dynamic equations for an isotropic spherical shell using the power series method and surface differential operators dynamic equations for an isotropic spherical shell are derived by using a series expansion technique the displacement field is split into a scalar radial part and a vector tangential part surface differential operators are introduced to decrease the length of the shell equations the starting point is a power series expansion of the displacement components in the thickness coordinate relative to the mid surface of the shell by using the expansions of the displacement components the three dimensional elastodynamic equations yield a set of recursion relations among the expansion functions that can be used to eliminate all but the four of lowest order and to express higher order expansion functions in terms of these of lowest orders applying the boundary conditions on the surfaces of the spherical shell and eliminating all but the four lowest order expansion functions give the shell equations as a power series in the shell thickness after lengthy manipulations the final four shell equations are obtained in a more compact form which can be represented explicitly in terms of the surface differential operators the method is believed to be asymptotically correct to any order the eigenfrequencies are compared to exact three dimensional theory and membrane theory

a note on the error analysis of time compression approximations the accuracy of the time compression analysis tca is analyzed by comparison with a numerical solution both the standard tca and a new modified tca are considered for a power law diffusivity and constant surface flux as expected the error of the approximations decreases with increasing power and the error of the modified tca is about half the error of the standard tca in a second part the errors of the two tcas are measured using a simple analytical solution instead of a numerical solution it is shown that the conclusions remain the same for the analytical and numerical solutions the advantage of using the analytical solution is to obtain simple analytical expressions showing the influence of parameters this is done to estimate the maximum error of both tcas a practical estimate of the errors can be obtained from equations which only require knowledge of the soil water diffusivity it appears that for real soils the errors of the tca are always 1 and thus are a very reliable tool for practical problems although not studied systematically it also appears that gravity effects reduce the errors of the tca so that the error obtained in the absence of gravity provides a conservative estimate when gravity is present

a note on the time compression approximation in this paper the work by sivapalan and milly 1989 is extended beyond the time of ponding to estimate the errors of the time compression approximation tca when an exact solution exists the diffusion coefficient is set to be constant and gravitational effects are not considered here the largest error of standard tca in calculating cumulative infiltration is about 2 5 while its underestimate of the time to ponding is about 19 a modified tca is also proposed in which the exact time of ponding is used directly instead of the flux to improve the estimate of postponding infiltration the error for the modified tca is about half of the error for the standard tca in predicting cumulative infiltration and thus the modified tca should be preferred wherever ponding time is or can be measured

divisorial contractions in dimension three which contract divisors to smooth points we deal with a divisorial contraction in dimension three which contracts its exceptional divisor to a smooth point we prove that any such contraction can be obtained by a suitable weighted blow up

three dimensional divisorial extremal neighborhoods in this paper we study divisorial extremal neighborhoods open image in new window such that 0 x is a can type threefold terminal singularity and f e is a smooth curve where e is the f exceptional divisor we view a divisorial extremal neighborhood as a one parameter smoothing of certain surface singularities and based on this we give a classification of such neighborhoods

analysis of time compression approximations tca time compression approximation is a practical and often quite accurate tool to predict postponding infiltration for field applications a modified approximation mtca can be used just as easily and in general will reduce the error by about 50 this is based on two results 1 after ponding tca and mtca predict very close infiltration rates and 2 mtca but not tca uses the actual cumulative infiltration up to the ponding time thus tca has an additional error in its prediction of postponding infiltration previously those results including the 50 reduction in error were observed numerically for linear and burger s soils they are illustrated here numerically with an actual soil a grenoble sand more importantly we developed a general analytical approximation for this problem and showed that it can provide a very convenient predictive tool which can then be used for arbitrary soil properties

elementary contractions of gorenstein threefolds in this paper we show that a generalization of the classification theorem of mori in 113 can be easily obtained from the contraction theorem of 5 a fine analysis is made of the contractions of extremal rays on projective threefolds with normal gorenstein q factorial terminal singularities so that x is in fact factorial a solution of the minimal model problem for threefolds has recently been completed by mori in ll we will first establish notation and give some preliminary results all of the definitions used in this paper can be found in 7 let x be a normal gorenstein projective threefold with q factorial terminal singularities suppose that x is defined over an algebraically closed field k of characteristic zero let r be an extremal ray of x it follows from arguments in 5 or 7 that there is a morphism f x y onto a normal variety y such that f is given by the linear system induced by a cartier divisor h and such that 1 f tp x 9 r 2 for an arbitrary curve c on x d imf c 0 holds if and only if c er 3 the pair f y is uniquely determined by conditions 1 and 2 up to isomorphism 4 s 0 pic y c pic x i sexact for i c i e r

an asymptotic theory for spherical shells we derive the exact two dimensional equations for a spherical shell from the three dimensional elastic state by an asymptotic expansion the resulting equations are presented as a power series in the thickness of the shell results for which a three dimensional solution is known or can be determined show full agreement

q gorenstein deformations of nonnormal surfaces let delta subset h be the germ of a nonnormal surface along a proper curve with smooth components such that the high index points of h are semi log terminal and the gorenstein singular points are semi log canonical of embedding dimension at most 4 we describe the sheaf t 1 qg h of bbb q gorenstein deformations of h and we obtain criteria for delta subset h to have bbb q gorenstein terminal smoothings

families of d minimal models and applications to 3 fold divisorial contractions let x t be a one parameter family of canonical 3 folds and let d be a weil divisor on it flat over t we study the problem of when the d t minimal models of x t form a family and we obtain conditions for this to happen as an application of this we classify terminal divisorial contractions e subset y leftarrow c subset x contracting an irreducible surface e onto the smooth curve c in the case when the general section of x through c is a d 5 duval singularity

infiltration models for semi infinite soil profiles 1 infiltration models for hydrological applications are developed for rational forms of the soil hydraulic conductivity and moisture retention functions the models are based on the traveling and kinematic wave solutions of the governing equation that proved to be highly accurate in specific flow conditions the approximate solutions describe the one dimensional infiltration into a semi infinite medium for uniform initial conditions under either a time dependent flux or a constant head boundary condition they capture the profile development from early to late time accurately due to the proper derivation of the wetting front speed in terms of the time varying surface boundary potential and flux rate algebraic expressions of theoretical and practical importance are derived in terms of well defined soil water parameters and include the effect of the antecedent moisture content in a specific fashion practical results include simple expressions for the surface moisture variation for variable rainfall patterns time to ponding expressions and infiltration equations that account explicitly for the initial condition formulas for the depth of the wetting zone and algebraic equations for parameter estimation of the soil hydraulic parameters by inverse analysis

pluri canonical divisors on kahler manifolds soit p x m une application reguliere propre de varietes complexes a fibres connexes de dimension k o est un point de m on suppose que p 1 0 x 0 est dans la classe 7b c soit m un entier positif et on suppose le diviseur d une section non nulle dans h 0 x 0 xd 0 k m est lisse alors il y a un voisinage analytique u de o dans m tel que p l p 1 z p l x 0 pour l 1 m et pour tout z dans u

factoring 3 fold flips and divisorial contractions to curves flips flops and divisorial contractions are the elementary birational maps of the minimal model program divisorial contractions are the higher dimensional analog of the inverse of blowing up a smooth point on a surface flips are instead a new operation which consists of a surgery in codimension 2 which replaces certain kx negative curves by some kx positive curves flops are also surgeries in codimension 2 but they replace certain kx trivial curves by some new kx trivial curves not surprisingly the geometry of divisorial contractions is better understood than that of flips and flops in fact the proof of the existence of flips and flops cf 1 7 is very abstract and gives little insight to their geometry in dimension 3 these operations are reasonably well understood kollar has shown 23 that if x 99k x is a flop of terminal 3 folds then x and x have analytically isomorphic singularities in 34 mori gives a precise understanding of the geometry of all flips with irreducible flipping curve we would like to remark that 3 fold divisorial contractions may be subdivided into two classes those that map the divisor to a curve and those that map the divisor to a point divisorial contractions to a point are classified in 4 14 18 19 20 21 and 31 there are also several partial results on divisorial contractions to a curve cf 5 37 38 39 40 and 41 the purpose of this talk is try to understand what happened to the singularities under these elementary birational map in dimension three and how can we decompose these maps into simplers maps that explicit description of singularities is possible in fact we can factor flips and divisorial contractions to curves via the simpler operations

infiltration models for soil profiles bounded by a water table 1 approximate solutions of richards equation are developed for rational forms of the soil hydraulic conductivity and moisture retention functions using a perturbation expansion method a novel approach is devised in the perturbation technique whereby a priori introduced parameters are estimated in an optimal context to ensure the accuracy of the perturbation solution at all times and for all flow conditions the perturbation model describes the one dimensional nonlinear nonsteady infiltration for arbitrary initial conditions under either a time dependent surface flux or a constant head boundary condition into either a semi infinite or a finite medium bounded from below by a shallow water table the optimal perturbation approach proved to be an effective method by which closed form linear solutions can be adapted to nonlinear soils through proper scaling factors the results show that the first order linear term of the optimal perturbation solution is sufficiently accurate for practical applications especially for shallow water table conditions they offer the means to analyze the effect of nonuniform initial conditions and the influence of the water table on the infiltration process practical results in terms of well defined soil water parameters and the antecedent moisture content include algebraic expressions for the surface moisture content variation under variable rainfall conditions time to ponding expressions and infiltration equations for deep and shallow water table conditions and a prediction formula for the water table recharge rate

an asymptotic theory for circular cylindrical shells we derive the two dimensional shell equations for a circular cylindrical shell by means of an asymptotic expansion of the three dimensional elastic state the assumptions involved are of mathematical character only and concern the continuity differentiability and convergence of the series used a numerical comparison between the frequencies obtained by the two dimensional shell equations and the three dimensional state in the case of free vibrations is presented in a few examples