nils-herrmann/clean_scirepeval huggingface dataset:
A carrier-borne epidemic with two stages of infection
This paper examines an epidemic spread by carriers, in which infectives may be in stage I or stage II of infection, depending on the number of contacts between the susceptibles, stage I infectives and carriers. A formal matrix solution for the state probabilities of the process is obtained, and the probabilities of survivors derived. A partial differential equation for the probability generating function of the process is also found, and its solution obtained in terms of Laplace transforms. Once again, the probabilities of survivors can be derived from these. The Laplace transforms may be inverted to provide time dependent solutions for the model.

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: 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: OBITUARY: EDWARD JAMES HANNAN
Some Clarifications on the Transversality Condition
In this paper, the authors study a general concave discrete-time, infinite-horizon, optimal-control problem. They establish necessary and sufficient conditions for optimality in the weak sense of W. A. Brock and for optimality in the strong sense of D. Gale. The corresponding transversality conditions are general exhaustion properties of the limit value of the optimal state variables; these properties cover and extend the well-known results obtained in special cases.

title: Necessary Conditions for Optimality of Elliptic Systems with Positivity Constraints on the State
abstract: Recently, necessary conditions for optimality were established in the case of nonlinear elliptic multi-dimensional systems with integral constraints [P. Michel, Condition necessaire d’optimalite pour des systemes d’equations elliptiques non lineaires, Quatriemes journees de controle (Metz, 18–21 Mai 1976), polycopie Universite de Metz, 1976]. Here this problem is solved in the case of additional constraints of positivity of the state’s components on measurable sets.

title: Pour une extension du principe du maximum de Pontrjagin

title: On the Transversality Condition in Infinite Horizon Optimal Problems

title: Generalized controls: A necessary condition for optimality in a Banach space
abstract: A necessary condition is established for optimality in the case of problems where the constraints are simultaneously functions of the trajectory and the control (Problem 3.1, Theorem 5.7); this condition holds for generalized controls with values in a Hausdorff space and for a state space which is a Banach space. To demonstrate the result a new technique is used, based on the differentiability of the trajectory (Theorem 2.6) and the introduction of the notion of pseudosolution (Definition 2.8). These results are then applied to calculus of variations problems in a Banach space (Theorem 6.3).

title: Stricte ergodicite d’ensembles minimaux de substitution
abstract: On se propose de donner une demonstration de la stricte ergodicite des ensembles minimaux engendres par les substitutions de longueur non constante.

title: Average rank of families of elliptic curves and Sato-Tate laws
Generalized controls: A necessary condition for optimality in a Banach space
A necessary condition is established for optimality in the case of problems where the constraints are simultaneously functions of the trajectory and the control (Problem 3.1, Theorem 5.7); this condition holds for generalized controls with values in a Hausdorff space and for a state space which is a Banach space. To demonstrate the result a new technique is used, based on the differentiability of the trajectory (Theorem 2.6) and the introduction of the notion of pseudosolution (Definition 2.8). These results are then applied to calculus of variations problems in a Banach space (Theorem 6.3).

title: On the Transversality Condition in Infinite Horizon Optimal Problems

title: Pour une extension du principe du maximum de Pontrjagin

title: Necessary Conditions for Optimality of Elliptic Systems with Positivity Constraints on the State
abstract: Recently, necessary conditions for optimality were established in the case of nonlinear elliptic multi-dimensional systems with integral constraints [P. Michel, Condition necessaire d’optimalite pour des systemes d’equations elliptiques non lineaires, Quatriemes journees de controle (Metz, 18–21 Mai 1976), polycopie Universite de Metz, 1976]. Here this problem is solved in the case of additional constraints of positivity of the state’s components on measurable sets.

title: Stricte ergodicite d’ensembles minimaux de substitution
abstract: On se propose de donner une demonstration de la stricte ergodicite des ensembles minimaux engendres par les substitutions de longueur non constante.

title: Average rank of families of elliptic curves and Sato-Tate laws
Pour une extension du principe du maximum de Pontrjagin

title: Necessary Conditions for Optimality of Elliptic Systems with Positivity Constraints on the State
abstract: Recently, necessary conditions for optimality were established in the case of nonlinear elliptic multi-dimensional systems with integral constraints [P. Michel, Condition necessaire d’optimalite pour des systemes d’equations elliptiques non lineaires, Quatriemes journees de controle (Metz, 18–21 Mai 1976), polycopie Universite de Metz, 1976]. Here this problem is solved in the case of additional constraints of positivity of the state’s components on measurable sets.

title: On the Transversality Condition in Infinite Horizon Optimal Problems

title: Average rank of families of elliptic curves and Sato-Tate laws
Necessary Conditions for Optimality of Elliptic Systems with Positivity Constraints on the State
Recently, necessary conditions for optimality were established in the case of nonlinear elliptic multi-dimensional systems with integral constraints [P. Michel, Condition necessaire d’optimalite pour des systemes d’equations elliptiques non lineaires, Quatriemes journees de controle (Metz, 18–21 Mai 1976), polycopie Universite de Metz, 1976]. Here this problem is solved in the case of additional constraints of positivity of the state’s components on measurable sets.

title: On the Transversality Condition in Infinite Horizon Optimal Problems

title: Average rank of families of elliptic curves and Sato-Tate laws
ON THE RECURRENT TENSOR FIELDS OF FINSLER SPACES

title: RECURRENT FINSLER SPACE OF SECOND ORDER

title: ON RECURRENT SPACES OF SECOND ORDER IN FINSLER SPACES
abstract: By B. B. SINHA and S. P. SINGH ( Chaki and Roychowdhary have studied the Ricci recurrent spaces of second order in the Riemannian Geometry $[$ 1 $]$ . The object of present paper is to define the recurrent curvature tensor fields of second order and to study the properties of recurrence tensor field and the curvature tensor fields in the Finsler spaces.

title: NONPARAMETRIC ESTIMATION OF THE GENERALIZED VARIANCE
abstract: For multivariate distributions with finite second order moments, a nonparametric symmetric, unbiased estimator of the generalized variance is considered, and it is shown to be (nonparametric) optimal for the class of distributions having finite fourth order moments. A jackknifed version of the sample generalized variance is also considered as a contender; it is computationally more convenient and asymptotically equivalent to the former. It is also shown that the second estimator performs quite well (in large sample) relative to the optimal normal theory estimators under several loss functions.

title: A Bayesian Approach to Optimum Allocation in Regression Problems

title: Almost saturatedD-optimal main effect plans and allied results
abstract: The theory of unimodular matrices has been applied to deriveD-optimal main effect plans fors1 ×s2 factorials ins1 +s2 runs. Plans with highA-efficiency have also been given.

title: INADMISSIBILITY OF THE BEST EQUIVARIANT ESTIMATORS OF THE VARIANCE-COVARIANCE MATRIX, THE PRECISION MATRIX, AND THE GENERALIZED VARIANCE UNDER ENTROPY LOSS
abstract: Based on a data matrix X = (X^ X^): pi k with independent columns Χ.;~Νη(ξ., Σ), and an independent ρχ ρ Wishart matrix S~W_(n,E), ι ρ ι -1 " estimators dominating the best equi variant estimators of Σ, Σ and |Σ| are obtained under two types of entropy loss. For simultaneous estimation of the mean vector and the variance-covariance matrix of a multinormal population, a suitable entropy loss is developed and estimators dominating the pair consisting of the sample mean vector and the best multiple of the sample Wishart matrix are derived. A technique of Sinha  is heavily exploited.

title: On the Equivalence of Confidence Sets Based on Bayesian and Non­Bayesian Procedures*:
A Bayesian Approach to Optimum Allocation in Regression Problems

title: ESTIMATION OF A COMMON LOCATION OF SEVERAL EXPONENTIALS

title: INADMISSIBILITY OF THE BEST EQUIVARIANT ESTIMATORS OF THE VARIANCE-COVARIANCE MATRIX, THE PRECISION MATRIX, AND THE GENERALIZED VARIANCE UNDER ENTROPY LOSS
abstract: Based on a data matrix X = (X^ X^): pi k with independent columns Χ.;~Νη(ξ., Σ), and an independent ρχ ρ Wishart matrix S~W_(n,E), ι ρ ι -1 " estimators dominating the best equi variant estimators of Σ, Σ and |Σ| are obtained under two types of entropy loss. For simultaneous estimation of the mean vector and the variance-covariance matrix of a multinormal population, a suitable entropy loss is developed and estimators dominating the pair consisting of the sample mean vector and the best multiple of the sample Wishart matrix are derived. A technique of Sinha  is heavily exploited.

title: On the Equivalence of Confidence Sets Based on Bayesian and Non­Bayesian Procedures*:

title: ESTIMATION IN THE MULTIPARAMETER EXPONENTIAL FAMILY: ADMISSIBILITY AND INADMISSIBILITY RESULTS
abstract: The problem of estimating k(äl) l inear combinations of the component means in the multiparameter exponential family with possibly dependent coordinates i s treated for squared-error loss. I t i s shown ρ that i f the natural parameter space is the whole of 1R , the UMVUE i s always admissible i f k s 2 . Also, suff ic ient conditions for admiss ibi l i ty of an arbitrary generalized Bayes estimate are obtained. I f the natural parameter space i s not the entire JR* (e.g. in the gamma case), inadmi s s ib i l i t y results are proved to indicate that the admiss ibi l i ty pattern of the "natural" estimate may be different even when k = l . F ina l ly , the problem of estimating a vector of smooth parametric functions more general than the means i s considered and admissible generalized Bayes estimates are obtained; in part icular, a result of Ghosh and Meeden (1977) follows as a corollary. AMS 1970 Subject C lass i f icat ions: Primary 62 C 15, Secondary 62 F 10

title: ON RECURRENT SPACES OF SECOND ORDER IN FINSLER SPACES
abstract: By B. B. SINHA and S. P. SINGH ( Chaki and Roychowdhary have studied the Ricci recurrent spaces of second order in the Riemannian Geometry $[$ 1 $]$ . The object of present paper is to define the recurrent curvature tensor fields of second order and to study the properties of recurrence tensor field and the curvature tensor fields in the Finsler spaces.

title: RECURRENT FINSLER SPACE OF SECOND ORDER

title: Almost saturatedD-optimal main effect plans and allied results
abstract: The theory of unimodular matrices has been applied to deriveD-optimal main effect plans fors1 ×s2 factorials ins1 +s2 runs. Plans with highA-efficiency have also been given.
INADMISSIBILITY OF THE BEST EQUIVARIANT ESTIMATORS OF THE VARIANCE-COVARIANCE MATRIX, THE PRECISION MATRIX, AND THE GENERALIZED VARIANCE UNDER ENTROPY LOSS
Based on a data matrix X = (X^ X^): pi k with independent columns Χ.;~Νη(ξ., Σ), and an independent ρχ ρ Wishart matrix S~W_(n,E), ι ρ ι -1 " estimators dominating the best equi variant estimators of Σ, Σ and |Σ| are obtained under two types of entropy loss. For simultaneous estimation of the mean vector and the variance-covariance matrix of a multinormal population, a suitable entropy loss is developed and estimators dominating the pair consisting of the sample mean vector and the best multiple of the sample Wishart matrix are derived. A technique of Sinha  is heavily exploited.

title: On the Equivalence of Confidence Sets Based on Bayesian and Non­Bayesian Procedures*:

title: ESTIMATION OF A COMMON LOCATION OF SEVERAL EXPONENTIALS

title: ESTIMATION IN THE MULTIPARAMETER EXPONENTIAL FAMILY: ADMISSIBILITY AND INADMISSIBILITY RESULTS
abstract: The problem of estimating k(äl) l inear combinations of the component means in the multiparameter exponential family with possibly dependent coordinates i s treated for squared-error loss. I t i s shown ρ that i f the natural parameter space is the whole of 1R , the UMVUE i s always admissible i f k s 2 . Also, suff ic ient conditions for admiss ibi l i ty of an arbitrary generalized Bayes estimate are obtained. I f the natural parameter space i s not the entire JR* (e.g. in the gamma case), inadmi s s ib i l i t y results are proved to indicate that the admiss ibi l i ty pattern of the "natural" estimate may be different even when k = l . F ina l ly , the problem of estimating a vector of smooth parametric functions more general than the means i s considered and admissible generalized Bayes estimates are obtained; in part icular, a result of Ghosh and Meeden (1977) follows as a corollary. AMS 1970 Subject C lass i f icat ions: Primary 62 C 15, Secondary 62 F 10

title: Almost saturatedD-optimal main effect plans and allied results
abstract: The theory of unimodular matrices has been applied to deriveD-optimal main effect plans fors1 ×s2 factorials ins1 +s2 runs. Plans with highA-efficiency have also been given.

title: ON RECURRENT SPACES OF SECOND ORDER IN FINSLER SPACES
abstract: By B. B. SINHA and S. P. SINGH ( Chaki and Roychowdhary have studied the Ricci recurrent spaces of second order in the Riemannian Geometry $[$ 1 $]$ . The object of present paper is to define the recurrent curvature tensor fields of second order and to study the properties of recurrence tensor field and the curvature tensor fields in the Finsler spaces.

title: RECURRENT FINSLER SPACE OF SECOND ORDER
ON RECURRENT SPACES OF SECOND ORDER IN FINSLER SPACES
By B. B. SINHA and S. P. SINGH ( Chaki and Roychowdhary have studied the Ricci recurrent spaces of second order in the Riemannian Geometry $[$ 1 $]$ . The object of present paper is to define the recurrent curvature tensor fields of second order and to study the properties of recurrence tensor field and the curvature tensor fields in the Finsler spaces.

title: RECURRENT FINSLER SPACE OF SECOND ORDER

title: On the Equivalence of Confidence Sets Based on Bayesian and Non­Bayesian Procedures*:
On the Equivalence of Confidence Sets Based on Bayesian and Non­Bayesian Procedures*:

title: ESTIMATION OF A COMMON LOCATION OF SEVERAL EXPONENTIALS

title: ESTIMATION IN THE MULTIPARAMETER EXPONENTIAL FAMILY: ADMISSIBILITY AND INADMISSIBILITY RESULTS
abstract: The problem of estimating k(äl) l inear combinations of the component means in the multiparameter exponential family with possibly dependent coordinates i s treated for squared-error loss. I t i s shown ρ that i f the natural parameter space is the whole of 1R , the UMVUE i s always admissible i f k s 2 . Also, suff ic ient conditions for admiss ibi l i ty of an arbitrary generalized Bayes estimate are obtained. I f the natural parameter space i s not the entire JR* (e.g. in the gamma case), inadmi s s ib i l i t y results are proved to indicate that the admiss ibi l i ty pattern of the "natural" estimate may be different even when k = l . F ina l ly , the problem of estimating a vector of smooth parametric functions more general than the means i s considered and admissible generalized Bayes estimates are obtained; in part icular, a result of Ghosh and Meeden (1977) follows as a corollary. AMS 1970 Subject C lass i f icat ions: Primary 62 C 15, Secondary 62 F 10

title: RECURRENT FINSLER SPACE OF SECOND ORDER
On the Picard property of lacunary power series

title: A kernel associated with certain multiply connected domains and its applications to factorization theorems

title: Complex Methods in Harmonic Analysis

title: H CLASSES OF HOLOMORPHIC FUNCTIONS IN TUBE DOMAINS.

title: A derivation of the main results of the theory of Hp spaces

title: The representation of regular linear systems on Hilbert spaces

title: Tables of Abscissas and Weights for Numerical Evaluation of Integrals of the Form ∞ 0 e -x x n f(x) dx

title: On the Inversion of the Specific-Heat Function
abstract: In this paper we present a method for the inversion of specific heat data to find the vibrational frequency spectrum of a solid. Our results are given in terms of a power series in UJ, the frequency. In this series the coefficients depend on C v (T) and its d~rivatives at T=O. The series thus derived is valid only in an asymptotic sense, but represents an improvement over inversions by Montroll and Kroll which require a knowledge of functions formed from the data, and the evaluation of double integrals over these functions, A method for forming the successive values of Cv(n) (0) from experimental data is also presented. One of the most frequently measured physical characteristics of a solid is the specific heat at constant volume Cv (T), where T is the temperature. The behavior of this function has quite accurately been predicted by various characterizations of a lattice of atoms which have harmonic interactions. If it is assumed that the specific heat can be attributed solely to harmonic effects, then it can be written as an integral over the vibrational frequency spectrum 1 ;

title: Admissibility of unbounded control operators
abstract: For linear systems described by $\dot x(t) = Ax(t) + Bu(t)$, where A generates a semigroup on the state space X and B is an unbounded operator, some necessary as well as some sufficient conditions are given for B to be admissible, i.e., for any t, the state $x(t)$ should be in X and should depend continuously on the input $u \in L^p $. This approach begins with an axiomatic description of such a system in terms of a functional equation. The results are applied to the wave equation on a bounded interval.

title: The metric Fuglede property and normality
A derivation of the main results of the theory of Hp spaces

title: Complex Methods in Harmonic Analysis

title: H CLASSES OF HOLOMORPHIC FUNCTIONS IN TUBE DOMAINS.

title: A kernel associated with certain multiply connected domains and its applications to factorization theorems

title: Admissibility of unbounded control operators
abstract: For linear systems described by $\dot x(t) = Ax(t) + Bu(t)$, where A generates a semigroup on the state space X and B is an unbounded operator, some necessary as well as some sufficient conditions are given for B to be admissible, i.e., for any t, the state $x(t)$ should be in X and should depend continuously on the input $u \in L^p $. This approach begins with an axiomatic description of such a system in terms of a functional equation. The results are applied to the wave equation on a bounded interval.

title: Tables of Abscissas and Weights for Numerical Evaluation of Integrals of the Form ∞ 0 e -x x n f(x) dx

title: The representation of regular linear systems on Hilbert spaces

title: Calculation of certain multiple generating functions

title: On the Inversion of the Specific-Heat Function
abstract: In this paper we present a method for the inversion of specific heat data to find the vibrational frequency spectrum of a solid. Our results are given in terms of a power series in UJ, the frequency. In this series the coefficients depend on C v (T) and its d~rivatives at T=O. The series thus derived is valid only in an asymptotic sense, but represents an improvement over inversions by Montroll and Kroll which require a knowledge of functions formed from the data, and the evaluation of double integrals over these functions, A method for forming the successive values of Cv(n) (0) from experimental data is also presented. One of the most frequently measured physical characteristics of a solid is the specific heat at constant volume Cv (T), where T is the temperature. The behavior of this function has quite accurately been predicted by various characterizations of a lattice of atoms which have harmonic interactions. If it is assumed that the specific heat can be attributed solely to harmonic effects, then it can be written as an integral over the vibrational frequency spectrum 1 ;