a sufficient condition for global regularity of the neumann operator abstract a theory of global regularity of the neumann operator is developed which unifies the two principal approaches to date namely the one via compactness due to kohn nirenberg j j kohn l nirenberg non coercive boundary value problems comm pure appl math 18 1965 443 492 and catlin david catlin global regularity of the neumann problem in y t siu ed complex analysis of several variables in proc sympos pure math vol 41 amer math soc providence ri 1984 pp 39 49 and the one via plurisubharmonic defining functions and or vector fields that commute approximately with due to boas and the author harold p boas emil j straube sobolev estimates for the neumann operator on domains in c n admitting a defining function that is plurisubharmonic on the boundary math z 206 1 1991 81 88 harold p boas emil j straube de rham cohomology of manifolds containing the points of infinite type and sobolev estimates for the neumann problem j geom anal 3 3 1993 225 235

when are multidegrees positive abstract let k be an arbitrary field p p k m 1 k k p k m p be a multiprojective space over k and x p be a closed subscheme of p we provide necessary and sufficient conditions for the positivity of the multidegrees of x as a consequence of our methods we show that when x is irreducible the support of multidegrees forms a discrete algebraic polymatroid in algebraic terms we characterize the positivity of the mixed multiplicities of a standard multigraded algebra over an artinian local ring and we apply this to the positivity of mixed multiplicities of ideals furthermore we use our results to recover several results in the literature in the context of combinatorial algebraic geometry

l 2 estimates for the boundary laplacian operator on hypersurfaces on donne une condition necessaire pour l estimation maximale pour le laplacien limite sur une hypersurface lisse m dans c n 1 non necessairement pseudoconvexe pour certaines classes d hypersurfaces on montre que la condition est aussi suffisante

estimates for the bar partial neumann problem in pseudoconvex domains of finite type in c2problem in pseudoconvex domains of finite type in c2

extended rees algebras and mixed multiplicities the aim of this paper is to study mixed multiplicities of ideals and use them to calculate multiplicities of certain homogeneous ideals of extended rees algebras and to give a complete characterization of those parameter ideals whose extended rees algebras are cohen macaulay with minimal multiplicity at their maximal homogeneous ideals let r m be a local ring of dimension d let i be an m primary ideal it is well known that the length of the artinian ring r f i r f is a polynomial of degree d in r for all large r the coefficient of nd d in this polynomial called the multiplicity of i denoted by e i is a well understood and useful invariant of suppose j is another m primary ideal then it is natural to consider l r fj s for positive integers r and s it is proved in b that for large values of r and s i r fj is given by a polynomial p r s of total degree d in r and s moreover the terms of total degree d in p r s have the form

microlocalisation et estimations pour mathtype mtef 2 1 feaafiart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbagafyoaiyrbae badawgaawcbagaamoyaaqabaaaaa 387e bar partial _b dans quelques hypersurfaces pseudoconvexes nous etudions des estimations precises pour bar partial b sur des hypersurfaces dont la matrice de levi dans une base a une certaine forme en particulier nous donnons par la methode de microlocalisation une demonstration tres simple des estimations dites maximales lorsque les valeurs propres sont comparables nous obtenons en fait une precision supplementaire inegalite 3 17 qui permet de considerer des cas plus generaux finalement de telles estimations on deduit des estimations sous elliptiques optimales pour bar partial b

hardy spaces and the szegő projection of the non smooth worm domain dβ we define hardy spaces hp d p 1 on the non smooth worm domain d z1 z2 c2 imz1 log z2 2 2 log z2 2 2 and we prove a series of related results such as the existence of boundary values on the distinguished boundary d of the domain and a fatou type theorem i e pointwise convergence to the boundary values thus we study the szeg projection operator s and the associated szeg kernel kd more precisely if hp d denotes the space of functions which are boundary values for functions in hp d we prove that the operator s extends to a bounded linear operator s lp d hp d for every p 1 and s wk p d wk p d for every k 0 here wk p denotes the sobolev space of order k and underlying lp norm p 1 as a consequence of the lp boundedness of s we prove that hp d c d is a dense subspace of hp d

lp and weighted estimates for barred derivatives abstract we generalize the basic l 2 inequality for barred derivatives that holds on bounded pseudoconvex domains the analogue in l p sobolev norms is established for smooth bounded pseudoconvex domains of finite type with comparable levi eigenvalues a weighted l 2 version and l p estimates with loss are obtained on any smooth bounded weakly q convex domain where the weights are fractional powers of the distance to the boundary

on maximal sobolev and holder estimates for the tangential cauchy riemann operator and boundary laplacian let m be the boundary of a smoothly bounded pseudoconvex domain in c n n 3 or more generally any compact pseudoconvex cr manifold of dimension 2 n 1 for which the range of inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i is closed in l 2 in this article we study the l p sobolev and holder regularity properties of inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i and b near a point of finite type under a comparable eigenvalues condition on the levi form we show that if all possible sums of q 0 eigenvalues of the levi matrix are comparable to its trace near a point of finite commutator type condition d q 0 then the inverse k q of b on 0 q forms for q 0 q n 1 q 0 satisfies sharp kernel estimates in terms of the quasi distance associated to the hormander sum of squares operator in particular we obtain the maximal l p estimates for b which were conjectured in the 1980s we also prove sharp estimates for certain parts of the kernels of k q 0 1 and k n q 0 and give some applications concerning domains with at most one degenerate eigenvalue finally we establish the composition and mapping properties of a class of singular integral nonisotropic smoothing operators that arises naturally in complex analysis these results yield optimal regularity of k q and related operators in the sobolev and lipschitz norms both isotropic and nonisotropic

the szegő kernel as a singular integral kernel on a family of weakly pseudoconvex domains the szego kernels on the weakly pseudoconvex domains im z2 izl12k k e z have been computed by greiner and stein after constructing a global nonisotropic pseudometric suitable for calderon zygmund singular integral theory on the boundaries of the domains we study principal value operators associated to these szego kernels we prove that the principal value operators are bounded on lp for 1 p oo and that they preserve certain nonisotropic lipschitz classes we then derive a plemelj formula that relates the principal value operators to the szego projections from this formula we deduce that the szego projections are also bounded on lp for 1 p oo and that they preserve the same nonisotropic lipschitz classes

a geometric theory of the buchsbaum rim multiplicity abstract we develop a self contained theory of a generalized buchsbaum rim multiplicity based on elementary abstract algebraic geometry we define the multiplicity as the sum of certain natural intersection numbers and recover the traditional definition in terms of the leading coefficient of the polynomial that gives the appropriate lengths we interpret the partial sums as the multiplicities in certain closely associated cases we prove an additivity formula in the rings and relate constancy to a generalized notion of reductions we establish a polar multiplicity formula and a mixed multiplicity formula and we determine when each of the four types of multiplicities vanish we end by generalizing the height inequality for maximal minors and a celebrated theorem of boger

the diederich fornaess index and the global regularity of the bar partial neumann problem we describe along the guidelines of kohn quantitative estimates for global regularity analysis and geometry in several complex variables pp 97 128 trend math birkhauser boston 1999 the constant mathcal e s which is needed to control the commutator of a totally real vector field t mathcal e with bar partial in order to have h s a priori estimates for the bergman projection b k k ge q 1 on a smooth q convex domain d subset subset mathbb c n this statement not explicit in kohn quantitative estimates for global regularity analysis and geometry in several complex variables pp 97 128 trend math birkhauser boston 1999 yields regularity of b k in specific sobolev degree s next we refine the pseudodifferential calculus at the boundary in order to relate for a defining function r of d the operators t frac delta 2 and r frac delta 2 we are thus able to extend to general degree k ge 0 of b k the conclusion of quantitative estimates for global regularity analysis and geometry in several complex variables pp 97 128 trend math birkhauser boston 1999 which only holds for q 1 and k 0 if for the diederich fornaess index delta of d we have 1 delta frac 1 2 le mathcal e s then b k is h s regular

a parametrix for the neumann problem on pseudoconvex domains of finite type abstract we construct a parametrix for the neumann problem on any pseudoconvex domain of finite type which reduces completely the study of isotropic lp sobolev and holder estimates to those for b and b we also establish the maximal nonisotropic estimates in the case of d q domains and provide a precise comparison of the bergman and szego projections and of the canonical solutions to with respect to these two operators the argument is substantially simpler than the known ones for the cases of strongly pseudoconvex domains and pseudoconvex domains of finite type in c 2

mixed multiplicities of ideals versus mixed volumes of polytopes the main results of this paper interpret mixed volumes of lattice polytopes as mixed multiplicities of ideals and mixed multiplicities of ideals as samuel s multiplicities in particular we can give a purely algebraic proof of bernstein s theorem which asserts that the number of common zeros of a system of laurent polynomial equations in the torus is bounded above by the mixed volume of their newton polytopes

a note on plurisubharmonic defining functions in mathbb c n let omega subset subset mathbb c n n 3 be a smoothly bounded domain suppose that admits a smooth defining function which is plurisubharmonic on the boundary of then a diederich fornaess exponent can be chosen arbitrarily close to 1 and the closure of admits a stein neighborhood basis

a note on plurisubharmonic defining functions in mathbb c 2 let mathbb c 2 be a smoothly bounded domain suppose that admits a smooth defining function which is plurisubharmonic on the boundary of then the diederich fornaess exponent can be chosen arbitrarily close to 1 and the closure of admits a stein neighborhood basis

the szegő projection sobolev estimates in regular domains the szego projection preserves global smoothness in weakly pseudoconvex domains that are regular in the sense of diederich fornxess and catlin it preserves local smoothness near boundary points of finite type the bergman projection being linked to the 8 problem plays an important role in several complex variables as demonstrated by recent applications to the boundary behavior of holomorphic maps 7 16 the szego projection is interesting both by analogy and by its connection with the ab problem and hence with unsolvable equations of lewy type while in strictly pseudoconvex domains the bergman and szego projections are both well understood in general much more is known about the bergman projection this is no surprise for the theory of the 8 problem is further advanced than the theory of the 8b problem nonetheless i believe that the szego projection ought not be any more mysterious than the bergman projection this paper is intended to support this contention the most important domains for which the bergman projection is known to be regular are domains with a good a neumann operator here it is shown that in such domains the szego projection also is regular more precisely in smooth bounded pseudoconvex domains satisfying catlin s property p the most general condition presently known that guarantees global regularity of the neumann operator the szego projection is shown to be globally regular theorem 4 1 moreover at boundary points of finite type the szego projection is locally regular theorem 5 1 in both cases the szego projection exactly preserves the degree of differentiability measured in sobolev norms the method of proof is not the obvious one of directly generalizing from the strictly peudoconvex case for there are serious obstacles to such a generalization for instance the approach of analysis on the heisenberg group used by phong and stein 29 to derive estimates for both the bergman and szego projections cannot yet be extended because the theory of singular integrals on weakly pseudoconvex surfaces is still in its early stages 28 15 similarly one does not know how to carry over the fourier integral operator approach of boutet de monvel and sjostrand 10 to the weakly pseudoconvex case explicit construction of cauchy fantappie forms received by the editors march 11 1986 paper presented april 11 1986 to the 826th meeting of the american mathematical society indianapolis special session on several complex variables 1980 mathematics subject classification 1985 revision primary 32a25 32h10 partially supported by national science foundation grants mcs 8201063 and dms 8501758 1987 american mathematical society 0002 9947 87 1 00 25 per page

parameter estimation in flow through partially saturated porous materials a class of numerical simulators were developed and critically evaluated to be incorporated as the solver of a forward problem in the framework of an inverse modeling strategy the strategy couples a mass lumped galerkin linear finite element solution of the mixed form richards equation with an experimental time space series and the osborne more revised form of the levenberg marquardt algorithm to retrieve hydraulic parameters of a partially saturated porous medium the numerical simulator shows excellent agreement with a reference solution obtained on a dense grid and infinitesimal time step in terms of fluid pressure head fluid content and fluid volumetric flux density and perfectly conserves the global mass an adaptive algorithm was implemented to estimate sensitivity matrix in the inverse algorithm a multi criterion stopping rule was developed and successfully implemented to end the inverse code at the solution the result of the optimization was compared with a large scale in situ soil moisture space time series measured during the course of a drainage experiment and excellent agreements were found analysis of the parameter response surfaces and hyper space plots closeness of the gradient of the penalty function at minimum to zero and positive definiteness of the approximation for the hessian at the solution eigs h 0 indicate that the obtained solution is a strong local minimum a state of the art sensitivity analysis carried out to quantify sensitivity of the state variable with respect to uncertainty and changes in different model parameters

maximal hypoellipticity for the neumann problem abstract we establish maximal hypoellipticity for the neumann problem on smooth bounded pseudoconvex domains in c n under the weakest possible condition on the levi form in particular maximal hypoellipticity holds on the level of n 1 forms for pseudoconvex domains of finite commutator type

estimates for the bergman and szego kernels in mathbf c 2 the purpose of this paper some of whose conclusions were announced in nrsw is to study the bergman and szegd projection operators on pseudoconvex domains q of finite type in c2 the results we obtain are of three kinds i the size estimates of the bergman and szeg6 kernels and their derivatives ii the cancellation properties of those kernels expressed in terms of the actions of these operators on suitable bump functions these properties have an interest in their own right but are also crucial in iii below iii the sharp mapping properties of these operators on functions spaces such as lp the nonisotropic sobolev spaces and the nonisotropic lipschitz spaces which are naturally attached to the geometry of the boundary this also leads ultimately to sharp results in the regularity properties of solutions of the equation du f in q and 9bu f on the boundary let us describe these matters in more detail our starting points are certain basic geometric constructs associated to q a metric p defined in terms of the vector fields x1 and x2 which are the real and imaginary parts of the tangential levi vector field on d 2 and a function a p 8 a polynomial in 8 for p e d 2 which represents the higher levi invariant attached to d 9 the significance of these to the geometry of d q can be understood from the following facts the ball b p 8 c d q centered at p of radius 8 in the metric p when viewed in the appropriate coordinates has width 8 in the complex tangential directions but its width is a p 8 in the complementary direction thus the volume of the ball is 82a p 8 among other crucial properties

hilbert polynomials of non standard bigraded algebras this paper investigates hilbert polynomials of bigraded algebras which are generated by elements of bidegrees 1 0 d 1 1 ldots d r 1 where d 1 ldots d r are non negative integers the obtained results can be applied to study rees algebras of homogeneous ideals and their diagonal subalgebras

milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs the chromatic polynomial g q of a graph g counts the num ber of proper colorings of g we give an affirmative answer to the conjecture of read and rota heron welsh that the absolute values of the coefficients of the chromatic polynomial form a log concave sequence the proof is obtained by identifying g q with a sequence of numerical invariants of a projective hypersurface analogous to the milnor number of a local analytic hypersurface as a by product of our approach we obtain an analogue of kouchnirenko s

a sufficient condition for compactness of the neumann operator we show that the existence of a certain family of plurisubharmonic functions on a bounded domain in cn implies that the neumann operator associated to the domain is compact our condition generalizes previous work of catlin on compactness of the neumann operator

regularity of canonical operators and nebenhulle hartogs domains abstract we relate the regularity of the bergman projection operator and the canonical solution operator to the nebenhulle of complete hartogs domains

comparing the bergman and szego projections on domains with subelliptic boundary laplacian we prove that the difference between the bergman and szego projections on a bounded pseudoconvex domain with c boundary is smoothing whenever the boundary laplacian is subelliptic an equivalent statement is that the bergman projection can be represented as a composition of the szego and harmonic bergman projections along with the restriction and poisson extension operators modulo an error that is smoothing we give several applications to the study of optimal mapping properties for these projections and their difference

combining multiobjective optimization and bayesian model averaging to calibrate forecast ensembles of soil hydraulic models 1 most studies in vadose zone hydrology use a single conceptual model for predictive inference and analysis focusing on the outcome of a single model is prone to statistical bias and underestimation of uncertainty in this study we combine multiobjective optimization and bayesian model averaging bma to generate forecast ensembles of soil hydraulic models to illustrate our method we use observed tensiometric pressure head data at three different depths in a layered vadose zone of volcanic origin in new zealand a set of seven different soil hydraulic models is calibrated using a multiobjective formulation with three different objective functions that each measure the mismatch between observed and predicted soil water pressure head at one specific depth the pareto solution space corresponding to these three objectives is estimated with amalgam and used to generate four different model ensembles these ensembles are postprocessed with bma and used for predictive analysis and uncertainty estimation our most important conclusions for the vadose zone under consideration are 1 the mean bma forecast exhibits similar predictive capabilities as the best individual performing soil hydraulic model 2 the size of the bma uncertainty ranges increase with increasing depth and dryness in the soil profile 3 the best performing ensemble corresponds to the compromise or balanced solution of the three objective pareto surface and 4 the combined multiobjective optimization and bma framework proposed in this paper is very useful to generate forecast ensembles of soil hydraulic models

regularity of the bergman projection on forms and plurisubharmonicity conditions let omega subset subset mathbb c n be a smoothly bounded domain suppose has a defining function such that the sum of any q eigenvalues of its complex hessian is non negative we show that this implies global regularity of the bergman projection b j 1 and the bar partial neumann operator n j acting on 0 j forms for j in q ldots n

mixed multiplicities segre numbers and segre classes abstract based on classical results of rees and on multivariate hilbert polynomials we define new mixed multiplicities of two arbitrary ideals in a local ring a m and use them to express the local degrees of all varieties appearing in the gaffney gassler construction of segre cycles we prove that the classical mixed multiplicities of m and an arbitrary ideal i which are a special case of the new ones are equal to the generalized samuel multiplicities of an ideal in the rees algebra r i a this equality is used to improve a result of jeffries montano and varbaro on the degree of the fiber cone of an ideal we conclude the paper with formulas and their inverses which express the degrees of segre classes of subschemes of arbitrary projective varieties by generalized samuel multiplicities or by classical mixed multiplicities using the mixed multiplicities of balanced rational normal scrolls which have been computed by hoang and lam we find the mixed multiplicities of all rational normal scrolls as well as their segre classes and their generalized samuel multiplicities

asymptotic vanishing of homogeneous components of multigraded modules and its applications abstract in this article we give a condition on the vanishing of finitely many homogeneous components which must imply the asymptotic vanishing for multigraded modules we apply our result to multi rees algebras of ideals as a consequence we obtain a result on normality of monomial ideals which extends and improves the results of reid roberts and vitulli 14 singla 16 and sarkar and verma 15

positivity of mixed multiplicities let r u v n2r u v be a standard bigraded algebra over an artinian local ring k r 0 0 standard means r is generated over k by a finite number of elements of degree 1 0 and 0 1 since the length r u v of r u v is finite we can consider r u v as a function in two variables u and v this function was first studied by van der waerden w and bhattacharya b who proved that there is a polynomial pr u v of total degree dimr 2 such that r u v pr u v for u and v large enough katz mandal andverma kmv found out that the degree of pr u v is equal to rdimr 2 where rdimr is the relevant dimension of r defined as follows let r denote the ideal generated by the homogeneous elements of degree u v with u 1 v 1 let projr be the set of all homogeneous prime ideals r of r then rdimr max dimr projr if projr and rdimr can be any negative integer if projr if we write

sobolev estimates for the cauchy riemann complex on c1 pseudoconvex domains let omega subset mathbb c n be a bounded pseudoconvex domain with c k boundary k 1 in this paper we will prove that the cauchy riemann operator overline partial has a bounded solution operator in the sobolev space w s p q omega for all 0 leq s k frac 1 2

three parameter lognormal distribution model for soil water retention many models for soil water retention have been proposed however most of these models are curve fitting equations and do not emphasize the physical significance of their empirical parameters a new retention model that exhibits increased flexibility was developed by applying three parameter lognormal distribution laws to the pore radius distribution function r and to the water capacity function which was taken to be the pore capillary pressure distribution function this model contains three parameters that are closely related to the statistics of the bubbling pressure c the mode 0 of and the standard deviation of transformed by comparison of this model with three existing models the van genuchten model the brooks corey model and the modified tani model it was shown that c 0 and are all essential for a general retention model

boundary invariants of pseudoconvex domains the purpose of this paper is to describe an invariant ax z which is associated with each point z in the boundary of a smoothly bounded pseudoconvex domain in cn the motivation for defining the invariant ax z referred to as the multitype of z comes from the study of the boundary regularity properties of solutions of the d neumann problem on domains of finite type by a domain of finite type we mean one that satisfies the definition given by d angelo 5 namely a domain such that at any boundary point the maximum order of contact of one dimensional complex analytic varieties with the boundary is bounded in 4 the author showed how one can give a proof of global regularity of the a neumann problem for pseudoconvex domains of finite type if there is an invariant such as the one described in this paper in a forthcoming article this invariant will be used to obtain a proof of subelliptic estimates for the same class of domains before giving the definition of the multitype ax z we must introduce some

the hilbert function of generic plane sections of curves of ℙ3 a characteristic condition is given on a zero dimensional differentiable 0 sequenceh hi i 0 h1 3 in order to be the hilbert function of a generic plane section of a reduced irreducible curve of 3 hence of points of 2 with the uniform position property in this way an answer is given to some question stated by harris in ha2

sobolev estimates for the bar partial neumann operator on domains inc n admitting a defining function that is plurisubharmonic on the boundary neumann operator on domains inc n admitting a defining function that is plurisubharmonic on the boundary

analyses of infiltration events in relation to determining soil hydraulic properties by inverse problem methodology at the field scale because of the relatively large number of observation points required to estimate the spatial distributions of hydraulic properties application of inversion procedures must be based on a characteristic of the flow that for a given point in the field can be measured with relative ease and can be used as input for the inversion procedure suggesting the use of infiltration data for this purpose and recognizing the fact that a basic requirement for the design of a transient flow experiment is that the resulting inverse problem be sufficiently well posed to allow solution this paper addresses the question under which circumstances the resulting inverse problem is well posed utilizing the concepts of identifiability uniqueness and stability for this purpose three different models of the soil hydraulic properties were analyzed the main conclusion of this study is that when infiltration data measured at the darcy scale are used as input for the inversion procedure the inclusion of prior information on a single measurable parameter the saturated conductivity ks in the estimation criterion will enhance the likelihood of uniqueness and stability of the inverse solution provided that the structure of the hydraulic model is sufficiently simple however since for a particular situation it is impossible to determine a priori whether the resultant inverse problem is well posed or not this must be carried out only a posteriori by solving the problem several times with different initial parameter estimates accompanied by an analysis of the associated estimation errors

lognormal distribution model for unsaturated soil hydraulic properties the soil water retention model developed by kosugi was modified to be compatible with mualem s model in order to derive an analytical expression for the relative hydraulic conductivity kr the modified water retention model is to be derived by applying a lognormal distribution law to the soil pore radius distribution function parameters of this retention model have physical significance on the water content capillary pressure curve and are related directly to the statistics of the pore radius distribution the accuracy of the resulting combined water retention hydraulic conductivity model is verified for observed data sets for six soils results showed that the proposed model produces acceptable matches with observed water retention curves and adequate predictions of hydraulic conductivities in five out of six cases the and kr or kr curves generated by this model are generally similar to those generated by van genuchten s model

determining soil hydraulic properties by parameter estimation on the selection of a model for the hydraulic properties parameter estimation procedures involving solution of the inverse flow problem pertinent to a transient experiment constitute a powerful method of determining the soil hydraulic properties one of the problems associated with these procedures is the selection of an appropriate model to describe the soil hydraulic properties three different models were considered those of van genuchten vg and brooks and corey bc model and the exponential model of gardner for the hydraulic conductivity soil water pressure relationships coupled with a new expression for the soil water content soil water pressure relationship gr model for a given model the soil hydraulic properties were determined from simulated and measured outflow experiments supplemented with water content at a soil water pressure head of 15 000 cm h2o using the parameter estimation procedure of kool et al 1985a and data from two soils a hypothetical sandy loam soil assumed to be described by the vg model and a silt loam soil model validation tests were performed and the most appropriate model was selected from the candidate models by discrimination tests using the akaike information criterion aic in the case of the hypothetical sandy loam the vg model was found to be the most accurate and most consistent with the data the performance of both the bc and the gr models in terms of the aic was less good but very similar to each other in the case of the silt loam soil the vg model with additional parameter m which accounts for the correlation between pores and for the flow path tortuosity m 2 02 rather than a constant m 0 5 was found to be most accurate and most consistent with the data the performance of the bc and the gr models was similar when m was considered as an unknown parameter instead of a constant

statistical analysis of spatial variability in unsaturated flow parameters core scale estimates of soil parameters of the gardner russo and van gemachten models of the hydraulic conductivity and water retention functions were obtained for 417 undisturbed soil cores taken from a wall of a trench 20 m long 2 5 m deep using a procedure based on inverse problem methodology these estimates were used to evaluate the first two statistical moments of the underlying random space functions rsfs using the restricted maximum likelihood estimation procedure coupled with the weighted least squares procedure to estimate parameters of models of the covariance and the drift functions of the pertinent rsfs the fitted models were used to evaluate the mean and covariance functions of the hydraulic conductivity and water rentention functions for given water saturations covariance functions of log saturated conductivity log ks and the shape parameters of the gardner russo and van genuchten models exhibited statistical anisotropy characterized by aspect ratios that vary between 3 to 4 correlation scales of log ks were larger than those of the shape parameters consequently the product of the variance of log unsaturated conductivity and its correlation scale remained essentially invariant for a considerable range of water saturation the implications of these results regarding stochastic modeling of transport in heterogeneous porous formations and possible applications of the results of this study are discussed briefly

a smoothing property of the bergman projection let b be the bergman projection associated to a domain on which the bar partial neumann operator is compact we show that arbitrary l 2 derivatives of bf are controlled by derivatives of f taken in a single distinguished direction as a consequence functions not contained in c infty overline omega that are mapped by b to c infty overline omega are explicitly described

global regularity for the neumann operator and bounded plurisubharmonic exhaustion functions abstract for a smooth bounded pseudoconvex domain c n we derive a new sufficient condition for global regularity of the neumann operator that generalizes mcneal s property p the approximately holomorphic vector fields of boas and straube and a condition involving bounded plurisubharmonic exhaustion functions due to kohn

necessary conditions for subellipticity of the overline partial neumann problem let a be a a closed form of type p q with l2 coefficients on a smoothly bounded domain q in c the problem of determining both the existence and regularity properties of the solution u of au a where u is orthogonal to the null space of a on p q l forms is known as the a neumann problem one of the principal methods used in the investigation of this problem is the proof of certain a priori subelliptic estimates let u be a neighborhood of a point z0 in the boundary of q a subelliptic estimate is said to hold in u if the estimate

real hypersurfaces orders of contact and applications a fundamental problem in the modem theory of several complex variables concerns the boundary behavior of the cauchy riemann equations suppose that d is an open domain in cn and that its boundary m is a smooth real submanifold of cn how does the geometry of m influence the function theory on d one approach to this question is the a neumann problem 6 there one studies the inhomogeneous cauchy riemann equations au a where a is a 0 q form with distribution coefficients on the closed domain d u m satisfying the necessary compatibility condition a a 0 the a neumann problem constructs a particular solution u which is orthogonal to the null space of the complex laplacian kohn 10a has solved this problem and has shown that good local regularity properties for u in terms of a follow from so called subelliptic estimates it is natural to seek geometric conditions on m that are necessary and sufficient for these estimates in this paper we will be concerned with a certain geometric condition on m that we feel is the right one for subellipticity although the motivation for the questions discussed here comes from partial differential equations the techniques come from algebraic geometry to see why we state theorems of kohn greiner and catlin concerning subellipticity kohn 1oa has discovered a sufficient condition for a subelliptic estimate near a fixed point p in m in case d is pseudoconvex and is contained in c2 this condition is equivalent to the finiteness of order of tangency of every complex analytic one dimensional manifold with m at p greiner 13 established the necessity of this condition in

comparison of the bergman and szego kernels abstract the quotient of the szego and bergman kernels for a smooth bounded pseudoconvex domains in c n is bounded from above by a constant multiple of log p for any p n where is the distance to the boundary for a class of domains that includes those of d angelo finite type and those with plurisubharmonic defining functions the quotient is also bounded from below by a constant multiple of log p for any p 1 moreover for convex domains the quotient is bounded from above and below by constant multiples of

boundary regularity of proper holomorphic mappings it s main result is formulated in theorem 2 below although the answer to the conjecture in the general case is still unknown it has been shown to hold in many special cases a fairly detailed history of this subject will be contained in 14 one class of positive answers deals with cases in which one knows that f21 and 2 posses fairly large classes of holomorphic automorphisms that extend holomorphically across the boundaries like for instance reinhardt domains see e g h cartan 8 w kaup 16 and st bell 6 in these situations one even often does not need a smoothness assumption on the boundaries of 1 and 22 on the other hand the first result without a priori knowledge on automorphisms which gave c extendability was proved by ch fefferman in 1974 in 15 and says

parameter estimation of hydraulic properties from one step outflow data the one step outflow method was presented by kool et al 1985a b as a fast procedure to estimate unsaturated soil hydraulic properties many investigators however encountered difficulties obtaining a unique solution to the problem the purpose of this paper is to evaluate some of the problems related to this method by looking at response surfaces and to make recommendations for improvements in the methodology the one step outflow procedure was investigated using synthetic data sets generated for 7 6 cm diameter by 7 6 cm high soil cores a finite difference solution of richards equation was used to generate the synthetic data sets response surfaces were calculated for the van genuchten parameters n and ks for various combinations of matric potential water content and outflow data from initially saturated soil cores subjected to a step change in pressure at one of its boundaries the results clearly show that with outflow data alone the parameter estimation procedure will have difficulty converging however if matric potential data are available for a point in the core at some distance from the outflow boundary parameter estimation sensitivity is greatly improved the procedure used was found to be most helpful for determining which auxiliary variables should be measured for parameter estimation from outflow experiments

superlogarithmic estimates on pseudoconvex domains and cr manifolds this paper is concerned with proving superlogarithmic estimates for the operator r b on pseudoconvex cr manifolds and using them to establish hypoellipticity of lb and of the neumann problem these estimates are established under the assumption that subellipticity degenerates in certain specified ways

reduction numbers and multiplicities of multigraded structures the aim of this paper is twofold first we want to relate the cohen macaulay property of r i i to the cohen macaulay propa 1 r erty of the ordinary rees rings r i j s 1 r then we determine a j the multiplicities of multi rees and form rings in particular we ask when minimal multiplicity occurs for i s s i s i the multi rees algebras r i s r i i 1 r a r a behave to some extent like the ordinary rees algebras r i in particua lar the cohen macaulay property of such multi rees algebras can be characterized in terms of conditions on the local cohomology of the form ring gr i including the condition a gr i 0 where a gr i denotes a a a w x the a invariant of gr i see hhr 1 the a invariant has in certain a w cases been related to the reduction exponent r i of the ideal i see t2 x gh moreover the cohen macaulay property of r i implies that of a w x r i for all r 1 the converse is not true in general see hhr1 but a r in certain applications the assumption r i is cohen macaulay can be a

boundary behavior of functions holomorphic in domains of finite type abstract we study several notions of distance and ball on the boundary of domains of finite type in cn we use these notions to develop a theory of maximal functions and area integrals for functions holomorphic in such domains

a new model for soil hydraulic properties based on a stochastic conceptualization of porous media 1 the nature and distribution of soil particles and pores plays a strong role in determining the soil hydraulic properties specifically the soil water retention curve and the relative hydraulic conductivity curve that govern water movement a new mathematical model for these hydraulic properties was developed by conceptualizing the soil as a random assemblage of soil particles represented by randomly sized overlapping spheres fully penetrable spheres the spatial arrangement of the spheres was assumed to follow a homogeneous poisson process a stochastic analysis was utilized to obtain analytical expressions for soil water retention curves and relative conductivity at varying water contents unlike the existing models of soil hydraulic properties this new model incorporates soil porosity in estimating model parameters furthermore because of this conceptualization we are able to determine the types of soils for which the model is appropriate a quantitative evaluation of the new model was performed by examining data on hydraulic properties for several soils in addition quantitative and qualitative comparisons were made with currently used expressions such as the van genuchten model brooks corey relationship and kosugi model for the same data sets results show that the new model provides reasonable fits with the observed water retention curve and good predictions of the hydraulic conductivity particularly for soils exhibiting a distinct air entry pressure