twistor spaces of hypercomplex manifolds are balanced abstract a hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations if in addition there exists a metric on the manifold which is hermitian with respect to the three structures and such that the corresponding hermitian forms are closed the manifold is said to be hyperkahler in the paper non hermitian yang mills connections 13 kaledin and verbitsky proved that the twistor space of a hyperkahler manifold admits a balanced metric these were first studied in the article on the existence of special metrics in complex geometry 17 by michelsohn in the present article we review the proof of this result and then generalize it and show that twistor spaces of general compact hypercomplex manifolds are balanced

global smoothing of calabi yau threefolds yoshinori namikawa i j h m steenbrink 2 i department of mathematics sophia university kioi cho tokyo 102 japan 2 mathematical institute university of nijmegen toernooiveld 6525 ed nijmegen the netherlands oblatum 10 x 1994 13 vi 1995 introduction friedman fr has studied the relationship between local and global deforma tions of a threefold z with isolated hypersurface singularities which admits small resolutions one of his main results is as follows let z be a moishezon threefold with only ordinary double points pl p assume that the canon ical line bundle

balanced metrics on non kahler calabi yau threefolds we construct balanced metrics on the family of non kahler calabi yau threefolds that are obtained by smoothing after contracting 1 1 rational curves on a kahler calabi yau threefold as an application we construct balanced metrics on complex manifolds diffeomorphic to the connected sum of k ge 2 copies of s 3 s 3

kahlerian twistor spaces the work of r penrose has shown the deep relationship between the conformal structure of minkowski space and the complex geometry of lines in projective three space this transformation applies to a more general class of conformal structures and in particular there is a riemannian version described in 5 which is itself of interest to mathematical physicists basically to each oriented riemannian 4manifold x one associates canonically a 6 manifold z the twistor space of x together with an almost complex structure if this structure is integrable then z becomes a complex 3 manifold with a distinguished family of projective lines on it whose geometry describes the conformal geometry of the manifold x it is natural to ask what sort of complex manifold one obtains by this process in this paper we ask the more specific question which compact 4c manifolds have ka hlerian twistor spaces 1 the answer rather surprisingly is that there are just two examples the 4 sphere s and the complex projective plane p2 c each with their standard homogeneous conformal structures the twistor space of s 4 is the 3 dimensional projective space p3 c and that of p 2 q is the manifold f2 c of flags in c 3 the essential point of the proof of this result is the remark that if z is a twistor space with a kahler metric then the canonical bundle k is negative using vanishing theorems and the riemann roch theorem we then narrow down the possibilities for z to four cases projective space the flag manifold the intersection of two quadrics in p5 and the double covering of p3 branched over a non singular quartic surface the last two candidates cannot be realized however because the value of their euler characteristic is incompatible with their being twistor spaces throughout the proof we make essential use of a real structure on z which reduces considerably the occurrence of singularities at various stages aside from this our methods are the standard ones of algebraic geometry the four examples to which the proof leads us are all fano threefolds if we drop the requirement of compactness on x then it is quite possible for an open set of a fano threefold to be a twistor space in particular we show that the family of conies lying on the intersection of two

theory and applications of q ary interleaved sequences a new class of q ary sequences called interleaved sequence is introduced their periods shift equivalence linear spans and autocorrelation functions are derived the interleaved sequences include a large number of popular sequences such as multiplexed sequences clock controlled sequences kasami 1966 sequences gmw sequences geometric sequences and no 1989 sequences a special class of the interleaved sequences is constructed by mapping gf q sup m sequences into gf q sequences in terms of different bases of gf q sup m over gf q as an application of the theory of interleaved sequences some new families of binary pseudo random sequences are constructed which have large linear spans optimal periodic cross autocorrelation functions balance and the rapidly hopped properties a complete comparison of the new family of sequences with the gold sequence family the kasami small and large set sequence families the bent function sequence family and the no sequence family is discussed this shows that the new sequence families have important advantages for use in spread spectrum multiple access communication systems

enumeration and criteria for cyclically shift distinct gmw sequences gordon mills welch gmw sequences also called cascaded gmw sequences have two level autocorrelations this property makes them widely used in various communication and cryptographic systems the generation of q ary gmw sequences of period q sup n 1 involves three types of parameters to determine whether gmw sequences are cyclically shift distinct for differing parameters has remained an open question until now in this paper we completely solve this problem for varying all three types of parameters we find a criterion for cyclically shift distinct q ary gmw sequences of period q sup n 1 and obtain the number of such sequences for the special case of q 2 this solution facilitates counting the number of cyclic hadamard difference sets which correspond to binary gmw sequences of period 2 sup n 1

regularity of the geodesic equation in the space of sasakian metrics abstract in this paper we study a geodesic equation in the space of sasakian metrics h the equation leads to the dirichlet problem of a complex monge ampere type equation on the kahler cone this equation differs from the standard complex monge ampere equation in a significant way with gradient terms involved in the 1 1 symmetric tensor of the operator we establish appropriate regularity estimates for this complex monge ampere type equation as geometric application we show that the space of sasakian metrics h is a metric space and the constant transversal scalar curvature metric realizes the global minimum of k energy if the first basic chern class c 1 b 0 we also prove that the constant transversal scalar curvature metric is unique in each basic kahler class if the first basic chern class is either strictly negative or zero

calabi yau generalized complete intersections and aspects of cohomology of sheaves we consider generalized complete intersection manifolds in the product space of projective spaces and work out useful aspects pertaining to the cohomology of sheaves over them first we present and prove a vanishing theorem on the cohomology groups of sheaves for subvarieties of the ambient product space of projective spaces we then prove a birational equivalence between configuration matrices of complete intersection calabi yau manifolds we also present a formula of the genus of curves in generalized complete intersection manifolds some of these curves arise as the fixed point locus of certain symmetry group action on the generalized complete intersection calabi yau manifolds we also make a blowing up along curves by which one can generate new calabi yau manifolds moreover an approach on spectral sequences is used to compute hodge numbers of generalized complete intersection calabi yau manifolds and the genus of curves therein

the fu yau equation with negative slope parameter the fu yau equation is an equation introduced by fu and yau as a generalization to arbitrary dimensions of an ansatz for the strominger system as in the strominger system it depends on a slope parameter alpha prime the equation was solved in dimension 2 by fu and yau in two successive papers for alpha prime 0 and for alpha prime 0 in the present paper we solve the fu yau equation in arbitrary dimension for alpha prime 0 to our knowledge these are the first non trivial solutions of the fu yau equation in any dimension strictly greater than 2

properties of manifolds with skew symmetric torsion and special holonomy abstract in this paper we provide examples of hypercomplex manifolds which do not carry hkt structures thus answering a question in grantcharov and poon comm math phys 213 2000 19 we also prove that the existence of an hkt structure is not stable under small deformations similarly we provide examples of compact complex manifolds with vanishing first chern class which do not admit a hermitian structure whose bismut connection has restricted holonomy in su n thus providing a counter example to the conjecture in gutowski et al deformations of generalized calibrations and compact non kahler manifolds with vanishing first chern class math dg 0205012 asian j math to appear again we prove that such a property is not stable under small deformations

infinitesimal moduli for the strominger system and killing spinors in generalized geometry we construct the space of infinitesimal variations for the strominger system and an obstruction space to integrability using elliptic operator theory we initiate the study of the geometry of the moduli space describing the infinitesimal structure of a natural foliation on this space the associated leaves are related to generalized geometry and correspond to moduli spaces of solutions of suitable killing spinor equations on a courant algebroid as an application we propose a unifying framework for metrics with holonomy mathrm su 3 and solutions of the strominger system

a new positivity condition for the curvature of hermitian manifolds in this note we introduce a new type of positivity condition for the curvature of a hermitian manifold which generalizes the notion of nonnegative quadratic orthogonal bisectional curvature to the non kahler case we derive a bochner formula for closed 1 1 forms from which this condition appears naturally and prove that if a hermitian manifold satisfies our positivity condition then any class alpha in h 1 1 bc x can be represented by a closed 1 1 form which is parallel with respect to the bismut connection lastly we show that such a curvature positivity condition holds on certain generalized hopf manifolds and on certain vaisman manifolds

on the noether lefschetz theorem and some remarks on codimension two cycles here of general moduli means that there is a countable union v of subvarieties of the space pn of surfaces of degree d in p3 such that the statement pie s z holds for s p n v noether it would seem stated this theorem but never completely proved it instead he gave a plausibility argument based on the following construction 1 let g be the hilbert scheme of curves of degree n and genus 9 in p3 l gr3 d l ip n the space of surfaces of degree d in p3 and zc t the incidence correspondence s o a c s c z s

geometry of compact complex homogeneous spaces with vanishing first chern class abstract we prove that any compact complex homogeneous space with vanishing first chern class after an appropriate deformation of the complex structure admits a homogeneous calabi yau with torsion structure provided that it also has an invariant volume form a description of such spaces among the homogeneous c spaces is given as well as many examples and a classification in the 3 dimensional case we calculate the cohomology ring of some of the examples and show that in dimension 14 there are infinitely many simply connected spaces admitting such a structure with the same hodge numbers and torsional chern classes we provide also an example solving the strominger s equations in heterotic string theory

extremal bundles on calabi yau threefolds we study constructions of stable holomorphic vector bundles on calabi yau threefolds especially those with exact anomaly cancellation which we call extremal by going through the known databases we find that such examples are rare in general and can be ruled out for the spectral cover construction for all elliptic threefolds we then introduce a general hartshorne serre construction and use it to find extremal bundles of general ranks and study their stability as well as computing their chern numbers based on both existing and our new constructions we revisit the dry conjecture for the existence of stable sheaves on calabi threefolds and provide theoretical and numerical evidence for its correctness our construction can be easily generalized to bundles with no extremal conditions imposed

arbitrarily high order convected scheme solution of the vlasov poisson system abstract the convected scheme cs is a forward trajectory semi lagrangian method for solution of transport equations which has been most often applied to the kinetic description of plasmas and rarefied neutral gases in its simplest form the cs propagates the solution forward in time by advecting the so called moving cells along their characteristic trajectories and by remapping them on the mesh at the end of the time step the cs is conservative positivity preserving simple to implement and it is not subject to time step restriction to maintain stability recently guclu and hitchon 2012 1 a new methodology was introduced for reducing numerical diffusion based on a modified equation analysis the remapping error was compensated by applying small corrections to the final position of the moving cells prior to remapping while the spatial accuracy was increased from 2nd to 4th order the new scheme retained the important properties of the original method and was shown to be extremely simple and efficient for constant advection problems here the cs is applied to the solution of the vlasov poisson system which describes the evolution of the velocity distribution function of a collection of charged particles subject to reciprocal coulomb interactions the vlasov equation is split into two constant advection equations one in configuration space and one in velocity space and high order time accuracy is achieved by proper composition of the operators the splitting procedure enables us to use the constant advection solver which we extend to arbitrarily high order of accuracy in time and space a new improved procedure is given which makes the calculation of the corrections straightforward focusing on periodic domains we describe a spectrally accurate scheme based on the fast fourier transform the proposed implementation is strictly conservative and positivity preserving the ability to correctly reproduce the system dynamics as well as resolving small scale features in the solution is shown in classical 1d 1v test cases both in the linear and the non linear regimes

a high order time splitting method based on integral deferred correction for semi lagrangian vlasov simulations semi lagrangian schemes with various splitting methods and with different reconstruction interpolation strategies have been applied to kinetic simulations for example the order of spatial accuracy of the algorithms proposed in qiu and christlieb 2010 29 is very high as high as ninth order however the temporal error is dominated by the operator splitting error which is second order for strang splitting it is therefore important to overcome such low order splitting error in order to have numerical algorithms that achieve higher orders of accuracy in both space and time in this paper we propose to use the integral deferred correction idc method to reduce the splitting error specifically the temporal order accuracy is increased by r with each correction loop in the idc framework where r 1 2r 1 2 for coupling the first order splitting and the strang splitting respectively the proposed algorithm is applied to the vlasov poisson system the guiding center model and two dimensional incompressible flow simulations in the vorticity stream function formulation we show numerically that the idc procedure can automatically increase the order of accuracy in time we also investigate numerical stability of the proposed algorithm via performing fourier analysis to a linear model problem

the fu yau equation on compact astheno kahler manifolds abstract in this paper we study the fu yau equation on compact hermitian manifolds and prove the existence of solutions of equation on astheno kahler manifolds we also prove the uniqueness of solutions of fu yau equation when the slope parameter is negative

q ary cascaded gmw sequences cascaded gmw sequences over gf q of arbitrary characteristic are investigated their periods are derived as compared with the existing results on such sequences substantially extended and improved theorems concerning their linear spans and autocorrelation functions are obtained a criterion and an algorithm for constructing cascaded gmw sequences that have much larger linear spans than gmw sequences with the same periods are given these provide a new class of complex valued sequences which have larger linear spans and two valued autocorrelation functions

invariant solutions to the strominger system on complex lie groups and their quotients using canonical 1 parameter family of hermitian connections on the tangent bundle we provide invariant solutions to the strominger system on certain complex lie groups and their quotients both flat and non flat cases are discussed in detail this paper answers a question proposed by andreas and garcia fernandez in comm math phys 332 3 1381 1383 2014

outflow boundary conditions for the fourier transformed two dimensional vlasov equation in order to facilitate numerical simulations of plasma phenomena where kinetic processes are important we have studied the technique of fourier transforming the vlasov equation analytically in velocity space and solving the resulting equation numerically particular attention has been paid to the boundary conditions of the fourier transformed system by using outgoing wave boundary conditions in the fourier transformed space small scale information in velocity space is carried outside the computational domain and is removed representing a dissipative loss mechainsm thereby the so called recurrence phenomenon is reduced in the present article a previously developed method in one spatial and one velocity dimension plus time is generalised to two spatial and two velocity dimensions plus time different high order methods are used for computing derivatives as well as for the time stepping

lie groups with flat gauduchon connections we pursue the research line proposed in yang and zheng acta math sinica english series 34 8 1259 1268 2018 about the classification of hermitian manifolds whose s gauduchon connection nabla s 1 frac s 2 nabla c frac s 2 nabla b is flat where s in mathbb r and nabla c and nabla b are the chern and the bismut connections respectively we focus on lie groups equipped with a left invariant hermitian structure such spaces provide an important class of hermitian manifolds in various contexts and are often a valuable vehicle for testing new phenomena in complex and hermitian geometry more precisely we consider a connected 2n dimensional lie group g equipped with a left invariant complex structure j and a left invariant compatible metric g and we assume that its connection nabla s is flat our main result states that if either n 2 or there exits a nabla s parallel left invariant frame on g then g must be kahler this result demonstrates rigidity properties of some complete hermitian manifolds with nabla s flat hermitian metrics

on integrability in grassmann geometries integrable systems associated with fourfolds in gr 3 5 let gr d n be the grassmannian of d dimensional linear subspaces of an n dimensional vector space v n a submanifold x gr d n gives rise to a differential system x that governs d dimensional submanifolds of v n whose gaussian image is contained in x systems of the form x appear in numerous applications in continuum mechanics theory of integrable systems general relativity and differential geometry they include such wellknown examples as the dispersionless kadomtsev petviashvili equation the boyer finley equation plebansky s heavenly equations and so on in this paper we concentrate on the particularly interesting case of this construction where x is a fourfold in gr 3 5 our main goal is to investigate differential geometric and integrability aspects of the corresponding systems x we demonstrate the equivalence of several approaches to dispersionless integrability such as the method of hydrodynamic reductions the method of dispersionless lax pairs integrability on solutions based on the requirement that the characteristic variety of system x defines an einstein weyl geometry on every solution integrability on equation meaning integrability in twistor theoretic sense of the canonical gl 2 r structure induced on a fourfold x gr 3 5 all these seemingly different approaches lead to one and the same class of integrable systems x we prove that the moduli space of such systems is 6 dimensional we give a complete description of linearisable systems the corresponding fourfold x is a linear section of gr 3 5 and linearly degenerate systems the corresponding fourfold x is the image of a quadratic map p4 99k gr 3 5 the fourfolds corresponding to generic integrable systems are not algebraic and can be parametrised by generalised hypergeometric functions

a flow of conformally balanced metrics with kahler fixed points while the anomaly flow was originally motivated by string theory its zero slope case is potentially of considerable interest in non kahler geometry as it is a flow of conformally balanced metrics whose stationary points are precisely kahler metrics we establish its convergence on kahler manifolds for suitable initial data we also discuss its relation to some current problems in complex geometry

symplectic conifold transitions we introduce a symplectic surgery in six dimensions which collapses lagrangian three spheres and replaces them by symplectic two spheres under mirror symmetry it corresponds to an operation on complex 3 folds studied by clemens friedman and tian we describe several examples which show that there are either many more calabi yau manifolds e g rigid ones than previously thought or there exist symplectic calabi yaus non kahler symplectic 6 folds with c1 0 the analogous surgery in four dimensions with a generalisation to ade trees of lagrangians implies that the canonical class of a minimal complex surface contains symplectic forms if and only if it has positive square

lines on the fermat quintic threefold and the infinitesimal generalized hodge conjecture we study the deformation theory of lines on the fermat quintic threefold we formulate an infinitesimal version of the generalized hodge conjecture and use our analysis of lines to prove it in a special case

two sphere partition functions and gromov witten invariants many n 2 2 two dimensional nonlinear sigma models with calabi yau target spaces admit ultraviolet descriptions as n 2 2 gauge theories gauged linear sigma models we conjecture that the two sphere partition function of such ultraviolet gauge theories recently computed via localization by benini et al and doroud et al yields the exact kahler potential on the quantum kahler moduli space for calabi yau threefold target spaces in particular this allows one to compute the genus zero gromov witten invariants for any such calabi yau threefold without the use of mirror symmetry more generally when the infrared superconformal fixed point is used to compactify string theory this provides a direct method to compute the spacetime kahler potential of certain moduli e g vector multiplet moduli in type iia exactly in we compute these quantities for the quintic and for rodland s pfaffian calabi yau threefold and find agreement with existing results in the literature we then apply our methods to a codimension four determinantal calabi yau threefold in p 7 recently given a nonabelian gauge theory description by the present authors for which no mirror calabi yau is currently known we derive predictions for its gromov witten invariants and verify that our predictions satisfy nontrivial geometric checks

balanced hermitian metrics from su 2 structures we study the intrinsic geometrical structure of hypersurfaces in six manifolds carrying a balanced hermitian su 3 structure which we call balanced su 2 structure we provide sufficient conditions in terms of suitable evolution equations which imply that a five manifold with such structure can be isometrically embedded as a hypersurface in a balanced hermitian su 3 manifold any five dimensional compact nilmanifold has an invariant balanced su 2 structure and we show how some of them can be evolved to give new explicit examples of balanced hermitian su 3 structures moreover for n 3 4 we present examples of compact solvmanifolds endowed with a balanced su n structure such that the corresponding bismut connection has holonomy equal to su n

connecting moduli spaces of calabi yau threefolds we demonstrate that many families of calabi yau threefolds consist generically of small resolutions of nodal forms in other families and in fact that a large class of families is connected by this relation our result resonates with a conjecture of reid that calabi yau threefolds may have a universal moduli space even though they are of different homotopy types such ideas tie quite naturally to alluring prospects of unifying super string models

2 2 superconformal field theories near orbifold points a thorough analysis of the blowing up modes of the 6 based on the lie algebraa2 d4 is presented we discover that the descriptions of these modes in the language of superconformal field theory and calabi yau compactification are not immediately in agreement a solution to this apparent inconsistency is offered which leads to the possibility of differentiably distinct calabi yau manifolds giving isomorphic physics

convergence of calabi yau manifolds abstract in this paper we study the convergence of calabi yau manifolds under kahler degeneration to orbifold singularities and complex degeneration to canonical singularities including the conifold singularities and the collapsing of a family of calabi yau manifolds

regularity estimates of solutions to complex monge ampere equations on hermitian manifolds in this paper we obtain the bedford taylor interior c2 estimate and local calabi c3 estimate for the solutions to complex monge ampere equations on hermitian manifolds

quasi kahler manifolds with trivial chern holonomy in this paper we study almost complex manifolds admitting a quasi kahler chern flat metric chern flat means that the holonomy of the chern connection is trivial we prove that in the compact case such manifolds are all nilmanifolds some partial classification results are established and we prove that a quasi kahler chern flat structure can be tamed by a symplectic form if and only if the ambient space is isomorphic to a flat torus

note on solutions of the strominger system from unitary representations of cocompact lattices of sl 2 mathbb c this note is motivated by a recently published paper biswas and mukherjee in commun math phys 322 2 373 384 2013 we prove a no go result for the existence of suitable solutions of the strominger system in a compact complex parallelizable manifold for this we assume g to be non abelian the hermitian metric to be induced from a right invariant metric on g the bianchi identity to be satisfied using the chern connection and furthermore the gauge field to be flat in biswas and mukherjee commun math phys 322 2 373 384 2013 it is claimed that one such solution exists on our result contradicts the main result in biswas and mukherjee commun math phys 322 2 373 384 2013

gmw sequences corresp the difference set design of gordon mills and welch gmw is adapted for use as a pseudorandom number generator statistical properties of the generated binary sequences including periodic correlation linear span and k tuple statistics are derived one mechanization of a gmw sequence generator is suggested and the number of sequences that can be generated with a fixed number of shift register stages and read only memory rom size is evaluated

on estimates for the fu yau generalization of a strominger system we study an equation proposed by fu and yau as a natural n dimensional generalization of a strominger system that they solved in dimension 2 it is a complex hessian equation with right hand side depending on gradients building on the methods of fu and yau we obtain c0 c2 and c2 a priori estimates we also identify difficulties in extending the fu yau arguments for non degeneracy from dimension 2 to higher dimensions

solutions of the strominger system via stable bundles on calabi yau threefolds we prove that a given calabi yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the strominger system provided that the second chern class of the vector bundle is equal to the second chern class of the tangent bundle if the calabi yau threefold has strict su 3 holonomy then the equations of motion derived from the heterotic string effective action are also satisfied by the solutions we obtain

vanishing theorems on l k strong kahler manifolds with torsion abstract we derive sufficient conditions for the vanishing of plurigenera p m j m 0 on compact l k strong l k 0 kahler manifolds with torsion in particular we show that the plurigenera of closed l k strong manifolds k n 1 for which hol s u n vanish where is the hermitian connection with skew symmetric torsion as a consequence all generalized k gauduchon manifolds for which hol s u n do not admit holomorphic n 0 forms furthermore we show that all conformally balanced l k strong kahler manifolds with torsion k n 1 are kahler we also give several examples of l k strong kahler and calabi yau manifolds with torsion

geometric model for complex non kahler manifolds with su 3 structure for a given complex n fold m we present an explicit construction of all complex n 1 folds which are principal holomorphic t2 fibrations over m for physical applications we consider the case of m being a calabi yau 2 fold we show that for such m there is a subclass of the 3 folds that we construct which has natural families of non kahler su 3 structures satisfying the conditions for open image in new window supersymmetry in the heterotic string theory compactified on the 3 folds we present examples in the aforementioned subclass with m being a k3 surface and a 4 torus

mirror symmetry and rational curves on quintic threefolds a guide for mathematicians we give a mathematical account of a recent string theory calcula tion which predicts the number of rational curves on the generic quintic three fold our account involves the interpretation of yukawa couplings in terms of variations of hodge structure a new q expansion principle for functions on the moduli space of calabi yau manifolds and the mirror symmetry phe nomenon recently observed by string theorists department of mathematics duke university durham north carolina 27706 e mail address drm math duke edu this content downloaded from 157 55 39 224 on wed 14 dec 2016 04 59 36 utc all use subject to http about jstor org terms

convergence of a difference scheme for the vlasov poisson fokker planck system in one dimension a finite difference scheme is proposed for the periodic one dimensional vlasov poisson fokker planck system which is related to the scheme in c cheng and g knorr em j comp phys 22 1976 pp 330 351 the density f left t x v right and the electric field e left t x right are shown to converge to the exact solution values in l 2 and l infty respectively the rate of convergence is essentially first order this scheme has been implemented in j schaeffer center for nonlinear analysis research report 97 na 004 carnegie mellon university 1997 and compares favorably with a random particle method

asymptotic behavior of an initial boundary value problem for the vlasov poisson fokker planck system the asymptotic behavior for the vlasov poisson fokker planck system in bounded domains is analyzed in this paper boundary conditions defined by a scattering kernel are considered it is proven that the distribution of particles tends for large time to a maxwellian determined by the solution of the poisson boltzmann equation with dirichlet boundary condition in the proof of the main result the conservation law of mass and the balance of energy and entropy identities are rigorously derived an important argument in the proof is to use a lyapunov type functional related to these physical quantities

fully nonlinear elliptic equations for conformal deformations of chern ricci forms abstract we study a general class of fully nonlinear elliptic equations of second order on hermitian manifolds we derive a priori estimates and prove some existence results for these equations in particular we prove interior estimates for the complex hessian which in general do not hold for other types of equations we apply our results to draw geometric conclusions on conformal deformations of the mixed chern ricci forms a notion we introduced in the article our work is motivated by the close connections of these equations to problems in non kahler geometry and the fact that there have been increasing interests in fully nonlinear pde s beyond the complex monge ampere equation from complex geometry

synthesis and uniqueness of m sequences over gf q sup n as n phase sequences over gf q the construction of m sequences over gf q sup n from known m sequences over gf q is discussed an algorithm is given which generates m sequences over gf q sup n from m sequences over gf q where n phase shifts of known m sequences over gf q are determined by the iterative polynomials it is shown that n shift distinct m sequences over gf q sup n generated by the same m sequences over gf q are unique when the elements of gf q sup n are represented by n tuples of the elements from gf q

stability and regularity of solutions of the monge ampere equation on hermitian manifolds abstract we prove stability of solutions of the complex monge ampere equation on compact hermitian manifolds when the right hand side varies in a bounded set in l p p 1 and it is bounded away from zero such solutions are shown to be holder continuous as an application we extend a recent result of szekelyhidi and tosatti on kahler einstein equation from kahler to hermitian manifolds

the numerical analysis of random particle methods applied to vlasov poisson fokker planck kinetic equations we devise and study a random particle method for approximating vlasov poisson fokker planck systems such a proposed scheme takes into account the fact that the trajectories of a particle undergoing brownian motion due to collisions with the medium or background particles can be obtained as the solutions of stochastic differential equations i e the langevin equations these equations are the precise analogs of the deterministic hamiltonian system in the collisionless model the particle approximation in particular simulates the action of viscosity by the use of independent wiener processes brownian motions the error analysis generalizes that of ganguly and victory siam j numer anal 26 1989 pp 249 288 by incorporating into the consistency estimates the sampling errors generated by the random motion of the particles these particular errors are the dominant component of the consistency errors and are estimated by applying bennett s inequality for estimating tail probabilities for standard

a construction of non kahler calabi yau manifolds and new solutions to the strominger system abstract we propose a new construction of compact non kahler calabi yau manifolds with balanced metrics and study the strominger system on them in particular we obtain explicit solutions to the strominger system with degeneracies on g t 4 where g is an immersed minimal surface of genus g 3 in flat t 3

a splitting algorithm for vlasov simulation with filamentation filtration a fourier fourier transformed version of the splitting algorithm for simulating solutions of the vlasov poisson system of equations is introduced it is shown that with the inclusion of filamentation filtration in this transformed algorithm it is both faster and more stable than the standard splitting algorithm it is further shown that in a scalar computer environment this new algorithm is approximately equal in speed and far less noisy than its particle in cell counterpart it is conjectured that in a multiprocessor environment the filtered splitting algorithm would be faster while producing more precise results

heterotic string compactification and new vector bundles we propose a construction of kahler and non kahler calabi yau manifolds by branched double covers of twistor spaces in this construction we use the twistor spaces of four manifolds with self dual conformal structures with the examples of connected sum of n mathbb p 2 s we also construct k3 fibered calabi yau manifolds from the branched double covers of the blow ups of the twistor spaces these manifolds can be used in heterotic string compactifications to four dimensions we also construct stable and polystable vector bundles some classes of these vector bundles can give rise to supersymmetric grand unified models with three generations of quarks and leptons in four dimensions

a splitting fourier pseudospectral method for vlasov poisson fokker planck system abstract in this paper we propose a splitting fourier pseudospectral method for vlasov poisson fokker planck vpfp system which describes the motion of charged particles in plasma the numerical integration for the system is performed by employing the splitting method in time fourier galerkin method in space direction and fourier collocation method in phase direction respectively the algorithm has spectral accuracy in both space and phase directions and can be implemented efficiently with the fast fourier transform and technique of diagonalization respectively extensive numerical results in one dimensional phase space or 1 x 1 v from the proposed numerical method are shown and have proven the good agreement with the theory and previous studies numerical algorithm for the vpfp system in two dimensional phase space or 2 x 2 v has been summarized in appendix

relationships between m sequences over gf q and gf q sup m it is shown that m sequences over gf q sup m of length q sup nm 1 corresponding to primitive polynomials in gf q sup m x of degree n can be generated from known m sequences over gf q of length q sup nm 1 obtained from primitive polynomials in gf q x of degree mn a procedure for generating the m sequences over gf q sup 2 from m sequences over gf q was given which enables the generation of m sequences over gf p sup 2n in addition it was shown that all of the primitive polynomials in gf q sup m x can be obtained from a complete set of the primitive polynomials in gf q x

a new class of nonlinear pn sequences over gf q sup n a new class of pseudo random sequences called cascaded gmw type permutation polynomial cgpp sequences over gp q sup n is constructed using a system of n orthogonal cascaded gmw functions in gf q their statistical properties are given classification evaluation and implementation of the cgpp sequences are derived a sequence generated by mapping elements of a cgpp sequence into gf q is also presented

on a conjecture of candelas and de la ossa we prove that the metric completion of a canonical ricci flat kahler metric on the nonsingular part of a projective calabi yau variety x with ordinary double point singularities is a compact metric length space homeomorphic to the projective variety x itself as an application we prove a conjecture of candelas and de la ossa for conifold flops and transitions

a critical comparison of eulerian grid based vlasov solvers a common problem with direct vlasov solvers is ensuring that the distribution function remains positive a related problem is to guarantee that the numerical scheme does not introduce false oscillations in velocity space in this paper we use a variety of schemes to assess the importance of these issues and to determine an optimal strategy for eulerian split approaches to vlasov solvers from these tests we conclude that maintaining positivity is less important than correctly dissipating the fine scale structure which arises naturally in the solution to many vlasov problems furthermore we show that there are distinct advantages to using high order schemes i e third order rather than second a natural choice which satisfies all of these requirements is the piecewise parabolic method ppm which is applied here to vlasov s equation for the first time

on global existence and trend to the equilibrium for the vlasov poisson fokker planck system with exterior confining potential we prove a global existence result with initial data of low regularity and prove the trend to the equilibrium for the vlasov poisson fokker planck system with small non linear term but with a possibly large exterior confining potential in dimension d 2 and d 3 the proof relies on a fixed point argument using sharp estimates at short and long time scales of the semi group associated to the fokker planck operator which were obtained by the first author

geometric flows and strominger systems a geometric flow on 2 2 forms is introduced which preserves the balanced condition of metrics and whose stationary points satisfy the anomaly equation in strominger systems the existence of solutions for a short time is established using hamilton s version of the nash moser implicit function theorem

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

the complex hessian equations with gradient terms on hermitian manifolds abstract in this paper we consider the complex hessian equation involving additional gradient terms on both left and right hand sides we derive the second order estimates for plurisubharmonic solutions to this equation on compact hermitian manifolds such an estimate may be helpful to study the existence and regularity for the solution of the equation

complex sequences over gf p sup m with a two level autocorrelation function and a large linear span new complex sequences with elements are proposed that have constant absolute values of 1 the periodic autocorrelation functions of these sequences are shown to be two level the sequences are generated by three consecutive mapping processes the number of sequences of fixed length is determined which is larger than the number of binary sequences for cryptographical reasons the large linear span of the sequences is of great interest the linear span of the new sequences is examined and is proven to be larger than the linear span of complex m sequences if the parameters of the mapping processes are appropriately chosen the formula for generating the sequences is generalized to enlarge the linear span of sequences

numerical approximation of the vlasov poisson fokker planck system in two dimensions a numerical method is developed for approximating the solution to the vlasov poisson fokker planck system in two spatial dimensions the method generalizes the approximation for the system in one dimension given in s wollman e ozizmir numerical approximation of the vlasov poisson fokker planck system in one dimension j comput phys 202 2005 602 644 the numerical procedure is based on a change of variables that puts the convection diffusion equation into a form so that finite difference methods for parabolic type partial differential equations can be applied the computational cycle combines a type of deterministic particle method with a periodic interpolation of the solution along particle trajectories onto a fixed grid computational work is done to demonstrate the accuracy and effectiveness of the approximation method parts of the numerical procedure are adapted to run on a parallel computer

transverse fully nonlinear equations on sasakian manifolds and applications abstract we prove a priori estimates for a class of transverse fully nonlinear equations on sasakian manifolds and give some geometric applications such as the transversion calabi yau theorem for transverse balanced and strongly gauduchon metrics we also explain that similar results hold on compact oriented taut transverse hermitian foliated manifold of complex co dimension n and give some geometric applications such as the transverse calabi yau theorems for transverse hermitian and strongly gauduchon metrics