a new benes network control algorithm a new benes network control algorithm is presented unlike the original looping algorithm the new algorithm is not recursive in this algorithm n x n benes network is viewed as a concatenation of two subnetworks sn1 and sn2 the first log n 1 stages of a benes network correspond to sn1 and the remaining log n stages correspond to sn2 sn1 is controlled by a full binary tree of set partitioning functions called a complete residue partition tree and sn2 is bit controlled the new control algorithm sets switches one stage at a time stage by stage

bifurcation from stability to instability for a free boundary problem arising in a tumor model we consider a time dependent free boundary problem with radially symmetric initial data t 0 if open image in new window and r 0 0 r in r then the stationary solution is unstable

asymptotic behavior of solutions of a free boundary problem modeling tumor spheroid with gibbs thomson relation abstract in this paper we study a free boundary problem modeling the growth of solid tumor spheroid it consists of two elliptic equations describing nutrient diffusion and pressure distribution within tumor respectively the new feature is that nutrient concentration on the boundary is less than external supply due to a gibbs thomson relation and the problem has two radial stationary solutions which differs from widely studied tumor spheroid model with surface tension effect we first establish local well posedness by using a functional approach based on fourier multiplier method and analytic semigroup theory then we investigate stability of each radial stationary solution by employing a generalized principle of linearized stability we prove that the radial stationary solution with a smaller radius is always unstable and there exists a positive threshold value of cell to cell adhesiveness such that the radial stationary solution with a larger radius is asymptotically stable for and unstable for 0

a new approach to analyticity of dirichlet neumann operators this paper outlines the theoretical background of a new approach towards an accurate and well conditioned perturbative calculation of dirichlet neumann operators dnos on domains that are perturbations of simple geometries previous work on the analyticity of dnos has produced formulae that as we have found are very ill conditioned we show how a simple change of variables can lead to recursions that satisfy analyticity estimates without relying on subtle cancellation properties at the heart of previous formulae

on a class of rearrangeable networks benes networks are nonblocking rearrangeable networks that can realize arbitrary permutations without conflict a class of 2 log sub b n stage networks which are equivalent to the benes networks is introduced networks in this class can be either symmetric or asymmetric in their structure regular or irregular in their interstage connections and even 2 log sub b n or 2 log sub b n 1 stages all networks in this class are nonblocking rearrangeable a switch labeling scheme is proposed to provide testing of the topological and functional equivalency for this class of networks this switch labeling scheme can also provide a novel matrix representation for network configuration this representation introduces a portability concept for the routing scheme on this class of networks with this representation a general routing scheme is also developed this routing scheme can realize arbitrary permutation for the whole class of 2 log sub b n stage networks

analysis of mathematical models for the growth of tumors with time delays in cell proliferation we study two mathematical models for the growth of tumors with time delays in cell proliferation one for nonnecrotic tumors in the presence of inhibitors and the other for necrotic tumors mathematical formulations of these models are retarded differential equations by using a comparison method we make rigorous analysis of these models the results show that dynamical behavior of solutions of these models are similar to that of solutions for corresponding nonretarded problems and the tumor will tend to a dormant state as time goes to infinity in favorable conditions nutrient sufficient inhibitor less while it will finally disappear in unfavorable conditions nutrient insufficient inhibitor much

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

rearrangeability of 2 protectn 1 stage shuffle exchange networks rearrangeable networks can realize each and every permutation in one pass through the network shuffle exchange networks provide an efficient interconnection scheme for implementing various types of parallel processes whether 2n stage shuffle exchange networks with n 2n inputs outputs are rearrangeable has remained an open question for approximately three decades this question has been answered affirmatively in this paper an important corollary of the main result is the proof that two passes through an omega network are sufficient and necessary to implement any permutation in obtaining the main results of this paper frames that look like grids with horizontal links of different lengths are shown to be remarkable tools for identifying and characterizing the binary matrix representations of permutations

a three dimensional steady state tumor system abstract the growth of tumors can be modeled as a free boundary problem involving partial differential equations we consider one such model and compute steady state solutions for this model these solutions include radially symmetric solutions where the free boundary is a sphere and nonradially symmetric solutions linear and nonlinear stability for these solutions are determined numerically

analysis of a free boundary tumor model with angiogenesis we consider a free boundary problem for a spherically symmetric tumor with free boundary r 0 if liminft t 0 surprisingly we exhibit solutions when is not small where t 0 exponentially in t while r t exponentially in t finally we prove the global asymptotic stability of steady state when is sufficiently small

stationary solutions of a free boundary problem modeling the growth of tumors with gibbs thomson relation abstract in this paper we study a free boundary problem modeling tumor growth the model consists of two elliptic equations describing nutrient diffusion and pressure distribution within tumors respectively and a first order partial differential equation governing the free boundary on which a gibbs thomson relation is taken into account we first show that the problem may have none one or two radial stationary solutions depending on model parameters then by bifurcation analysis we show that there exist infinite many branches of non radial stationary solutions bifurcating from given radial stationary solution the result implies that cell to cell adhesiveness is the key parameter which plays a crucial role on tumor invasion

the kr benes network a control optimal rearrangeable permutation network the benes network has been used as a rearrangeable network for over 40 years yet the uniform n 2 log n 1 control complexity of the n spl times n benes is not optimal for many permutations in this paper we present a novel o log n depth rearrangeable network called kr benes that is permutation specific control optimal the kr benes routes every permutation with the minimal control complexity specific to that permutation and its worst case complexity for arbitrary permutations is bounded by the benes thus it replaces the benes when considering control complexity latency we design the kr benes by first constructing a restricted 2log k 2 depth rearrangeable network called k benes for routing k bounded permutations with control 2n log k 0 spl les k spl les n 4 we then show that the n spl times n benes network itself with one additional stage contains every kr benes network as a subgraph and use this property to construct the kr benes network with regard to the control optimality of the kr benes we show that any optimal network for rearrangeably routing k bounded permutations must have depth 2log k 2 and therefore the k benes and hence the kr benes is optimal

symmetry breaking bifurcation of analytic solutions to free boundary problems an application to a model of tumor growth in this paper we develop a general technique for establishing analyticity of solutions of partial differential equations which depend on a parameter e the technique is worked out primarily for a free boundary problem describing a model of a stationary tumor we prove the existence of infinitely many branches of symmetry breaking solutions which bifurcate from any given radially symmetric steady state these asymmetric solutions are analytic jointly in the spatial variables and in e 1 the model and main result in this paper we present a general technique for establishing analyticity of solutions of systems of partial differential equations which depend analytically on a parameter e the method works not only for boundary value problems but also for free boundary problems in this latter context it can be used to establish long time existence of transient solutions and also to study the existence of spatially asymmetric steady solutions since free boundary problems are typically more challenging than their boundary value counterparts we shall concentrate here on a free boundary problem from developmental biology namely a model of tumor growth to further exemplify the generality of our approach an instance of a boundary value problem in a fixed domain is presented in the last section of the paper a variety of other problems are amenable to the same analysis including in particular the hele shaw model of fluid flow 11 within the last several decades a number of mathematical models have been developed that aimed at describing the evolution of carcinomas see e g 1 5 6 8 12 13 and the references cited there the main objective of these models has been to qualitatively describe under various simplifying assumptions the growth and stability of tumor tissue analysis and simulations of such models are helping to assess the relative importance of various mechanisms affecting tumor growth as well as the efficacy of certain cancer treatments on the other hand the description of the stationary dormant configurations that arise from the models has only been addressed in the case of spherical tumors but otherwise it remains largely unexplored in this paper we develop a method for establishing analyticity of received by the editors august 17 1999 1991 mathematics subject classification primary 35b32 35r35 secondary 35b30 35b60 35c10 35j85 35q80 92c15 95c15

bifurcation from stability to instability for a free boundary problem modeling tumor growth by stokes equation we consider a free boundary problem modeling tumor growth in fluid like tissue the model equations include a diffusion equation for the nutrient concentration and the stokes equation with a source which represents the proliferation of tumor cells the proliferation rate and the cell to cell adhesiveness which keeps the tumor intact are two parameters which characterize the aggressiveness of the tumor for any positive radius r there exists a unique radially symmetric stationary solution with radius r r for a sequence mn r there exist symmetry breaking bifurcation branches of solutions with free boundary r r eyn 0 o e 2 n even 2 for small e w hereyn 0 is the spherical harmonic of mode n 0 furthermore the smallest mn r s aymn r is such that n n r as r in this paper we prove that the radially symmetric stationary solution with r rs is linearly stable if n rs w heren rs mn rs and we prove that strict inequality holds if is small or if is large the biological implications of these results are discussed at the end of the paper

bifurcation for a free boundary problem with surface tension modeling the growth of multi layer tumors this paper is devoted to the study of the bifurcation of a free boundary problem modeling the growth of tumors with the effect of surface tension being considered the existence of infinitely many branches of bifurcation solutions is proved the method of analysis is based on reducing the problem to an operator equation in certain holder space with a nonlinear fredholm operator of index 0 the desired result then follows from the crandall rabinowitz bifurcation theorem

free boundary problems with surface tension conditions abstract in this paper we consider free boundary problems with a surface tension condition at the free boundary the simplest of these problems is the classical hele shaw problem which describes viscous flow between two parallel plates with small spacing we shall consider models which describe tumor growth and are expressed by systems of pdes we shall also consider the hele shaw problem constrained in a half space

a center manifold analysis for the mullins sekerka model abstract the mullins sekerka model is a nonlocal evolution model for hypersurfaces which arises as a singular limit for the cahn hilliard equation we show that classical solutions exist globally and tend to spheres exponentially fast provided that they are close to a sphere initially our analysis is based on center manifold theory and on maximal regularity

characterization of admissible linear estimators in the general growth curve model with respect to an incomplete ellipsoidal restriction abstract in this paper we study the characterization of admissible linear estimators of regression coefficients in the general growth curve model with respect to an incomplete ellipsoidal restriction under the loss function d y kbl d y kbl by the methods of linear algebra and matrix theory when kbl is estimable the necessary and sufficient conditions for linear estimators to be admissible in the homogeneous and non homogeneous linear classes are given if kbl is inestimable we obtain the necessary and sufficient conditions for linear estimators to be admissible in the homogeneous and non homogeneous linear classes using orthogonal projection approach

les aspects fondamentaux de l admissibilite en approximation quadratique d applications lineaires abstract the quadratic approximation of a linear mapping under affine constraints is a central problem in linear statistical inference it is based on two fundamental orderings on the set of quadratic forms defined on a finite dimensional vector space e one is loewner ordering and the other based on the trace of linear mappings of e into e the direction of the affine subspace of constraints is a tensor product of two vector spaces the search for minimum solutions is now replaced by investigation of minimal solutions called optimal or admissible according to the ordering a functional approach shows that we can obtain many identical results which often only depend on the linear structure of the considered vector spaces we prove thereby two results the first is a significant generalization of a theorem due to a olsen j seely and d birkes 11 on the completeness of the set of optimal or admissible solutions and the second is theorem containing some necessary conditions of admissibility this theorem is a consequence of an extension of an important theorem due to l r lamotte 9 proof of which has already been given in this general framework 18 19

a free boundary problem for a singular system of differential equations an application to a model of tumor growth first published in transactions of the american mathematical society in volume 355 issue 9 published by the american mathematical society

on rearrangeability of tandem connection of banyan type networks a multistage interconnection network min consisting of 2 times 2 nodes constructs a nonblocking switch if the network is rearrangeable when a 2n times 2n bit permuting network is rearrangeable with the minimum depth of 2n 1 the initial resp final n stages of the network form a banyan type network and hence the network is equivalent to the tandem connection between two banyan type networks let gamma denote the guide permutation of a 2n times 2n banyan type network and tau the trace permutation of another these are permutations on numbers from 1 to n this paper proves that when the permutation gammatau 1 is the transposition between the number n and some number k n the tandem connection between the two networks is rearrangeable this sufficient condition for rearrangeability covers a wide class of tandem connections for example the first network in tandem can be the omega network appended with the banyan exchange of any rank while the second is the reversed omega network

stability and instability of liapunov schmidt and hopf bifurcation for a free boundary problem arising in a tumor model first published in transactions of the american mathematical society in volume 360 issue 10 published by the american mathematical society

rearrangeability of bit permutation networks in this paper we introduce the concept of routing grid as a tool for analyzing realizability of permutations on bit permutation networks bpns we extend a result by linial and tarsi which characterizes permutations realizable on shuffle exchange networks to any bpns a necessary condition for a bpn to he rearrangeable is given and the rearrangeability of two families of bpns are explored finally we present a method which may help to tackle one kind of balanced matrix problems whose solution implies an answer to benes conjecture hopefully our treatment brings some new insight into the problem of permutation routing

bifurcation for a free boundary problem modeling the growth of tumors with a drug induced nonlinear proliferation rate abstract in this paper we study a free boundary model describing growth of tumors under action of drugs to our knowledge in theoretical discussion for free boundary problems the proliferation rate in tumor models discussed in previous bifurcation results is a linear function of nutrients and inhibitors whereas in this paper we consider the net proliferation rate as a nonlinear function depending on both nutrients and drugs first the existence and the uniqueness of radially symmetric stationary solutions are obtained second we prove that symmetry breaking solutions bifurcate from the radially symmetric stationary solutions when the concentration of drug on the boundary of tumor is less than one in the rescaled model

lie group action and stability analysis of stationary solutions for a free boundary problem modelling tumor growth abstract in this paper we study asymptotic behavior of solutions for a free boundary problem modelling tumor growth we first establish a general result for differential equations in banach spaces possessing a lie group action which maps a solution into new solutions we prove that a center manifold exists under certain assumptions on the spectrum of the linearized operator without assuming that the space in which the equation is defined is of either d a or d a type by using this general result and making delicate analysis of the spectrum of the linearization of the stationary free boundary problem we prove that if the surface tension coefficient is larger than a threshold value then the unique stationary solution is asymptotically stable modulo translations provided the constant c is sufficiently small whereas if then this stationary solution is unstable

a parabolic hyperbolic system modeling the growth of a tumor abstract in this paper we consider a model with tumor microenvironment involving nutrient density extracellular matrix and matrix degrading enzymes which satisfy a coupled system of pdes with a free boundary for this coupled parabolic hyperbolic free boundary problem we prove that there is a unique radially symmetric solution globally in time the stationary problem involves an ode system which is transformed into a singular integro differential equation we establish a well posed theorem for such general types of equations by the shooting method the theorem is then applied to our problem for the existence of a stationary solution in addition for this highly nonlinear problem we also prove the uniqueness of the stationary solution which is a nontrivial result moreover numerical simulations indicate that the stationary solution is likely locally asymptotically stable for reasonable range of parameters

a new routing algorithm for a class of rearrangeable networks this paper presents a routing algorithm for a class of multistage interconnection networks specifically the concatenation of two omega networks which has 2 log sub 2 n stages is treated it is shown that this kind of asymmetric omega omega network can be converted into a symmetric omega sup 1spl times omega network or a symmetric omega spl times omega sup 1 network however they have butterfly connections between the two center stages a general algorithm is developed which routes a class of symmetric networks the algorithm routes the network from center stages to outer stages at both the input and the output sides simultaneously the algorithm presented is simpler and more flexible than the well known looping algorithm in that it can be applied adaptively according to the structure of the network it can be applied to routing the omega based networks regardless of the center stage connection patterns i e straight skewed straight simple butterfly or skewed butterfly as long as the networks are symmetric the sufficient conditions for proper routing are shown and proved in addition an example is shown to demonstrate the algorithm

admissibility of linear estimators with respect to inequality constraints under matrix loss function in this paper we investigate the admissibility of linear estimators in the multivariate linear model with respect to inequality constraints under matrix loss function the necessary and sufficient conditions for a linear estimator to be admissible in the class of homogeneous linear estimators and the class of inhomogeneous linear estimators are obtained respectively

analysis of an elliptic parabolic free boundary problem modelling the growth of non necrotic tumor cord abstract we study a free boundary problem modelling the growth of a tumor cord in which tumor cells live around and receive nutrient from a central blood vessel the evolution of the tumor cord surface is governed by darcy s law together with a surface tension equation the concentration of nutrient in the tumor cord satisfies a reaction diffusion equation in this paper we first establish a well posedness result for this free boundary problem in some sobolev besov spaces with low regularity by using the analytic semigroup theory we next study asymptotic stability of the unique radially symmetric stationary solution by making delicate spectrum analysis for the linearized problem we prove that this stationary solution is locally asymptotically stable provided that the constant c representing the ratio between the diffusion time of nutrient and the birth time of new cells is sufficiently small

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

asymptotic stability for a free boundary problem arising in a tumor model abstract we consider a tumor model in which all cells are proliferating at a rate and their density is proportional to the nutrient concentration the model consists of a coupled system of an elliptic equation and a parabolic equation with the tumor boundary as a free boundary it is known that for an appropriate choice of parameters there exists a unique spherically symmetric stationary solution with radius r s which is independent of it was recently proved that there is a function r s such that the spherical stationary solution is linearly stable if r s and linearly unstable if r s in this paper we prove that the spherical stationary solution is nonlinearly stable or asymptotically stable if r s

analysis of a tumor model free boundary problem with a nonlinear boundary condition abstract in this paper we study a free boundary problem modeling the growth of nonnecrotic tumors with angiogenesis this model differs from the other tumor models studied in existing literatures at the point that it has a nonlinear boundary value condition for the nutrient concentration we first study spherically symmetric version of this model we prove that there exists a unique spherically symmetric stationary solution which is asymptotically stable under spherically symmetric perturbation next we make rigorous analysis to the spherically asymmetric version of this model by using some abstract theory of parabolic differential equations in banach manifold we prove that this free boundary problem is locally well posed in little holder spaces and the radial stationary solution is asymptotically stable in case the surface tension coefficient is larger than a threshold value whereas unstable in case is less than this threshold value

on eigenvalues of the linearization of a free boundary problem modeling two phase tumor growth abstract in this paper we study eigenvalues of the linearization of a free boundary problem modeling the growth of a tumor containing two species of cells proliferating cells and quiescent cells such eigenvalues are potential bifurcation points from which nonradial solutions of the free boundary problem might bifurcate from the radial solution a special feature of this problem is that it contains a singular ordinary differential equation which causes the main difficulty of this problem by using the spherical harmonic expansion method combined with some techniques for solving singular differential integral equations developed in some previous literature eigenvalues of the linearized problem are completely determined invertibility of some linear operators related to the linearized problem in suitable function spaces is also studied which might be useful in the analysis of the original free boundary problem

well posedness and stability of a free boundary problem modeling the growth of multi layer tumors abstract in this paper we study well posedness and stability of a free boundary problem modeling the growth of multi layer tumors under the action of external inhibitors an important feature of this problem is that the surface tension of the free boundary is taken into account we first reduce this free boundary problem into an evolution equation in little holder space and use the well posedness theory for differential equations in banach spaces of parabolic type i e equations which are treatable by using the analytic semi group theory to prove that this free boundary problem is locally well posed for initial data belonging to a little holder space next we study flat solutions of this problem we obtain all flat stationary solutions and give a precise description of asymptotic stability of these stationary solutions under flat perturbations finally we investigate asymptotic stability of flat stationary solutions under non flat perturbations by carefully analyzing the spectrum of the linearized stationary problem and employing the theory of linearized stability for differential equations in banach spaces of parabolic type we give a complete analysis of stability and instability of all flat stationary solutions under small non flat perturbations

regularity of solutions to a free boundary problem modeling tumor growth by stokes equation in this paper we investigate regularity of solutions to a free boundary problem modeling tumor growth in fluid like tissues the model equations include a quasi stationary diffusion equation for the nutrient concentration and a stokes equation with a source representing the proliferation density of the tumor cells subject to a boundary condition with stress tensor effected by surface tension this problem is a fully nonlinear problem involving nonlocal terms based on the employment of the functional analytic method and the theory of maximal regularity we prove that the free boundary of this problem is real analytic in temporal and spatial variables for initial data of less regularity

the universality of the shuffle exchange network this paper has focused on the realization of every arbitrary permutation with the shuffle exchange network permutation properties of shuffle exchange networks are studied and are used to demonstrate several universal networks it is concluded that 3 log2 n 1 passes through a single stage regular shuffle exchange network are sufficient to realize every arbitrary permutation where n is network size a routing algorithm is also developed to calculate control settings of the shuffle exchange switches for the permutation realization three optimal universal networks namely expanded direct connection shuffle exchange network multiple pass omega network and modified shuffle exchange network are then exploited for better interconnection purposes in addition this work specifies the inherent relationship between the shuffle exchange network and the benes binary network so that designers can have a broad prospect

on the correctness of inside out routing algorithm recently a new routing algorithm called inside out routing algorithm was proposed for routing an arbitrary permutation in the omega based 2log sub 2 n stage networks this paper discusses the problems of the inside out routing algorithm and shows that the suggested condition for proper routing in the omega omega network is insufficient an extended necessary and sufficient condition for proper routing in the omega omega network is also suggested however it is unknown if any permutation can be successfully routed by a heuristic algorithm which follows the condition thus the rearrangeability of the omega omega network still remains an open problem

admissible linear estimators in linear models with respect to inequality constraints abstract admissibility of linear estimators is characterized in linear models e y x d y v with an unknown multidimensional parameter v varying in the cartesian product c v where c is a halfspace and v is a given set of nonnegative definite symmetric matrices the relation between admissibility of inhomogeneous and homogeneous linear estimators is discussed and some sufficient and necessary conditions for admissibility of an inhomogeneous linear estimator are given some results were extended to the case where c is a given polyhedral convex cone

on a reaction diffusion equation with robin and free boundary conditions this paper studies the following problem ut uxx f u 0 0 u 0 t bux 0 t t 0 u h t t 0 h t ux h t t t 0 h 0 h0 u x 0 x 0 x h0 where f is an unbalanced bistable nonlinearity b 0 0 and is a compactly supported c2 function we prove that there exists 0 such that vanishing happens when 0 and u t converges as t to 0 uniformly in 0 h t spreading happens when i e h t c t tends to a constant for some c 0 u t converges to a positive stationary solution locally uniformly in 0 and to a traveling semi wave with speed c near x h t in the transition case when u t v t h2 0 h t tends to 0 as t where t is a maximum point of u t and v is the unique even positive solution of v f v 0 subject to v 0 moreover with respect to b and f t pln t q o 1 for some p 0 and q r or t z for some root z of v z bv z

bifurcation for a free boundary problem modeling the growth of multi layer tumors abstract in this paper we study bifurcations for a free boundary problem modeling the growth of multi layer tumors under the action of inhibitors an important feature of this problem is that the surface tension effect of the free boundary is taken into account by reducing this problem into an abstract bifurcation equation in a banach space overcoming some technical difficulties and finally using the crandall rabinowitz bifurcation theorem we prove that this problem has infinitely many branches of bifurcation solutions bifurcating from the flat solution

simultaneous regression shrinkage variable selection and supervised clustering of predictors with oscar variable selection can be challenging particularly in situations with a large number of predictors with possibly high correlations such as gene expression data in this article a new method called the oscar octagonal shrinkage and clustering algorithm for regression is proposed to simultaneously select variables while grouping them into predictive clusters in addition to improving prediction accuracy and interpretation these resulting groups can then be investigated further to discover what contributes to the group having a similar behavior the technique is based on penalized least squares with a geometrically intuitive penalty function that shrinks some coefficients to exactly zero additionally this penalty yields exact equality of some coefficients encouraging correlated predictors that have a similar effect on the response to form predictive clusters represented by a single coefficient the proposed procedure is shown to compare favorably to the existing shrinkage and variable selection techniques in terms of both prediction error and model complexity while yielding the additional grouping information

stationary shapes for 2 d water waves and hydraulic jumps a hydraulic jump is a physical phenomenon commonly observed in nature such as in open channel flows or spillways and is dependent upon the relation between the initial upstream fluid speed and a critical speed characterized by a dimensionless number f known as the froude number in this paper we prove the existence of hydraulic jumps for stationary water waves as a consequence of the existence of bifurcation branches of non flat liquid interfaces originated from each of a sequence of upstream velocities f1 f2 fr fr 0 as r we further establish explicitly for f 0 f fr r the existence and uniqueness of the solution of a perfect incompressible irrotational free surface flow over a flat bottom under the influence of gravity as well as the corresponding hydraulic jump

solution of a boundary value problem for the helmholtz equation via variation of the boundary into the complex domain in this paper we deal with the problem of diffraction of electromagnetic waves by a periodic interface between two materials this corresponds to a two dimensional quasi periodic boundary value problem for the helmholtz equation we prove that solutions behave analytically with respect to variations of the interface the interest of this result is both theoretical the legitimacy of power series expansions in the parameters of the problem has indeed been questioned and perhaps more importantly practical we have found that the solution can be computed on the basis of this observation the simple algorithm that results from such boundary variations is described to establish the property of analyticity of the solution for the grating with respect to the height we present a holomorphic formulation of the problem using surface potentials we show that the densities entering into the potential theoretic formulation are analytic with respect to variations of the boundary or in other words that the integral operator that results from the transmission conditions at the interface is invertible in a space of holomorphic functions of the variables x y this permits us to conclude in particular that the partial derivatives of u with respect to at 0 satisfy certain boundary value problems for the helmholtz equation in regions with plane boundaries which can be solved in a closed form

analysis of a free boundary problem modeling the growth of multicell spheroids with angiogenesis abstract in this paper we study a free boundary problem modeling the growth of vascularized tumors the model is a modification to the byrne chaplain tumor model that has been intensively studied during the past two decades the modification is made by replacing the dirichlet boundary value condition with the robin condition which causes some new difficulties in making rigorous analysis of the model particularly on existence and uniqueness of a radial stationary solution in this paper we successfully solve this problem we prove that this free boundary problem has a unique radial stationary solution which is asymptotically stable for large surface tension coefficient whereas unstable for small surface tension coefficient tools used in this analysis are the geometric theory of abstract parabolic differential equations in banach spaces and spectral analysis of the linearized operator

existence of three dimensional toroidal mhd equilibria with nonconstant pressure we establish an existence result for the three dimensional mhd equations x b x b p b 0 b n t 0 with p const in tori t without symmetry more precisely our theorems insure the existence of sharp boundary solutions for tori whose departure from axisymmetry is sufficiently small they allow for solutions to be constructed with an arbitrary number of pressure jumps

a hyperbolic free boundary problem modeling tumor growth asymptotic behavior first published in transactions of the american mathematical society in volume 357 issue 12 published by the american mathematical society

frames a simple characterization of permutations realized by frequently used networks rearrangeable multistage networks such as the benes network realize any permutation yet their routing algorithms are not cost effective on the other hand there exist inexpensive routing algorithms for nonrearrangeable networks but no simple technique exists to characterize all the permutations realized on these networks this paper introduces the concept of frame and shows how it can be used to characterize all the permutations realized on various multistage interconnection networks they include subnetworks of baseline benes and cascaded baseline and shuffle exchange networks

boundary element method for a free boundary problem modeling three dimensional tumor growth abstract in the mathematical model of tumor growth the initial boundary surface of the three dimensional tumor domain is known but the tumor domain and its boundary surface change over time in a way that is unknown in advance people are concerned whether the tumor is likely to spread or shrink and how the tumor will change in this article by the boundary element method the free boundary problem in the three dimensional tumor domain will be solved via the integration on a two dimensional boundary surfaces at the expense of singularity in the green s functions we will numerically compute and graphically show the changing boundary surfaces of the three dimensional tumor domain over time we will numerically analyze the trend of tumor growth with varying proliferation rate our numerical approach professor bei hu proposed is new and our numerical experiments contribute to the prediction of tumor growth in clinical medicine

analysis of a mathematical model for tumor growth with gibbs thomson relation abstract in this paper we study a mathematical model for the growth of nonnecrotic solid tumor the tumor is assumed to be radially symmetric and its radius r t is an unknown function of time t as tumor growth and the model is in the form of a free boundary problem the feature of the model is that a gibbs thomson relation is taken into account which results an interesting phenomenon that there exist two stationary solutions depending on the model parameters the global existence and uniqueness of solution are established by denoting c the ratio of the diffusion time scale to the tumor doubling time scale we prove that for sufficiently small c 0 the stationary solution with the larger radius is asymptotically stable and the other smaller one is unstable

bifurcation for a free boundary problem modeling a protocell abstract in this paper we consider a free boundary problem for a physico chemical model of a protocell this model of a self maintaining unity or a protocell is based on the reaction and diffusion process and a mechanism of self control of the boundary for any positive radius r there exists a radially symmetric solution with radius r r in the more realistic three space dimensional case we give a proof that there exist symmetry breaking bifurcation branches of solutions with free boundary r r y n 0 o 2 n 2 even for small where y n 0 is the spherical harmonic of mode n 0

bifurcation for a free boundary tumor model with extracellular matrix and matrix degrading enzymes abstract we study a free boundary problem modeling solid tumor growth with ecm and mde interactions the production rate of mde by tumor cells is a nonlinear function depending on nutrients and mde this nonlinear term is more complicated for this model we can not give the explicit expressions or integral expressions for mde terms while we only get the existence and uniqueness at first we show the existence and the uniqueness of radially symmetric stationary solutions then the existence of symmetry breaking solutions bifurcating from the radially symmetric stationary solutions is obtained

topologies of combined 2 log n 1 stage interconnection networks a combined 2 log n 1 stage interconnection network denoted by spl delta spl oplus spl delta is constructed by concatenating two omega equivalent networks spl delta and spl delta with the rightmost stage of spl delta and the leftmost stage of spl delta overlapped benes network and the 2 log n 1 stage shuffle exchange network are two examples of such networks although these two networks have received intensive studies the research on the topology of entire class of spl delta spl oplus spl delta networks is very limited so far in this paper we study the topological structure of spl delta spl oplus spl delta networks and propose an algorithm for determining topological equivalence between two given spl delta spl oplus spl delta networks we also present a simplified spl omega equivalence checking algorithm as a supporting result

a penalized method for multivariate concave least squares with application to productivity analysis abstract we propose a penalized method for the least squares estimator of a multivariate concave regression function this estimator is formulated as a quadratic programing qp problem with o n2 constraints where n is the number of observations computing such an estimator is a very time consuming task and the computational burden rises dramatically as the number of observations increases by introducing a quadratic penalty function we reformulate the concave least squares estimator as a qp with only non negativity constraints this reformulation can be adapted for estimating variants of shape restricted least squares i e the monotonic concave convex least squares the experimental results and an empirical study show that the reformulated problem and its dual are solved significantly faster than the original problem the matlab and r codes for implementing the penalized problems are provided in the paper

a free boundary problem modeling the cell cycle and cell movement in multicellular tumor spheroids abstract this paper deals with a mathematical model describing the cell cycle dynamics and chemotactic driven cell movement in a multicellular tumor spheroid tumor cells consist of two types of cells proliferating cells and quiescent cells which have different chemotactic responses to an extracellular nutrient supply the model is a free boundary problem for a nonlinear system of reaction diffusion advection equations where the free boundary is the outer boundary of the spheroid the free boundary condition is quite novel due to different velocity of two types of cells the global existence and uniqueness of solutions to the model is proved the proof is based on a fixed point argument together with the l p theory for parabolic equations with the third boundary condition

well posedness and stability of a multi dimensional tumor growth model we study a moving boundary problem modeling the growth of in vitro tumors this problem consists of two elliptic equations describing the distribution of the nutrient and the internal pressure respectively and a first order partial differential equation describing the evolution of the moving boundary an important feature is that the effect of surface tension on the moving boundary is taken into account we show that this problem is locally well posed for a large class of initial data by using analytic semi group theory we also prove that if the surface tension coefficient is larger than a threshold value then the unique flat equilibrium is asymptotically stable whereas in the case this flat equilibrium is unstable

bifurcation solutions of a free boundary problem modeling tumor growth with angiogenesis abstract in this paper we study bifurcation solutions from the unique radial solution of a free boundary problem modeling stationary state of tumors with angiogenesis this model comprises two elliptic equations describing the distribution of the nutrient concentration x and the inner pressure p p x unlike similar tumor models that have been intensively studied in the literature where dirichlet boundary condition for is imposed in this model the boundary condition for is a robin boundary condition existence and uniqueness of a radial solution of this model have been successfully proved in a recently published paper 20 in this paper we study existence of nonradial solutions by using the bifurcation method let k k 2 be the sequence of eigenvalues of the linearized problem we prove that there exists a positive integer k 2 such that in the two dimension case for any k k k is a bifurcation point and in the three dimension case for any even k k k is also a bifurcation point