the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

simultaneous confidence intervals for comparing binomial parameters summary to compare proportions with several independent binomial samples we recommend a method of constructing simultaneous confidence intervals that uses the studentized range distribution with a score statistic it applies to a variety of measures including the difference of proportions odds ratio and relative risk for the odds ratio a simulation study suggests that the method has coverage probability closer to the nominal value than ad hoc approaches such as the bonferroni implementation of wald or exact small sample pairwise intervals it performs well even for the problematic but practically common case in which the binomial parameters are relatively small for the difference of proportions the proposed method has performance comparable to a method proposed by piegorsch 1991 biometrics 47 45 52

comparing the areas under two or more correlated receiver operating characteristic curves a nonparametric approach methods of evaluating and comparing the performance of diagnostic tests are of increasing importance as new tests are developed and marketed when a test is based on an observed variable that lies on a continuous or graded scale an assessment of the overall value of the test can be made through the use of a receiver operating characteristic roc curve the curve is constructed by varying the cutpoint used to determine which values of the observed variable will be considered abnormal and then plotting the resulting sensitivities against the corresponding false positive rates when two or more empirical curves are constructed based on tests performed on the same individuals statistical analysis on differences between curves must take into account the correlated nature of the data this paper presents a nonparametric approach to the analysis of areas under correlated roc curves by using the theory on generalized u statistics to generate an estimated covariance matrix

partial auc estimation and regression accurate diagnosis of disease is a critical part of health care new diagnostic and screening tests must be evaluated based on their abilities to discriminate diseased from nondiseased states the partial area under the receiver operating characteristic roc curve is a measure of diagnostic test accuracy we present an interpretation of the partial area under the curve auc which gives rise to a nonparametric estimator this estimator is more robust than existing estimators which make parametric assumptions we show that the robustness is gained with only a moderate loss in efficiency we describe a regression modeling framework for making inference about covariate effects on the partial auc such models can refine knowledge about test accuracy model parameters can be estimated using binary regression methods we use the regression framework to compare two prostate specific antigen biomarkers and to evaluate the dependence of biomarker accuracy on the time prior to clinical diagnosis of prostate cancer

parallel permutation and sorting algorithms and a new generalized connection network o k log n algorithms are obtained to permute and sort n data items on cube and perfect shuffle computers with n sup 1 1 k processing elements 1 k log n these algorithms lead directly to a generalized connection network construction having o k log n delay and o kn sup 1 1 k log n contact pairs this network has the advantage that the switches can be set in o k log n time by either a cube or perfect shuffle computer with n sup 1 1 k processing elements 23 references

analytical and numerical investigations of spontaneous imbibition in porous media we present semi analytical solutions for co current displacements with some degree of counter current flow the solution assumes a one dimensional horizontal displacement of two immiscible incompressible fluids with arbitrary viscosities and saturation dependent relative permeability and capillary pressures we address the impact of the system length on the degree of counter current flow when there is no pressure drop in the non wetting phase across the system assuming negligible capillary back pressure at the inlet boundary of the system it is shown that in such displacements the fractional flow can be used to determine a critical water saturation from which regions of both co current and counter current flow are identified this critical saturation changes with time as the saturation front moves into the porous medium furthermore the saturation profile in the approach presented here is not necessarily a function of distance divided by the square root of time we also present approximate solutions using a perturbative approach which is valid for a wide range of flow conditions this approach requires less computational power and is much easier to implement than the implicit integral solutions used in previous work finally a comprehensive comparison between analytical and numerical solutions is presented numerical computations are performed using traditional finite difference formulations and convergence analysis shows a generally slow convergence rate for water imbibition rates and saturation profiles this suggests that most coarsely gridded simulations give a poor estimate of imbibition rates while demonstrating the value of these analytical solutions as benchmarks for numerical studies complementing buckley leverett analysis this article is protected by copyright all rights reserved

painleve test and exact similarity solutions of a class of nonlinear diffusion equations for 1 1 dimensional diffusion equations where the diffusion coefficient is an arbitrary power of the dependent variable a painleve test is performed on both the partial differential equation and the similarity reductions the invariance of the painleve property under a large class of similarity reductions is shown for the reductions with the painleve property the explicit similarity solutions are given it is demonstrated how results of a painleve analysis can be used to obtain further exact similarity solutions even in cases without the painleve property

construction of confidence limits about effect measures a general approach it is widely accepted that confidence interval construction has important advantages over significance testing for the presentation of research results as now facilitated by readily available software however for a number of effect measures procedures are either not available or not satisfactory in samples of small to moderate size in this paper we describe a general approach for estimating a difference between effect measures which can also be used to obtain confidence limits for a risk ratio and a lognormal mean numerical evaluation shows that this closed form procedure outperforms existing methods including the bootstrap

exact similarity solutions to some nonlinear diffusion equations the author gives new closed form similarity solutions to n dimensional radially symmetric nonlinear diffusion equations with power law and exponential diffusivities these solutions are generalisations of known similarity solutions

new variable separation approach application to nonlinear diffusion equations the concept of the derivative dependent functional separable solution ddfss as a generalization to the functional separable solution is proposed as an application it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach as a consequence a complete list of canonical forms for such equations which admit the ddfss is obtained and some exact solutions to the resulting equations are described

multicasting in quantum switching networks in this paper we present a quantum multicasting network called a generalized quantum connector n gqc which can be used to multicast quantum information from n inputs to n outputs this network is recursively constructed using n 2 gqcs and consists of o n log2 n quantum gates the key component of the n gqc is another network called an n quantum concentrator n qc this concentrator is also an n n quantum network and can route arbitrary quantum states on any m of its inputs to its top m outputs for any m 1 m n its quantum gate complexity is o n log n the quantum gate level depths of n qc and n gqc are o log2 n and o log3 n respectively both n qc and n gqc are based on the classical self routing concentrators and generalized connection networks given by lee and oruc 1 while these networks work for multicasting classical packets they cannot be used to multicast quantum packets as they employ balancer switches with both forward and backward propagation of packets we introduce a quantum balancer switch that works using a forward propagation of packets only thereby facilitating the n qc and n gqc designs presented in the paper

symmetry reductions and exact solutions of a class of nonlinear heat equations abstract classical and nonclassical symmetries of the nonlinear heat equation ut uxx f u are considered the method of differential grobner bases is used both to find the conditions on f u under which symmetries other than the trivial spatial and temporal translational symmetries exist and to solve the determining equations for the infinitesimals a catalogue of symmetry reductions is given including some new reductions for the linear heat equation and a catalogue of exact solutions of the nonlinear heat equation for cubic f u in terms of the roots of f u 0

new similarity reductions of the boussinesq equation some new similarity reductions of the boussinesq equation which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering are presented these new similarity reductions including some new reductions to the first second and fourth painleve equations cannot be obtained using the standard lie group method for finding group invariant solutions of partial differential equations they are determined using a new and direct method that involves no group theoretical techniques

bipartite perfect matching is in quasi nc we show that the bipartite perfect matching problem is in quasi mathsf nc 2 that is it has uniform circuits of quasi polynomial size n o log n and o log 2 n depth previously only

exact solutions for water infiltration with an arbitrary surface flux or nonlinear solute adsorption several authors have now used the backlund transformation to linearize richard s equation and so obtain analytical solutions for infiltration and redistribution processes for the linearizable class of diffusivities and hydraulic conductivities after transformation a convection diffusion equation is obtained to date all the analytical results making use of the backlund transform have been based on a specified constant flux that is assumed to exist at the surface boundary we generalize the previous work by removing this restriction and obtain a general solution for an arbitrary temporal variation in surface flux the solution contains a function that is specified by a volterra integral equation in practice the volterra equation must be evaluated numerically this task is accomplished using a relatively straightforward algorithm the analytical results for infiltration can be applied to the process of solute transport subject to a nonlinear adsorption isotherm since these two phenomena are equivalent under another mapping our new analytical results therefore also apply to this class of solute transport processes the general form of the adsorption isotherm for which exact results can be obtained is derived this isotherm appears capable of representing a relatively large family of physically relevant cases although this topic remains open for future investigation

integrability of hamiltonians with third and fourth degree polynomial potentials the weak painleve property as a criterion of integrability is applied to the case of simple hamiltonians describing the motion of a particle in two dimensional polynomial potentials of degree three and four this allows a complete identification of all the integrable cases of cubic potentials in the case of quartic potentials although our results are not exhaustive some new integrable cases are discovered in both cases the integrability is explicited by a direct calculation of the second integral of motion of the system

lie transformations similarity reduction and solutions for the nonlinear madelung fluid equations with external potential the application of lie group methods to a system of coupled nonlinear partial differential equations representing what is usually called a madelung fluid is shown the generating operators of the transformation group that depends on five arbitrary group constants will be constructed and all subclasses of systems of ordinary differential equations derived by similarity reduction will be presented in tabular form two subclasses of physical interest are investigated in detail and the similarity solutions are compared with solutions found earlier by the application of inverse scattering transform techniques to the cubic nonlinear schrodinger equation similarity solutions for the madelung equations with linear external potential x f0x are presented

symmetries and integrability of generalized diffusion reaction equations using lie group methods and the painleve test the authors analyse nonlinear diffusion reaction equations ut d u u f u with power law diffusion coefficients d approximately uv and arbitrary nonlinear reaction terms f u which have a wide spectrum of applications in many areas of science the lie group based similarity method leads to a classification of the reaction terms according to its symmetry properties with the help of the adjoint representation the optimal system of similarity reductions is calculated to check the integrability of the partial differential equation the existence of generalized lie backlund symmetries is investigated apart from three known cases no further cases with third order symmetries exist examining the integrability of the second order ordinary differential equations resulting from the reductions only a few parameter combinations can be found for which the painleve property is given however they are able to construct unknown integrals of motion for a much larger range of parameter values from the integrals exact similarity solutions may be derived this is demonstrated by examples corresponding to the important moving wave reduction

when nonlinear differential equations are equivalent to linear differential equations a necessary and sufficient condition is established for the existence of a 1 1 transformation of a system of nonlinear differential equations to a system of linear equations the obtained theorems enable one to construct such transformations from the invariance groups of differential equations the hodograph transformation the legendre transformation and lie s transformation of the monge ampsre equation are shown to be special cases noninvertible transformations are also considered examples include burgers equation a nonlinear diffusion equation and the liouville equation introduction in this work we study transformations mapping nonlinear differen tial equations to linear differential equations in a 1 1 manner based upon the group analysis of differential equations we obtain necessary and sufficient conditions for the existence of such transformations the established theorems not only allow us to determine the existence of the transformations but also enable us to actually construct these transformations from invariance groups of the nonlinear equations in the following analysis two types of transformations are considered 1 the invariance groups of differential equations and 2 the mappings which transform nonlinear differential equations to linear differential equations theorems will be proved based upon the following observations clearly if there exists a 1 1 mapping between any two differential equations it must inject properties of one equation into the other including their invariance properties for this reason the often ignored fact that any linear differential equation admits an invariance group related to the superpo sition principle becomes very significant the generator of this particular group depends upon an arbitrary solution of the linear equation it follows then that any nonlinear equation transformable to a linear equation by a 1 1 mappingmust admit an invariance group whose generator depends upon an arbitrary solution of some linear differential equation the idea of comparing invariance groups of differential equations in the search of mappings connecting the equations was first used by bluman in his study of burgers equation 1 and it was applied to the study of the mappings of one dimensional linear parabolic equations to the heat equation 2 in the first section of this paper some basic properties of various transformations are summarized the theorems are presented in the second section the examples in the third section include the hodograph transformation the legendre transformation lie s transformation of themonge ampre equation and the equation ux uxx uyy 0 in the last section we examine properties of noninvertible mappings of burgers equation the diffusion equation u 2ux uy 0 and the liouville equation u y e u respectively into linear equations

confidence intervals for an effect size measure based on the mann whitney statistic part 2 asymptotic methods and evaluation several asymptotic confidence interval methods for u mn the mann whitney u statistic divided by the product of the two sample sizes are developed and evaluated alongside published methods novel methods derived from gaussian and beta models perform well though overall a modification of the hanley mcneil approach method 5 in this evaluation performed better and is recommended for calculating confidence intervals for u mn for continuously distributed data

graph expansion and communication costs of fast matrix multiplication the communication cost of algorithms also known as i o complexity is shown to be closely related to the expansion properties of the corresponding computation graphs we demonstrate this on strassen s and other fast matrix multiplication algorithms and obtain the first lower bounds on their communication costs in the sequential case where the processor has a fast memory of size m too small to store three n by n matrices the lower bound on the number of words moved between fast and slow memory is for a large class of matrix multiplication algorithms n m 0 m where 0 is the exponent in the arithmetic count e g 0 lg 7 for strassen and 0 3 for conventional matrix multiplication with p parallel processors each with fast memory of size m the lower bound is asymptotically lower by a factor of p these bounds are attainable both for sequential and for parallel algorithms and hence optimal

efficient parallel convex hull algorithms parallel algorithms are presented to identify i e detect and enumerate the extreme points of the convex hull of a set of planar points using a hypercube pyramid tree mesh of trees mesh with reconfigurable bus exclusive read exclusive write parallel random access machine erew pram and modified aks network it is shown that the problem of identifying the convex hull for a set of planar points given arbitrarily cannot be solved faster than sorting

an impes scheme for a two phase flow in heterogeneous porous media using a structured grid abstract we develop a numerical scheme for a two phase immiscible flow in heterogeneous porous media using a structured grid finite element method which has been successfully used for the computation of various physical applications involving elliptic interface equations li et al 2003 2004 chou et al 2010 kwak et al 2010 chang and kwak 2011 the proposed method is based on the implicit pressure explicit saturation procedure to solve the pressure equation we use an ifem based on the rannacher turek rannacher and turek 1992 nonconforming space which is a modification of the work in kwak et al 2010 where broken p 1 nonconforming element of crouzeix raviart 1973 1 was developed for the darcy velocity we apply the mixed finite volume method studied in chou et al 2003 and kwak et al 2010 on the basis of immersed finite element method ifem in this way the darcy velocity of the flow can be computed cheaply locally after we solve the pressure equation the computed darcy velocity is used to solve the saturation equation explicitly the whole procedure can be implemented on a structured grid which is independent of the underlying heterogeneous porous media in fact we apply a new version of multigrid algorithm to solve the pressure equation for which the cpu time grows like o n numerical tests for analytic problems show that our method is almost optimal in all variables problem with sources sinks is also computed and it seems to work well

algorithms for finding and updating minimum depth spanning trees in parallel abstract fast parallel algorithms are presented for finding and updating the minimum depth spanning trees of graphs the computational model used is a parallel random access machine that allows simultaneous access to the same memory location during both read and write operations the parallel minimum depth spanning tree algorithm is based on a partial spanning tree doubling technique which is also found to be useful in updating the minimum depth spanning tree when a new node or edge is added to the graph the parallel minimum depth spanning tree algorithm runs in o log n log log n time with o n 2 n loglog n processors the most notable results are o loglog n time parallel algorithms for updating the minimum depth spanning tree solution when a new node edge is added to an n node graph whose minimum depth spanning tree is known

self routing technique in perfect shuffle networks using control tags the self routing technique using control tags on multiple pass perfect shuffle networks is generalized in particular they show that bit permute complement permutations can be realized and unscrambled in 2n 1 passes or less where n log sub 2 n n being the number of terminals on either side they also show that most of the frequently used permutations are in the intersection of omega realizing and inverse omega realizing sets and can be realized and unscrambled in n passes

a self routing benes network and parallel permutation algorithms a benes permutation network capable of setting its own switches dynamically is presented the total switch setting and delay time for the n input utput self routing network is o log n it is shown that the network is capable of performing a rich class of permutations the self routing scheme leads to efficient o log n parallel algorithms to perform the same class of permutations on cube connected and perfect shuffle computers

separation of variables of a generalized porous medium equation with nonlinear source this paper considers a general form of the porous medium equation with nonlinear source term ut d u u n x f u n 1 the functional separation of variables of this equation is studied by using the generalized conditional symmetry approach we obtain a complete list of canonical forms for such equations which admit the functional separable solutions as a consequence some exact solutions to the resulting equations are constructed and their behavior are also investigated 2002 elsevier science usa all rights reserved

extended group analysis of variable coefficient reaction diffusion equations with exponential nonlinearities abstract the group classification of a class of variable coefficient reaction diffusion equations with exponential nonlinearities is carried out up to both the equivalence generated by the corresponding generalized equivalence group and the general point equivalence the set of admissible transformations of this class is exhaustively described via finding the complete family of maximal normalized subclasses and associated conditional equivalence groups limit processes between variable coefficient reaction diffusion equations with power nonlinearities and those with exponential nonlinearities are simultaneously studied with limit processes between objects related to these equations including lie symmetries exact solutions and conservation laws

an efficient parallel dynamic programming algorithm abstract antonio tsai and huang proposed a scheme in 1991 to parallelize the standard dynamic programming approach to solve combinatorial multistage problems however their dynamic programming approach is restricted to those multistage problems where the decision made at each stage depends only on decisions made in the stage immediately preceding it for many interesting problems the decision at each stage depends on the decisions made at all the previous stages and therefore their approach doesn t apply the matrix chain multiplication problem longest common subsequence problem and optimal polygon triangulation problem are some examples of such problems we also present techniques for parallelizing the dynamic programming solution to such problems the parallel algorithm we develop for a pram has complexity n employing n 2 processors since the traditional sequential algorithm for such problems is n 3 our parallel algorithm is an optimal parallel algorithm based on this traditional algorithm we also describe the results of our experiments that are in conformity with our theoretical complexity results we also compare and contrast our result with results obtained by earlier researchers and show that our parallel algorithm has optimal efficiency of 100 with respect to the traditional dynamic programming algorithm

singular point analysis and integrals of motion for coupled nonlinear schrodinger equations for a system of two coupled nonlinear schrodinger equations and the corresponding madelung fluid equations we calculate the similarity transformation and reductions to ordinary differential equations the symmetries can be used to classify several types of solutions besides a system of coupled painleve ii equations we obtain a two dimensional quartic hamiltonian system using noether s theorem and performing a painleve test we identify those parameters which lead to regular motion on tori using the results of the p test we obtain heretofore undiscovered integrals of motion for the madelung fluid by direct calculations investigating the dynamics of the system for parameters that are different from those obtained by the painleve test we calculate numerically the surface of section kam tori and study the transition into chaotic behaviour

isogroup and general similarity solution of a nonlinear diffusion equation for a class of one dimensional nonlinear diffusion equations where the diffusion coefficient varies as some power of the dependent variable the invariance group and its lie algebra are given the isovector fields which generate the isogroup are then used to derive a general similarity solution for a particular case the solution can be reduced to a one parameter group solution which is in full agreement with previously published results

new classes of symmetries for partial differential equations new classes of symmetries for partial differential equations are introduced by writing a given partial differential equation s in a conserved form a related system t with potentials as additional dependent variables is obtained the lie group of point transformations admitted by t induces a symmetry group of s new symmetries may be obtained for s that are neither point nor lie backlund symmetries they are determined by a completely algorithmic procedure significant new symmetries are found for the wave equation with a variable wave speed and the nonlinear diffusion equation

the efficiency of simulation based multiple comparisons a frequently encountered problem in practice is that of simultaneous interval estimation of p linear combinations of a parameter beta in the setting of or equivalent to a univariate linear model this problem has been solved adequately only in a few settings when the covariance matrix of the estimator is diagonal in other cases conservative solutions can be obtained by the methods of scheffe bonferroni or sidak 1967 journal of the american statistical association 62 626 633 here we investigate the efficiency of using a simulated critical point for exact intervals which has been suggested before but never put to serious test we find the simulation based method to be completely reliable and essentially exact sample size savings are substantial in our settings 3 19 over the sidak method 4 37 over the bonferroni method and 27 33 over the scheffe method we illustrate the efficiency and flexibility of the simulation based method with case studies in physiology and marine ecology

simultaneous confidence intervals using ordinal effect measures for ordered categorical outcomes when outcomes are ordered categorical a model using an ordinal effect size measure is a good alternative of the cumulative logit model to compare several independent group differences we present a method of constructing simultaneous confidence intervals for the ordinal effect size measures using the studentized range distribution with the score test statistic a simulation study shows that the proposed method performs well in terms of coverage probability and it seems better than the method using a bonferroni correction for wald type statistics and methods that account for the dependencies among pairwise ordinal effect size measures using the multivariate normal distribution or the multivariate t distribution for small samples

a taxonomy of problems with fast parallel algorithms the class nc consists of problems solvable very fast in time polynomial in log n in parallel with a feasible polynomial number of processors many natural problems in nc are known in this paper an attempt is made to identify important subclasses of nc and give interesting examples in each subclass the notion of nc 1 reducibility is introduced and used throughout problem r is nc 1 reducible to problem s if r can be solved with uniform log depth circuits using oracles for s problems complete with respect to this reducibility are given for many of the subclasses of nc a general technique the parallel greedy algorithm is identified and used to show that finding a minimum spanning forest of a graph is reducible to the graph accessibility problem and hence is in nc 2 solvable by uniform boolean circuits of depth o log 2 n and polynomial size the class logcfl is given a new characterization in terms of circuit families the class det of problems reducible to integer determinants is defined and many examples given a new problem complete for deterministic polynomial time is given namely finding the lexicographically first maximal clique in a graph this paper is a revised version of s a cook 1983 in proceedings 1983 intl found comut sci conf lecture notes in computer science vol 158 pp 78 93 springer verlag berlin new york

optimal parallel hypercube algorithms for polygon problems we present parallel techniques on hypercubes for solving optimally a class of polygon problems we thus obtain optimal o log n time n processor hypercube algorithms for the problems of computing the portions of an n vertex simple polygonal chain c that are visible from a given source point computing the convex hull of c testing an n vertex simple polygon p for monotonicity and other related problems as well previously it was not known how to achieve these complexity bounds on hypercubes one of the main difficulties being that there is no known optimal sorting hypercube algorithm that achieves these bounds in fact these are the first optimal geometric hypercube algorithms that do not assume that the input is given already sorted by x or y coordinates the hypercube model we use is the standard one with o 1 local memory per processor and with one port communication

a logarithmic time sort for linear size networks a randomized algorithm that sorts on an n node network with constant valence in o log n time is given more particularly the algorithm sorts n items on an n node cube connected cycles graph and for some constant k for all large enough it terminates within k log n time with probability at least 1 n

divide and conquer algorithms on the hypercube abstract we show how to implement divide and conquer algorithms without undue overhead on a wide class of networks we give an optimal generic divide and conquer implementation on hypercubes for the class of divide and conquer algorithms for which the total size of the subproblems on any level of the recursion does not exceed the parent problem size for this implementation appropriately sized subcubes have to be allocated to the subproblems generated by the dividesteps we take care that these allocation steps do not cause any unbalanced distribution of work and that asymptotically they do not increase the running time variants of our generic algorithm also work for the butterfly network and by a general simulation for the class of hypercubic networks including the shuffle exchange and the cube connected cycles network our results can also be applied to optimally solve various types of routing problems

a classification of pseudospherical surface equations of type ut uxxx g u ux uxx the equations of type ut uxxx g u ux uxx which describe pseudospherical surfaces are characterized a new class of such equations is obtained this class together with the korteweg de vries kdv equation the modified korteweg de vries mkdv equation and the linear equation completes the classification

some non local transformations between nonlinear diffusion equations generalized backlund transformations are applied to derive links between a large number of different types of nonlinear diffusion equations including many which are of physical significance some new exactly linearizable forms are determined

a self stabilizing algorithm for minimum depth search of graphs abstract this paper presents a self stabilizing algorithm for the minimum depth search mds of a connected undirected graph on an asynchronous distributed or network model of computation the algorithm produces a minimum depth spanning tree mdst of the given graph in a distributed manner so that each node of the graph knows its depth and parent the algorithm is resilient to transient faults and does not require initialization it has been proved that the algorithm is correct and requires o n 2 time where n is the number of nodes of the graph

parallel matrix and graph algorithms matrix multiplication algorithms for cube connected and perfect shuffle computers are presented it is shown that in both these models two n times n matrices can be multiplied in o n m log m time when n 2 m 1 leqq m leqq n processing elements pes are available when only m 2 1 leqq m leqq n pes are available two n times n matrices can be multiplied in o n 2 m m n m 2 61 time it is shown that many graph problems can be solved efficiently using the matrix multiplication algorithms

exact solutions to a nonlinear diffusion equation similarity solutions are derived for the nonlinear diffusion equation ct del c del c in one dimension and with cylindrical symmetry some applications are indicated

the equivalence problem for the heat equation in this note we ask for the classes of equations of the second order which can be transformed into the heat equation ut uxx to give a partial answer to the question we express the heat equation by differential forms and prolong it by the estabrook wahlquist method this is motivated by the fact that our analysis is based upon conservation laws for which ideals of differential forms are a very suitable framework necessary conditions are derived for deciding whether a given equation can be transformed by some invertible point transformation into the heat equation or into its prolongation in particular the prolongation method enables us to understand the connection of various equations to the heat equation

using confidence intervals to compare several correlated areas under the receiver operating characteristic curves the performance of a diagnostic tool yielding quantitative or ordinal measurements is often assessed in terms of its area under the receiver operating characteristic curve auc as new diagnostic tools are constantly being developed a frequently occurring task is to compare multiple aucs as derived from the same group of subjects for this purpose previous methods have usually used an omnibus chi square test which may not be very informative we present here methods for comparing several correlated aucs using simultaneous confidence intervals to improve small sample properties we adopt the method of variance estimates recovery in which confidence limits for each auc are obtained on the basis of the logit and inverse hyperbolic sine transformations a simulation study demonstrates the superior performance of the proposed approach the methods are illustrated with two examples

painleve conjecture revisited the discovery of new integrable two dimensional hamiltonian systems is reported the analytic structure of the solutions makes necessary the generalization of the painlev e conjecture a widely used integrability criterion such a generalization is presented which the authors believe should replace the usual conjecture for two dimensional hamiltonian systems it is indeed compatible with all the systems already found and in addition leads to still new integrable cases

immiscible two phase flow in a porous medium utilization of a laplace transform boost a boost operator is defined for the laplace transform it is used in conjunction with the laplace transform to solve the diffusion equation on a domain with multiple moving boundaries this problem arises in the study of immiscible multiphase flow in a finite medium including end effects extensions of this method to the solution of other linear differential equations are conceivable

a local sparing design methodology for fault tolerant multiprocessors abstract we present a comprehensive design methodology for constructing low cost multiprocessors that use local spares to tolerate the failure of either processor clusters or individual processors we first formalize the concepts of global and local sparing in terms of graph automorphisms we then present a method for partitioning a multiprocessor graph by its automorphisms and for incorporating local sparing to tolerate faults we emphasize local sparing designs since they offer higher reliability to cost ratios and can reconfigure faster and in a localized manner when the spare clusters in each local subsystem are certain sizes our designs are optimal in the number of spare intersubsystem links they are all efficient optimal in some cases in terms of the number of spare intrasubsystem links we present switch based implementations that significantly reduces the spare link complexities of the designs these implementations are equally efficient for any spare cluster size so they yield efficient local sparing designs that can tolerate individual processor faults cluster size of one algorithms for fast localized and incremental reconfiguration of our ft designs are also developed finally we demonstrate that our local sparing designs have higher reliability to cost ratios than previous designs

two sided confidence intervals for the single proportion comparison of seven methods simple interval estimate methods for proportions exhibit poor coverage and can produce evidently inappropriate intervals criteria appropriate to the evaluation of various proposed methods include closeness of the achieved coverage probability to its nominal value whether intervals are located too close to or too distant from the middle of the scale expected interval width avoidance of aberrations such as limits outside 0 1 or zero width intervals and ease of use whether by tables software or formulae seven methods for the single proportion are evaluated on 96 000 parameter space points intervals based on tail areas and the simpler score methods are recommended for use in each case methods are available that aim to align either the minimum or the mean coverage with the nominal 1 alpha

on the exactly solvable equation s_t beta s gamma 2 s_x _x alpha beta s gamma 2 s_x occurring in two phase flow in porous media the symmetry approach of fokas j math phys 21 1980 pp 1318 1325 is used to show that the most general equation of the form s t g s s xx f s s x dg ds ne 0 which is exactly solvable is equivalent to the equation s t beta s gamma 2 s x x alpha beta s gamma 2 s x this equation is then mapped to the linear heat equation through a series of backlund transformations the above result is used to solve an initial boundary value problem modeling the process of waterflooding i e the displacement of oil initially in a porous reservoir by continuously injected water

the dirichlet to neumann map for a nonlinear diffusion convection equation a method for constructing the dirichlet to neumann map for a nonlinear diffusion convection equation is presented the problem is reduced to the solution of a nonlinear integral equation in one independent variable existence and uniqueness of the solution may be proven for small times via a contraction mapping technique