a general formula for channel capacity a formula for the capacity of arbitrary single user channels without feedback not necessarily information stable stationary etc is proved capacity is shown to equal the supremum over all input processes of the input output inf information rate defined as the liminf in probability of the normalized information density the key to this result is a new converse approach based on a simple new lower bound on the error probability of m ary hypothesis tests among equiprobable hypotheses a necessary and sufficient condition for the validity of the strong converse is given as well as general expressions for spl epsiv capacity

uniqueness and short time regularity of the weak kahler ricci flow let x be a compact kahler manifold we prove that the kahler ricci flow starting from arbitrary closed positive 1 1 currents is smooth outside some analytic subset this regularity result is optimal meaning that the flow has positive lelong numbers for short time if the initial current has we also prove that the flow is unique when starting from currents with zero lelong numbers

a mesh independence principle for operator equations and their discretizations the mesh independence principle asserts that when newton s method is applied to a nonlinear equation between some banach spaces as well as to some finite dimensional discretization of that equation then the behavior of the discretized process is asymptotically the same as that for the original iteration and as a consequence the number of steps required by the two processes to converge to within a given tolerance is essentially the same so far this result has been proved only for certain classes of boundary value problems in this paper a proof is presented for a general class of operator equations and discretizations it covers the earlier results and extends them well beyond the cases that have been considered before

convergence of the multilevel full approximation scheme including thev cycle the multilevel full approximation scheme fas ml is a well known solver for nonlinear boundary value problems in this paper we prove local quantitative convergence statements for a class of fas ml algorithms in a general hilbertspace setting this setting clearly exhibits the structure of fas ml we prove local convergence of a nested iteration for a rather concrete class of fas ml algorithms in whichv cycles and only one jacobilike pre and post smoothing on each level are used

regularizing properties of complex monge ampere flows ii hermitian manifolds we prove that a general complex monge ampere flow on a hermitian manifold can be run from an arbitrary initial condition with zero lelong number at all points using this property we confirm a conjecture of tosatti weinkove the chern ricci flow performs a canonical surgical contraction finally we study a generalization of the chern ricci flow on compact hermitian manifolds namely the twisted chern ricci flow

convergence of the multigrid full approximation scheme for a class of elliptic mildly nonlinear boundary value problems the multigrid full approximation scheme fas mg is a well known solver for nonlinear boundary value problems in this paper we restrict ourselves to a class of second order elliptic mildly nonlinear problems and we give local conditions e g a local lipschitz condition on the derivative of the continuous operator under which the fas mg with suitably chosen parameters locally converges we prove quantitative convergence statements and deduce explicit bounds for important quantities such as the radius of a ball of guaranteed convergence the number of smoothings needed the number of coarse grid corrections needed and the number of fas mg iterations needed in a nested iteration these bounds show well known features of the fas mg scheme

the weighted monge ampere energy of quasiplurisubharmonic functions abstract we study degenerate complex monge ampere equations on a compact kahler manifold x we show that the complex monge ampere operator d d c n is well defined on the class e x of plurisubharmonic functions with finite weighted monge ampere energy the class e x is the largest class of psh functions on which the monge ampere operator is well defined and the comparison principle is valid it contains several functions whose gradient is not square integrable we give a complete description of the range of the operator d d c n on e x as well as on some of its subclasses we also study uniqueness properties extending calabi s result to this unbounded and degenerate situation and we give applications to complex dynamics and to the existence of singular kahler einstein metrics

weak solutions to degenerate complex monge ampere flows ii abstract studying the long term behavior of the kahler ricci flow on mildly singular varieties one is naturally led to study weak solutions of degenerate parabolic complex monge ampere equations the purpose of this article the second of a series on this subject is to develop a viscosity theory for degenerate complex monge ampere flows on compact kahler manifolds our general theory allows in particular to define and study the normalized kahler ricci flow on varieties with canonical singularities generalizing results of song and tian

global and uniform convergence of subspace correction methods for some convex optimization problems this paper gives some global and uniform convergence estimates for a class of subspace correction based on space decomposition iterative methods applied to some unconstrained convex optimization problems some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems

sharp estimates for multigrid rates of convergence with general smoothing and acceleration in this paper we prove the convergence of the multilevel iterative method for solving linear equations that arise from elliptic partial differential equations our theory is presented entirely in terms of the generalized condition number kappa of the matrix a and the smoothing matrix b this leads to a completely algebraic analysis of the method as an iterative technique for solving linear equations the properties of the elliptic equation and discretization procedure enter only when we seek to estimate kappa just as in the case of most standard iterative methods here we consider the fundamental two level iteration and the v and w cycles of the j level iteration j 2 we prove that the v and w cycles converge even when only one smoothing iteration is used we present several examples of the computation of kappa using both fourier analysis and standard finite element techniques we compare the predictions of our theorems with the actual rate of convergence our analysis also shows that

analysis of a multilevel iterative method for nonlinear finite element equations the multilevel iterative technique is a powerful technique for solving the systems of equations associated with discretized partial differential equations we describe how this technique can be combined with a globally convergent approximate newton method to solve nonlinear partial differential equations we show that asymptotically only one newton iteration per level is required thus the complexity for linear and nonlinear problems is essentially equal

a new convergence proof for the multigrid method including the v cycle for a positive definite finite element equation we describe a multigrid iteration and prove convergence under natural assumptions on the discretization and the elliptic problem hitherto existing convergence proofs require a sufficiently large number of smoothing iterations and exclude the v cycle the presented proof applies to procedures with any number of smoothing iterations and to the v cycle

regularizing properties of complex monge ampere flows we study the regularizing properties of complex monge ampere flows on a kahler manifold x when the initial data are psh functions with zero lelong number at all points we prove that the general monge ampere flow has a solution which is immediately smooth we also prove the uniqueness and stability of solution

a gradient estimate in the calabi yau theorem we prove a c 1 estimate for the complex monge ampere equation on a compact kahler manifold directly from the c 0 estimate without using a c 2 estimate this was earlier done only under additional assumption of non negative bisectional curvature

on the capacity of time varying channels with periodic feedback the capacity of time varying channels with periodic feedback at the transmitter is evaluated it is assumed that the channel state information csi is perfectly known at the receiver and is fed back to the transmitter at the regular time intervals the system capacity is investigated in two cases 1 finite state markov channel and 2 additive white gaussian noise channel with time correlated fading in the first case it is shown that the capacity is achievable by multiplexing multiple codebooks across the channel in the second case the channel capacity and the optimal adaptive coding is obtained it is shown that the optimal adaptation can be achieved by a single gaussian codebook while adaptively allocating the total power based on the side information at the transmitter

a two level method with backtracking for the navier stokes equations we consider a two level method for resolving the nonlinearity in finite element approximations of the equilibrium navier stokes equations the method yields l2 and h1 optimal velocity approximations and an l2 optimal pressure approximation the two level method involves solving one small nonlinear coarse mesh system one oseen problem hence linear with positive definite symmetric part on the fine mesh and one linear correction problem on the coarse mesh the algorithm we study produces an approximate solution with the optimal asymptotic in h accuracy for any fixed reynolds number we do not consider the behavior of the error for fixed h as re rightarrow infty i e for flows in transition to turbulence

analysis of a damped nonlinear multilevel method in this paper we present a new algorithm that is obtained by introducing a damping parameter in the classical nonlinear multilevel method we analyse this damped nonlinear multilevel method in particular we prove global convergence and local efficiency for a suitable class of problems

nonlinear multigrid methods for second order differential operators with nonlinear diffusion coefficient nonlinear multigrid methods such as the full approximation scheme fas and newton multigrid newton mg are well established as fast solvers for nonlinear pdes of elliptic and parabolic type in this paper we consider newton mg and fas iterations applied to second order differential operators with nonlinear diffusion coefficient under mild assumptions arising in practical applications an approximation shown to be sharp of the execution time of the algorithms is derived which demonstrates that newton mg can be expected to be a faster iteration than a standard fas iteration for a finite element discretisation results are provided for elliptic and parabolic problems demonstrating a faster execution time as well as greater stability of the newton mg iteration results are explained using current theory for the convergence of multigrid methods giving a qualitative insight into how the nonlinear multigrid methods can be expected to perform in practice