on energy functionals kahler einstein metrics and the moser trudinger onofri neighborhood abstract we prove that the existence of a kahler einstein metric on a fano manifold is equivalent to the properness of the energy functionals defined by bando chen ding mabuchi and tian on the set of kahler metrics with positive ricci curvature we also prove that these energy functionals are bounded from below on this set if and only if one of them is this answers two questions raised by x x chen as an application we obtain a new proof of the classical moser trudinger onofri inequality on the two sphere as well as describe a canonical enlargement of the space of kahler potentials on which this inequality holds on higher dimensional fano kahler einstein manifolds

polynomial division using left shift register abstract in this short note we describe a simple polynomial division circuit based on a left shift register the circuit essentially performs the modulo operation f x mod p x it is shown how the same circuit can be used to perform f x g x mod p x applications to standard basis multiplication and encoding and decoding of systematic cyclic codes are also described

remarks on the existence problem of positive kahler einstein metrics on introduit un invariant m qui donne un critere pour l existence de metriques de kahler einstein

double basis multiplicative inversion over gf 2 sup m inversion over galois fields is much more difficult than the corresponding multiplication efficient computation of inverses in gf 2 sup m is considered by solving a set of linear equations over the ground field gf 2 the proposed algorithm uses two separate bases for the representation of its input and output elements and has low computational complexity the algorithm is also suitable for hardware implementation using vlsi technologies

bit serial systolic divider and multiplier for finite fields gf 2 sup m a systolic structure for bit serial division over the field gf 2 sup m is developed consideration is given to avoid global data communications and dependency of the time step duration on m this is important for applications where the value of m is large the divider requires only three basic processors and one simple control signal and its circuit and time complexities are proportional to m sup 2 and m respectively it does not depend on the irreducible polynomial and can be expanded easily moreover with m additional simple processors a bit serial systolic multiplier is developed which uses part of the divider structure this is advantageous from the implementation point of view as both the divider and multiplier can be fabricated on a single chip resulting in a reduction of area

a systolic reed solomon encoder an architecture for a reed solomon rs encoder is presented consisting of r 1 systolic cells where r is the redundancy of the code the systolic encoder is systematic does not contain any feedback or other global signals its systolic cells are of low complexity and it is easily reconfigurable for variable redundancy and changes in the choice of generator polynomial of the code the encoding algorithm is based on the cauchy representation of the generator matrix of the code this architecture is suitable for very high speed applications where global signals such as the feedback line present in the traditional rs encoder design and the need for global synchronization may pose restrictions on the achievable switching speed of the encoder

a thermodynamical formalism for monge ampere equations moser trudinger inequalities and kahler einstein metrics we develop a variational calculus for a certain free energy functional on the space of all probability measures on a kahler manifold x this functional can be seen as a generalization of mabuchi s k energy functional and its twisted versions to more singular situations applications to monge ampere equations of mean field type twisted kahler einstein metrics and moser trudinger type inequalities on miller manifolds are given tian s alpha invariant is generalized to singular measures allowing in particular a proof of the existence of kahler einstein metrics with positive ricci curvature that are singular along a given anti canonical divisor which combined with very recent developments concerning miller metrics with conical singularities confirms a recent conjecture of donaldson as another application we show that if the calabi flow in the anti canonical class exists for all times then it converges to a kahler einstein metric when a unique one exists which is in line with a well known conjecture c 2013 elsevier inc all rights reserved

yau tian donaldson correspondence for k semistable fano manifolds in this paper using the recent compactness results of tian and chen donaldson sun we prove the k semistable version of yau tian donaldson correspondence for fano manifolds

curvature of vector bundles associated to holomorphic fibrations let l be a semi positive line bundle over a kahler manifold x fibered over a complex manifold y assuming the fibers are compact and nonsingular we prove that the hermitian vector bundle e over y whose fibers over points y are the spaces of global sections over xy to l kx y endowed with the l2 metric is semi positive in the sense of nakano we also discuss various applications among them a partial result on a conjecture of griffiths on the positivity of ample bundles

smooth p adic analytic spaces are locally contractible 0 introduction 293 1 piecewise rs linear spaces 298 2 r colored polysimplicial sets 308 3 r colored polysimplicial sets of length l 313 4 the skeleton of a nondegenerate pluri stable formal scheme 327 5 a colored polysimplicial set associated with a nondegenerate poly stable fibration 336 6 p adic analytic and piecewise linear spaces 346 7 strong local contractibility of smooth analytic spaces 355 8 cohomology with coefficients in the sheaf of constant functions 362

on kahler einstein metrics on certain kahler manifolds with c1 m 0 on demontre qu il existe une metrique de kahler einstein sur une hypersurface de fermat a m dimensions de degre superieur a m 1

partial pluricomplex energy and integrability exponents of plurisubharmonic functions we first prove a quantitative estimate of the volume of the sublevel sets of a plurisubharmonic function in a hyperconvex domain with boundary values 0 in a quite general sense in terms of its monge ampere mass in the domain then we deduce a sharp sufficient condition on the monge ampere mass of such a plurisubharmonic function for exp 2 to be globally integrable as well as locally integrable

kahler einstein metrics and the generalized futaki invariant in 1983 futaki introduced his famous invariant this invariant generalizes the obstruction of kazdan warner to prescribing gauss curvature on s 2 cf ful l the futaki invariant is defined for any compact k ihler manifold with positive first chern class that has nontrivial holomorphic vector fields it is a lie algebraic character from the lie algebra of holomorphic vector fields into and its vanishing is a necessary condition for the existence of a k ihler einstein metric on the underlying manifold therefore it can be used to test the existence of k ihlereinstein metrics on a given compact k ihler manifold with positive first chern class an excellent reference on the futaki invariant is futaki s book fu2 until now all known nontrivial obstructions to k ihler einstein metrics come from holomorphic vector fields this suggests the following conjecture

bergman kernels and the pseudoeffectivity of relative canonical bundles a criterion for the pseudoeffectivity of twisted relative canonical bundles of surjective projective maps

architecture for a low complexity rate adaptive reed solomon encoder multiple error correcting reed solomon rs codes have many practical applications the complexity of an rs encoder depends on multiplications in the finite field over which the code is defined we consider a triangular basis for representing the field elements and present an architecture for a rate adaptive rs encoder using a triangular basis multiplication algorithm the architecture supports pipeline and bit serial operations and has a low circuit complexity

on the structure of almost einstein manifolds in this paper we study the structure of the limit space of a sequence of almost einstein manifolds which are generalizations of einstein manifolds roughly speaking such manifolds are the initial manifolds of some normalized ricci flows whose scalar curvatures are almost constants over space time in the l1 sense ricci curvatures are bounded from below at the initial time under the non collapsed condition we show that the limit space of a sequence of almost einstein manifolds has most properties which is known for the limit space of einstein manifolds as applications we can apply our structure results to study the properties of kahler manifolds

kahler einstein metrics with positive scalar curvature in this paper we prove that the existence of kahler einstein metrics implies the stability of the underlying kahler manifold in a suitable sense in particular this disproves a long standing conjecture that a compact kahler manifold admits kahler einstein metrics if it has positive first chern class and no nontrivial holomorphic vector fields we will also establish an analytic criterion for the existence of kahler einstein metrics our arguments also yield that the analytic criterion is satisfied on stable kahler manifolds provided that the partial c 0 estimate posed in t6 is true

conical kahler einstein metrics revisited in this paper we introduce the interpolation degeneration strategy to study kahler einstein metrics on a smooth fano manifold with cone singularities along a smooth divisor that is proportional to the anti canonical divisor by interpolation we show the angles in 0 2 that admit a conical kahler einstein metric form a connected interval and by degeneration we determine the boundary of the interval in some important cases as a first application we show that there exists a kahler einstein metric on mathbb p 2 with cone singularity along a smooth conic degree 2 curve if and only if the angle is in 2 2 when the angle is 2 3 this proves the existence of a sasaki einstein metric on the link of a three dimensional a2 singularity and thus answers a question posed by gauntlett martelli sparks yau as a second application we prove a version of donaldson s conjecture about conical kahler einstein metrics in the toric case using song wang s recent existence result of toric invariant conical kahler einstein metrics

algebraic estimates stability of local zeta functions and uniform estimates for distribution functions a method of algebraic estimates is developed and used to study the stability properties of integrals of the form r b jf z j i dv under small deformations of the function f the estimates are described in terms of a stratiflcation of the space of functionsfr z jp z j jq z j g by algebraic varieties on each of which the size of the integral of r z is given by an explicit algebraic expression the method gives an independent proof of a result on stability of tian in 2 dimensions as well as a partial extension of this result to 3 dimensions in arbitrary dimensions combined with a key lemma of siu it establishes the continuity of the mapping c r b jf z c j i dv1 dvn when f z c is a holomorphic function of z c in particular the leading pole is semicontinuous in f strengthening also an earlier result of lichtin

division and accumulation over gf 2 sup m the galois field division is a complex arithmetic operation the corresponding division and accumulation daa is not only complex but also a time consuming operation in this article the daa over gf 2 sup m is considered and a simple scheme for its sequential operation is presented a multiple stream daa structure is developed which supports pipeline operations and yields an increased throughput with only a modest increase in the hardware as an application the use of the sequential daa algorithm is shown for the high speed encoding of reed solomon codes

convex hulls of random walks large deviation properties we study the convex hull of the set of points visited by a two dimensional random walker of t discrete time steps two natural observables that characterize the convex hull in two dimensions are its perimeter l and area a while the mean perimeter and the mean area have been studied before analytically and numerically and exact results are known for large t brownian motion limit little is known about the full distributions p a and p l in this paper we provide numerical results for these distributions we use a sophisticated large deviation approach that allows us to study the distributions over a larger range of the support where the probabilities p a and p l are as small as 10 300 we analyze open random walks as well as closed brownian bridges on the two dimensional discrete grid as well as in the two dimensional plane the resulting distributions exhibit for large t a universal scaling behavior independent of the details of the jump distributions as a function of a t and l sqrt t respectively we are also able to obtain the rate function describing rare events at the tails of these distributions via a numerical extrapolation scheme and find a linear and square dependence as a function of the rescaled perimeter and the rescaled area respectively