ansatz this suggests geometric hypotheses which we call a constancy to impose upon the base metric g m and hermitian structure h in order that the scalar curvature of g be specified by solving an ode we show that constancy is necessary and sufficient for the calabi ansatz to work in the following sense under the assumption of constancy the disk bundle admits a one parameter family of complete kahler metrics of constant scalar curvature that restrict to g m on the zero section theorems b and d an analogous result holds for the punctured disk bundle theorem c a simple criterion determines when such a metric is einstein conversely in the absence of constancy the calabi ansatz yields at most one metric of constant scalar curvature in either the disk bundle or the punctured disk bundle theorem e many of the metrics constructed here seem to be new including a complete negative einstein kahler metric on the disk subbundle of a stable vector bundle over a riemann surface of genus at least two and a complete scalar flat kahler metric on c 2

on structures of quasi thin table algebras and applications to association schemes abstract in this paper we develop a structure theory for a class of table algebras i e the so called quasi thin table algebras they are direct generalizations of quasi thin association schemes although this class of table algebras is rather close to finite groups its structural properties are quite different from those of finite groups the thin radical and thin residue give rise to two group structures for every table algebra they play the central role in our discussions applications to association schemes are also discussed and some new results about quasi thin association schemes are obtained in particular we will give necessary and sufficient conditions under which a commutative quasi thin association scheme has multiplicities 1 or 2 we will need these results in the study of the characterization and classification of double quasi thin association schemes in 22

on morphisms of association schemes abstract in this paper we present a necessary and sufficient condition under which a combinatorial morphism between association schemes induces an algebra homomorphism between their scheme rings we will also discuss scheme ring homomorphisms of naturally valenced association schemes

varietal terwilliger algebras arising from wreath products of rank two association schemes abstract as abstractions of terwilliger algebras generalized terwilliger algebras and varietal terwilliger algebras have been studied in 5 6 17 in general it is difficult to determine the structure of a varietal terwilliger algebra as proposed in the concluding remarks in 4 in this paper we study the structures of those varietal terwilliger algebras arising from the wreath products of rank two association schemes in particular we give the explicit formulas for their central primitive idempotents applications to terwilliger algebras of association schemes are also discussed and an affirmative answer to the terwilliger conjecture mention in 4 is given

k energy on polarized compactifications of lie groups abstract in this paper we study mabuchi s k energy on a compactification m of a reductive lie group g which is a complexification of its maximal compact subgroup k we give a criterion for the properness of k energy on the space of k k invariant kahler potentials in particular it turns to give an alternative proof of delcroix s theorem for the existence of kahler einstein metrics in case of fano manifolds m we also study the existence of minimizers of k energy for general kahler classes of m

semi classical weights and equivariant spectral theory abstract we prove inverse spectral results for differential operators on manifolds and orbifolds invariant under a torus action these inverse spectral results involve the asymptotic equivariant spectrum which is the spectrum itself together with very large weights of the torus action on eigenspaces more precisely we show that the asymptotic equivariant spectrum of the laplace operator of any toric metric on a generic toric orbifold determines the equivariant biholomorphism class of the orbifold we also show that the asymptotic equivariant spectrum of a t n invariant schrodinger operator on r n determines its potential in some suitably convex cases in addition we prove that the asymptotic equivariant spectrum of an s 1 invariant metric on s 2 determines the metric itself in many cases finally we obtain an asymptotic equivariant inverse spectral result for weighted projective spaces as a crucial ingredient in these inverse results we derive a surprisingly simple formula for the asymptotic equivariant trace of a family of semi classical differential operators invariant under a torus action

kahler metrics on toric orbifolds a theorem of e lerman and s tolman generalizing a result of t delzant states that compact symplectic toric orbifolds are classified by their moment polytopes together with a positive integer label attached to each of their facets in this paper we use this result and the existence of global actionangle coordinates to give an effective parametrization of all compatible toric complex structures on a compact symplectic toric orbifold by means of smooth functions on the corresponding moment polytope this is equivalent to parametrizing all toric kahler metrics and generalizes an analogous result for toric manifolds a simple explicit description of interesting families of extremal kahler metrics arising from recent work of r bryant is given as an application of the approach in this paper the fact that in dimension four these metrics are self dual and conformally einstein is also discussed this gives rise in particular to a one parameter family of self dual einstein metrics connecting the well known eguchi hanson and taub nut metrics

toric generalized kahler ricci solitons with hamiltonian 2 form we show that the generalized kahler ricci soliton equation on 4 dimensional toric kahler orbifolds reduces to odes assuming there is a hamiltonian 2 form this leads to an explicit resolution of this equation on labelled triangles and convex labelled quadrilaterals in particular we give the explicit expression of the kahler ricci solitons of weighted projective planes as well as new examples

on a class of integral table algebras abstract in this paper we give the classification for a class of integral table algebras and their duals as well then we give an application of this classification to association schemes

irreducible characters of wreath products in reality based algebras and applications to association schemes abstract wreath products in reality based algebras are generalizations of wreath products of table algebras and generalized camina frobenius pairs of c algebras in this paper we present characterizations of the wreath product in a reality based algebra by its irreducible characters and by the size of the zero submatrix of its character table applications to finite groups table algebras and association schemes are also discussed in particular we will show that the wreath product of one class association schemes is characterized by the zeros in its first eigenmatrix

quasi potentials and kahler einstein metrics on flag manifolds ii abstract for a homogeneous space g p where p is a parabolic subgroup of a complex semisimple group g an explicit kahler einstein metric on it is constructed the einstein constant for the metric is 1 therefore the intersection number of the first chern class of the holomorphic tangent bundle of g p coincides with the volume of g p with respect to this kahler einstein metric thus enabling us to compute volume for this metric and for all kahlerian metrics on g p invariant under the action of a maximal compact subgroup of g

interior estimates for the n dimensional abreuʼs equation abstract we study the abreu s equation in n dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform k stability

pseudo direct sums and wreath products of loose coherent algebras with applications to coherent configurations abstract we introduce the notion of a loose coherent algebra which is a special semisimple subalgebra of the matrix algebra and define two operations to obtain new loose coherent algebras from the old ones the pseudo direct sum and the wreath product for two arbitrary coherent configurations c d and their wreath product c d it is difficult to express the terwilliger algebra t x y c d in terms of the terwilliger algebras t x c and t y d by using the concept and operations of loose coherent algebras we find a very simple such expression as a direct consequence of this expression we obtain the central primitive idempotents of t x y c d in terms of the central primitive idempotents of t x c and t y d many results in 4 6 10 12 are special cases of the results in this paper

a generalization of the terwilliger algebra abstract p m terwilliger 1992 j algebraic combin 1 363 388 considered the c algebra generated by a given bose mesner algebra m and the associated dual bose mesner algebra m this algebra is now known as the terwilliger algebra and is usually denoted by t terwilliger showed that each vanishing intersection number and krein parameter of m gives rise to a relation on certain generators of t these relations determine much of the structure of t thought not all of it in general to illuminate the role these relations play we consider a certain generalization t of t to go from t to t we replace m and m with a pair of dual character algebras c and c we define t by generators and relations intuitively t is the associative c algebra with identity generated by c and c subject to the analogues of terwilliger s relations t is infinite dimensional and noncommutative in general we construct an irreducible t module which we call the primary module the dimension of this module is the same as that of c and c we find two bases of the primary module one diagonalizes c and the other diagonalizes c we compute the action of the generators of t on these bases we show t is a direct sum of two sided ideals t 0 and t 1 with t 0 isomorphic to a full matrix algebra we show that the irreducible module associated with t 0 is isomorphic to the primary module we compute the central primitive idempotent of t associated with t 0 in terms of the generators of t

optimal global approximation of sdes with time irregular coefficients in asymptotic setting we investigate strong approximation of solutions of scalar stochastic differential equations sdes with irregular coefficients in przybylowicz 2015 23 an approximation of solutions of sdes at a single point is considered such kind of approximation is also called a one point approximation comparing to that article we are interested here in a global reconstruction of trajectories of the solutions of sdes in a whole interval of existence we assume that a drift coefficient a 0 t r r is globally lipschitz continuous with respect to a space variable but only measurable with respect to a time variable a diffusion coefficient b 0 t r is only piecewise holder continuous with holder exponent 0 1 the algorithm and results concerning lower bounds from przybylowicz 2015 23 cannot be applied for this problem and therefore we develop a suitable new technique in order to approximate solutions of sdes under such assumptions we define a discrete type randomized euler scheme we provide the error analysis of the algorithm showing that its error is o n min 1 2 moreover we prove that roughly speaking the error of an arbitrary algorithm for fixed a and b that uses n values of the diffusion coefficient cannot converge to zero faster than n min 1 2 as n hence the proposed version of the randomized euler scheme achieves the established best rate of convergence

efficient approximate solution of jump diffusion sdes via path dependent adaptive step size control abstract we provide a construction of a method based on path dependent adaptive step size control for global approximation of jump diffusion sdes the discretization points and the number of them are chosen in adaptive way with respect to trajectories of the driving poisson and wiener processes the resulting algorithm is in many cases much more efficient than methods based on nonuniform meshes obtained from adaptive but path independent sampling

nilpotent fusion categories abstract in this paper we extend categorically the notion of a finite nilpotent group to fusion categories to this end we first analyze the trivial component of the universal grading of a fusion category c and then introduce the upper central series of c for fusion categories with commutative grothendieck rings e g braided fusion categories we also introduce the lower central series we study arithmetic and structural properties of nilpotent fusion categories and apply our theory to modular categories and to semisimple hopf algebras in particular we show that in the modular case the two central series are centralizers of each other in the sense of m muger

decomposition of products in nilpotent table algebras abstract two theorems on the decomposition of products in nilpotent commutative table algebras are established this generalizes several results of adan bante on the decomposition of products of irreducible characters and of conjugacy classes of finite p groups and extends these results to fusion rule algebras and association schemes

on thin residues and basis digraphs of nilpotent table algebras and applications to nilpotent groups abstract in this paper we study characterizations of nilpotent table algebras in terms of thin residues thin residue matrices thin residue digraphs and basis digraphs we will also discuss applications to nilpotent groups in particular we give a conceptual explanation of the results in takegahara and yoshida 2008 ty

terwilliger algebras of wreath products by quasi thin schemes abstract the structure of terwilliger algebras of wreath products by thin schemes or one class schemes was studied in a hanaki k kim y maekawa terwilliger algebras of direct and wreath products of association schemes j algebra 343 2011 195 200 in this paper we will consider the structure of terwilliger algebras of wreath products by quasi thin schemes this gives a generalization of their result

optimal pointwise approximation of sdes from inexact information we study a pointwise approximation of solutions of systems of stochastic differential equations we assume that an approximation method can use values of the drift and diffusion coefficients which are perturbed by some deterministic noise let 1 20 be the precision levels for the drift and diffusion coefficients respectively we give a construction of the randomized euler scheme and we prove that it has the error o nmin 1 2 1 2 where n is the number of discretization points and is the hlder exponent of the diffusion coefficient we also investigate lower bounds on the error of an arbitrary algorithm and establish optimality of the defined randomized euler algorithm finally we report some numerical results

some structure theory of table algebras and applications to association schemes abstract in this paper we prove some basic structure theorems for arbitrary table algebras in particular we prove a krull schmidt theorem for arbitrary table algebras and give applications to association schemes

nilpotency property in table algebras abstract table algebras form an important class of c algebras the dual of a table algebra may not be a table algebra but just a c algebra it is not known under what conditions the dual of a table algebra is also a table algebra in this paper we prove that if a table algebra has nilpotency property then its dual also is a table algebra finally we conclude that if a b is a nilpotent table algebra then its dual also is a nilpotent table algebra

terwilliger algebras of direct and wreath products of association schemes abstract we will consider structures of terwilliger algebras of direct and wreath products of association schemes in general it is difficult to determine the structure of the terwilliger algebras though they are known to be semisimple c algebras but we get the structure of terwilliger algebras of these cases under some assumptions

quotient structures homomorphisms and partial wreath products in reality based algebras abstract homomorphisms and quotient structures of reality based algebras are presented and described related central idempotents and quotient sets are characterized and the extent to which a homomorphism preserves the given anti automorphisms of the algebras is determined the notion of a partial wreath product an algebraic abstraction of the wedge product of association schemes is developed prototypical results previously obtained for various special cases including table algebras and commutative c algebras are thus uniformly generalized

the recognition problem for table algebras and reality based algebras given a finite dimensional noncommutative semisimple algebra a over c with involution we show that a always has a basis b for which a b is a reality based algebra for algebras that have a one dimensional representation we show that there always exists an rba basis for which is a positive degree map we characterize all rba bases of the 5 dimensional noncommutative semisimple algebra for which the algebra has a positive degree map and give examples of rba bases of c mn c for which the rba has a positive degree map for all n 2

numerical kahler einstein metric on the third del pezzo the third del pezzo surface admits a unique kahler einstein metric which is not known in closed form the manifold s toric structure reduces the einstein equation to a single monge ampere equation in two real dimensions we numerically solve this nonlinear pde using three different algorithms and describe the resulting metric the first two algorithms involve simulation of ricci flow in complex and symplectic coordinates respectively the third algorithm involves turning the pde into an optimization problem on a certain space of metrics which are symplectic analogues of the algebraic metrics used in numerical work on calabi yau manifolds our algorithms should be applicable to general toric manifolds using our metric we compute various geometric quantities of interest including laplacian eigenvalues and a harmonic 1 1 form the metric and 1 1 form can be used to construct a klebanov tseytlin like supergravity solution

schur rings and association schemes whose thin residues are thin abstract the thin residue is an important concept in the theory of association schemes association schemes whose thin residues are thin have been studied in several papers in this paper we construct a new class of association schemes whose thin residues are thin and give a characterization of their automorphism groups in particular we give a formula for the order of the automorphism group and a necessary and sufficient condition under which the association scheme is schurian schur rings are used as a tool in our approach

on quasi thin association schemes abstract an association scheme is called quasi thin if each of its basic relations has valency 1 or 2 a quasi thin scheme is called kleinian if its thin residue is the klein four group with respect to relational multiplication it is proved that any kleinian quasi thin scheme arises from a near pencil on 3 points from an affine plane of order 2 or from a projective plane of order 2 the main result in this paper is that any non kleinian quasi thin scheme is schurian and separable we also construct an infinite family of kleinian quasi thin schemes which is neither schurian nor separable

fusion rings with few degrees abstract the main result characterizes fusion rings whose degree set consists of 1 and a fixed prime p a well known theorem of isaacs and passman on finite groups whose irreducible character degrees are 1 and p follows as a corollary numerically compatible nc fusion rings are defined as a potential generalization of the grothendieck rings of fusion categories and the nc fusion rings of order p p 2 p 3 pq and p q 2 where p q are primes are classified in terms of certain standard table algebras as another application of the main theorem

the cauchy problem for the homogeneous monge ampere equation ii legendre transform abstract we continue our study of the cauchy problem for the homogeneous real and complex monge ampere equation hrma hcma in the prequel y a rubinstein and s zelditch 27 a quantum mechanical approach for solving the hcma was developed and was shown to coincide with the well known legendre transform approach in the case of the hrma in this article that uses tools of convex analysis and can be read independently we prove that the candidate solution produced by these methods ceases to solve the hrma even in a weak sense as soon as it ceases to be differentiable at the same time we show that it does solve the equation on its dense regular locus and we derive an explicit a priori upper bound on its monge ampere mass the technique involves studying regularity of legendre transforms of families of non convex functions

terwilliger algebras of wreath products of association schemes abstract the terwilliger algebra of an association scheme of order n introduced in 13 is a subalgebra of the matrix algebra of all n n matrices terwilliger algebras of wreath products of special association schemes are studied in several papers in this paper we study the terwilliger algebra of the wreath product t s of two arbitrary association schemes s and t we will express the terwilliger algebra of t s and its primitive central idempotents in terms of the terwilliger algebras of s and t and their primitive central idempotents the known results of hanaki kim etc cf 7 10 are special cases of our results

t duality and homological mirror symmetry for toric varieties abstract let x be a complete toric variety the coherent constructible correspondence of fang et al 2011 14 equates p erf t x with a subcategory sh c c m r of constructible sheaves on a vector space m r the microlocalization equivalence of nadler and zaslow 2009 27 and nadler 2009 25 relates these sheaves to a subcategory fuk t m r of the fukaya category of the cotangent t m r when x is nonsingular taking the derived category yields an equivariant version of homological mirror symmetry dcoh t x dfuk t m r which is an equivalence of triangulated tensor categories the nonequivariant coherent constructible correspondence of treumann preprint 33 embeds p erf x into a subcategory s h c t r of constructible sheaves on a compact torus t r when x is nonsingular the composition of and microlocalization yields a version of homological mirror symmetry dcoh x dfuk t t r which is a full embedding of triangulated tensor categories when x is nonsingular and projective the composition is compatible with t duality in the following sense an equivariant ample line bundle l has a hermitian metric invariant under the real torus whose connection defines a family of flat line bundles over the real torus orbits this data produces a t dual lagrangian brane l on the universal cover t m r of the dual real torus fibration we prove l l in fuk t m r thus equivariant homological mirror symmetry is determined by t duality

on semisimple varietal terwilliger algebras whose non primary ideals are 1 dimensional abstract as an abstraction of the terwilliger algebra of a commutative association scheme the notion of a varietal terwilliger algebra was introduced in 11 in this paper we first prove that there exists a varietal terwilliger algebra defined by any given standard c algebra and a generalized terwilliger algebra 6 is also a varietal terwilliger algebra then we present a necessary and sufficient condition under which a quotient algebra of a varietal terwilliger algebra is also a varietal terwilliger algebra we will also give a characterization of a semisimple varietal terwilliger algebra whose non primary ideals are all 1 dimensional and prove that a semisimple regular varietal terwilliger algebra with 1 dimensional non primary ideals is characterized by the structure of its base c subalgebra as direct consequences we obtain some results in 18 for finite association schemes and a conceptual explanation of the results in 9

fusion algebras for imprimitive complex reflection groups abstract we prove that the fourier matrices for the imprimitive complex reflection groups introduced by malle in gunter malle unipotente grade imprimitiver komplexer spiegelungsgruppen j algebra 177 3 1995 768 826 define fusion algebras with not necessarily positive but integer structure constants hence they define z algebras as a result we obtain that all known fourier matrices belonging to spetses define algebras with integer structure constants

on quasi thin association schemes with odd number of points abstract let x r be an association scheme in the sense of p h zieschang 1996 an algebraic approach to association schemes lecture notes in mathematics vol 1628 springer new york berlin where x is a finite set and r is a partition of x x we say that x r is quasi thin if each element of r has a valency of at most two in this paper we focus on quasi thin association schemes with an odd number of points and obtain that x r has a regular automorphism group when n o r is square free

the character values of commutative quasi thin schemes the main result of this article shows that all character values of commutative quasi thin schemes are cyclotomic algebraic integers in particular all of the eigenvalues of the adjacency matrices corresponding to relations in these association schemes are cyclotomic algebraic integers

on nakayama automorphisms of double frobenius algebras abstract double frobenius algebras or df algebras were recently introduced by the author the concept generalizes finite dimensional hopf algebras adjacency algebras of non commutative association schemes and c algebras or character algebras this paper studies basic properties of various nakayama automorphisms in a df algebra as an application the theorem of d e radford stating that the antipode s of a finite dimensional hopf algebra is of finite order is generalized to df algebras and so is his formula for s 4 n in terms of certain group like elements

hamiltonian 2 forms in kahler geometry ii global classification we present a classification of compact kahler manifolds admitting a hamiltonian 2 form which were classified locally in part i of this work this involves two components of independent interest the first is the notion of a rigid hamiltonian torus action this natural condition for torus actions on a kahler manifold was introduced locally in part i but such actions turn out to be remarkably well behaved globally leading to a fairly explicit classification up to a blow up compact kahler manifolds with a rigid hamiltonian torus action are bundles of toric kahler manifolds the second idea is a special case of toric geometry which we call orthotoric we prove that orthotoric kahler manifolds are diffeomorphic to complex projective space but we extend our analysis to orthotoric orbifolds where the geometry is much richer we thus obtain new examples of kahler einstein 4 orbifolds combining these two themes we prove that compact kahler manifolds with hamiltonian 2 forms are covered by blow downs of projective bundles over kahler products and we describe explicitly how the kahler metrics with a hamiltonian 2 form are parameterized we explain how this provides a context for constructing new examples of extremal kahler metrics in particular a subclass of such metrics which we call weakly bochner flat we also provide a self contained treatment of the theory of compact toric kahler manifolds since we need it and find the existing literature incomplete

optimal approximation of stochastic integrals in analytic noise model abstract we study approximate stochastic ito integration of processes belonging to a class of progressively measurable stochastic processes that are holder continuous in the rth mean inspired by increasing popularity of computations with low precision used on graphics processing units gpus and standard computer processing units cpus we introduce a suitable analytic noise model of standard noisy information about x and w in this model we show that the upper bounds on error of the riemann maruyama quadrature are proportional to n 1 2 where n is a number of noisy evaluations of x and w 0 1 is a holder exponent of x and 1 2 0 are precision parameters for values of x and w respectively moreover we show that the error of any algorithm based on at most n noisy evaluations of x and w is at least c n 1 finally we report numerical experiments performed on both cpu and gpu together with some computational performance comparison between those two architectures

hamiltonian constructions of kahler einstein metrics and kahler metrics of constant scalar curvature assuming the existence of a real torus acting through holomorphic isometries on a kahler manifold we construct an ansatz for kahler einstein metrics and an ansatz for kahler metrics with constant scalar curvature using this hamiltonian approach we solve the differential equations in special cases and find in particular a family of constant scalar curvature kahler metrics describing a non linear superposition of the bergman metric the calabi metric and a higher dimensional generalization of the lebrun kahler metric the superposition contains kahler einstein metrics and all the geometries are complete on the open disk bundle of some line bundle over the complex projective spacepn we also build such kahler geometries on kahler quotients of higher cohomogeneity