a new formula for the analytical solution of the radial dispersion problem a new formula is presented for the analytical solution of the radial dispersion problem which analyzes the dispersive transport of a tracer in radial flow from a recharge well this formula is simpler than a solution presented by previous investigators but the two solutions are shown to be equivalent because the analytical solution consists of an integral of an oscillatory function it is evaluated as an alternating series the terms of which are the integrals over successive half cycles of the integrand an efficient algorithm is used to accelerate convergence of the series the accuracies of previous solutions obtained by finite difference numerical laplace transform and perturbation methods are examined by comparison with the analytical solution numerical values of the solution are tabulated for readers interested in checking the accuracies of solute transport codes

validity of the local equilibrium assumption for modeling sorbing solute transport through homogeneous soils sorption processes that occur during reactive solute movement through porous media can be modeled using either an equilibrium or kinetic approach because of the resulting conceptual and mathematical simplification many transport models assume local chemical equilibrium is valid for describing sorption reactions this paper presents quantitative criteria to assess the validity of the local equilibrium assumption for one dimensional steady flow through homogeneous soils a method is described whereby formulas for solute breakthrough curve time moments can be determined without knowledge of the nalytical solution to the mass transport model this method is applied to several commonly used nonequilibrium formulations as well as the standard linear equilibrium model the formulations considered include both the physical nonequilibrium models where the sorption rate is controlled by diffusive solute transfer between mobile and stagnant fluid zones and the chemical nonequilibrium models where the overall sorption rate is governed by the rate of reaction at the soil solution interfaces criteria for local equilibrium to be valid are derived by comparing the time moment formulas for the nonequilibrium and equilibrium models these criteria explicitly show that basic system parameters e g seepage velocity dispersion coefficient distribution coefficient sorption rate boundary conditions have a significant influence on the attainment of local equilibrium

on the construction of graphs determined by their generalized characteristic polynomials abstract given a graph g with adjacency matrix a g the generalized characteristic polynomial of g is defined as g g t det i a g t d g d g is the degree diagonal matrix g is said to be determined by generalized characteristic polynomial ds for short if for any graph h g h implies that h is isomorphic to g in this paper we show that a connected graph g is ds if and only if the subdivision graph g s is ds this gives a simple method to construct large ds graph from smaller ones some further generalization of this result as wells as some non trivial examples of constructing ds graphs are also provided

source terms in eulerian lagrangian contaminant transport simulation standard eulerian treatment of source terms in eulerian lagrangian numerical simulations results in poor performance at higher courant numbers to regain the customary high accuracy of eulerian lagrangian methods under these conditions a lagrangian treatment of source terms is needed it is also important to include the effects of fluid sources as well as contaminant sources a new lagrangian source formulation is presented which has been implemented in a finite element simulator for contaminant transport in rivers and estuaries test problems demonstrate the high accuracy of the technique under a range of conditions and its applicability to general multi dimensional problems and unstructured grids copyright 2004 john wiley sons ltd

enumeration of graphs with the same ihara zeta function abstract we enumerate all connected graphs with minimal vertex degree 2 on at most 11 vertices and determine their ihara zeta functions we also count the number of such graphs for which there is another graph with the same zeta function we then use these graphs to conjecture properties of the graphs determined by the zeta function in addition we study switching constructions proposed by godsil and mckay to determine whether they preserve the zeta function we show that gm switching is not strong enough to preserve the zeta function but gm switching following the notation of haemers and spence does preserve the zeta function

zeta functions of discrete groups acting on trees abstract this paper generalizes bass work on zeta functions for uniform tree lattices using the theory of von neumann algebras machinery is developed to define the zeta function of a discrete group of automorphisms of a bounded degree tree the main theorems relate the zeta function to determinants of operators defined on edges or vertices of the tree a zeta function associated to a non uniform tree lattice with appropriate hilbert representation is defined zeta functions are defined for infinite graphs with a cocompact or finite covolume group action

graphs determined by their generalized characteristic polynomials abstract for a given graph g with 0 1 adjacency matrix a g the generalized characteristic polynomial of g is defined to be g g t det i a g td g where i is the identity matrix and d g is the diagonal degree matrix of g in this paper we are mainly concerned with the problem of characterizing a given graph g by its generalized characteristic polynomial g we show that graphs with the same generalized characteristic polynomials have the same degree sequence based on which a unified approach is proposed to show that some families of graphs are characterized by g we also provide a method for constructing graphs with the same generalized characteristic polynomial by using gm switching

weighted zeta functions of digraphs abstract we define a weighted zeta function of a digraph and a weighted l function of a symmetric digraph and give determinant expressions of them furthermore we give a decomposition formula for the weighted zeta function of a g cyclic cover of a symmetric digraph for any finite group and g a decomposition formula for the weighted zeta function of an oriented line graph l g of a regular covering g of a graph g is given furthermore we define a weighted l function of an oriented line graph l g of g and present a factorization formula for the weighted zeta function of l g by weighted l functions of l g as a corollay we obtain a factorization formula for the multiedge zeta function of g given by stark and terras

on the ihara zeta function and resistance distance based indices abstract we show that the ihara zeta function of a graph determines a resistance distance based invariant which is a linear combination of the kirchhoff index additive degree kirchhoff index and multiplicative degree kirchhoff index

distinguishing graphs with zeta functions and generalized spectra abstract conjecturally almost all graphs are determined by their spectra this problem has also been studied for variants such as the spectra of the laplacian and signless laplacian here we consider the problem of determining graphs with ihara and bartholdi zeta functions which are also computable in polynomial time these zeta functions are geometrically motivated but can be viewed as certain generalizations of characteristic polynomials after discussing some graph properties determined by zeta functions we show that large classes of cospectral graphs can be distinguished with zeta functions and enumerate graphs distinguished by zeta functions on 11 vertices this leads us to conjecture that almost all graphs which are not determined by their spectrum are determined by zeta functions along the way we make some observations about the usual types of spectra and disprove a conjecture of setyadi and storm about ihara zeta functions determining degree sequences

ruelle zeta functions for finite digraphs abstract three types of expressions for combinatorial zeta functions are considered we investigate conditions for reformulating the exponential expression to the euler product expression and the euler product expression to the determinant expression of hashimoto type the existence of the determinant expression of hashimoto type enables one to unify those zetas within a single framework that is the ruelle zeta functions for quasi finite dynamical systems constructed on finite digraphs which we call the combinatorial zeta functions

the supremum of gaussian processes with a constant variance we obtain an estimate of the distribution of the large values of the supremum of a sample bounded gaussian process having a constant variance this estimate uses the entropy function of the parameter space endowed as usual with the pseudo metric induced by the l2 norm of the increments of the process

a numerical inversion of the laplace transform solution to radial dispersion in a porous medium a special form of the numerical inversion of the laplace transform described by stehfest 1970 is applied to the transformed solution of dispersion in a radial flow system in a porous medium the inversion is extremely simple to use because the weighting coefficients depend only on the number of terms used in the computation and not upon the transform solution as required by most numerical inversion techniques the result obtained by use of this approximate inversion of the radial dispersion problem reproduced the curves obtained previously by hoopes and harleman 1967 with a finite difference scheme

statistical properties of generalized discrepancies when testing that a sample of n points in the unit hypercube 0 1 d comes from a uniform distribution the kolmogorov smirnov and the cramer von mises statistics are simple and well known procedures to encompass these measures of uniformity hickernell introduced the so called generalized p discrepancies these discrepancies can be used in numerical integration through monte carlo and quasi monte carlo methods design of experiments uniformity testing and goodness of fit tests the aim of this paper is to derive the statistical asymptotic properties of these statistics under monte carlo sampling in particular we show that under the hypothesis of uniformity of the sample of points the asymptotic distribution is a complex stochastic integral with respect to a pinned brownian sheet on the other hand if the points are not uniformly distributed then the asymptotic distribution is gaussian

solute transport in divergent radial flow with multistep pumping 1 an efficient approach is developed to analytically evaluate solute transport in a horizontal divergent radial flow field with a multistep injection flow rate and an arbitrary input concentration history by assuming a piecewise steady state flow and transforming the time domain to the cumulative injected flow domain the concentration distribution is found to be completely determined by the total volume of injected flow and independent of specific flow rates thus on the cumulative flow domain the transport problem with a temporally varying velocity field can be transformed into a steady state flow problem linear convolution can then be applied on the cumulative injected flow domain to evaluate the solution for an arbitrarily time dependent input concentration solutions on the regular time domain can be conveniently obtained by mapping the solution on the cumulative injected flow domain to the time domain furthermore we theoretically examine the conditions for the assumption of piecewise steady state flow to be valid on the basis of the critical time scale of the pseudosteady state condition defined as when velocity changes accomplish 99 of their steady state differences and the relative error in the mean travel time of plume front we obtain conditions for neglecting the transitional period between two pumping steps such conditions include the following 1 the duration of a pumping step tp must be longer than the critical time scale tc i e tp tc 25r2s t where r is the radial distance s is the storage coefficient and t is the transmissivity or similarly a maximum problem domain needs to be defined for a given pumping strategy 2 the maximum well pumping rate qmax should satisfy qmax t 25s where is the effective porosity when both conditions are satisfied transitional periods may be neglected

zeta functions of several corona type graphs abstract in this paper we present the decomposition formulae for the zeta functions of families of graphs obtained through corona type construction furthermore we construct some families of graphs with the same zeta function by the spectra of these graphs

zeta functions of digraphs abstract we define a zeta function of a digraph and an l function of a symmetric digraph and give determinant expressions of them furthermore we give a decomposition formula for the zeta function of a g cyclic cover of a symmetric digraph for any finite group and g

weighted zeta functions for quotients of regular coverings of graphs abstract let g be a connected graph we reformulate stark and terras galois theory for a quotient h of a regular covering k of a graph g by using voltage assignments as applications we show that the weighted bartholdi l function of h associated to the representation of the covering transformation group of h is equal to that of g associated to its induced representation in the covering transformation group of k furthermore we express the weighted bartholdi zeta function of h as a product of weighted bartholdi l functions of g associated to irreducible representations of the covering transformation group of k we generalize stark and terras galois theory to digraphs and apply to weighted bartholdi l functions of digraphs

zeta equivalent digraphs simultaneous cospectrality abstract we introduce a zeta function of digraphs that determines and is determined by the spectra of all linear combinations of the adjacency matrix its transpose the out degree matrix and the in degree matrix in particular zeta equivalence of graphs encompasses simultaneous cospectrality with respect to the adjacency the laplacian the signless laplacian and the normalized laplacian matrix in addition we express zeta equivalence in terms of markov chains and in terms of invasions where each edge is replaced by a fixed digraph we finish with a method for constructing zeta equivalent digraphs

the characteristic polynomial of a generalized join graph abstract for a graph g with adjacency matrix a g and degree diagonal matrix d g cvetkovic et al introduced a bivariate polynomial g x t d e t x i a g t d g where i is the identity matrix the polynomial g x t not only generalizes the characteristic polynomials of some well known matrices related to g such as the adjacency the laplacian matrices but also has an elegant combinatorial interpretation as being equivalent to the bartholdi zeta function let g h g 1 g 2 g k be the generalized join graph of g 1 g 2 g k determined by graph h in this paper we first give a decomposition formula for g x t the decomposition formula provides us a new method to construct infinitely many pairs of non regular cospectral graphs then as applications explicit expressions for g x t of some special kinds of graphs are given

zeta functions of finite graphs and coverings iii abstract a graph theoretical analog of brauer siegel theory for zeta functions of number fields is developed using the theory of artin l functions for galois coverings of graphs from parts i and ii in the process we discuss possible versions of the riemann hypothesis for the ihara zeta function of an irregular graph

which graphs are determined by their spectrum for almost all graphs the answer to the question in the title is still unknown here we survey the cases for which the answer is known not only the adjacency matrix but also other types of matrices such as the laplacian matrix are considered

ihara zeta functions of coronae abstract we derive a factorization formula for the ihara zeta function of the corona of two graphs when the two graphs are regular this factorization formula involves the graphs adjacency spectra as an application we show that if each composing graph of a corona of regular graphs is replaced with a cospectral mate then the ihara zeta function of the corona does not change we also give a formula for the weighted kirchhoff index of the corona of two regular graphs

bartholdi zeta and l functions of weighted digraphs their coverings and products since a zeta function of a regular graph was introduced by ihara y ihara on discrete subgroups of the two by two projective linear group over p adic fields j math soc japan 19 1966 219 235 many kinds of zeta functions and l functions of a graph or a digraph have been defined and investigated most of the works concerning zeta and l functions of a graph contain the following 1 defining a zeta function 2 defining an l function associated with a regular graph covering 3 providing their determinant expressions and 4 computing the zeta function of a graph covering and obtaining its decomposition formula as a product of l functions as a continuation of those works we introduce a zeta function of a weighted digraph and an l function associated with a weighted digraph bundle a graph bundle is a notion containing a cartesian product of graphs and a regular or irregular graph covering also we provide determinant expressions of the zeta function and the l function moreover we compute the zeta function of a weighted digraph bundle and obtain its decomposition formula as a product of the l functions