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

new algorithms for singly linearly constrained quadratic programs subject to lower and upper bounds there are many applications related to singly linearly constrained quadratic programs subjected to upper and lower bounds in this paper a new algorithm based on secant approximation is provided for the case in which the hessian matrix is diagonal and positive definite to deal with the general case where the hessian is not diagonal a new efficient projected gradient algorithm is proposed the basic features of the projected gradient algorithm are 1 a new formula is used for the stepsize 2 a recently established adaptive non monotone line search is incorporated and 3 the optimal stepsize is determined by quadratic interpolation if the non monotone line search criterion fails to be satisfied numerical experiments on large scale random test problems and some medium scale quadratic programs arising in the training of support vector machines demonstrate the usefulness of these algorithms

an exact test for multiple inequality and equality constraints in the linear regression model abstract in this article we consider the linear regression model y x e where e is n 0 2i in this context we derive exact tests of the form h r r versus k rk for the case in which 2 is unknown we extend these results to consider hypothesis tests of the form h r1 r1 and r2 r2 versus k rk for each of these hypotheses tests we derive several equivalent forms of the test statistics using the duality theory of the quadratic programming for both tests we derive their exact distribution as a weighted sum of snedecor s f distributions normalized by the numerator degrees of freedom of each f distribution of the sum a methodology for computing critical values as well as probability values for the tests is discussed the relationship between this testing framework and the multivariate one sided hypothesis testing literature is also discussed in this context we show that for any size of the hypothesis test h 0 versus k rk the test statistic and critical value obtained a

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

on tests against one sided hypotheses in some generalized linear models one sided hypotheses arise naturally in many situations when testing against such hypotheses it is desirable to take the available one sided information into account rather than simply applying a two sided test what we expect to gain by applying a one sided test instead of a two sided test is an increase in the power of the test we consider various tests of one sided hypotheses in a class of models that includes generalized linear and cox regression models the tests are likelihood ratio wald score generalized distance and a pearson chi square it is shown that these test statistics are asymptomatically equivalent in terms of local power this is a generalization of the well known corresponding result for two sided alternatives two examples are also discussed they are on 1 testing for interaction in binomial response models and 2 comparison of treatments with ordinal categorical responses

optimization based remap and transport a divide and conquer strategy for feature preserving discretizations this paper examines the application of optimization and control ideas to the formulation of feature preserving numerical methods with particular emphasis on the conservative and bound preserving remap constrained interpolation and transport advection of a single scalar quantity we present a general optimization framework for the preservation of physical properties and specialize it to a generic optimization based remap obr of mass density the latter casts remap as a quadratic program whose optimal solution minimizes the distance to a suitable target quantity subject to a system of linear inequality constraints the approximation of an exact mass update operator defines the target quantity which provides the best possible accuracy of the new masses without regard to any physical constraints such as conservation of mass or local bounds the latter are enforced by the system of linear inequalities in so doing the generic obr formulation separates accuracy considerations from the enforcement of physical properties we proceed to show how the generic obr formulation yields the recently introduced flux variable flux target fvft 1 and mass variable mass target mvmt 2 formulations of remap and then follow with a formal examination of their relationship using an intermediate flux variable mass target fvmt formulation we show the equivalence of fvft and mvmt optimal solutions to underscore the scope and the versatility of the generic obr formulation we introduce the notion of adaptable targets i e target quantities that reflect local solution properties extend fvft and mvmt to remap on the sphere and use obr to formulate adaptable conservative and bound preserving optimization based transport algorithms for cartesian and latitude longitude coordinate systems a selection of representative numerical examples on two dimensional grids demonstrates the computational properties of our approach

a reflective newton method for minimizing a quadratic function subject to bounds on some of the variables we propose a new algorithm a reflective newton method for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables this method applies to a general indefinite quadratic function for which a local minimizer subject to bounds is required and is particularly suitable for the large scale problem our new method exhibits strong convergence properties global and quadratic convergence and appears to have significant practical potential strictly feasible points are generated experimental results on moderately large and sparse problems support the claim of practicality for large scale problems

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

locally constrained projections on grids a technique is formulated for projecting vector fields from one unstructured computational grid to another grid so that a constraint condition such as a conservation property holds at the cell or element level on the receiving grid the approach is based on ideas from constrained optimization and certain mixed or multiplier type finite element methods in which lagrange multipliers are introduced on the elements to enforce the constraint a theoretical analysis and estimates for the associated saddle point problem are developed and a new algorithm is proposed for efficient solution of the resulting discretized problem in the algorithm a reduced schur s complement problem is constructed for the multipliers and the projected velocity computation reduces to a post processing calculation in some instances the reduced system matrix can be factored so that repeated projections involve little more than forward and backward substitution sweeps numerical tests with an element of practical interest demonstrate optimal rate of convergence for the projected velocities and verify the local conservation property to expected machine precision a practical demonstration for environmental simulation of florida bay concludes the study copyright 2001 john wiley sons ltd

a practical two step method for testing moment inequalities this paper considers the problem of testing a finite number of moment inequalities we propose a two step approach in the first step a confidence region for the moments is constructed in the second step this set is used to provide information about which moments are negative a bonferonni type correction is used to account for the fact that with some probability the moments may not lie in the confidence region it is shown that the test controls size uniformly over a large class of distributions for the observed data an important feature of the proposal is that it remains computationally feasible even when the number of moments is large the finite sample properties of the procedure are examined via a simulation study which demonstrates among other things that the proposal remains competitive with existing procedures while being computationally more attractive

on bootstrap inconsistency and bonferroni based size correction for the subset anderson rubin test under conditional homoskedasticity abstract we focus on the linear instrumental variable model with two endogenous regressors under conditional homoskedasticity and study the subset anderson and rubin 1949 ar test when the nuisance structural parameter the unrestricted slope coefficient of endogenous regressor may be weakly identified weak identification leads to nonstandard null limiting distributions and alternative to the usual chi squared critical value is needed we first investigate the bootstrap validity for the subset ar test based on various plug in estimators and show that the bootstrap provides asymptotic refinement when the nuisance structural parameter is strongly identified but is inconsistent when it is weakly identified this is in contrast to the result of bootstrap validity in moreira et al 2009 then we propose a bonferroni based size correction method that yields correct asymptotic size for all the test statistics considered the power performance of size corrected tests can be further improved by applying the mapping between structural and endogenous parameters in the model monte carlo experiments confirm the bootstrap inconsistency and demonstrate that all the subset tests based on our correction technique control the size

asymptotic performance analysis of bayesian target recognition this article investigates the asymptotic performance of bayesian target recognition algorithms using deformable template representations rigid computer aided design cad models represent the underlying targets low dimensional matrix lie groups rotation and translation extend them to particular instances remote sensors observing the targets are modeled as projective transformations converting three dimensional scenes into random images bayesian target recognition corresponds to hypothesis selection in the presence of nuisance parameters its performance is quantified as the bayes error analytical expressions for this error probability in small noise situations are derived yielding asymptotic error rates for exponential error probability decay

association schemes in which the thin residue is an elementary abelian p group of rank 2 abstract in this article we investigate the existence and schurity problem of association schemes whose thin residues are isomorphic to an elementary abelian p group of rank 2

design and analysis of group sequential tests based on the type i error spending rate function summary lan demets 1983 devised a method of constructing discrete group sequential boundaries by using the type i error spending rate function it is extended so as to generate asymmetric as well as symmetric two sided boundaries for clinical trials the design aspect of this procedure is explored in terms of the maximum sample size needed to achieve a desired level of power and the expected stopping times under both null and alternative hypotheses finally these properties are employed in search of appropriate type i error spending rate functions for differing situations

on p schemes of order p 3 abstract let x s be a p scheme of order p 3 and t the thin residue of s assuming that t has valency p 2 one of the following holds i t p 2 and t c p 2 ii t p 2 and t c p c p iii t p 2 it is known that x s is schurian if i holds in case ii we define a partial linear space on x t and prove that the sizes of its lines coincide with the character degrees of x s in case iii we give a construction of non schurian p schemes which are algebraically isomorphic to a schurian p scheme of order p 3

variable density saturated flow with modified darcy s law the salt lake problem and circulation 1 for unsteady variable density seepage flow alternative solutions are obtained by taking respectively the curl and the divergence of a linear form of darcy s law and solving each problem directly using compatible boundary conditions this gives a vector potential formulation depending upon the horizontal density gradient and a pressure formulation depending upon the vertical density gradient resulting in two complementary solutions two velocity fields are obtained by taking the curl of the vector potential solution and by solving darcy s law using the gradient of the pressure solution and corresponding vector potentials are obtained fairly symmetrically from these velocities the novelty is that a linear combination of the two solutions can be made by simple addition or subtraction with independent scalar coefficients having broader scope than each of the alternative solutions alone a two dimensional model based on convective plumes in a hele shaw experiment with a macroscopic rayleigh number of 3975 is treated as a benchmark salt lake problem having a uniform evaporation layer with 1 noise along one third part of the upper boundary with appropriate saline recharge the coefficients are optimized for maximum circulation this determines the ratio of the pressure based solution to the vector potential based solution modifying the rayleigh number downward to an effective value of 3455 numerical streamlines reveal secondary flow typical of henry circulation measured by a peak stream function equal to the circulation flux from finger geometry there is better agreement between the numerically calculated plumes and the experimental plumes than has been achieved previously

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

a maximum principle satisfying modification of triangle based adaptive stencils for the solution of scalar hyperbolic conservation laws a modified triangle based adaptive difference stencil for the numerical approximation of scalar hyperbolic conservation laws in two space dimensions is constructed the scheme satisfies the maximum principle and approximates the flux with second order accuracy

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

a maximum principle preserving finite element method for scalar conservation equations this paper introduces a first order viscosity method for the explicit approximation of scalar conservation equations with lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension provided the lumped mass matrix is positive definite the method is shown to satisfy the local maximum principle under a usual cfl condition the method is independent of the cell type for instance the mesh can be a combination of tetrahedra hexahedra and prisms in three space dimensions

bad behavior of godunov mixed methods for strongly anisotropic advection dispersion equations we study the performance of godunov mixed methods which combine a mixed hybrid finite element solver and a godunov like shock capturing solver for the numerical treatment of the advection dispersion equation with strong anisotropic tensor coefficients it turns out that a mesh locking phenomenon may cause ill conditioning and reduce the accuracy of the numerical approximation especially on coarse meshes this problem may be partially alleviated by substituting the mixed hybrid finite element solver used in the discretization of the dispersive diffusive term with a linear galerkin finite element solver which does not display such a strong ill conditioning to illustrate the different mechanisms that come into play we investigate the spectral properties of such numerical discretizations when applied to a strongly anisotropic diffusive term on a small regular mesh a thorough comparison of the stiffness matrix eigenvalues reveals that the accuracy loss of the godunov mixed method is a structural feature of the mixed hybrid method in fact the varied response of the two methods is due to the different way the smallest and largest eigenvalues of the dispersion diffusion tensor influence the diagonal and off diagonal terms of the final stiffness matrix one and two dimensional test cases support our findings

an improved multislope muscl scheme for solving shallow water equations on unstructured grids 2018 elsevier ltd this paper describes an improved vector manipulation multislope monotone upstream centred scheme for conservation laws muscl reconstruction for solving the shallow water equations on unstructured grids this improved muscl reconstruction method includes a bigger stencil for the interpolation and saves time for determining the geometric relations compared to the original vector manipulation method so it is computationally more efficient and straightforward to implement four examples involving an analytical solution laboratory experiments and field scale measurements are used to test the performance of the proposed scheme it has been proven that the proposed scheme can provide comparable accuracy and higher efficiency compared to the original vector manipulation method with the increasing of the number of cells the advantage of the proposed scheme becomes more apparent

maximum likelihood estimation of intraclass correlation in the analysis of familial data estimating equation approach summary we introduce a generalized model for estimating intraclass correlation in the analysis of familial data this model incorporates the models of donner koval 1980 donner bull 1983 rosner 1984 and miunoz rosner carey 1986 as special cases we then obtain the maximum likelihood estimates of the parameters of the model in particular we obtain a single estimating equation to be solved iteratively for the estimation of the intraclass correlation p and discuss all the special cases asymptotic variance for the estimate of the intraclass correlation is obtained for all the models and some examples are given

schurity and separability of quasiregular coherent configurations abstract a permutation group is said to be quasiregular if each of its transitive constituents is regular and a quasiregular coherent configuration can be thought as a combinatorial analog of such a group the transitive constituents are replaced by the homogeneous components in this paper we are interested in the question when the configuration is schurian i e formed by the orbitals of a permutation group or and separable i e uniquely determined by the intersection numbers in these terms an old result of hanna neumann is in a sense dual to the statement that the quasiregular coherent configurations with cyclic homogeneous components are schurian in the present paper we a establish the duality in a precise form and b generalize the latter result by proving that a quasiregular coherent configuration is schurian and separable if the groups associated with the homogeneous components have distributive lattices of normal subgroups

robust bounded influence tests in linear models abstract a robust test that we call an aligned generalized m test for testing subhypotheses in general linear models is developed and its asymptotic properties are studied the test is a robustification of the well known f test and it is an elegant alternative to ronchetti s 1982 class of tests p values associated with it can be approximated readily using existing chi square tables the test is based on an appropriately constructed quadratic form and uses the generalized m estimators of the parameters in the reduced model under the null hypothesis the asymptotic distribution is a central chi square and under contiguous alternatives it is a noncentral chi square with the same degrees of freedom the test can be viewed as a generalization of sen s 1982 m test for linear models the influence function of the test is bounded the bound not only applies to the influence of residuals but to the influence of position in the factor space as well on the other hand sen s test has bounded influence only

the repair paradigm new algorithms and applications to compressible flow the repair paradigm leads to several algorithms for redistributing mass momentum and energy while adhering to local maximum principles as an adjunct to the remapping step in certain compressible flow codes that use remapping such as arbitrary lagrangian eulerian codes or for just redistributing mass in advection codes in the case of advection of a concentration repair keeps the newly computed concentration in a cell between the maximum and minimum concentrations in neighboring old cells thus guaranteeing at least that the new concentration is between zero and one for compressible flow density velocity and internal energy are similarly constrained while maintaining conservation of mass momentum and total energy in this way positive density and internal energy are achieved as a side effect we propose a new algorithm combining both local and global repair that maintains causality and is efficient in a parallel computational setting the local global algorithm is independent of the order in which the distribution is performed and it maintains 1d symmetry this is applied to advection in two dimensions and to among others the leblanc problem the sedov problem and an interacting 2d blast wave problem the latter is done with a lagrangian code for which rezoning remapping and repair are essential

direction aware slope limiter for three dimensional cubic grids with adaptive mesh refinement abstract in the context of finite volume methods for hyperbolic systems of conservation laws slope limiters are an effective way to suppress creation of unphysical local extrema and or oscillations near discontinuities we investigate properties of these limiters as applied to piecewise linear reconstructions of conservative fluid quantities in three dimensional simulations in particular we are interested in linear reconstructions on cartesian adaptively refined meshes where a reconstructed fluid quantity at a face center depends on more than a single gradient component of the quantity we design a new slope limiter which combines the robustness of a minmod limiter with the accuracy of a van leer limiter the limiter is called direction aware limiter dal because the combination is based on a principal flow direction in particular dal is useful in situations where the barth jespersen limiter for general meshes fails to maintain global linear functions such as on cubic computational meshes with stencils including only face neighboring cells we verify the new slope limiter on a suite of standard hydrodynamic test problems on cartesian adaptively refined meshes we demonstrate reduced mesh imprinting for radially symmetric problems such as the sedov blast wave or the noh implosion test cases the results with dal show better preservation of radial symmetry compared to the other standard methods on cartesian meshes

compatible energy conserving bounds preserving remap of hydrodynamic fields for an extended ale scheme abstract from the very origins of numerical hydrodynamics in the lagrangian work of von neumann and richtmyer 83 the issue of total energy conservation as well as entropy production has been problematic because of well known problems with mesh deformation lagrangian schemes have evolved into arbitrary lagrangian eulerian ale methods 39 that combine the best properties of lagrangian and eulerian methods energy issues have persisted for this class of methods we believe that fundamental issues of energy conservation and entropy production in ale require further examination the context of the paper is an ale scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity the principal design goals for a remap method then consist of total energy conservation bounded internal energy and compatibility of kinetic energy and momentum we also have secondary objectives of limiting velocity and stress in a non directional manner keeping primitive variables monotone and providing a higher than second order reconstruction of remapped variables in particular the new contributions fall into three categories associated with energy conservation and entropy production reconstruction and bounds preservation of scalar and tensor fields and conservative remap of nonlinear fields the paper presents a derivation of the methods details of implementation and numerical results for a number of test problems the methods requires volume integration of polynomial functions in polytopal cells with planar facets and the requisite expressions are derived for arbitrary order

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

mixed finite element and finite volume discretization for heavy brine simulations in groundwater recently a new theory of high concentration brine transport in groundwater has been developed this approach is based on two nonlinear mass conservation equations one for the fluid flow equation and one for the salt transport equation both having nonlinear diffusion terms in this paper we present and analyze a numerical technique for the solution of such a model the approach is based on the mixed hybrid finite element method for the discretization of the diffusion terms in both the flow and transport equations and a high resolution tvd finite volume scheme for the convective term this latter technique is coupled to the discretized diffusive flux by means of a time splitting approach a commonly used benchmark test elder problem is used to verify the robustness and nonoscillatory behavior of the proposed scheme and to test the validity of two different formulations one based on using pressure head and concentration c as dependent variables and one using pressure p and mass fraction as dependent variables it is found that the latter formulation gives more accurate and reliable results in particular at large times the numerical model is then compared against a semi analytical solution and the results of a laboratory test these tests are used to verify numerically the performance and robustness of the proposed numerical scheme when high concentration gradients i e the double nonlinearity are present

a note on permutation tests for variance components in multilevel generalized linear mixed models in many applications of generalized linear mixed models to multilevel data it is of interest to test whether a random effects variance component is zero it is well known that the usual asymptotic chi square distribution of the likelihood ratio and score statistics under the null does not necessarily hold in this note we propose a permutation test based on randomly permuting the indices associated with a given level of the model that has the correct type i error rate under the null results from a simulation study suggest that it is more powerful than tests based on mixtures of chi square distributions the proposed test is illustrated using data on the familial aggregation of sleep disturbance

association schemes in which the thin residue is a finite cyclic group abstract in this article we investigate association schemes s on finite sets in which each element s satisfies s s s s it is shown that these schemes are schurian if the partially ordered set of the intersections of the closed subsets s s of s with s s is distributive a scheme is said to be schurian if it arises in a well understood way from a transitive permutation group it is also shown that if these schemes are schurian the transitive permutation group from which they arise have subnormal one point stabilizers as a consequence of the first result one obtains that schemes are schurian if their thin residue is thin and has a distributive normal closed subset lattice normal subgroup lattice this implies for instance that schemes are schurian if their thin residue is a cyclic group

a second order maximum principle preserving lagrange finite element technique for nonlinear scalar conservation equations this paper proposes an explicit at least second order maximum principle sat isfying lagrange finite element method for solving nonlinear scalar conservation equations the technique is based on a new viscous bilinear form introduced in guermond and nazarov com put methods appl mech engrg 272 2014 pp 198 213 a high order entropy viscosity method and the boris book zalesak flux correction technique the algorithm works for arbitrary meshes in any space dimension and for all lipschitz fluxes the formal second order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems

good neighborhoods for multidimensional van leer limiting van leer limiting uses nearby cell means of a function integral mean values weighted by a prescribed positive density that are taken over each of a collection of nearby computational cells to restrict the range of values allowed to a linear approximation of the function on a given central cell these nearby cells whose cell means are actually involved in the limiting are called the central cell s neighbors and the set of these neighbors is called the central cell s neighborhood the use of certain neighborhoods in multidimensional van leer limiting can force even linear functions to be subject to restriction over the central cell a simple geometric property characterizes those neighborhoods whose use would not require that any linear functions be limited such a neighborhood is called a good neighborhood for van leer limiting since its use would not preclude second order accuracy in the local linear approximation of a smooth function by one that is van leer limited unless the additional here unspecified details for obtaining the approximation preclude it by themselves the characterization is as follows where it is presumed that the cells lie in a finite dimensional vector space one has chosen a good neighborhood for a given central cell if and only if the convexmore hull of the centroids of its associated neighbors contains that central cell details are given less

a globally and superlinearly convergent algorithm for convex quadratic programs with simple bbounds a globally and superlinearly convergent algorithm for solving convex quadratic programs with simple bounds is presented the algorithm is developed using a new formulation of the problem the minimization of an unconstrained piecewise quadratic function that has the same optimality conditions as the original problem the major work at each iteration is the cholesky factorization of a positive definite matrix with the size and structure of the hessian of the quadratic hence the algorithm is suitable for solving large sparse problems and for implementation on parallel computers the numerical results indicate that the new approach has promise

a subcell remapping method on staggered polygonal grids for arbitrary lagrangian eulerian methods we describe a new remapping algorithm for use in arbitrary lagrangian eulerian ale simulations the new features of this remapper are designed to complement a staggered mesh lagrangian phase in which the cells may be general polygons in two dimensions and which uses subcell discretizations to control unphysical mesh distortion and hourglassing our new remapping algorithm consists of three stages a gathering stage in which we interpolate momentum internal energy and kinetic energy to the subcells in a conservative way a subcell remapping stage in which we conservatively remap mass momentum internal and kinetic energy from the subcells of the lagrangian mesh to the subcells of the new rezoned mesh a scattering stage in which we conservatively recover the primary variables subcell density nodal velocity and cell centered specific internal energy on the new rezoned mesh we prove that our new remapping algorithm is conservative reversible and satisfies the debar consistency condition we also demonstrate computationally that our new remapping method is robust and accurate for a series of test problems in one and two dimensions

the analysis of multiple endpoints in clinical trials treatment comparisons in randomized clinical trials usually involve several endpoints such that conventional significance testing can seriously inflate the overall type i error rate one option is to select a single primary endpoint for formal statistical inference but this is not always feasible another approach is to apply bonferroni correction i e multiply each p value by the total number of endpoints its conservatism for correlated endpoints is examined for multivariate normal data a third approach is to derive an appropriate global test statistic and this paper explores one such test applicable to any set of asymptotically normal test statistics quantitative binary and survival endpoints are all considered within this general framework two examples are presented and the relative merits of the proposed strategies are discussed

convex quadratic programming with one constraint and bounded variables in this paper we propose an iterative algorithm for solving a convex quadratic program with one equality constraint and bounded variables at each iteration a separable convex quadratic program with the same constraint set is solved two variants are analyzed one that uses an exact line search and the other a unit step size preliminary testing suggests that this approach is efficient for problems with diagonally dominant matrices

coherent configurations associated with ti subgroups let x be a coherent configuration associated with a transitive group g in terms of the intersection numbers of x a necessary condition for the point stabilizer of g to be a ti subgroup is established furthermore under this condition x is determined up to isomorphism by the intersection numbers it is also proved that asymptotically this condition is also sufficient more precisely an arbitrary homogeneous coherent configuration satisfying this condition is associated with a transitive group the point stabilizer of which is a ti subgroup as a byproduct of the developed theory recent results on pseudocyclic and quasi thin association schemes are generalized and improved in particular it is shown that any scheme of prime degree p and valency k is associated with a transitive group whenever p 1 6k k 1 2

a variable explicit implicit numerical method for calculating advection on unstructured meshes a variable explicit implicit numerical method is presented for calculating fluid advection on hybrid unstructured meshes the method is intended for unsteady flows that have a large range of advective time scales with subregions where the flow may be quasi steady on time scales of interest the method generalizes the method of collins collela and glaz by providing an explicit to implicit switching criterion that is suitable for use on unstructured meshes no directional splitting is used upwinding is in the direction of the material velocity and thus we define and use a new multidimensional limited gradient that generalizes van leer s muscl limiting 7 after reviewing the one dimensional method of collins collela and glaz we present the generalization to hybrid unstructured grids and detail the results of four example calculations that demonstrate the accuracy and flexibility of the new method

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

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

randomization based inference within principal strata in randomized studies treatment comparisons conditional on intermediate postrandomization outcomes using standard analytic methods do not have a causal interpretation an alternative approach entails treatment comparisons within principal strata defined by the potential outcomes for the intermediate outcome that would be observed under each treatment assignment in this article we develop methods for randomization based inference within principal strata we compare our proposed methods with existing large sample methods as well as traditional intent to treat approaches this research is motivated by hiv prevention studies where few infections are expected and inference is desired within the always infected principal stratum that is all individuals who would become infected regardless of randomization assignment

high order godunov mixed methods on tetrahedral meshes for density driven flow simulations in porous media two dimensional godunov mixed methods have been shown to be effective for the numerical solution of density dependent flow and transport problems in groundwater even when concentration gradients are high and the process is dominated by density effects this class of discretization approaches solves the flow equation by means of the mixed finite element method thus guaranteeing mass conserving velocity fields and discretizes the transport equation by mixed finite element and finite volumes techniques combined together via appropriate time splitting in this paper we extend this approach to three dimensions employing tetrahedral meshes and introduce a spatially variable time stepping procedure that improves computational efficiency while preserving accuracy by adapting the time step size according to the local courant friedrichs lewy cfl constraint careful attention is devoted to the choice of a truly three dimensional limiter for the advection equation in the time splitting technique so that to preserve second order accuracy in space in the sense that linear functions are exactly interpolated the three dimensional elder problem and the saltpool problem recently introduced as a new benchmark for testing three dimensional density models provide assessments with respect to accuracy and reliability of this numerical approach

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

high order multi material ale hydrodynamics we present a new approach for multi material arbitrary lagrangian eulerian ale hydrodynamics simulations based on high order finite elements posed on high order curvilinear meshes the method builds on and extends our previous work in the lagrangian v a dobrev t v kolev and r n rieben siam j sci comput 34 2012 pp b606 b641 and remap r w anderson et al internat j numer methods fluids 77 2015 pp 249 273 phases of ale and depends critically on a functional perspective that enables subzonal physics and material modeling v a dobrev et al internat j numer methods fluids 82 2016 pp 689 706 curvilinear mesh relaxation is based on node movement which is determined through the solution of an elliptic equation the remap phase is posed in terms of advecting state variables between two meshes over a fictitious time interval the resulting advection equation is solved by a discontinuous galerkin dg formulation combined with a customized flux corrected transpor

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

characterization of p valenced schemes of order p2q abstract in p h zieschang association schemes in which the thin residue is a finite cyclic group j algebra 324 2010 3572 3578 it was shown that association schemes are schurian if their thin residues are finite groups and have a distributive normal subgroup lattice however in the case that their thin residues are elementary abelian groups they do not have a distributive normal subgroup lattice actually they are not necessarily schurian due to the non schurian quasi thin scheme of order 28 in this paper we investigate association schemes such that their thin residues are elementary abelian groups of order p 2 it is shown that these schemes are schurian if the number of elements with valency p is 2p and the factor scheme over the thin residue is a cyclic group of prime order we also construct non schurian p schemes of order p 3

a flux corrected transport algorithm for handling the close packing limit in dense suspensions convection of a scalar quantity by a compressible velocity field may give rise to unbounded solutions or nonphysical overshoots at the continuous and discrete level in this paper we are concerned with solving continuity equations that govern the evolution of volume fractions in eulerian models of disperse two phase flows an implicit galerkin finite element approximation is equipped with a flux limiter for the convective terms the fully multidimensional limiting strategy is based on a flux corrected transport fct algorithm this nonlinear high resolution scheme satisfies a discrete maximum principle for divergence free velocities and ensures positivity preservation for arbitrary velocity fields to enforce an upper bound that corresponds to the maximum packing limit an fct like overshoot limiter is applied to the converged convective fluxes at the end of each time step this postprocessing step imposes an additional physical constraint on the numerical solution to the unconstrained mathematical model numerical results for 2d implosion problems illustrate the performance of the proposed limiting procedure

formulation analysis and numerical study of an optimization based conservative interpolation remap of scalar fields for arbitrary lagrangian eulerian methods we develop and study the high order conservative and monotone optimization based remap obr of a scalar conserved quantity mass between two close meshes with the same connectivity the key idea is to phrase remap as a global inequality constrained optimization problem for mass fluxes between neighboring cells the objective is to minimize the discrepancy between these fluxes and the given high order target mass fluxes subject to constraints that enforce physically motivated bounds on the associated primitive variable density in so doing we separate accuracy considerations handled by the objective functional from the enforcement of physical bounds handled by the constraints the resulting obr formulation is applicable to general unstructured heterogeneous grids under some weak requirements on grid proximity but not on the cell types we prove that the obr algorithm is linearity preserving in one two and three dimensions the paper also examines connections between the obr and the recently proposed flux corrected remap fcr liska et al 1 we show that the fcr solution coincides with the solution of a modified version of obr m obr which has the same objective but a simpler set of box constraints derived by using a worst case scenario because m obr fcr has a smaller feasible set preservation of linearity may be lost and accuracy may suffer for some grid configurations our numerical studies confirm this and show that obr delivers significant increases in robustness and accuracy preliminary efficiency studies of obr reveal that it is only a factor of 2 1 slower than fcr but admits 1 5 times larger time steps

a score test against one sided alternatives abstract a score type statistic t s is introduced for testing h 0 against k 0 and more general one sided hypotheses when nuisance parameters may be present is a vector parameter the main advantages of t s are that it requires estimation of the model only under the null hypothesis and that it is asymptotically equivalent to the likelihood ratio statistic these are precisely the reasons for the popularity of the score tests for testing against two sided alternatives in this sense t s preserves the main attractive features of the classical two sided score test the theoretical results are presented in a general framework where the likelihood based score function is replaced by an estimating function so that the test is applicable even if the exact population distribution is unknown computation of t s is simplified by the fact that it can be computed easily once the corresponding two sided statistic has been computed the relevance and simplicity of t s are illustrated by discussing

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

three dimensional adaptive mesh refinement for hyperbolic conservation laws a local adaptive mesh refinement algorithm for solving hyperbolic systems of conservation laws in three space dimensions is described the method is based on the use of local grid patches superimpo

fast optimization based conservative remap of scalar fields through aggregate mass transfer abstract we develop a fast efficient and accurate optimization based algorithm for the high order conservative and local bound preserving remap constrained interpolation of a scalar conserved quantity between two close meshes with the same connectivity the new formulation is as robust and accurate as the flux variable flux target optimization based remap fvft obr 1 2 yet has the computational efficiency of an explicit remapper the coupled system of linear inequality constraints resulting from the flux form of remap is the main efficiency bottleneck in fvft obr while advection based remappers use the flux form to directly enforce mass conservation the optimization setting allows us to treat mass conservation as one of the constraints to take advantage of this fact we consider an alternative mass variable mass target mvmt obr formulation in which the optimization variables are the net mass updates per cell and a single linear constraint enforces the conservation of mass in so doing we change the structure of the obr problem from a global linear inequality constrained qp to a singly linearly constrained qp with simple bounds using the structure of the mvmt obr problem and the fact that in remap the old and new grids are close we are able to develop a simple efficient and easily parallelizable optimization algorithm for the primal mvmt obr qp numerical studies on a variety of affine and non affine grids confirm that mvmt obr is as accurate and robust as fvft obr but has the same computational cost as the explicit state of the art fcr

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

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

analysis and computation of a least squares method for consistent mesh tying in the finite element method a standard approach to mesh tying is to apply lagrange multipliers if the interface is curved however discretization generally leads to adjoining surfaces that do not coincide spatially straightforward lagrange multiplier methods lead to discrete formulations failing a first order patch test t a laursen m w heinstein consistent mesh tying methods for topologically distinct discretized surfaces in non linear solid mechanics internat j numer methods eng 57 2003 1197 1242 this paper presents a theoretical and computational study of a least squares method for mesh tying p bochev d m day a least squares method for consistent mesh tying internat j numer anal modeling 4 2007 342 352 applied to the partial differential equation email protected email protected email protected f f we prove optimal convergence rates for domains represented as overlapping subdomains and show that the least squares method passes a patch test of the order of the finite element space by construction to apply the method to subdomain configurations with gaps and overlaps we use interface perturbations to eliminate the gaps theoretical error estimates are illustrated by numerical experiments

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

a test in the presence of nuisance parameters abstract we are interested in testing 0 against an alternative in the presence of some nuisance parameter the usual procedure for such problems is to use a test statistic that is a function of the data only let q denote the p value at a given value if q does not depend on then in principle we can apply this procedure however a major difficulty that arises in many situations is that q depends on and therefore cannot be used as a p value in such cases the usual approach is to define the p value as the supremum of q over the nuisance parameter space because this approach ignores sample information about it may be unnecessarily conservative this is a serious problem in order restricted inference to overcome this i propose the following obtain say a 99 confidence region for under the null hypothesis now for a given let t be a test statistic and r be the p value the test procedure is to reject the null hypothesis if 0 01 supremum of r over the 99 c

possible indices for a class of association schemes with thin residue equal to the thin radical abstract we consider association schemes with thin radical isomorphic to an elementary abelian p group of rank 2 such that the thin residue coincides with the thin radical and all non thin elements have valency p we show that when the order of the thin quotient of such schemes exceeds p 2 it must be equal to p 2 p 1 a known upper bound and we show that there exist examples whose thin quotient has order p 2 1 we also show that if the thin quotient has order at least 10 then one can always find a non schurian example with the same thin quotient

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

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

modified lagrange multiplier tests for problems with one sided alternatives abstract a modified lagrange multiplier test statistic is proposed which takes explicit account of the one sided nature of the alternative in problems where the null hypothesis specifies that the true value of the parameter vector lies on the boundary of the parameter space computation of this statistic requires only the constrained maximum likelihood estimator conditions for the consistency of tests based on this statistic are examined and it is shown that the distribution of the statistic is not affected of nuisance parameters are allowed to lie on the boundary of the parameter space

isotropic finite differences new finite differences called isotropic finite differences where the lowest order error terms are without any directional bias are proposed an accurate simulation of 6 fold symmetric dendritic solidification is presented using a numerical scheme based on these finite differences