nils-herrmann/clean_scirepeval huggingface dataset:
Fixed points of polynomial maps. Part II. Fixed point portraits
— Douady, Hubbard and Branner have introduced the concept of a "limb" in the Mandelbrot set. A quadratic map f(z) = z + c belongs to the p/q-limb if and only if there exist q external rays of its Julia set which land at a common fixed point of/, and which are permuted by/with combinatorial rotation number ^^Q/Z, p / q ^ O . ( This note will make a similar analysis of higher degree polynomials by introducing the concept of the "fixed point portrait" of a monic polynomial map.

title: On the shape of the unit sphere in Q(Δ)
abstract: We show that the unit sphere in the Banach space of L 1 holomorphic quadratic differentials on the disk is weakly uniformly convex with exponent 1/2 at certain points

title: Uniformization of attracting basins for exponential maps
abstract: Soit la famille exponentielle complexe Eλ(Z)=λ exp(Z). Il y a un ensemble ouvert de valeurs de λ dans le plan complexe pour lesquelles Eλ a un point fixe attractif unique; Ωλ est le bassin d'attraction pour ces valeurs. On considere l'uniformisation Φλ de Ωλ et on etudie la dynamique induite par Φλ sur le disque unite

title: A finiteness theorem for a dynamical class of entire functions

title: On the multiplier of a repelling fixed point
abstract: We estimate the multiplier λ of a repelling fixed point with rational rotation number for a polynomial in one complex variable. We show that a canonical branch of the logarithm of λ lies in a small disk tangent to the imaginary axis. The radius of the disk is determined by the degree of the polynomial, the rotation number of the fixed point and the escape rates and external arguments of the critical values.

title: Volatility of the short rate in the rational lognormal model
abstract: A recent article of Flesaker and Hughston introduces a one factor interest rate model called the rational lognormal model. This model has a lot to recommend it including guaranteed finite positive interest rates and analytic tractability. Consequently, it has received a lot of attention among practioners and academics alike. However, it turns out to have the undesirable feature of predicting that the asymptotic value of the short rate volatility is zero. This theoretical result is proved rigorously in this article. The outcome of an empirical study complementing the theoretical result is discussed at the end of the article. European call options are valued with the rational lognormal model and a comparably calibrated mean reverting Gaussian model. unsurprisingly, rational lognormal option values are considerably lower than the analogous mean reverting Gaussian option values. In other words, the volatility in the rational lognormal model declines so quickly that options are severely undervalued.
A finiteness theorem for a dynamical class of entire functions

title: Uniformization of attracting basins for exponential maps
abstract: Soit la famille exponentielle complexe Eλ(Z)=λ exp(Z). Il y a un ensemble ouvert de valeurs de λ dans le plan complexe pour lesquelles Eλ a un point fixe attractif unique; Ωλ est le bassin d'attraction pour ces valeurs. On considere l'uniformisation Φλ de Ωλ et on etudie la dynamique induite par Φλ sur le disque unite

title: On the multiplier of a repelling fixed point
abstract: We estimate the multiplier λ of a repelling fixed point with rational rotation number for a polynomial in one complex variable. We show that a canonical branch of the logarithm of λ lies in a small disk tangent to the imaginary axis. The radius of the disk is determined by the degree of the polynomial, the rotation number of the fixed point and the escape rates and external arguments of the critical values.

title: Catalan numbers and branched coverings by the Riemann sphere
abstract: We prove that the number of PGL(2, C) equivalence classes of degree d rational maps with a fixed branch set is generically equal to the “Catalan number” ϱ(d) = ( 1 d )( 2d−2 d−1 ) . Several (previously known) applications of Catalan numbers to combinatorics and algebraic geometry are discussed throughout the course of the article.

title: On the shape of the unit sphere in Q(Δ)
abstract: We show that the unit sphere in the Banach space of L 1 holomorphic quadratic differentials on the disk is weakly uniformly convex with exponent 1/2 at certain points

title: Volatility of the short rate in the rational lognormal model
abstract: A recent article of Flesaker and Hughston introduces a one factor interest rate model called the rational lognormal model. This model has a lot to recommend it including guaranteed finite positive interest rates and analytic tractability. Consequently, it has received a lot of attention among practioners and academics alike. However, it turns out to have the undesirable feature of predicting that the asymptotic value of the short rate volatility is zero. This theoretical result is proved rigorously in this article. The outcome of an empirical study complementing the theoretical result is discussed at the end of the article. European call options are valued with the rational lognormal model and a comparably calibrated mean reverting Gaussian model. unsurprisingly, rational lognormal option values are considerably lower than the analogous mean reverting Gaussian option values. In other words, the volatility in the rational lognormal model declines so quickly that options are severely undervalued.
On the uniqueness of the solution of the evolution dam problem

title: On the dam problem
abstract: This paper is concerned with the qualitative behavior of solutions of the "dam problem'' for flow of an incompressible fluid through a two-dimensional porous medium. The cross section of the flow region is allowed to have a complicated boundary (the flow domain is assumed to have a Lipschitz boundary and minimal assumptions are made on the parts where various boundary conditions are to be satisfied). The main contribution of the paper is to determine the corresponding properties of the solution. After giving a concise proof of the known result that a solution exists, the authors introduce the so-called "S 3 -connected''solutions (S 3 is the impervious part of the boundary), and prove several interesting results about them. Solutions which do not have these properties are such that there are pools of fluid not in contact with the outside reservoir, and they prove that any solution can be written as a sum of an S 3 -connected solution and pools. Also, it is shown that S 3 -connected solutions are unique. For some boundaries it can be shown that only S 3 -connected solutions exist, so that uniqueness holds without qualification.

title: The dam problem with leaky boundary conditions
abstract: The goal of this paper is to study the fluid flow through a two-dimensional porous medium when we impose a leaky boundary condition. We show in particular that the situation is quite different from the one with the usual Dirichlet boundary condition.

title: On some nonlinear elliptic equations involving derivatives of the nonlinearity
abstract: The existence of weak solutions of the Dirichlet problem for nonlinear elliptic equations of the type −(∂/∂x j )(a ij (x)u x i +b j (u))+a(x)u=f is proved for nonlinearities b j which are only continuous. The proof is based on the observation that an L ∞ a priori estimate is valid which is independent of b j . The second part contains several uniqueness results and counterexamples, showing that uniqueness may fail in general.

title: Entropy Solutions for Nonlinear Degenerate Problems
abstract: We consider a class of elliptic‐hyperbolic degenerate equations 
$$g(u)-\Delta b(u) +\divg\phi (u) =f$$ with Dirichlet homogeneous boundary conditions and a class of elliptic‐parabolic‐hyperbolic degenerate equations 
$$g(u)_t-\Delta b(u) +\divg\phi (u) =f$$ with homogeneous Dirichlet conditions and initial conditions. Existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function φ satisfying rather general conditions. Comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for φ continuous.

title: Uniqueness of Renormalized Solutions of Degenerate Elliptic–Parabolic Problems
abstract: We consider a general class of degenerate elliptic-paraboic problems associated with the equation b(v)(t) = div a(v, Dv) + f. Using Kruzhkov's method of doubling variables both in space and time we prove uniqueness and a comparison principle in L-1 for renormalized solutions
Uniqueness of Renormalized Solutions of Degenerate Elliptic–Parabolic Problems
We consider a general class of degenerate elliptic-paraboic problems associated with the equation b(v)(t) = div a(v, Dv) + f. Using Kruzhkov's method of doubling variables both in space and time we prove uniqueness and a comparison principle in L-1 for renormalized solutions

title: Entropy Solutions for Nonlinear Degenerate Problems
abstract: We consider a class of elliptic‐hyperbolic degenerate equations 
$$g(u)-\Delta b(u) +\divg\phi (u) =f$$ with Dirichlet homogeneous boundary conditions and a class of elliptic‐parabolic‐hyperbolic degenerate equations 
$$g(u)_t-\Delta b(u) +\divg\phi (u) =f$$ with homogeneous Dirichlet conditions and initial conditions. Existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function φ satisfying rather general conditions. Comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for φ continuous.

title: On some nonlinear elliptic equations involving derivatives of the nonlinearity
abstract: The existence of weak solutions of the Dirichlet problem for nonlinear elliptic equations of the type −(∂/∂x j )(a ij (x)u x i +b j (u))+a(x)u=f is proved for nonlinearities b j which are only continuous. The proof is based on the observation that an L ∞ a priori estimate is valid which is independent of b j . The second part contains several uniqueness results and counterexamples, showing that uniqueness may fail in general.

title: The dam problem with leaky boundary conditions
abstract: The goal of this paper is to study the fluid flow through a two-dimensional porous medium when we impose a leaky boundary condition. We show in particular that the situation is quite different from the one with the usual Dirichlet boundary condition.
On some nonlinear elliptic equations involving derivatives of the nonlinearity
The existence of weak solutions of the Dirichlet problem for nonlinear elliptic equations of the type −(∂/∂x j )(a ij (x)u x i +b j (u))+a(x)u=f is proved for nonlinearities b j which are only continuous. The proof is based on the observation that an L ∞ a priori estimate is valid which is independent of b j . The second part contains several uniqueness results and counterexamples, showing that uniqueness may fail in general.

title: The dam problem with leaky boundary conditions
abstract: The goal of this paper is to study the fluid flow through a two-dimensional porous medium when we impose a leaky boundary condition. We show in particular that the situation is quite different from the one with the usual Dirichlet boundary condition.

title: On the dam problem
abstract: This paper is concerned with the qualitative behavior of solutions of the "dam problem'' for flow of an incompressible fluid through a two-dimensional porous medium. The cross section of the flow region is allowed to have a complicated boundary (the flow domain is assumed to have a Lipschitz boundary and minimal assumptions are made on the parts where various boundary conditions are to be satisfied). The main contribution of the paper is to determine the corresponding properties of the solution. After giving a concise proof of the known result that a solution exists, the authors introduce the so-called "S 3 -connected''solutions (S 3 is the impervious part of the boundary), and prove several interesting results about them. Solutions which do not have these properties are such that there are pools of fluid not in contact with the outside reservoir, and they prove that any solution can be written as a sum of an S 3 -connected solution and pools. Also, it is shown that S 3 -connected solutions are unique. For some boundaries it can be shown that only S 3 -connected solutions exist, so that uniqueness holds without qualification.

title: Entropy Solutions for Nonlinear Degenerate Problems
abstract: We consider a class of elliptic‐hyperbolic degenerate equations 
$$g(u)-\Delta b(u) +\divg\phi (u) =f$$ with Dirichlet homogeneous boundary conditions and a class of elliptic‐parabolic‐hyperbolic degenerate equations 
$$g(u)_t-\Delta b(u) +\divg\phi (u) =f$$ with homogeneous Dirichlet conditions and initial conditions. Existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function φ satisfying rather general conditions. Comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for φ continuous.
Processus stochastiques de population

title: Some population and epidemic models revisited.
abstract: Three problems of population and epidemic models formulated between ten and thirty years ago are reconsidered. In each case, a modified approach to the problem leads to its solution. For the two-sex population model, the solution of a Riccati equation results in an expression for the generating function of the process. The fully stochastic, as against the previously studied semistochastic, model of population growth with random catastrophes yields to hard analysis. Finally a generalized form of the general stochastic epidemic is solved using matrix geometric methods.

title: Stochastic Models for Type Counts in a Literary Text

title: Modelling the spread of HIV in prisons
abstract: This paper is concerned with models for the spread of HIV in prisons. We first consider a single prison of size N in which there is homogeneous mixing, and where there is an inflow and outflow of n< N prisoners at times t= 0, 1, 2,... Conditions are derived for the stability of the system. The interaction of such a prison with the outside world is then studied, and stability conditions obtained for this case. Finally, a quarantine policy is examined and its cost analyzed, both in the non-stable and stable cases.

title: A simple deterministic epidemic in several related growing communities
abstract: This paper first considers a simple deterministic epidemic in a growing population. It then examines a simple deterministic epidemic in several related growing communities, where infection is transmitted between individuals both within and across the communities. An explicit parametric solution is derived for the number of susceptibles in these communities as a function of time.

title: Random Allocation Methods in an Epidemic Model
abstract: A random allocation model is developed for the numbers of susceptibles in a group of n IVDU’s who become infected by i HIV-infectives sharing needles. A comparison of this model and the classical Reed-Frost model is outlined.

title: OBITUARY: EDWARD JAMES HANNAN
Stochastic Models for Type Counts in a Literary Text

title: Modelling the spread of HIV in prisons
abstract: This paper is concerned with models for the spread of HIV in prisons. We first consider a single prison of size N in which there is homogeneous mixing, and where there is an inflow and outflow of n< N prisoners at times t= 0, 1, 2,... Conditions are derived for the stability of the system. The interaction of such a prison with the outside world is then studied, and stability conditions obtained for this case. Finally, a quarantine policy is examined and its cost analyzed, both in the non-stable and stable cases.

title: A simple deterministic epidemic in several related growing communities
abstract: This paper first considers a simple deterministic epidemic in a growing population. It then examines a simple deterministic epidemic in several related growing communities, where infection is transmitted between individuals both within and across the communities. An explicit parametric solution is derived for the number of susceptibles in these communities as a function of time.

title: Point Processes in Epidemiology
abstract: The paper consists of six sections. The first is devoted to chain binomial methods and their use in the statistical analysis of measles and hepatitis data. A second considers time dependent results for carrier-borne epidemics, and the use of matrix methods in computing probabilities of their final size. The third surveys the application of perturbation techniques to the general stochastic epidemic, and the estimation of infection and removal parameters in this model on the basis of smallpox data. The fourth section summarizes asymptotic results for the general stochastic epidemic when the initial populations of susceptibles and infectives are both very large. In the fifth, some recent results are outlined on the costs of epidemics; these depend on the stochastic path integral under the infective curve. Finally, a brief account is given of the analysis of space-time interactions in epidemic processes.

title: Some population and epidemic models revisited.
abstract: Three problems of population and epidemic models formulated between ten and thirty years ago are reconsidered. In each case, a modified approach to the problem leads to its solution. For the two-sex population model, the solution of a Riccati equation results in an expression for the generating function of the process. The fully stochastic, as against the previously studied semistochastic, model of population growth with random catastrophes yields to hard analysis. Finally a generalized form of the general stochastic epidemic is solved using matrix geometric methods.

title: Random Allocation Methods in an Epidemic Model
abstract: A random allocation model is developed for the numbers of susceptibles in a group of n IVDU’s who become infected by i HIV-infectives sharing needles. A comparison of this model and the classical Reed-Frost model is outlined.

title: OBITUARY: EDWARD JAMES HANNAN
Problems of epidemic modelling
This note gives a brief review of some aspects of epidemic modelling which I have found of interest. The field is now very broad, and it is difficult to provide more than a partial flavor of recent developments. We shall concentrate on three topics: epidemic data fitting, matrix-geometric methods for general epidemics, and the duration of an epidemic in an immigration type model. These will provide a sample of current research problems.

title: Some population and epidemic models revisited.
abstract: Three problems of population and epidemic models formulated between ten and thirty years ago are reconsidered. In each case, a modified approach to the problem leads to its solution. For the two-sex population model, the solution of a Riccati equation results in an expression for the generating function of the process. The fully stochastic, as against the previously studied semistochastic, model of population growth with random catastrophes yields to hard analysis. Finally a generalized form of the general stochastic epidemic is solved using matrix geometric methods.

title: Processus stochastiques de population

title: Stochastic Models for Type Counts in a Literary Text

title: Random Allocation Methods in an Epidemic Model
abstract: A random allocation model is developed for the numbers of susceptibles in a group of n IVDU’s who become infected by i HIV-infectives sharing needles. A comparison of this model and the classical Reed-Frost model is outlined.

title: Modelling the spread of HIV in prisons
abstract: This paper is concerned with models for the spread of HIV in prisons. We first consider a single prison of size N in which there is homogeneous mixing, and where there is an inflow and outflow of n< N prisoners at times t= 0, 1, 2,... Conditions are derived for the stability of the system. The interaction of such a prison with the outside world is then studied, and stability conditions obtained for this case. Finally, a quarantine policy is examined and its cost analyzed, both in the non-stable and stable cases.

title: OBITUARY: EDWARD JAMES HANNAN
Approaches to the Modelling of Aids
The spread of AIDS in Africa, Europe, North America and elsewhere in the world is causing considerable concern. It is known that the human immunodeficiency virus (HIV) attacks T-4lymphocytes in the bloodstream, thus causing a decline in the immune system. Serious infection by organisms usually kept under control follows: patients develop Pneumocystis carinii pneumonia, Kaposi’s sarcoma, chronic lymphadenopathy, dementia and various opportunistic infections. Infection by the HIV almost always leads to overt AIDS symptoms, which appear to be inevitably fatal; one problem of interest is the length of the incubation period, that is the time between HIV infection and the diagnosis of AIDS.

title: A simple deterministic epidemic in several related growing communities
abstract: This paper first considers a simple deterministic epidemic in a growing population. It then examines a simple deterministic epidemic in several related growing communities, where infection is transmitted between individuals both within and across the communities. An explicit parametric solution is derived for the number of susceptibles in these communities as a function of time.

title: Stochastic Models for Type Counts in a Literary Text

title: Random Allocation Methods in an Epidemic Model
abstract: A random allocation model is developed for the numbers of susceptibles in a group of n IVDU’s who become infected by i HIV-infectives sharing needles. A comparison of this model and the classical Reed-Frost model is outlined.

title: Processus stochastiques de population

title: Modelling the spread of HIV in prisons
abstract: This paper is concerned with models for the spread of HIV in prisons. We first consider a single prison of size N in which there is homogeneous mixing, and where there is an inflow and outflow of n< N prisoners at times t= 0, 1, 2,... Conditions are derived for the stability of the system. The interaction of such a prison with the outside world is then studied, and stability conditions obtained for this case. Finally, a quarantine policy is examined and its cost analyzed, both in the non-stable and stable cases.

title: OBITUARY: EDWARD JAMES HANNAN