chow groups of projective varieties of very small degree see 12 5 and the references given there these facts together with various conjectures on the cohomology and chow groups of algebraic varieties suggest that the chow groups of x might satisfy chl x q chl pk q q for l 1 compare with remark 5 6 and corollary 5 7 this is explicitly formulated by v srinivas and k paranjape in 16 conjecture 1 8 the chain of reasoning goes roughly as follows suppose x is smooth one expects a good filtration 0 f j 1 f j f 0 ch x x q whose graded pieces f f l 1 are controlled by h2j l x x see 10 according to grothendieck s generalized conjecture 8 the groups h x should be generated by the image under the gysin morphism of the homology of a codimension subset together with the classes coming from p applying this to the diagonal in x x should then force the triviality of the chow groups in the desired range for zero cycles the conjecture follows from roitman s theorem see 17 and 18

the system point method in exponential queues a level crossing approach the purpose of this paper is to describe the new system point method for analyzing queues it considers the stationary probability distribution of the waiting time in variations of the m m r queue with first come first served discipline for a large class of service mechanisms it is shown that the stationary probability density function of the waiting time evaluated at w 0 can be interpreted as the long run average of the number of times that the virtual wait becomes less than w per unit time theorems are presented which establish this interpretation of the probability density function of the virtual waiting time in terms of point processes generated by level crossings in the state space these theorems in combination with the principle of stationary set balance generate a system of model equations that can be written directly in addition the forms of these equations are often linear volterra integral equations of the second kind with parameter which yield direct analytical solutions an analogous theorem is proved for a variant of m g 1 two illustrative examples are presented

maximum likelihood estimates via duality for log convex models when cell probabilities are subject to convex constraints the purpose of this article is to derive and illustrate a method for fitting models involving both convex and log convex constraints on the probability vector s of a product multinomial distribution we give a two step algorithm to obtain maximum likelihood estimates of the probability vector s and show that it is guaranteed to converge to the true solution some examples are discussed which illustrate the procedure

groupe de chow de codimension deux des varietes definies sur un corps de nombres un theoreme de finitude pour la torsion letx be a smooth projective variety defined over a number field and let ch2 x denote the chow group of codimension two cycles modulo rational equivalence we show that if the cohomology grouph2 x ox vanishes then the torsion subgroup of ch2 x is a finite group this result covers all previous results in this direction the hypothesish2 x ox 0 is used to lift line bundles

approximations for operating characteristics in a production inventory model with variable production rate this paper deals with production inventory control models with a variable production rate the demand process is a compound poisson process the production rate is controlled by the well known m m policy simple and accurate approximations are given for operating characteristics of the system it turns out that a sequential determination of m m and m yields a rule that minimizes average costs subject to a service level constraint numerical results are given to show the accuracy of the approximations

a discrete time model for common lifetime inventory systems we consider a discrete time s s inventory model in which the stored items have a random common lifetime with a discrete phase type distribution demands arrive in batches following a discrete phase type renewal process with zero lead time and allowing backlogs we construct a multidimensional markov chain to model the inventory level process we obtain a closed form expected cost function numerical results demonstrate some properties of optimal ordering policies and cost functions when compared with the results for the constant lifetime model the variance of the lifetime significantly affects the system behavior thus the formalism that we create here adds a new dimension to the research in perishable inventory control under uncertainty in lifetime

profile likelihood inference for highly accurate diagnostic tests nous envisageons une inference sur la vraisemblance de profil basee sur la distribution multinomiale pour evaluer la precision d un test diagnostic la methode s applique a des donnees ordinales quand la precision est evaluee au moyen de l aire sous la courbe caracteristique du receveur courbe roc des resultats de simulation suggerent que les intervalles de confiance derives ont vies probabilites de couverture acceptables meme lorsque les tailles d echantillons sont petites et que le test diagnostic a une haute precision les methodes s etendent a des contextes stratifies et a des situations ou les evaluations sont correlees nous illustrons les methodes sur des donnees provenant d un essai clinique sur la detection du cancer de l ovaire

the arithmetic of zero cycles on surfaces with geometric genus and irregularity zero let x be a smooth projective geometrically irreducible surface over a perfect field f throughout this paper it will be assumed that the geometric genus pg and the irregularity q of x both vanish denote the separable closure of f by f let x x be the surface obtained from x by base extension it will also be assumed that the group ao x of rational equivalence classes of zero cycles of degree zero on x vanishes this is a technical hypothesis which could presumably be eliminated at the expense of working with ker ao x ao x for want of a better name and for ease in stating various results any surface which satisfies these three hypotheses will be called a pseudo rational surface bloch 2 has conjectured that the vanishing of ao x should follow from the assumption that po q 0 this was proven by bloch kas and lieberman 5 for all such surfaces which are not of general type i e which have kodaira dimension less than 2 it has also been proven for particular surfaces of general type by inose and mizukami 23 barlow 1 and keum 25 consequently the class of pseudo rational surfaces includes rational surfaces enriques surfaces elliptic surfaces with q 0 the classical godeaux surface burniat inoue surfaces campedelti surfaces and the surfaces of barlow and of keum this paper will study ao x for pseudo rational surfaces defined over fields of number theoretic interest bloch 4 introduced k theoretic techniques into the study of zero cycles on rational surfaces his work was extended 7 12 15 27 28 32 36 to achieve a thorough understanding of such cycles colliot th616ne and raskind 10 developed this machinery further to study codimension two cycles on any variety the author 14 applied these techniques to enriques surfaces raskind 30 used them to study zero cycles on pseudo rational surfaces one of the main results of this paper is a new proof of the following theorem of raskind 31

unirational threefolds with no universal codimension 2 cycle we prove that the general quartic double solid with k le 7 nodes does not admit a chow theoretic decomposition of the diagonal or equivalently has a nontrivial universal mathrm ch 0 group and the same holds if we replace in this statement chow theoretic by cohomological in particular it is not stably rational we also deduce that the general quartic double solid with seven nodes does not admit a universal codimension 2 cycle parameterized by its intermediate jacobian and even does not admit a parametrization with rationally connected fibers of its jacobian by a family of 1 cycles this finally implies that its third unramified cohomology group is not universally trivial

examples of smash nilpotent cycles on rationally connected varieties abstract voevodsky has conjectured that numerical and smash equivalence coincide on a smooth projective variety we prove this conjecture holds for uniruled 3 folds 4 folds whose mrcc quotient has dimension 2 and for smooth complete intersections with very small degree

motives and filtrations on chow groups in this paper sequential to sa we discuss a philosophy of bloch and beilinson concerning filtrations on chow groups of algebraic vareties which provides us with a good understanding on the structure of at least certain portions of chow groups let k be a fixed ground field and let c be the category of smooth projective schemes over k with a fixed suitable weil cohomology theory cf notations x in mathcal c rightsquigarrow h x mathop oplus limits i in z h i x

rost nilpotence and higher unramified cohomology abstract we develop an approach to proving the rost nilpotence principle involving higher unramified cohomology along with a decomposition of the diagonal technique we use this to prove the principle for certain threefolds over a perfect field

optimal and simple approximate solutions to a production inventory system with stochastic and deterministic demand abstract we consider a continuous review production inventory system where demand is a mixture of a deterministic component and a random component which follows a compound poisson process demand is satisfied by a production facility which may be in production or idle while in production the facility produces at a constant rate a two number s s policy is used to control production when inventory reaches level s production is turned off and when inventory drops below level s production is turned on a level crossing approach is used to derive the steady state distribution of inventory level from which the exact total expected cost function consisting of setup inventory holding and backorder costs is determined the optimal s s policy can be found through a search of the expected cost function we propose approximations that give simple closed form solutions with near optimal performance

an iterative procedure for obtaining i projections onto the intersection of convex sets abstract a frequently occuring problem is to find that probability distribution pd lying within a convex set which minimizes the i divergence between it and given pd r this document proposes an iterative procedure which requires only that the set be convex and not necessarily linear which under general conditions will converge to the desired i projection

positivity of the diagonal abstract we study how the geometry of a projective variety x is reflected in the positivity properties of the diagonal x considered as a cycle on x x we analyze when the diagonal is big when it is nef and when it is rigid in each case we give several implications for the geometric properties of x for example when the cohomology class of x is big we prove that the hodge groups h k 0 x vanish for k 0 we also classify varieties of low dimension where the diagonal is nef and big

complex multiplication cycles and a conjecture of beilinson and bloch a generalization of the conjecture of birch and swinnerton dyer is investigated using complex multiplication cycles on a particular kuga fiber variety a weak finiteness result consistent with the conjecture is proved the image of complex multiplication cycles under the abel jacobi map is computed explicitly the results provide numerical evidence supporting the conjecture they also give evidence for a relationship between complex multiplication cycles and a modular form of weight 5 2 and raise questions for further investigation

2 cycles sur les hypersurfaces cubiques de dimension 5 we study 2 cycles of a smooth cubic hypersurface of dimension 5 we show that the griffiths group of 2 cycles is trivial and the abel jacobi map induces an isomorphism between the chow group of algebraically trivial 2 cycles and the intermediate jacobian

a hyper kahler compactification of the intermediate jacobian fibration associated with a cubic 4 fold let x be a general cubic fourfold it was observed by donagi and markman that the relative intermediate jacobian fibration j u with u p5 x associated to the smooth hyperplane sections of x carries a natural holomorphic symplectic form making the fibration lagrangian in this paper we obtain a smooth projective compactification j of j with the property that the holomorphic symplectic form on j extends to a holomorphic symplectic form on j in particular j is a 10 dimensional compact hyper kahler manifold which we show to be deformation equivalent to the exceptional example of o grady this proves a conjecture by markushevich

a pencil of enriques surfaces with non algebraic integral hodge classes we prove that there exists a pencil of enriques surfaces defined over mathbb q with non algebraic integral hodge classes of non torsion type this gives the first example of a threefold with the trivial chow group of zero cycles on which the integral hodge conjecture fails as an application we construct a fourfold which gives the negative answer to a classical question of murre on the universality of the abel jacobi maps in codimension three

the hodge conjecture for a certain class of singular varieties in j there is stated a version of the hodge conjecture for complex singular varieties reduced separated algebraic schemes over c generalizing the popular version of the conjecture a statement of the general hodge conjecture for the singular case extending the amended version by grothendieck is given in l2 using the techniques in j the statement is this let z be a reduced separated algebraic scheme over c the lowest weight part w i hi z q of the borelmoore homology hi z q defines a hodge structure of weight i recall the filtration by niveau given by

rost nilpotence and etale motivic cohomology abstract a smooth projective scheme x over a field k is said to satisfy the rost nilpotence principle if any endomorphism of x in the category of chow motives that vanishes on an extension of the base field k is nilpotent we show that an etale motivic analogue of the rost nilpotence principle holds for all smooth projective schemes over a perfect field this provides a new approach to the question of rost nilpotence and allows us to obtain an elegant proof of rost nilpotence for surfaces as well as for birationally ruled threefolds over a field of characteristic 0

production inventory systems with lost sales and compound poisson demands this paper considers a continuous review single product production inventory system with a constant replenishment rate compound poisson demands and lost sales two objective functions that represent metrics of operational costs are considered 1 the sum of the expected discounted inventory holding costs and lost sales penalties both over an infinite time horizon given an initial inventory level and 2 the long run time average of the same costs the goal is to minimize these cost metrics with respect to the replenishment rate it is however not possible to obtain closed form expressions for the aforementioned cost functions directly in terms of positive replenishment rate prr to overcome this difficulty we construct a bijection from the prr space to the space of positive roots of lundberg s fundamental equation to be referred to as the lundberg positive rootlpr space this transformation allows us to derive closed form expressions for the aforementioned cost metrics with respect to the lpr variable in lieu of the prr variable we then proceed to solve the optimization problem in the lpr space and finally recover the optimal replenishment rate from the optimal lpr variable via the inverse bijection for the special cases of constant or loss proportional penalty and exponentially distributed demand sizes we obtain simpler explicit formulas for the optimal replenishment rate

rational curves on complete intersections in positive characteristic abstract we study properties of rational curves on complete intersections in positive characteristic it has long been known that in characteristic 0 smooth calabi yau and general type varieties are not uniruled in positive characteristic however there are well known counterexamples to this statement we will show that nevertheless a general calabi yau or general type complete intersection in projective space is not uniruled we will also show that the space of complete intersections of degree d 1 d k containing a rational curve has codimension at least i 1 k d i 2 n 2 and give similar results for hypersurfaces containing higher genus curves

a fluid eoq model of perishable items with intermittent high and low demand rates we consider a stochastic fluid eoq type model with demand rates operating in a two state random environment this environment alternates between exponentially distributed periods of high demand and generally distributed periods of low demand the inventory level starts at some level q and decreases linearly at rate h during the periods of high demand and at rate l h at periods of low demand refilling of the inventory level to level q is required when the first of two events takes place either the buffer level reaches zero or the buffer content becomes outdated if such an event occurs during a high demand period an order is instantaneously placed otherwise ordering is postponed until the beginning of the next high demand period we determine the steady state distribution of the inventory level as well as other quantities of interest such as the distribution of the time until a refill is required finally for a given cost revenue structure we determine the long run average profit and we co

cohomologie non ramifiee et conjecture de hodge entiere en nous appuyant sur la conjecture de bloch kato en k theorie de milnor nous etablissons un lien general entre le defaut de la conjecture de hodge entiere pour la cohomologie de degre 4 et le troisieme groupe de cohomologie non ramifiee a coefficients q z ceci permet de montrer que sur un solide en anglais threefold uniregle le troisieme groupe de cohomologie non ramifiee a coefficients q z s annule ce que la k theorie algebrique ne permet d obtenir que dans certains cas ceci permet a l inverse de deduire d exemples ayant leur source en k theorie que la conjecture de hodge entiere pour la cohomologie de degre 4 peut etre en defaut pour les varietes rationnellement connexes pour certaines familles a un parametre de surfaces on etablit un lien entre la conjecture de hodge entiere et l indice de la fibre generique

a production inventory model with randomly changing environmental conditions we consider a limited capacity production inventory system with linear production rate and compound poisson demand in which both production and demand processes are subject to independently and randomly changing environmental conditions assuming that these conditions are represented by two continuous time homogeneous markov chains and shortages are lost we derive the limiting distribution of the inventory level and present some numerical results in terms of the ensuing performance measures

2 cycles on higher fano hypersurfaces let x d be a smooth hypersurface of degree d in mathbb p mathbb c n suppose that the fano variety mathrm f x d of lines of x d is smooth we prove that the griffiths group mathrm griff 1 mathrm f mathrm x d of mathrm f x d is trivial if the hypersurface mathrm x d is of 2 fano type as a result we give a positive answer to a question of professor voisin about the first griffiths groups of fano varieties in some cases base on this result we prove that mathrm ch 2 mathrm x d mathbb z for a smooth 3 fano hypersurface mathrm x d subseteq mathbb p n mathbb c with smooth fano variety of lines

the compensation method applied to a one product production inventory problem this paper considers a one product one machine production inventory problem demand requests for the product are governed by a poisson process with demand size being an exponential random variable the production facility may be in production or idle while in production the facility produces continuously at a constant rate the objective is to minimize system costs consisting of setup costs inventory holding costs and backorder costs given a two critical number policy the problem is analyzed as a constrained markov process using the compensation method a closed form expression is found for system cost as a function of the policy parameters this cost function may then be searched to find an optimal policy the production inventory problem is related to a server backlog process for an m m 1 system in which the server departs when the system empties and returns when the backlog exceeds a specified threshold the application of the compensation method to this server backlog process is discussed

lawson homology for varieties with small chow groups and the induced filtration on the griffiths groups these groups form an intriguing set of invariants despite the vast literature on this subject the groups have been calculated only in very few cases such as for the projective spaces one of the goals of this note is to understand these invariants in case the variety has few cycles in the sense that rational and homological equivalence coincide for all m cycles up to a certain rank m s actually the results only deal with that part of lawson homology that is not visible in ordinary homology in that it is in the kernel of the cycle class maps cm k 2m lmhk 2m x hk 2m x

tamagawa numbers of diagonal cubic surfaces numerical evidence a refined version of manin sconjecture aboutthe asymptotics of points of bounded height on fano varieties has been developped by batyrev and the authors we test numerically this refined conjecture for some diagonal cubic surfaces

optimal control of production rate in a failure prone manufacturing system we address the problem of controlling the production rate of a failure prone manufacturing system so as to minimize the discounted inventory cost where certain cost rates are specified for both positive and negative inventories and there is a constant demand rate for the commodity produced the underlying theoretical problem is the optimal control of a continuous time system with jump markov disturbances with an infinite horizon discounted cost criterion we use two complementary approaches first proceeding informally and using a combination of stochastic coupling linear system arguments stable and unstable eigenspaces renewal theory parametric optimization etc we arrive at a conjecture for the optimal policy then we address the previously ignored mathematical difficulties associated with differential equations with discontinuous right hand sides singularity of the optimal control problem smoothness and validity of the dynamic programming equation etc to give a rigorous proof of optimality of the conjectured policy it is hoped that both approaches will find uses in other such problems also we obtain the complete solution and show that the optimal solution is simply characterized by a certain critical number which we call the optimal inventory level if the current inventory level exceeds the optimal one should not produce at all if less one should produce at the maximum rate while if exactly equal one should produce exactly enough to meet demand we also give a simple explicit formula for the optimal inventory level

non trivial elements in the abel jacobi kernels of higher dimensional varieties abstract the purpose of this paper is to construct non trivial elements in the abel jacobi kernels in any codimension by specializing correspondences with non trivial hodge theoretical invariants at points with different transcendence degrees over a subfield in c

on the fibration method for zero cycles and rational points conjectures on the existence of zero cycles on arbitrary smooth projective varieties over number elds were proposed by colliot th el ene sansuc kato and saito in the 1980 s we prove that these conjectures are compatible with brations for brations into rationally connected varieties over a curve in particular they hold for the total space of families of homogeneous spaces of linear groups with connected geometric stabilisers we prove the analogous result for rational points conditionally on a conjecture on locally split values of polynomials which a recent work of matthiesen establishes in the case of linear polynomials over the rationals

permutation modules and chow motives of geometrically rational surfaces abstract we prove that the chow motive with integral coefficient of a geometrically rational surfaces s over a perfect field k is zero dimensional if and only if the picard group of k k s where k is an algebraic closure of k is a direct summand of a gal k k permutation module and s possesses a zero cycle of degree one as shown by colliot thelene in a letter to the author which we have reproduced in the appendix this is in turn equivalent to s having a zero cycle of degree 1 and ch 0 k s k s being torsion free

decomposition of small diagonals and chow rings of hypersurfaces and calabi yau complete intersections abstract on the one hand for a general calabi yau complete intersection x we establish a decomposition up to rational equivalence of the small diagonal in x x x from which we deduce that any decomposable 0 cycle of degree 0 is in fact rationally equivalent to 0 up to torsion on the other hand we find a similar decomposition of the smallest diagonal in a higher power of a hypersurface which provides us an analogous result on the multiplicative structure of its chow ring

production control of a manufacturing system with multiple machine states the production control of a single product manufacturing system with arbitrary number of machine states failure modes is discussed the objective is to find a production policy that would meet the demand for the product with minimum average inventory or backlog cost the optimal production policy has a special structure and is called a hedging point policy if the hedging points are known the optimal production rate is readily specified assuming a set of tentative hedging points the simple structure of the optimal policy is utilized to find the steady state probability distribution of the surplus inventory or backlog once this function is determined the average surplus cost is easily calculated in terms of the values of the hedging points the average cost is then minimized to find the optimum hedging points

nonparametric estimation of convex models via mixtures we present a general approach to estimating probability measures constrained to lie in a convex set we represent constrained measures as mixtures of simple known extreme measures and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure convex constraints arise in many modeling situations such as estimation of the mean and estimation under stochastic ordering constraints we describe mixture representation techniques for these and other situations and discuss applications to maximum likelihood and bayesian estimation

on the integral hodge conjecture for real varieties i we formulate the real integral hodge conjecture a version of the integral hodge conjecture for real varieties and raise the question of its validity for cycles of dimension 1 on uniruled and calabi yau threefolds and on rationally connected varieties we relate it to the problem of determining the image of the borel haefliger cycle class map for 1 cycles with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the chow group of 1 cycles of real threefolds new results about these problems are obtained along the way

sporadic and continuous clearing policies for a production inventory system under an m g demand process a production inventory system is filled continuously at rate 1 and satisfies demands of i i d random sizes that arrive at poisson times for this system we consider two clearing policies under sporadic review clearing takes place after a random time independent of the content process under continuous review the system is cleared as soon as the inventory level reaches some pre specified threshold we derive explicit results for the associated expected discounted cost functionals under both types of clearing

levels of function fields of surfaces over number fields we study the level of nonformally real function fields of surfaces over number fields and show that it is at most 4 for a large class of surfaces

unreliable production inventory model with a two phase erlang demand arrival process a production inventory system is studied in which an unreliable machine is susceptible to failure following which it must be repaired to make it operative again the demand for the product is governed by a two phase erlang process and demand sizes are independent and identically distributed random variables a two critical number policy m m is used to control a machine s setups and shutdowns namely the machine is shut down whenever the inventory level reaches m and is resumed to operate only when the inventory level falls below the critical number m m m we obtain the steady state distribution of the inventory process and some performance measures of the process

potential density of rational points on the variety of lines of a cubic fourfold we prove the potential density of rational points on the variety of lines of a sufficiently general cubic fourfold defined over a number field where sufficiently general means that a condition of terasoma type is satisfied these varieties have trivial canonical bundle and have geometric picard number equal to one

bloch s conjecture for catanese and barlow surfaces catanese surfaces are regular surfaces of general type with pg 0 they specialize to double covers of barlow surfaces we prove that the ch0 group of a catanese surface is equal to z which implies the same result for the barlow surfaces

on the unramified cohomology of certain quotient varieties in this note we consider unramified cohomology with mathbb z 2 coefficients for some degree two quotient varieties and describe a method that allows one to prove the non vanishing of these groups under certain conditions we apply this method to prove a non vanishing statement in the case of kummer varieties combining this with work of colliot thelene and voisin we obtain a new type of three dimensional counterexample to the integral hodge conjecture

rationally connected varieties over local fields let x be a proper variety defined over a field k following ma we say that two points x x x k are r equivalent if they can be connected by a chain of rational curves defined over k cf 4 1 in essence two points are r equivalent if they are obviously rationally equivalent several authors have proved finiteness results over local and global fields cubic hypersurfaces ma sd linear algebraic groups ct sa vo1 gi vo2 rational surfaces ct co ct1 ct sk1 quadric bundles and intersections of two quadrics ct sa sd pa su r equivalence is only interesting if there are plenty of rational curves on x at least over k such varieties have been studied in the series of papers komi mo1 ko mi mo3 see also ko1 there are many a priori different ways of defining what plenty of rational curves should mean fortunately many of these turn out to be equivalent and this leads to the notion of rationally connected varieties see ko mi mo2 ko1 iv 3 ko2 4 1 2

on the action of symplectic automorphisms on the mathrm ch _0 groups of some hyper kahler fourfolds we prove that for any polarized symplectic automorphism of the fano variety of lines of a smooth cubic fourfold equipped with the plucker polarization the induced action on the chow group of 0 cycles is identity as predicted by bloch beilinson conjecture we also prove the same result for the chow group of homologically trivial 2 cycles up to torsion

some results on green s higher abel jacobi map this paper is devoted to the study of the flrst higher abel jacobi invariant deflned by m green in 4 for zero cycles on a surface green s work is a very original attempt to understand at least over the graded pieces of the conjecturally deflned flltration on chow groups ch p x f 0 ch p x ae f 1 ch p x c h p x hom ae ae f p 1 ch p x 0

maximum likelihood methods for log linear models when expected frequencies are subject to linear constraints abstract hypotheses relating to log linear models may be defined in terms of constraints on the frequencies or on the logarithms of the frequencies a two step algorithm is developed to allow fitting models containing constraints of both types this algorithm is shown to yield maximum likelihood estimates of the log linear parameters three examples are presented to illustrate cases in which these models are of interest

inference for likelihood ratio ordering in the two sample problem abstract we obtain the maximum likelihood estimators of two multinomial probability vectors under the constraint that they are likelihood ratio ordered we extend this estimation approach to the case of two univariate distributions and show strong consistency of the estimators we also derive and study the asymptotic distribution of the likelihood ratio statistic for testing the equality of two discrete probability distributions against the alternative that one distribution is greater than the other in the likelihood ratio ordering sense finally we examine a data set pertaining to average daily insulin dose from the boston collaborative drug surveillance program and compare our testing procedure to testing procedures for other stochastic orderings