derived category automorphisms from mirror symmetry inspired by the homological mirror symmetry conjecture of kontsevich 30 we construct new classes of automorphisms of the bounded derived category of coherent sheaves on a smooth quasi projective variety msc 2000 18e30 14j32

optimization of an acoustic horn with respect to efficiency and directivity we consider the problem of designing an acoustic horn in order to efficiently transmit the incoming wave energy and favorably distribute the energy in the far field a finite element solution of the helmholtz equation in planar or cylindrical symmetry models the wave propagation the transmission efficiency is monitored by measuring the back reflections into the feeding waveguide and the far field directivity pattern is computed using an integral expression known from scattering theory the design problem is formulated as a non linear least squares problem which is solved using a gradient based algorithm where the gradients are provided by solutions of the associated adjoint equations the results demonstrate that this approach can generate horns with almost perfect transmission in a wide frequency band due to the improved transmission properties at the lower frequency region the optimization with respect to efficiency also generates improved far field directivity patterns that is patterns that vary less with frequency it is possible to obtain even more uniform directivity patterns by explicitly including directivity requirements in the optimization however those improvements in directivity seem to be associated with a substantial loss of efficiency copyright 2007 john wiley sons ltd

the grothendieck duality theorem via bousfield s techniques and brown representability grothendieck proved that if f x y is a proper morphism of nice schemes then rf has a right adjoint which is given as tensor product with the relative canonical bundle the original proof was by patching local data deligne proved the existence of the adjoint by a global argument and verdier showed that this global adjoint may be computed locally in this article we show that the existence of the adjoint is an immediate consequence of brown s representability theorem lit follows almost as imme diately by smashing arguments that the adjoint is given by tensor product with a dualising complex verdier s base change theorem is an easy conse quence department of mathematics university of virginia charlottesville virginia 22903 e mail address an3rqvirginia edu this content downloaded from 157 55 39 27 on wed 07 sep 2016 06 26 19 utc all use subject to http about jstor org terms

coupling of boundary element and wave based methods for the efficient solution of complex multiple scattering problems a novel hybrid method for the efficient solution of complex acoustic multiple scattering problems is proposed in this paper the wave based method and the boundary element method are coupled to benefit from the strengths of both the former is an indirect trefftz approach which has a faster convergence rate and lower computational load compared to element based methods when applied on geometries of moderate complexity the latter is the state of the art technique for unbounded acoustic problems and can handle very complex geometries the idea behind the hybrid method is to take advantage of the fast wbm solution for scatterers of moderate complexity and take advantage of the bem s capability for handling scatterers of high complexity for the bem part the indirect variational formulation is used which allows modeling of open boundary problems zero thickness walls in addition the wbm makes it possible to easily add heterogeneities domain inclusions to the problem therefore the hybrid method does not only aim for better efficiency but also for extending the variety of configurations that can be tackled by both methods with ease the accuracy and the performance of the method are demonstrated with three examples both in 2d and 3d it is shown that when complex and simple scatterers coexist the hybrid method is more efficient than the wbm the bem and the fast multipole bem while it is able to provide accuracy of similar level

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

on uniqueness properties of solutions of the k generalized kdv equations in this paper we study uniqueness properties of solutions of the so called k generalized korteweg de vries equations our goal is to obtain sufficient conditions on the behavior of the difference u1 u2 of two solutions u1 u2 of 1 1 at two different times t0 0 and t1 1 which guarantee that u1 u2

fourier mukai transforms for gorenstein schemes we extend to singular schemes with gorenstein singularities or fibered in schemes of that kind bondal and orlov s criterion for an integral functor to be fully faithful we also prove that the original condition of characteristic zero cannot be removed by providing a counterexample in positive characteristic we contemplate a criterion for equivalence as well in addition we prove that for locally projective gorenstein morphisms a relative integral functor is fully faithful if and only if its restriction to each fibre is also fully faithful these results imply the invertibility of the usual relative fourier mukai transform for an elliptic fibration as a direct corollary

complex surfaces with equivalent derived categories we examine the extent to which a smooth minimal complex projective surface x is determined by its derived category of coherent sheaves dx to do this we find for each such surface x the set of surfaces y for which there exists a fourier mukai transform d y to d x

d equivalence and k equivalence let x and y be smooth projective varieties over they are called d equivalent if their derived categories of bounded complexes of coherent sheaves are equivalent as triangulated categories and k equivalent if they are birationally equivalent and the pull backs of their canonical divisors to a common resolution coincide we expect that the two equivalences coincide for birationally equivalent varieties we shall provide a partial answer to the above problem in this paper

on uniqueness and decay of solution for hirota equation abstract we address the question of the uniqueness of solution to the initial value problem associated to the equation t u i x 2 u x 3 u i u 2 u u 2 x u u 2 x u 0 x t r and prove that a certain decay property of the difference u1 u2 of two solutions u1 and u2 at two different instants of times t 0 and t 1 is sufficient to ensure that u1 u2 for all the time

fast direct solution of the helmholtz equation with a perfectly matched layer or an absorbing boundary condition we consider the efficient numerical solution of the helmholtz equation in a rectangular domain with a perfectly matched layer pml or an absorbing boundary condition abc standard bilinear trilinear finite element discretization on an orthogonal mesh leads to a separable system of linear equations for which we describe a cyclic reduction type fast direct solver we present numerical studies to estimate the reflection of waves caused by an absorbing boundary and a pml and we optimize certain parameters of the layer to minimize the reflection copyright 2003 john wiley sons ltd

fourier mukai transforms for elliptic surfaces we compute a large number of moduli spaces of stable bun dles on a general algebraic elliptic surface using a new class of relative fourier mukai transforms

filters in topology optimization in this article a modified filtered version of the minimum compliance topology optimization problem is studied the direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field by the mean of a convolution operator in this setting it is possible to establish the existence of solutions moreover convergence of an approximation by means of finite elements can be obtained this is illustrated through some numerical experiments the filtering technique is also shown to cope with two important numerical problems in topology optimization checkerboards and mesh dependent designs copyright 2001 john wiley sons ltd

shape optimization of an acoustic horn the shape of an acoustic horn is optimized with respect to its ability to provide impedance matching to the surrounding air the resulting minimization problem is solved using a bfgs quasi newton algorithm the wave propagation is modeled by a finite element approximation of the helmholtz equation and the necessary objective function gradient is calculated from the solution of the associated adjoint equation local solutions to the optimization problem corresponding to irregular horn contours are avoided by using a filtering technique that applies smoothing to the design updates and the gradient the method converges fast to a smooth solution and the resulting horn has good impedance properties throughout the entire frequency band of interest

unique continuation for some evolution equations this work is concerned with unique continuation results for some evolution equations essentially of parabolic type to be more precise let l be an evolution operator acting on functions defined on some connected open set b of r r x r l is said to have the unique continuation property if every solution u of lu 0 which vanishes one some nonempty open set u i of fl vanishes in the horizontal component of o in 0 i e in x t e 0 3x x t e co the first general result of this type was established by mizohata 6 in the case where l is a second order parabolic operator with smooth coefficients however mizohata s proof is somewhat delicate it is based in particular on an extended class of calderon zygmund operators and does not lead obviously to a weakening of the smoothness of the coefficients on the other hand it is important for the applications to deal with nonsmooth coefficients since l is often obtained as the linearization of some nonlinear operator at a nonnecessarily smooth solution we refer to lions 4 and kernevez and lions 3 for applications to control theory and to 1 l for applications to transversality techniques let us now describe the content of this work in the first section we prove a unique continuation theorem when l is a second order parabolic equation our proof is simple and based on the derivation of a carleman estimate which is reminiscent of the classical carleman estimates for second order elliptic operators see 121 this carleman inequality allows the weakening of the 118 0022 0396187 3 00

three dimensional flops and noncommutative rings limburgs univ ctr dept math b 3590 diepenbeek belgium van den bergh m limburgs univ ctr dept math univ campus b 3590 diepenbeek belgium vdbergh luc ac be

flops and equivalences of derived categories for threefolds with only terminal gorenstein singularities the main purpose of this paper is to show that bridgeland s moduli space of perverse point sheaves for certain flopping contractions gives the flops and the fourier mukai transform given by the birational correspondence of the flop is an equivalence between bounded derived categories

a note on the unique continuation property for zakharov kuznetsov equation we prove that if a sufficiently smooth solution to the initial value problem associated with the zakharov kuznetsov equation ut uxx uyy x uux 0 x y r 2 t r

shape and topology optimization of an acoustic horn lens combination using gradient based optimization combined with numerical solutions of the helmholtz equation we design an acoustic device with high transmission efficiency and even directivity throughout a two octave wide frequency range the device consists of a horn whose flare is subject to boundary shape optimization together with an area in front of the horn where solid material arbitrarily can be distributed using topology optimization techniques effectively creating an acoustic lens

large scale three dimensional acoustic horn optimization we consider techniques that enable large scale gradient based shape optimization of wave guiding devices in the context of three dimensional time domain simulations the approach relies on a memory efficient boundary representation of the shape gradient together with primal and adjoint solvers semiautomatically generated by the fenics framework the hyperbolic character of the governing linear wave equation written as a first order system is exploited through systematic use of the characteristic decomposition both to define the objective function and to obtain stable numerical fluxes in the discontinuous galerkin spatial discretization the methodology is successfully used to optimize the shape of a midrange acoustic horn described by 1 762 design variables for maximum transmission efficiency where the parallel computations involve a total of 3 5 times10 9 unknowns

unique continuation property for a higher order nonlinear schrodinger equation abstract we prove that if a sufficiently smooth solution u to the initial value problem associated with the equation t u i x 2 u x 3 u i u 2 u u 2 x u e u 2 x u 0 x t r is supported in a half line at two different instants of time then u 0 to prove this result we derive a new carleman type estimate by extending the method introduced by kenig et al in ann inst h poincare anal non lineaire 19 2002 191 208

optimization of a variable mouth acoustic horn by using boundary shape optimization on the end part of a semi infinite waveguide for acoustic waves we design transmission efficient interfacial devices without imposing an upper bound on the mou

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

optical solitons in a monomode fiber we discuss the propagation of optical solitons in a monomode fiber as a model of long distance high bit rate transmission system we give several new results which did not appear in our previous papers on this subject such as 1 a derivation of the perturbed nonlinear schrodinger equation from the maxwell equation 2 on the integrability of the perturbed nonlinear schrodinger equation 3 a discussion of the soliton as a stable fixed point of certain infinite dimensional map generated by a transmission system with periodic excitations