brauer groups and quotient stacks a natural question is to determine which algebraic stacks are quotient stacks in this paper we give some partial answers and relate it to the question of whether for a scheme x the natural map from the brauer group equivalence classes of azumaya algebras to the cohomological brauer group the torsion subgroup of h 2 x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i m is surjective

degeneration of l adic weight spectral sequences the degeneracy of the l adic weight spectral sequence over any trait with no assumptions on its residue field is proved by the method of log geometry in the sense of fontaine illusie

decomposable markov decision processes a fluid optimization approach decomposable markov decision processes mdps are problems where the stochastic system can be decomposed into multiple individual components although such mdps arise naturally in many practical applications they are often difficult to solve exactly due to the enormous size of the state space of the complete system which grows exponentially with the number of components in this paper we propose an approximate solution approach to decomposable mdps that is based on re solving a fluid linear optimization formulation of the problem at each decision epoch this formulation tractably approximates the problem by modeling transition behavior at the level of the individual components rather than the complete system we prove that our fluid formulation provides a tighter bound on the optimal value function than three state of the art formulations the approximate linear optimization formulation the classical lagrangian relaxation formulation and a novel alternate lagrangian relaxation that is based on relax

on stepanov almost periodic semigroups and cosine functions of operators abstract in this paper we consider stepanov asymptotically almost periodic sp a a p mild solutions of first and second order abstract differential equations specifically we prove that a c0 semigroup is sp a a p if and only if it is asymptotically almost periodic and that a c0 cosine function of operators is sp a a p if and only if it is almost periodic

weighted pseudo almost periodic solutions of second order neutral delay differential equations with piecewise constant argument by introducing the method of decomposition of weighted pseudo almost periodic sequence we present some existence theorems of weighted pseudo almost periodic solutions for second order neutral differential equations with piecewise constant argument of the form d 2dt 2 x t px t 1 qx 2 t 12 f t where p 1 denotes the greatest integer function q is a nonzero constant and f t is weighted pseudo almost periodic our results are new and can be regarded as a complement of some known results even in the special cases of almost periodicity and pseudo almost periodicity

minimal sets of almost periodic motions les conditions de nemytskii stepanov et deysach sell pour un mouvement x sont equivalentes a la presque periodicite asymptotique de x r la presque periodicite asymptotique de x r n est pas necessaire afin que x soit un ensemble minimal de mouvements presque periodiques

a re solving heuristic with bounded revenue loss for network revenue management with customer choice we consider a network revenue management problem with customer choice and exogenous prices we study the performance of a class of certainty equivalent heuristic control policies these heuristics periodically re solve the deterministic linear program dlp that results when all future random variables are replaced by their average values and implement the solutions in a probabilistic manner we provide an upper bound for the expected revenue loss under such policies when compared to the optimal policy using this bound we construct a schedule of re solving times such that the resulting expected revenue loss obtained by re solving the dlp at these times and implementing the solution as a probabilistic scheme is bounded by a constant that is independent of the size of the problem

pathwise optimization for optimal stopping problems we introduce the pathwise optimization po method a new convex optimization procedure to produce upper and lower bounds on the optimal value the price of a high dimensional optimal stopping problem the po method builds on a dual characterization of optimal stopping problems as optimization problems over the space of martingales which we dub the martingale duality approach we demonstrate via numerical experiments that the po method produces upper bounds of a quality comparable with state of the art approaches but in a fraction of the time required for those approaches as a by product it yields lower bounds and suboptimal exercise policies that are substantially superior to those produced by state of the art methods the po method thus constitutes a practical and desirable approach to high dimensional pricing problems furthermore we develop an approximation theory relevant to martingale duality approaches in general and the po method in particular our analysis provides a guarantee on the quality of upper bounds resulting from these approaches and identifies three key determinants of their performance the quality of an input value function approximation the square root of the effective time horizon of the problem and a certain spectral measure of predictability of the underlying markov chain as a corollary to this analysis we develop approximation guarantees specific to the po method finally we view the po method and several approximate dynamic programming methods for high dimensional pricing problems through a common lens and in doing so show that the po method dominates those alternatives this paper was accepted by wei xiong stochastic models and simulation

asymptotically periodic solutions of abstract differential equations abstract in this paper we introduce the concept of s asymptotically periodicity in the stepanov sense we study some properties of the space consisting of s asymptotically periodic functions and we use this notion to establish the existence of s asymptotically periodic solutions to linear and semi linear first order abstract differential equations in particular we characterize the strongly continuous semigroups of bounded linear operators defined on reflexive spaces which are s asymptotically periodic as those semigroups which are the direct sum of an periodic and a strongly stable semigroup

on the shafarevich and tate conjectures for hyperkahler varieties 1 problems and results 2 polarized hyperk ihler varieties and cubic fourfoids 3 the period mapping 4 the kuga satake construction 5 the kuga satake construction in the relative setting 6 proof of theorem 1 5 1 7 proof of theorem 1 6 1 8 descent 9 proof of theorem 1 3 1 appendix 1 spinorial shimura varieties appendix 2 a short proof of the hodge conjecture for cubic fourfolds 205 210 212 216 220 224 229 233 240 244 245

uber die lokale zetafunktion von shimuravarietaten monodromiefiltration und verschwindende zyklen in ungleicher charakteristik

almost automorphic solutions of nonautonomous evolution equations abstract in this paper we establish some new theorems about the existence of almost automorphic solutions to nonautonomous evolution equations u t a t u t f t and u t a t u t f t u t in banach spaces as we will see our results allow for a more general a t to some extent an example is also given to illustrate our results in addition by means of an example we show that one cannot ensure the existence of almost automorphic solutions to u t a t u t f t even if the evolution family u t s generated by a t is exponentially stable and f a a x

an asymptotically optimal policy for a quantity based network revenue management problem we consider a canonical revenue management problem in a network setting where the goal is to find a customer admission policy to maximize the total expected revenue over a fixed finite horizon there is a set of resources each of which has a fixed capacity there are several customer classes each with an associated arrival process price and resource consumption vector if a customer is accepted it effectively removes the resources that it consumes from the system the exact solution cannot be obtained for reasonable sized problems due to the curse of dimensionality several approximate solution techniques have been proposed in the literature one way to analytically compare policies is via an asymptotic analysis where both resource sizes and arrival rates grow large many of the proposed policies are asymptotically optimal on the fluid scale however as we demonstrate in this paper these policies may fail to be optimal on the more sensitive diffusion scale even for quite simple problem instances we develop a new policy that achieves diffusion scale optimality the policy starts with a probabilistic admission rule derived from the optimization of the fluid model embeds a trigger function that tracks the difference between the actual and expected customer acceptance and sets threshold values for the trigger function the violation of which invokes the reoptimization of the admission rule we show that re solving the fluid model which needs to be performed at most once is required for extending the asymptotic optimality from the fluid scale to the diffusion scale we demonstrate the implementation of the policy by numerical examples

ordinary k3 surfaces over a finite field we give a description of the category of ordinary k3 surfaces over a finite field in terms of linear algebra data over z this gives an analogue for k3 surfaces of deligne s description of the category of ordinary abelian varieties over a finite field and refines earlier work by n o nygaard and j d yu our main result is conditional on a conjecture on potential semi stable reduction of k3 surfaces over p adic fields we give unconditional versions for k3 surfaces of large picard rank and for k3 surfaces of small degree

dynamic bid prices in revenue management we formally derive the standard deterministic linear program lp for bid price control by making an affine functional approximation to the optimal dynamic programming value function this affine functional approximation gives rise to a new lp that yields tighter bounds than the standard lp whereas the standard lp computes static bid prices our lp computes a time trajectory of bid prices we show that there exist dynamic bid prices optimal for the lp that are individually monotone with respect to time we provide a column generation procedure for solving the lp within a desired optimality tolerance and present numerical results on computational and economic performance

approximate dynamic programming via a smoothed linear program we present a novel linear program for the approximation of the dynamic programming cost to go function in high dimensional stochastic control problems lp approaches to approximate dp have typically relied on a natural projection of a well studied linear program for exact dynamic programming such programs restrict attention to approximations that are lower bounds to the optimal cost to go function our program the smoothed approximate linear program is distinct from such approaches and relaxes the restriction to lower bounding approximations in an appropriate fashion while remaining computationally tractable doing so appears to have several advantages first we demonstrate bounds on the quality of approximation to the optimal cost to go function afforded by our approach these bounds are in general no worse than those available for extant lp approaches and for specific problem instances can be shown to be arbitrarily stronger second experiments with our approach on a pair of challenging problems the game of tetris and a queueing network control problem show that the approach outperforms the existing lp approach which has previously been shown to be competitive with several adp algorithms by a substantial margin

a dynamic traveling salesman problem with stochastic arc costs we propose a dynamic traveling salesman problem tsp with stochastic arc costs motivated by applications such as dynamic vehicle routing in which the cost of a decision is known only probabilistically beforehand but is revealed dynamically before the decision is executed we formulate this as a dynamic program dp and compare it to static counterparts to demonstrate the advantage of the dynamic paradigm over an a priori approach we then apply approximate linear programming alp to overcome the dp s curse of dimensionality obtain a semi infinite linear programming lower bound and discuss its tractability we also analyze a rollout version of the price directed policy implied by our alp and derive worst case guarantees for its performance our computational study demonstrates the quality of a heuristically modified rollout policy using a computationally effective a posteriori bound

complete intersections moduli torelli and good reduction we study the arithmetic of complete intersections in projective space over number fields our main results include arithmetic torelli theorems and versions of the shafarevich conjecture as proved for curves and abelian varieties by faltings for example we prove an analogue of the shafarevich conjecture for cubic and quartic threefolds and intersections of two quadrics

optimal toll design a lower bound framework for the asymmetric traveling salesman problem we propose a framework of lower bounds for the asymmetric traveling salesman problem tsp based on approximating the dynamic programming formulation with different basis vector sets we discuss how several well known tsp lower bounds correspond to intuitive basis vector choices and give an economic interpretation wherein the salesman must pay tolls as he travels between cities we then introduce an exact reformulation that generates a family of successively tighter lower bounds all solvable in polynomial time we show that the base member of this family yields a bound greater than or equal to the well known held karp bound obtained by solving the linear programming relaxation of the tsp s integer programming arc based formulation

on the shafarevich conjecture for enriques surfaces enriques surfaces are minimal surfaces of kodaira dimension 0 with b 2 10 if we work with a field of characteristic away from 2 enriques surfaces admit double covers which are k3 surfaces in this paper we prove the shafarevich conjecture for enriques surfaces by reducing the problem to the case of k3 surfaces in our formulation of the shafarevich conjecture we use the notion admitting a cohomological good k3 cover which includes not only good reduction but also flower pot reduction

complete second order linear differential equations with almost periodic solutions abstract this paper characterizes equations of the type u t bu t au t 0 in a banach space where a b are densely defined closed linear operators and whose solutions are all almost periodic

perverse t structure on artin stacks in this paper we develop the theory of perverse sheaves on artin stacks continuing our earlier study of lisse etale sheaves on stacks in laszlo and olsson the six operations for sheaves on artin stacks i finite coefficients publ math ihes 2008 the six operations for sheaves on artin stacks ii adic coefficients publ math ihes 2008

the tate conjecture for k3 surfaces in odd characteristic we show that the classical kuga satake construction gives rise away from characteristic 2 to an open immersion from the moduli of primitively polarized k3 surfaces of any fixed degree to a certain regular integral model for a shimura variety of orthogonal type this allows us to attach to every polarized k3 surface in odd characteristic an abelian variety such that divisors on the surface can be identified with certain endomorphisms of the attached abelian variety in turn this reduces the tate conjecture for k3 surfaces over finitely generated fields of odd characteristic to a version of the tate conjecture for certain endomorphisms on the attached kuga satake abelian variety which we prove as a by product of our methods we also show that the moduli stack of primitively polarized k3 surfaces of degree 2d is quasi projective and when d is not divisible by p 2 is geometrically irreducible in characteristic p we indicate how the same method applies to prove the tate conjecture for co dimension 2 cycles on cubic fourfolds

optimal control of a high volume assemble to order system we consider an assemble to order system with a high volume of prospective customers arriving per unit time our objective is to maximize expected infinite horizon discounted profit by choosing product prices component production capacities and a dynamic policy for sequencing customer orders for assembly we prove that a myopic discrete review sequencing policy which allocates scarce components among orders for different products to minimize instantaneous physical and financial holding costs is asymptotically optimal furthermore we prove that optimal prices and production capacity nearly balance the supply and demand for components i e it is economically optimal to operate the system in heavy traffic so system performance is characterized by a diffusion approximation the diffusion approximation exhibits state space collapse its dimension equals the number of components rather than the number of components plus the number of products these results complement the existing assemble to order literature which focuses on managing component inventory and assumes fifo sequencing of orders for assembly

generalized polynomial approximations in markovian decision processes abstract fitting the value function in a markovian decision process by a linear superposition of m basis functions reduces the problem dimensionality from the number of states down to m with good accuracy retained if the value function is a smooth function of its argument the state vector this paper provides for both the discounted and undiscounted cases three algorithms for computing the coefficients in the linear superposition linear programming policy iteration and least squares

a p adic nonabelian criterion for good reduction of curves let k be a complete discrete valuation field of characteristic 0 with valuation ring ok and perfect residue field k of positive characteristic p we prove that a proper and smooth curve over k admitting a semistable model over ok has good reduction if and only if its unipotent p adic etale fundamental group is crystalline

using lagrangian relaxation to compute capacity dependent bid prices in network revenue management we propose a new method to compute bid prices in network revenue management problems the novel aspect of our method is that it explicitly considers the temporal dynamics of the arrivals of the itinerary requests and generates bid prices that depend on the remaining leg capacities our method is based on relaxing certain constraints that link the decisions for different flight legs by associating lagrange multipliers with them in this case the network revenue management problem decomposes by the flight legs and we can concentrate on one flight leg at a time when compared with the so called deterministic linear program we show that our method provides a tighter upper bound on the optimal objective value of the network revenue management problem computational experiments indicate that the bid prices obtained by our method perform significantly better than the ones obtained by standard benchmark methods

semigroups arising from elastic systems with dissipation abstract in this paper we investigate the properties norm continuity differentiability analyticity and exponential stability of semigroups arising from elastic systems with dissipation the resulting theorems are complete in a sense extensions of 1 theorem 1 1 and 2 theorem 1 1

existence results for some damped second order volterra integro differential equations abstract in this paper we make a subtle use of operator theory techniques and the well known schauder fixed point principle to establish the existence of pseudo almost automorphic solutions to some second order damped integro differential equations with pseudo almost automorphic coefficients in order to illustrate our main results we will study the existence of pseudo almost automorphic solutions to a structurally damped plate like boundary value problem

a linear programming approach to nonstationary infinite horizon markov decision processes nonstationary infinite horizon markov decision processes mdps generalize the most well studied class of sequential decision models in operations research namely that of stationary mdps by relaxing the restrictive assumption that problem data do not change over time linear programming lp has been very successful in obtaining structural insights and devising solution methods for stationary mdps however an lp approach for nonstationary mdps is currently missing this is because the lp formulation of a nonstationary infinite horizon mdp includes countably infinite variables and constraints and research on such infinite dimensional lps has traditionally faced several hurdles for instance duality results may not hold an extreme point may not be a basic feasible solution and in the context of a simplex algorithm a pivot operation may require infinite data and computations and a sequence of improving extreme points need not converge in value to optimal in this paper we tackle these challenges a

mild almost periodic solutions of abstract differential equations abstract necessary and sufficient conditions are established for the existence of mild almost periodic solutions of cauchy problems u au and u au f where a is the infinitesimal generator of a strongly continuous semigroup respectively a cosine function on a hilbert space and an almost periodic function

integrated semigroups and higher order abstract equations abstract let e be a banach space b 0 b n 1 closed linear operators on e and f 0 e this paper is devoted to the study of well posedness of the cauchy problem for higher order abstract differential equations formula using the theory of integrated semigroups we obtain some concise and useful criteria

analysis of deterministic control and its improvements for an inventory problem with multiproduct batch differentiation we consider a multiperiod planning problem faced by a biopharmaceutical firm that must coordinate the production and allocation of batches of intermediate products to end products for multiple markets this is a challenging problem to solve optimally so we derive a theoretical bound on the performance of a deterministic control dc in which all random variables are replaced by their expected values and the corresponding deterministic optimization problem is solved this is a variant of an approach that is widely used in practice we show that while dc can perform poorly in some instances simple reoptimizations of dc i e certainty equivalent control cec improve the performance of dc that said the benefit of reoptimization decreases as the magnitude of demand variation increases to address this and also to provide guidance for heuristic design we derive performance bounds for two additional heuristic controls 1 open loop feedback control olfc which reoptimizes a sequence of stochastic pro

hypersurfaces in projective schemes and a moving lemma let x s be a quasi projective morphism over an affine base we develop in this article a technique for proving the existence of closed subschemes h s of x s with various favorable properties we offer several applications of this technique including the existence of finite quasi sections in certain projective morphisms and the existence of hypersurfaces in x s containing a given closed subscheme c and intersecting properly a closed set f assume now that the base s is the spectrum of a ring r such that for any finite morphism z s pic z is a torsion group this condition is satisfied if r is the ring of integers of a number field or the ring of functions of a smooth affine curve over a finite field we prove in this context a moving lemma pertaining to horizontal 1 cycles on a regular scheme x quasi projective and flat over s we also show the existence of a finite surjective s morphism to psd for any scheme x projective over s when x s has all its fibers of a fixed dimension d

a characterization of norm continuity of propagators for second order abstract differential equations abstract in this paper we obtain a concise characterization of norm continuity for t 0 of propagators for the complete second order abstract differential equation on a banach space e u t bu t au t 0 t 0 where b l e as a consequence we discover that a strongly continuous cosine operator function or operator group is norm continuous for t 0 if and only if its generator is bounded

characterizations of almost periodic strongly continuous cosine operator functions abstract we characterize in terms of the infinitesimal generator those cosine operator functions which are almost periodic or uniformly almost periodic

asymptotically almost periodic solutions of abstract differential equations abstract in this paper we are concerned with the problem of existence and uniqueness of asymptotically almost periodic mild solutions of nonhomogeneous first order abstract differential equations essentially we obtain existence of asymptotically almost periodic solutions when the semigroup is asymptotically almost periodic or when the forcing term is an asymptotically stepanov almost periodic function

almost periodic and pseudo almost periodic solutions to fractional differential and integro differential equations abstract we study the existence of almost periodic resp pseudo almost periodic mild solutions for fractional differential and integro differential equations in the case when the forcing term belongs to the class of stepanov almost resp stepanov like pseudo almost periodic functions

the linear programming approach to approximate dynamic programming the curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large scale stochastic control problems we study an efficient method based on linear programming for approximating solutions to such problems the approach fits a linear combination of pre selected basis functions to the dynamic programming cost to go function we develop error bounds that offer performance guarantees and also guide the selection of both basis functions and state relevance weights that influence quality of the approximation experimental results in the domain of queueing network control provide empirical support for the methodology

good reduction criterion for k3 surfaces we prove a neron ogg shafarevich type criterion for good reduction of k3 surfaces which states that a k3 surface over a complete discrete valuation field has potential good reduction if its l adic cohomology group is unramified we also prove a p adic version of the criterion these are analogues of the criteria for good reduction of abelian varieties the model of the surface will be in general not a scheme but an algebraic space as a corollary of the criterion we obtain the surjectivity of the period map of k3 surfaces in positive characteristic

on a piecewise linear approximation for network revenue management the network revenue management rm problem arises in airline hotel media and other industries where the sale products use multiple resources it can be formulated as a stochastic dynamic program but the dynamic program is computationally intractable because of an exponentially large state space and a number of heuristics have been proposed to approximate its value function in this paper we show that the piecewise linear approximation to the network rm dynamic program is tractable specifically we show that the separation problem of the approximation can be solved as a relatively compact linear program moreover the resulting compact formulation of the approximate dynamic program turns out to be exactly equivalent to the lagrangian relaxation of the dynamic program an earlier heuristic method proposed for the same problem we perform a numerical comparison of solving the problem by generating separating cuts or as our compact linear program we discuss extensions to versions of the network rm prob

reductions of approximate linear programs for network revenue management the linear programming approach to approximate dynamic programming has received considerable attention in the recent network revenue management literature a major challenge of the approach lies in solving the resulting approximate linear programs alps which often have a huge number of constraints and or variables we show that the alps can be dramatically reduced in size for both affine and separable piecewise linear approximations to network revenue management problems under both independent and discrete choice models of demand our key result is the equivalence between each alp and a corresponding reduced program which is more compact in size and admits an intuitive probabilistic interpretation for the affine approximation to network revenue management under an independent demand model we recover an equivalence result known in the literature but provide an alternative proof our other equivalence results are new we test the numerical performance of solving the reduced programs directly using o

bid price controls for network revenue management martingale characterization of optimal bid prices we consider a continuous time rate based model of network revenue management under mild assumptions we construct a simple e optimal bid price control which can be viewed as a perturbation of a bid price control in the classical sense williamson e l 1992 airline network seat control ph d thesis mit cambridge ma we show that the associated bid price process forms a martingale and the corresponding booking controls converge in an appropriate sense to an optimal control as e tends to 0 moreover we show that there exists an optimal generalized bid price control where the bid price process forms a martingale and is used in conjunction with a capacity usage limit process we also discuss its connection to the bid price controls in the classical sense and sufficient conditions for the near optimality of the latter

hom stacks and restriction of scalars fix an algebraic space s and let x and y be separated artin stacks of finite presentation over s with finite diagonals over s we define a stack homs x y classifying morphisms between x and y assume that x is proper and flat over s and assume fppf locally on s that there exists a finite finitely presented flat cover z x with z an algebraic space then we show that homs x y is an artin stack with quasi compact and separated diagonal