quadratic model for reservoir management application to the central valley project a quadratic optimization model is applied to a large scale reservoir system to obtain operation schedules the model has the minimum possible dimensionality treats spillage and penstock releases as decision variables and takes advantage of system dependent features to reduce the size of the decision space an efficient and stable quadratic programming active set algorithm is used to solve for the optimal release policies the stability and convergence of the solution algorithm are ensured by the factorization of the reduced hessian matrix and the accurate computation of the lagrange multipliers the quadratic model is compared with a simplified linear model and it is found that optimal release schedules are robust to the choice of model both yielding an increase of nearly 27 in the total annual energy production with respect to conventional operation procedures although the quadratic model is more flexible and of general applicability the adequate fulfillment of other system functions such as flood control and water supply is guaranteed via constraints on storage and spillage variables

sur une conjecture de kato et kuzumaki concernant les hypersurfaces de fano resume nous montrons que le corps qp et les corps de nombres totalement imaginaires verifient la propriete c 1 conjecturee par kato et kuzumaki en 1986 autrement dit si k est l un de ces corps et f k x0 xn est un polynome homogene de degre d 6 n tout element de k s ecrit comme produit de normes depuis des extensions finies de k dans lesquelles f admet un zero non trivial nous etablissons aussi la conjecture d ax sur les corps pseudo algebriquement clos parfaits pour les corps dont le groupe de galois absolu est un pro p groupe

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

tame coverings of arithmetic schemes the objective of this paper is to investigate tame fundamental groups of schemes of finite type over spec z more precisely let x be a connected scheme of finite type over spec z and let x be a compactification of x i e a scheme which is proper and of finite type over spec z and which contains x as a dense open subscheme then the tame fundamental group of x classifies finite etale coverings of x which are tamely ramified along the boundary x x in particular the tame fundamental group 1 x x x is a quotient of the etale fundamental group 1 x our interest in the tame fundamental group arises from the observation that it seems to be the maximal quotient of 1 x which is visible via class field theory by algebraic cycle theories see s s1 s and s s2 for more precise statements on tame class field theory coverings of a regular scheme which are tamely ramified along a normal crossing divisor have been studied in sga1 g m in this paper we consider tame ramification along an arbitrary zariski closed subset the main reason for this is the lack of good desingularization theorems in positive and mixed characteristics a simple imitation of the definition of tame ramification in the normal crossing case proves to be not useful in the more general situation we give a definition of tameness in the general situation in section 1 and we show that it coincides with the previous one in the normal crossing case for galois coverings of normal schemes our definition of tameness coincides with that proposed by abbes ab and with the notion of numerical tameness defined by chinburg erez c e naturally the question ariseswhether the tame fundamental group 1 x x x is independent of the choice of the compactification x at themoment we can answer this question only for the maximal pro nilpotent quotient in section 2 we consider discrete valuations of higher rank associated to parshin chains we investigate the connection between the tameness of a covering and the behaviour of the associated higher dimensional henselian fields and we show that a finite covering of a regular arithmetic scheme with nilpotent galois group is tamely

on the kernel of the reciprocity map of varieties over local fields this thesis is about higher dimensional class field theory of varieties over local and finite fields their abelianized etale fundamental group is compared with an attached class group via the reciprocity map like in the classical case of a local or global field the main results in this thesis are about the structure of the kernel of their reciprocity maps and criteria for the vanishing of it resp

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

class field theory for arithmetic schemes let x be a regular arithmetic scheme i e a regular integral separated scheme flat and of finite type over spec mathbb z generalising classical class field theory for number fields we define a class group cx and show there is a natural surjective map c x rightarrow pi 1 ab x whose kernel is the connected component of 0

r equivalence in adjoint classical groups over fields of virtual cohomological dimension 2 let f be a field of characteristic not 2 whose virtual cohomological dimension is at most 2 let g be a semisimple group of adjoint type defined over f let rg f denote the normal subgroup of g f consisting of elements r equivalent to identity we show that if g is of classical type not containing a factor of type d n g f rg f 0 if g is a simple classical adjoint group of type d n we show that if f and its multi quadratic extensions satisfy strong approximation property then g f rg f 0 this leads to a new proof of the r triviality of f rational points of adjoint classical groups defined over number fields

weighted complementarity problems a new paradigm for computing equilibria this paper introduces the notion of a weighted complementarity problem wcp which consists of finding a pair of vectors x s belonging to the intersection of a manifold with a cone such that their product in a certain algebra x circ s equals a given weight vector w when w is the zero vector then wcp reduces to a complementarity problem the motivation for introducing the more general notion of a wcp lies in the fact that several equilibrium problems in economics can be formulated in a natural way as wcps moreover those formulations lend themselves to the development of highly efficient algorithms for solving the corresponding equilibrium problems for example fisher s competitive market equilibrium model can be formulated as a wcp that can be efficiently solved by interior point methods moreover it is shown that the quadratic programming and weighted centering problem which generalizes the notion of a linear programming and weighted centering problem recently proposed by anstreicher

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

unramified class field theory of arithmetical surfaces let k be an algebraic number field 9k its ring of integers and v a non empty open subscheme of spec ck let x be a projective smooth geometrically irreducible scheme over k and x a regular proper flat scheme over v such that x x vk x the purpose of this paper is to give an explicit description of the abelian fundamental groups ab x and 7t b x using some idele class groups attached to x and x by a k theoretical method its outline is as follows in general for a noetherian scheme z and i 0 or 1 we define the group ski z to be the cokernel of

the volumetric barrier for semidefinite programming we consider the volumetric barrier for semidefinite programming or generalized volumetric barrier as introduced by nesterov and nemirovskii we extend several fundamental properties of the volumetric barrier for a polyhedral set to the semidefinite case our analysis facilitates a simplified proof of self concordance for the semidefinite volumetric barrier as well as for the combined volumetric logarithmic barrier for semidefinite programming for both of these barriers we obtain self concordance parameters equal to those previously shown to hold in the polyhedral case

a generalization of serre s condition mathrm f f with applications to the finiteness of unramified cohomology in this paper we introduce a condition mathrm f m on a field k for a positive integer m that generalizes serre s condition f and which still implies the finiteness of the galois cohomology of finite galois modules annihilated by m and algebraic k tori that split over an extension of degree dividing m as well as certain groups of etale and unramified cohomology various examples of fields satisfying mathrm f m including those that do not satisfy f are given

volumetric path following algorithms for linear programming we consider the construction of small step path following algorithms using volumetric and mixed volumetric logarithmic barriers we establish quadratic convergence of a volumetric centering measure using pure newton steps enabling us to use relatively standard proof techniques for several subsequently needed results using a mixed volumetric logarithmic barrier we obtain an o n 1 4 m 1 4 l iteration algorithm for linear programs withn variables andm inequality constraints providing an alternative derivation for results first obtained by vaidya and atkinson in addition we show that the same iteration complexity can be attained while holding the work per iteration to o n 2 m as opposed to o nm 2 operations by avoiding use of the true hessian of the volumetric barrier our analysis also provides a simplified proof of self concordancy of the volumetric and mixed volumetric logarithmic barriers originally due to nesterov and nemirovskii

a new method for the real time operation of reservoir systems this paper introduces a new method for the real time operation of reservoir systems the system is represented by a set of stochastic differential equations describing the reservoir and river dynamics in state space form the formulated reservoir operation problem calls for finding policies which maximize the expected benefits of one system s objective while satisfying the remaining objectives at prespecified reliability levels the solution is obtained by a new method named extended linear quadratic gaussian elqg controller elqg draws on and extends stochastic control theory results and it is well suited for the optimization of constrained dynamical systems it is a trajectory iteration algorithm theoretically expected to exhibit reliability and computational efficiency the new method is tested and evaluated in a real world case study

ellipsoidal approximations of convex sets based on the volumetric barrier let c rn be a convex set we assume that x 1 for all x c and that c contains a ball of radius 1 r for x rn r r and b and n n symmetric positive definite matrix let ex b r y y xtby x r2 a rounding of c is an ellipsoid ex b r such that ex b r c ex b r in the case that c is characterized by a separation oracle it is well known that an on3 2 rounding of c can be obtained using the shallow cut ellipsoid method in on3 lnnr oracle calls we show that a modification of the volumetric cutting plane method obtains an on3 2 rounding of c in on2 lnnr oracle calls we also consider the problem of obtaining an on rounding of c when c has an explicit polyhedral description our analysis uses a new characterization of circumscribing ellipsoids centered at or near the volumetric center of a polyhedral set

class field theory for open curves over p adic fields we introduce the idele class group for quasi projective curves over p adic fields and show that the kernel of the reciprocity map is divisible this extends saito s class field theory for projective curves saito in j number theory 21 44 80 1985

on vaidya s volumetric cutting plane method for convex programming we describe a simplified and strengthened version of vaidya s volumetric cutting plane method for finding a point in a convex set x1d49e rn at each step the algorithm has a system of linear inequality constraints which defines a polyhedron x1d4ab x1d49e and an interior point x x1d4ab the algorithm then either drops one constraint or calls an oracle to check if x x1d49e and if not obtain a new constraint that separates x from x1d49e following the addition or deletion of a constraint the algorithm takes a small number of newton steps for the volumetric barrier v progress of the algorithm is measured in terms of changes in v the algorithm is terminated when either it is discovered that x x1d49e or v becomes large enough to demonstrate that the volume of x1d49e must be below some prescribed amount the complexity of the algorithm compares favorably with that of the ellipsoid method especially in terms of the number of calls to the separation oracle compared to vaidya s original analysis we decrease the total number

class field theory for a product of curves over a local field we prove that the kernel of the reciprocity map for a product of curves over a p adic field with split semi stable reduction is divisible we also consider the k1 of a product of curves over a number field

towards a practical volumetric cutting plane method for convex programming we consider the volumetric cutting plane method for finding a point in a convex set cal c subset re n that is characterized by a separation oracle we prove polynomiality of the algorithm with each added cut placed directly through the current point and show that this central cut version of the method can be implemented using no more than 25n constraints at any time

a new algorithm for minimizing convex functions over convex sets let s subseteq mathbb r n be a convex set for which there is an oracle with the following property given any pointz n the oracle returns a yes ifz s whereas ifz s then the oracle returns a no together with a hyperplane that separatesz froms the feasibility problem is the problem of finding a point ins the convex optimization problem is the problem of minimizing a convex function overs we present a new algorithm for the feasibility problem the notion of a volumetric center of a polytope and a related ellipsoid of maximum volume inscribable in the polytope are central to the algorithm our algorithm has a significantly better global convergence rate and time complexity than the ellipsoid algorithm the algorithm for the feasibility problem easily adapts to the convex optimization problem

optimal short term hydro scheduling from the principle of progressive optimality this paper presents an algorithm based on the principle of progressive optimality for determining the optimal short term scheduling of multireservoir power systems the method takes into account water head variations spilling and time delays between upstream and downstream reservoirs the method is computationally efficient and has minimal storage requirements the convergence is monotonic and a global solution is reached contrary to dynamic programing the state variables do not have to be discretized with this method an example consisting of four hydroplants in series is solved and the results are presented

tame class field theory for arithmetic schemes takagi s class field theory gave a decription of the abelian extensions of a number field k in terms of ideal groups in k in the 1980s it k kato and it s saito global class field theory of arithmetic schemes applications of algebraic k theory to algebraic geometry and number theory proc ams ims siam joint summer res conf boulder colo 1983 part i contemp math 55 255 331 1986 zbl 0614 14001 were able to generalize class field theory to higher dimensional fields and to describe their abelian extensions using a generalized idele class group whose definition is quite involved in the case of unramified extensions however the class fields can be described geometrically using chow groups for fields of positive characteristic a similarly geometric description for tamely ramified extensions was obtained by the author and it m spiess j reine angew math 527 13 36 2000 zbl 0961 14013 in this article an analogous result is proved for the case of mixed characteristic

cycles on curves over global fields of positive characteristic let k be a global field of positive characteristic and let x spec k be a smooth projective curve we study the zero dimensional cycle group v x ker sik 1 x k 1 k and the one dimensional cycle group w x coker k 2 k h 0 zar x k 2 addressing the conjecture that v x is torsion and w x is finitely generated the main idea is to use abhyankar s theorem on resolution of singularities to relate the study of these cycle groups to that of the k groups of a certain smooth projective surface over a finite field

some consequences of wiesend s higher dimensional class field theory we use a result of g wiesend to establish the relation between the integral singular homology in degree zero and the abelianized tame fundamental group of a regular connected scheme of finite type over spec mathbb z

a class of volumetric barrier decomposition algorithms for stochastic quadratic programming abstract ariyawansa and zhu have introduced a class of volumetric barrier decomposition algorithms k a ariyawansa y zhu a class of polynomial volumetric barrier decomposition algorithms for stochastic semidefinite programming available as technical report 2006 7 department of mathematics washington state university pullman wa submitted for publication available from for solving two stage stochastic semidefinite programs with recourse ssdps k a ariyawansa y zhu stochastic semidefinite programming a new paradigm for stochastic optimization 4or the quarterly journal of the belgian french and italian or societies in press available as technical report 2004 10 department of mathematics washington state university pullman wa october 2004 available from in this paper we utilize their work for ssdps to derive a class of volumetric barrier decomposition algorithms for solving two stage stochastic quadratic programs with recourse and to establish polynomial complexity of certain members of the class of algorithms

dimensional homotopy t structures in motivic homotopy theory the aim of this work is to construct certain homotopy t structures on various categories of motivic homotopy theory extending works of voevodsky morel deglise and ayoub we prove these t structures possess many good properties some analogous to those of the perverse t structure of beilinson bernstein and deligne we compute the homology of certain motives notably in the case of relative curves we also show that the hearts of these t structures provide convenient extensions of the theory of homotopy invariant sheaves with transfers extending some of the main results of voevodsky these t structures are closely related to gersten weight structures as defined by bondarko

zero cycles sur les fibrations au dessus d une courbe de genre quelconque resume soit x une variete propre et lisse sur un corps de nombres k des conjectures sur l image du groupe de chow des zero cycles de x dans le produit des memes groupes sur tous les completes de k ont ete proposees par colliot thelene kato et saito nous demontrons ces conjectures pour l espace total de fibrations en varietes rationnellement connexes verifiant l approximation faible au dessus de courbes dont le groupe de tate shafarevich est fini sous une hypothese d abelianite sur les fibres singulieres

optimization of hydropower systems operation with a quadratic model abstract this paper is devoted to the development and application of a reservoir optimization model that yields monthly release policies the generalization consists of the capability to handle nonlinear energy generation rates in the objective function maximization of system annual energy generation a quadratic model for the elevation storage average storage curve is used the optimization problem is described and formulated as the optimal control of a multivariable state space model in which the state and control vectors are constrained by sets of equality and inequality relations lagrange and kuhn tucker multipliers are used to adjoin these equality and inequality constraints to the objective functions the resulting cost functional is maximized by using the minimum norm formulation of the functional analysis numerical results are reported for a real system in operation consisting of three rivers each river has two series reservoirs

a polynomial method of approximate centers for linear programming we present a path following algorithm for the linear programming problem with a surprisingly simple and elegant proof of its polynomial behaviour this is done both for the problem in standard form and for its dual problem we also discuss some implementation strategies

voevodsky s motives and weil reciprocity we describe somekawa s k group associated to a finite collection of semiabelian varieties or more general sheaves in terms of the tensor product in voevodsky s category of motives while somekawa s definition is based on weil reciprocity voevodsky s category is based on homotopy invariance we apply this to explicit descriptions of certain algebraic cycles

a finer tate duality theorem for local galois symbols abstract let k be a finite extension of q p let a b be abelian varieties over k with good reduction for any integer m 1 we consider the galois symbol k k a b m h 2 k a m b m where k k a b is the somekawa k group attached to a b this map is a generalization of the galois symbol k 2 m k m h 2 k m 2 of the bloch kato conjecture where k 2 m k is the milnor k group of k in this paper we give a geometric description of the image of this generalized galois symbol by looking at the tate duality pairing h 2 k a m b m hom g k a m b m z m where b is the dual abelian variety of b under this perfect pairing we compute the exact annihilator of the image of the galois symbol in terms of an object of integral p adic hodge theory in this way we generalize a result of tate for h 1 moreover our result has applications to zero cycles on abelian varieties

the volumetric barrier for convex quadratic constraints let where and i is an n n positive semidefinite matrix we prove that the volumetric and combined volumetric logarithmic barriers for are and self concordant respectively our analysis uses the semidefinite programming sdp representation for the convex quadratic constraints defining and our earlier results on the volumetric barrier for sdp the self concordance results actually hold for a class of sdp problems more general than those corresponding to the sdp representation of

chow group of 0 cycles with modulus and higher dimensional class field theory one of the main results of this article is a proof of the rank one case of an existence conjecture on lisse q over bar l sheaves on a smooth variety u over a finite field due to deligne and drinfeld the problem is translated into the language of higher dimensional class field theory over finite fields which describes the abelian fundamental group of u by chow groups of 0 cycles with moduli a key ingredient is the construction of a cycle theoretic avatar of a refined artin conductor in ramification theory originally studied by kazuya kato