a spectral solver for the navier stokes equations in the velocity vorticity formulation for flows with two nonperiodic directions a novel pseudospectral solution procedure for the navier stokes equations in the velocity vorticity formulation suitable to simulate flows with two nonperiodic directions is proposed an influence matrix method including a tau correction procedure has been employed to elicit an algorithmic substitute for thea priorilacking boundary conditions for the vorticity following o daube j comput phys 103 402 1992 the influence matrix is built by enforcing either the definition of the vorticity or the continuity equation at the boundary of the domain the influence matrix is nonsingular in both cases the order of the influence matrix is twice larger than one would expect from analogous solution methods based on finite differences or finite elements the spatial discretization is based on a 2d chebyshev expansion on anonstaggeredgrid of collocation points and the boundary conditions are imposed via the lanczos tau procedure the time marching scheme is adams bashforth for the advection term and crank nicolson for the viscous term the proposed scheme yields machine accurate divergence free flow fields and the definition of the vorticity is satisfied within machine accuracy

holder estimates on cr manifolds with a diagonalizable levi form a for all e 0 the operator cl maps lip s po into lip s 2 m e po here lip s p denotes the space of square integrable forms of degree p q with 1 g q otheoperators o l o l q and0 map lip s p into lip s l m e po c for all e o the operators 8b8zo 8z8ho 1 q a aa cl 8 8 8 q 8 and 8 0 ab map lip s p into lip s p hebre aiag web asm acts on forms of type p q with 1 q 0 e zf f is a square integrable function on a with f e lip p then s f e lip s e p for all e 0 where s is the orthogonal projection on square integrable cr functions

proper holomorphic mappings of balanced domains in mathbb c n we extend a well known result about the unit ball by h alexander to a class of balanced domains in mathbb c n n 1 specifically we prove that any proper holomorphic self map of a certain type of balanced finite type domain in mathbb c n n 1 is an automorphism the main novelty of our proof is the use of a recent result of opshtein on the behaviour of the iterates of holomorphic self maps of a certain class of domains we use opshtein s theorem together with the tools made available by finiteness of type to deduce that the aforementioned map is unbranched the monodromy theorem then delivers the result

a parametrix for the neumann problem on pseudoconvex domains of finite type abstract we construct a parametrix for the neumann problem on any pseudoconvex domain of finite type which reduces completely the study of isotropic lp sobolev and holder estimates to those for b and b we also establish the maximal nonisotropic estimates in the case of d q domains and provide a precise comparison of the bergman and szego projections and of the canonical solutions to with respect to these two operators the argument is substantially simpler than the known ones for the cases of strongly pseudoconvex domains and pseudoconvex domains of finite type in c 2

hearing the type of a domain in c 2 with the neumann laplacian a smooth bounded pseudoconvex domain in c2 is of finite type if and only if the number of eigenvalues of its a neumann laplacian that are less than or equal to has at most polynomial growth as goes to infinity

a mixed spectral wavelet method for the solution of the stokes problem the paper presents a mixed wavelet spectral chebychev method for solving the unsteady 2d stokes equations in the vorticity stream function formulation with periodicity condition in one direction after an appropriate time discretisation of the equations one has to solve at each time step a stationary stokes like problem a capacitance matrix method is used to eliminate the problem of boundary conditions this leads to solving a series of helmholtz problems the spatial discretisation makes use of the wavelet method in the periodic direction and the spectral collocation chebychev method in the non periodic direction the resolution of the discrete helmholtz problem is done by means of the diagonalisation technique in the non periodic direction the system then splits into a sequence of one dimensionnal periodic helmholtz problems which are efficiently inverted using ffts numerical tests show both the stability and the accuracy of the method

a stochastic scheduling problem with intree precedence constraints we consider n jobs to be scheduled on two parallel machines the jobs are subject to intree precedence constraints that is each job except one which is the root of the tree has one successor the job of the root is at level 0 and a job is at level l if its predecessor is at level l 1 a job can start to be processed only after all its predecessors have finished job processing times are independent random variables with those at the same level being identically distributed the objective is to minimize the expected completion time of the last job such a model can be applied to assembly line and computational problems this paper generalizes a result of pinedo and weiss

two simulated annealing based heuristics for the job shop scheduling problem abstract in this paper we present two simulated annealing based algorithms for the classical general job shop scheduling problem where the objective is to minimize the makespan we consider sets of jobs consisting of tasks and sets of machines which can handle at most one task at a time to represent the problem we employ the model of disjunctive graphs simulated annealing has been applied to this problem earlier e g by van laarhoven et al where the neighborhood function is based on reversing a single arc of a longest path of the underlying graph in our approach we analyze a neighborhood function which involves a non uniform generation probability to obtain the neighbors of a schedule we reverse more than a single arc of longest paths and perform a control on the increase of the makespan the selection of the arcs depends on the number of longest paths to which a particular arc belongs furthermore we have designed two cooling schedules which employ a detailed analysis of the objective function depending on the specified neighborhood relation the expected run times can be either o n2 e or o n3 e m for the first cooling schedule and o n5 2 e m1 2 or o n7 2 e m1 2 for the second cooling schedule where n is the number of tasks m the number of machines and e represents o ln ln n ln n our computational experiments on small to large benchmark problems have shown that within short series of consecutive trials relatively stable results equal or close to optimal solutions are repeatedly obtained including the well known benchmark problems ft10 and la38 we could improve five upper bounds for the yn1 yn4 swv12 swv13 and swv15 benchmark problems e g for swv13 the gap between the lower and the former upper bound has been shortened by about 57 in our approach we rely only on basic information about the given problem instance

necessary geometric and analytic conditions for general estimates in the bar partial neumann problem we show the geometric and analytic consequences of a general estimate in the bar partial neumann problem a gain in the estimate yields a bound in the type of the boundary that is in its order of contact with an analytic curve as well as in the rate of the bergman metric we also discuss the potential theoretical consequence a gain implies a lower bound for the levi form of a bounded weight

construction of p s h functions on weakly pseudoconvex domains let q c c be a smoothly bounded pseudoconvex domain and let a q denote the functions holomorphic on q and continuous on sl a point p e aq is a peak point if there is a function f e a q such that f p 1 and if z i 2 were obtained by range 19 20 and hakim and sibony 12 these results do not extend automatically to arbitrary weakly pseudoconvex boundary points of q even if the boundary is real analytic an example of kohn and nirenberg 17 shows that a p e aq does not always have a separating function which is real analytic at p similarly this example does not have a peak function which is e at p see fornaess 6 here we show how peak functions and separating functions may be constructed for a large class of weakly pseudoconvex points on domains in c the results are most complete for domains in c2 so we state them here for that case

hearing pseudoconvexity with the kohn laplacian a bounded domain in open image in new window with connected lipschitz boundary is pseudoconvex if the bottom of the essential spectrum of the kohn laplacian on the space of 0 q forms 1 q n 1 with l2 coefficients is positive

on the optimal stochastic scheduling of out forests this paper presents new results on the problem of scheduling jobs on k 1 parallel processors to stochastically minimize the makespan the jobs are subject to out forest precedence constraints i e each job has at most one immediate predecessor and job running times are independent samples from a given exponential distribution we define a class of uniform out forests in which all subtrees are ordered by an embedding relation we prove that an intuitive greedy policy is optimal for k 2 and that if out forests satisfy an additional uniform root embedding constraint then the greedy policy is optimal for all k 2

scheduling flat graphs the problem of scheduling a partially ordered set of unit length tasks on m identical processors is known to be np complete there are efficient algorithms for only a few special cases of this problem in this paper we analyze the effect of the structure of the precedence graph and the availability of the processors on the construction of optimal schedules we prove that to find an optimal schedule it suffices to consider at each step only initial tasks which belong to the m 1 highest components of the precedence graph this result reduces the number of cases we have to check during the construction of an optimal schedule our method leads to polynomial algorithms if the number of processors is fixed and the precedence graph has a certain form in particular if the precedence graph contains only intrees and outtrees this result leads to linear algorithms for finding an optimal schedule on two or three processors

the bergman kernel on certain weakly pseudoconvex domains let c c be a bounded pseudoconvex domain with c p lur i superharmonic defining function 0 let az q be the space of square integrable ho lomorph ic functions on if 0 is any complete o r thonorma l basis for az g2 then the bergman kernel for o is given by k z w y o z o w except for some special cases 53 it is not possible at present to obta in a nice closed form for k however for domains of the form

compactness of the complex green operator on cr manifolds of hypersurface type the purpose of this article is to study compactness of the complex green operator on cr manifolds of hypersurface type we introduce cr pq a potential theoretic condition on 0 q forms that generalizes catlin s property pq to cr manifolds of arbitrary codimension we prove that if an embedded cr manifold of hypersurface type of real dimension at least five satisfies cr pq and cr pn 1 q then the complex green operator is a compact operator on the sobolev spaces h s 0 q m and h s 0 n 1 q m if 1 q n 2 and s 0 we use cr plurisubharmonic functions to build a microlocal norm that controls the totally real direction of the tangent bundle 1 introduction and results in this article we introduce property cr pq a potential theoretic condition on 0 q forms we show that if an embedded cr manifold of hypersurface type satisfies cr pq and cr pn 1 q then the complex green operator is a compact operator on the sobolev spaces h s 0 q m and h s 0 n 1 q m if 1 q n 2 we use cr plurisubharmonic functions to build a microlocal norm that controls the bad direction of the tangent bundle we first prove the closed range and compactness results on l 2 q m and use an elliptic regularization

application of vorticity integral conditioning to chebyshev pseudospectral formulation for the navier stokes equations a pseudospectral method based on the vorticity stream function formulation is proposed for the solution of two dimensional time dependent flow of an incompressible fluid it features the high resolution and computational economy of chebyshev collocation and the combined second order adams bashforth and crank nicolson time integration schemes precise treatment for the vorticity condition is accomplished by the use of conditions of integral type numerical experiments indicate that the pseudospectral method is capable of producing results comparable to those obtained by finite differences with fewer unknowns and is superior in accuracy for the same number of nodal points

boundary invariants of pseudoconvex domains the purpose of this paper is to describe an invariant ax z which is associated with each point z in the boundary of a smoothly bounded pseudoconvex domain in cn the motivation for defining the invariant ax z referred to as the multitype of z comes from the study of the boundary regularity properties of solutions of the d neumann problem on domains of finite type by a domain of finite type we mean one that satisfies the definition given by d angelo 5 namely a domain such that at any boundary point the maximum order of contact of one dimensional complex analytic varieties with the boundary is bounded in 4 the author showed how one can give a proof of global regularity of the a neumann problem for pseudoconvex domains of finite type if there is an invariant such as the one described in this paper in a forthcoming article this invariant will be used to obtain a proof of subelliptic estimates for the same class of domains before giving the definition of the multitype ax z we must introduce some

necessary conditions for subellipticity of the overline partial neumann problem let a be a a closed form of type p q with l2 coefficients on a smoothly bounded domain q in c the problem of determining both the existence and regularity properties of the solution u of au a where u is orthogonal to the null space of a on p q l forms is known as the a neumann problem one of the principal methods used in the investigation of this problem is the proof of certain a priori subelliptic estimates let u be a neighborhood of a point z0 in the boundary of q a subelliptic estimate is said to hold in u if the estimate

convex domains of finite type we construct bounded plurisubharmonic functions with maximally large hessians near the boundary of a smoothly bounded convex domain in cn as a corollary the equality of the order of contact of the boundary with complex analytic varieties the d angelo type and the order of contact with complex lines is demonstrated

real hypersurfaces orders of contact and applications a fundamental problem in the modem theory of several complex variables concerns the boundary behavior of the cauchy riemann equations suppose that d is an open domain in cn and that its boundary m is a smooth real submanifold of cn how does the geometry of m influence the function theory on d one approach to this question is the a neumann problem 6 there one studies the inhomogeneous cauchy riemann equations au a where a is a 0 q form with distribution coefficients on the closed domain d u m satisfying the necessary compatibility condition a a 0 the a neumann problem constructs a particular solution u which is orthogonal to the null space of the complex laplacian kohn 10a has solved this problem and has shown that good local regularity properties for u in terms of a follow from so called subelliptic estimates it is natural to seek geometric conditions on m that are necessary and sufficient for these estimates in this paper we will be concerned with a certain geometric condition on m that we feel is the right one for subellipticity although the motivation for the questions discussed here comes from partial differential equations the techniques come from algebraic geometry to see why we state theorems of kohn greiner and catlin concerning subellipticity kohn 1oa has discovered a sufficient condition for a subelliptic estimate near a fixed point p in m in case d is pseudoconvex and is contained in c2 this condition is equivalent to the finiteness of order of tangency of every complex analytic one dimensional manifold with m at p greiner 13 established the necessity of this condition in

galerkin spectral method for the vorticity and stream function equations a galerkin legendre spectral method for the solution of the vorticity and stream function equations in uncoupled form under no slip conditions in a square domain is presented which fully exploits the separation of variables in the two elliptic problems benefits from a nonsingular influence matrix and is able to solve the singular driven cavity problem modulo gibbs phenomenon even without regularizing the boundary condition at the corners

effective vanishing order of the levi determinant on a smooth domain in mathbb c n of finite d angelo q type at a point an effective upper bound for the vanishing order of the levi determinant rm coeff partial r wedge bar partial r wedge partial bar partial r n q at that point is given in terms of the d angelo q type the dimension of the space n and q itself the argument uses catlin s notion of a boundary system as well as techniques pioneered by john d angelo

stochastic scheduling with variable profile and precedence constraints in this paper we consider the stochastic profile scheduling problem of a partially ordered set of tasks on uniform processors the set of available processors varies in time the running times of the tasks are independent random variables with exponential distributions we obtain a sufficient condition under which a list policy stochastically minimizes the makespan within the class of preemptive policies this result allows us to obtain a simple optimal policy when the partial order is an interval order an in forest or an out forest

on stochastic scheduling with in tree precedence constraints we consider the problem of optimal scheduling of a set of jobs obeying in tree precedence constraints when a number m of processors is available it is assumed that the service times of different jobs are independent identically distributed random variables subject to a minor assumption on the service time distribution we show that policies of the highest level first type are optimal asymptotically as the number of jobs tends to infinity