a mathematical formulation for reactive transport that eliminates mineral concentrations we present a concise and general mathematical formulation for reactive transport in groundwater for general applications by means of linear algebraic manipulations of the stoichiometric coefficients of the chemical reactions we are able to reduce the number of unknowns of the equations to be solved to the number of degrees of freedom according to thermodynamic rules we present six formulations that differ from each other by number and type of unknowns and discuss their advantages and disadvantages with respect to the two most important numerical solution methods the sequential iteration approach sia and the direct substitution approach dsa our conclusion is that the proposed reduction of the number of variables is of special interest for the dsa we have applied one of these formulations to an example of the flushing of saline water by fresh water

total nonnegativity of finite hurwitz matrices and root location of polynomials abstract in 1970 b a asner jr proved that for a real quasi stable polynomial i e a polynomial whose zeros lie in the closed left half plane of the complex plane its finite hurwitz matrix is totally nonnegative i e all its minors are nonnegative and that the converse statement is not true in this work we explain this phenomenon in detail and provide necessary and sufficient conditions for a real polynomial to have a totally nonnegative finite hurwitz matrix

hermite biehler routh hurwitz and total positivity simple proofs of the hermite biehler and routh hurwitz theorems are presented the total nonnegativity of the hurwitz matrix of a stable real polynomial follows as an immediate corollary

borcherds products and arithmetic intersection theory on hilbert modular surfaces we prove an arithmetic version of a theorem of hirzebruch and zagier saying that hirzebruch zagier divisors on a hilbert modular surface are the coecients of an elliptic modular form of weight two moreover we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its petersson metric on a regular model of a hilbert modular surface and study faltings heights of arithmetic hirzebruch zagier divisors

a global strategy for solving reactive transport equations reactive transport models are complex nonlinear partial differential algebraic equations pdae coupling the transport engine with the geochemical operator we propose an efficient and robust global numerical method based on a method of lines and differential algebraic equations dae solvers combined with a newton method using a powerful sparse linear solver numerical experiments show the performances of the method we also propose a unified framework to describe classical methods such as sequential non iterative approach sequential iterative approach direct substitution approach and compare them with our global method

an explicit koppelman formula for ddc and green currents on mathbb p n we compute a quite explicit koppelman formula for dd c on projective space and obtain green currents for closed p p currents

a fixed point formula of lefschetz type in arakelov geometry iv the modular height of c m abelian varieties we give a new proof of a slightly weaker form of a theorem of p colmez c2 par 2 this theorem corollary 5 8 gives a formula for the faltings height of abelian varieties with complex multiplication by a c m eld whose galois group over q is abelian it reduces to the formula of chowla and selberg in the case of elliptic curves we show that the formula can be deduced from the arithmetic

a fixed point formula of lefschetz type in arakelov geometry i statement and proof we consider arithmetic varieties endowed with an action of the group scheme of n th roots of unity and we define equivariant arithmetic k 0 theory for these varieties we use the equivariant analytic torsion to define direct image maps in this context and we prove a riemann roch theorem for the natural transformation of equivariant arithmetic k 0 theory induced by the restriction to the fixed point scheme this theorem can be viewed as an analog in the context of arakelov geometry of the regular case of the theorem proved by p baum w fulton and g quart in bafq we show that it implies an equivariant refinement of the arithmetic riemann roch theorem in a form conjectured by j m bismut cf b2 par l p 353 and also ch soule s question in sabk 1 5 p 162

integrality of a ratio of petersson norms and level lowering congruences we prove integrality of the ratiof f g g outside an explicit finite set of primes where g is an arithmetically normalized holomorphic newform on a shimura curve f is a normalized hecke eigenform on gl 2 with the same hecke eigenvalues as g and denotes the petersson inner product the primes dividing this ratio are shown to be closely related to certain level lowering con gruences satisfied by f and to the central values of a family of rankin selberg l functions finally we give two applications the first to proving the integral ity of a certain triple product l value and the second to the computation of the faltings height of jacobians of shimura curves

total nonnegativity of matrices related to polynomial roots and poles of rational functions abstract in this paper totally nonnegative positive matrices are considered which are matrices having all their minors nonnegative positive the almost totally positive matrices form a class between the totally nonnegative matrices and the totally positive ones an efficient determinantal test based on the cauchon algorithm for checking a given matrix for falling in one of these three classes of matrices is applied to matrices which are related to roots of polynomials and poles of rational functions specifically the hankel matrix associated with the laurent series at infinity of a rational function and matrices of hurwitz type associated with polynomials in both cases it is concluded from properties of one or two finite sections of the infinite matrix that the infinite matrix itself has these or related properties then the results are applied to derive a sufficient condition for the hurwitz stability of an interval family of polynomials finally interval problems for a subclass of the rational functions viz r functions are investigated these problems include invariance of exclusively positive poles and exclusively negative roots in the presence of variation of the coefficients of the polynomials within given intervals

random walks kleinian groups and bifurcation currents let be a holomorphic family of representations of a finitely generated group g into psl 2 parameterized by a complex manifold we define a notion of bifurcation current in this context that is a positive closed current on describing the bifurcations of this family of representations in a quantitative sense it is the analogue of the bifurcation current introduced by demarco for holomorphic families of rational mappings on 1 our definition relies on the theory of random products of matrices so it depends on the choice of a probability measure on g

hadamard powers and totally positive matrices considered are continuous positive hadamard powers of entry wise positive nonnegative matrices those that are eventually in the sense of all hadamard powers beyond some point totally positive totally nonnegative doubly nonnegative and doubly positive are characterized for example for matrices with at least four rows and four columns hadamard powers greater than one of totally positive matrices need not be totally positive but they are eventually totally positive

intrinsic volumes and successive radii motivated by a problem of teissier to bound the intrinsic volumes of a convex body in terms of the inradius and the circumradius of the body we give upper and lower bounds for the intrinsic volumes of a convex body in terms of the elementary symmetric functions of the so called successive inner and outer radii these results improve on former bounds and in particular they also provide bounds for the elementary symmetric functions of the roots of steiner polynomials in terms of the elementary symmetric functions of these radii

analysis of box schemes for reactive flow problems key properties of the box scheme are shown to be advantageous for reactive flow problems unconditional stability and compact conservation are shown by a detailed modified equation analysis to enable the scheme to reflect exactly the reduced speed enhanced diffusion and dispersion which are typical of such hyperbolic conservation laws with relaxation a novel modified equation analysis is also used to show how the spurious checkerboard mode behaves and can be controlled numerical experiments for some nonlinear one dimensional problems and a two dimensional problem demonstrate that the behavior of the scheme deduced from a simple model problem has general validity

hermitian vector bundles and extension groups on arithmetic schemes i geometry of numbers we define and investigate extension groups in the context of arakelov geometry the arithmetic extension groups ext xi f g we introduce are extensions by groups of analytic types of the usual extension groups extxi f g attached to ox modules f and g over an arithmetic scheme x in this paper we focus on the first arithmetic extension group ext x1 f g the elements of which may be described in terms of admissible short exact sequences of hermitian vector bundles over x and we especially consider the case when x is an arithmetic curve namely the spectrum specok of the ring of integers in some number field k then the study of arithmetic extensions over x is related to old and new problems concerning lattices and the geometry of numbers namely for any two hermitian vector bundles f and g over x specok we attach a logarithmic sizesf g to any element of ext x1 f g and we give an upper bound on sf g in terms of slope invariants of f and g we further illustrate this notion by relating the sizes of restrictions to points in p1 z of the universal extension over pz1 to the geometry of psl2 z acting on poincare s upper half plane and by deducing some quantitative results in reduction theory from our previous upper bound on sizes finally we investigate the behaviour of size by base change i e under extension of the ground field k to a larger number field k when the base field k is q we establish that the size which cannot increase under base change is actually invariant when the field k is an abelian extension of k or when f g is a direct sum of root lattices and of lattices of voronoi s first kind the appendices contain results concerning extensions in categories of sheaves on ringed spaces and lattices of voronoi s first kind which might also be of independent interest

calculus on arithmetic surfaces in a2 and a3 arakelov introduces an intersection calculus for arithmetic surfaces that is for stable models of curves over a number field in this paper we intend to show that his intersection product has a lot of useful properties more precisely we show that the following properties from the theory of algebraic surfaces have an analogue in our situation

global representation of segre numbers by monge ampere products on a reduced analytic space x we introduce the concept of a generalized cycle which extends the notion of a formal sum of analytic subspaces to include also a form part we then consider a suitable equivalence relation and corresponding quotient mathcal b x that we think of as an analogue of the chow group and a refinement of de rham cohomology this group allows us to study both global and local intersection theoretic properties we provide many mathcal b analogues of classical intersection theoretic constructions for an analytic subspace v subset x we define a mathcal b segre class which is an element of mathcal b x with support in v it satisfies a global king formula and in particular its multiplicities at each point coincide with the segre numbers of v when v is cut out by a section of a vector bundle we interpret this class as a monge ampere type product for regular embeddings we construct a mathcal b analogue of the gysin morphism

structured matrices continued fractions and root localization of polynomials we give a detailed account of various connections between several classes of objects hankel hurwitz toeplitz vandermonde and other structured matrices stietjes and jacobi type continued fractions cauchy indices moment problems total positivity and root localization of univariate polynomials along with a survey of many classical facts we provide a number of new results

twisted hilbert modular surfaces arithmetic intersections and the jacquet langlands correspondence abstract we study arithmetic intersections on quaternionic hilbert modular surfaces and shimura curves over a real quadratic field our first main result is the determination of the degree of the top arithmetic todd class of an arithmetic twisted hilbert modular surface this quantity is then related to the arithmetic volume of a shimura curve via the arithmetic grothendieck riemann roch theorem and the jacquet langlands correspondence

on sufficient conditions for the total positivity and for the multiple positivity of matrices abstract the following theorem is proved theorem suppose m a i j be a k k matrix with positive entries and a i j a i 1 j 1 4 cos 2 k 1 a i j 1 a i 1 j 1 i k 1 1 j k 1 then det m 0 the constant 4 cos 2 k 1 in this theorem is sharp a few other results concerning totally positive and multiply positive matrices are obtained

heights and metrics with logarithmic singularities we prove lower bound and finiteness properties for arakelovian heights with respect to pre log log hermitian ample line bundles these heights were introduced by burgos kramer and kuhn in 2 in their extension of the arithmetic intersection theory of gillet and soule 8 aimed to deal with hermitian vector bundles equipped with metrics admitting suitable logarithmic singularities our results generalize the corresponding properties for the heights of cycles in bost gillet soule 1 as well as the properties established by faltings 7 for heights of points attached to hermitian ample line bundles whose metrics have logarithmic singularities we also discuss various geometric constructions where such pre log log hermitian ample line bundles naturally arise msc 14g40 primary 11j25 11j97 secondary

intersection theory in differential algebraic geometry generic intersections and the differential chow form in this paper an intersection theory for generic differential polynomials is presented the intersection of an irreducible differential variety of dimension d and order h with a generic differential hypersurface of order s is shown to be an irreducible variety of dimension d 1 and order h s as a consequence the dimension conjecture for generic differential polynomials is proved based on intersection theory the chow form for an irreducible differential variety is defined and most of the properties of the chow form in the algebraic case are established for its differential counterpart furthermore the generalized differential chow form is defined and its properties are proved as an application of the generalized differential chow form the differential resultant of n 1 generic differential polynomials in n variables is defined and properties similar to that of the macaulay resultant for multivariate polynomials are proved

computing green currents via the heat kernel let x be a compact kahler manifold for an analytic cycle y x of complex codimension k the poincare duality assigns a class in the de rham cohomology which can be represented by a harmonic k k form y a green current gy connects both objects by the equality ddgy y y thus we can reconstruct y and its harmonic projection y from this equation because y is the locus where ddgy is not smooth while y is determined by its values on the dense open set x y furthermore the above equality tells us that y and y differ only by some exact current green currents for varieties of arbitrary dimension were systematically developed by h gillet and c soule in 3 these currents play a central role in arakelov theory see 10 and 7 on the one hand the existence of green currents follows more or less formally from the hodge decomposition for currents to do intersection theory on the other hand we need currents which behave well green forms and green currents of logarithmic type are examples of these currents see 2 and 3 here we present a method to find a canonical green current gy which depends only on the kahler manifold x and the cycle y this current gy is given by k k forms with l coefficients which are smooth on x y we start with repeating some basic results on kahler manifolds in 1 which can be found in the textbooks 5 or 11 furthermore we recall the main properties of the heat kernel before we consider the heat flow of dirac currents in section 2 obtaining a green operator for these currents in 3 we define the canonical harmonic green current and show that its harmonic projection is zero in section 4 we apply the heat kernel to intersections of properly intersecting cycles this is needed to derive a formula for the product of green currents in 5 however we have to restrict to cycles that intersect properly hence our results are weaker than those of 3 as we used a different approach we decided to present them here in section 6 we give examples which we found by a good guess 6 1 or because we know all eigen functions of the laplace operator 6 2 or from the explicit formula of the heat kernel 6 3 the last example shows how our techniques can be extended to non compact kahler manifolds for which a heat kernel exists we conclude in section 7 with some questions and remarks acknowledgment the author wishes to thank w gubler j kramer and u kuhn for many discussions which contributed to this paper the comments of the referee helped to clarify the exposition

accuracy of operator splitting for advection dispersion reaction problems an operator splitting approach is often used for the numerical solution of advection dispersion reaction problems operationally this approach advances the solution over a single time step in two stages one involving the solution of the nonreactive advection dispersion equation and the other the solution of the reaction equations the first stage is usually solved with a finite difference finite element or related technique while the second stage is normally solved with an ordinary differential equation integrator the only generally published guidelines on numerical accuracy suggest that the discretization errors associated with each stage must be small in order to achieve high accuracy of the overall solution however in this note we demonstrate that there is an inherent mass balance error present in the operator splitting algorithm for problems involving continuous mass influx boundary conditions the mass balance error does not exist for instantaneous mass input problems these conclusions are based upon analysis of a simple first order decay problem for which each stage of the calculation can be performed analytically i e without discretization error for this linear decay problem we find that the product of the first order decay coefficient k times t must be less than approximately 0 1 in order for the mass balance error to be less than 5 we also present a variant of the normal operator splitting algorithm in which the order of solving the advection dispersion and reaction operators is reversed at each time step this modification reduces the mass balance error by more than a factor of 10 for a wide range of k t values

the wills functional and gaussian processes the wills functional from the theory of lattice point enumeration can be adapted to produce the following exponential inequality for zero mean gaussian processes formula math an application is a new proof of the deviation inequality for the supremum of a gaussian process above its mean formula math where a 0 and 2 sup t t 2

a sufficient condition for a polynomial to be stable abstract a real polynomial is called hurwitz stable if all its zeros have negative real parts for a given n n we find the smallest possible constant d n 0 such that if the coefficients of f z a 0 a 1 z a n z n are positive and satisfy the inequalities a k a k 1 d n a k 1 a k 2 for k 1 2 n 2 then f z is hurwitz

on the roots of the wills functional abstract we investigate the roots of wills polynomials of convex bodies we study the structure showing that the set of roots in the upper half plane is a convex cone monotonous with respect to the dimension in particular we give its precise description for dimensions n 2 3 we also show that for n 7 this cone is completely contained in the open left half plane which is not true in dimensions 14 moreover we study the size of the roots of the wills polynomial bounding them in terms of functionals like the in and circumradius of the set we also relate the roots of the steiner and the wills polynomials

faltings heights of cm cycles and derivatives of l functions we study the faltings height pairing of arithmetic special divisors and cm cycles on shimura varieties associated to orthogonal groups we compute the archimedean contribution to the height pairing and derive a conjecture relating the total pairing to the central derivative of a rankin l function we prove the conjecture in certain cases where the shimura variety has dimension 0 1 or 2 in particular we obtain a new proof of the gross zagier formula

modeling of chemically reactive groundwater transport a complete reactive groundwater transport model must account for both chemical and transport processes for the chemical processes one has to decide whether to formulate them kinetically or to assume a local chemical equilibrium state this decision in the chemical model part determines the mathematical structure of the overall model in a kinetic formulation the linear partial differential equations of the transport have to be coupled with a nonlinear system of ordinary differential equations describing the kinetic development whereas in an equilibrium formulation the equations of the transport are coupled to a nonlinear system of algebraic equations describing the equilibrium state basically two kinds of methods for solving reactive transport systems may be distinguished namely one step methods which simultaneously solve the transport and the chemical model parts and two step methods which solve these model parts separately we here present a sequential two step method for kinetic transport models and an iterative two step method for equilibrium transport models we conduct a timescale analysis to check whether the error of the sequential two step method is tolerable and whether a given kinetic transport system can be reduced to an equilibrium one the numerical methods and the timescale analysis are applied to two test cases zysset et al 1994 present a further application of the kinetic transport model to laboratory column experiments governed by biodegradation