Life-expectancy in a nonhomogeneous population

Mortality differentials exist even among people of the same age and environmental risks. These differences are due to individual frailty (risks due to biological or behavioural reasons) not considered in the computation of conventional life-tables (where populations are assumed to be homogeneous). This note seeks to show empirically that life-expectancies computed from homogeneous population models are overstated for ages less than the mean, and are understated for higher ages. It is also shown that life-expectancy curves for both homogeneous and nonhomogeneous populations intersect at the mean survival age (when the most frail would have all died off) and at the maximum age lived in the population (when the last members of the cohort would have died off).     

On a nonhomogeneous Bingham fluid

The nonstationary motion of a Bingham fluid, which is a special type of a non-Newtonian material, is considered. Usually one deals with the Eulerian velocity and the hydrodynamic pressure of the medium under the assumption that its density is constant. In this paper we are concerned with the initial-boundary value problem for bounded domains and nonconstant densities. This leads to a variational inequality coupled with the continuity equation for conservation of the mass, for which the existence of appropriately generalized solutions is proved. The problem of uniqueness and regularity of the solutions for the general problem remains open. Under special circumstances a partial answer can be given.     

Green's function of a weakly nonhomogeneous waveguide

One constructs the uniform asymptotic expansion, with respect to a small parameter , of the solution of the problem: [ + k² (x, y)]u(x,y) =(x–x_o)·(y–y_o), u(x,0)=u(x, H)=0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 128, pp. 139–148, 1983.The author expresses his gratitude to N. Sh. Uryson and B. P. Belinskii for interesting discussions.     

Calculation of a nonhomogeneous cylinder with a rigid inclusion

A method for the approximate solution of mixed problems of elasticity theory for nonhomogeneous bodies of revolution af finite size is proposed. Based on this method the stress-formed state of a cylinder wtih a rigid inclusion is determined.Translated from Matematicheskie Metody i Fiziko-mekhanicheskie Polya, No. 26, pp. 72–78, 1987.     

Limit theorems for a nonhomogeneous Ornstein-Uhlenbeck process

We describe a construction of a summation scheme with replacements of random variables. As the limit, we obtain a time nonhomogeneous generalization of the Ornstein-Uhlenbeck process. This generalization is described by a transform of Lamperti type in which an arbitrary continuous monotone function is used instead of the exponential one. Bibliography: 16 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 111–134.     

Boundary layer for 3D nonlinear parallel pipe flow of nonhomogeneous incompressible Navier‐Stokes equations

In this paper, we justify the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear parallel pipe flow of nonhomogeneous incompressible Navier‐Stokes equations. The convergence for velocity is shown under various Sobolev norms. In addition, the higher‐order asymptotic expansions are also considered. And the mathematical validity of the Prandtl boundary layer theory for nonlinear parallel pipe flow is generalized to the nonhomogeneous case.     

Convexity estimates for a nonhomogeneous mean curvature flow

We study the evolution of a closed immersed hypersurface whose speed is given by a function f(H){\phi(H)} (H) of the mean curvature asymptotic to H/ ln H for large H. Compared with other nonlinear functions of the curvatures, this speed has some good properties which allow for an easier study of the formation of singularities in the nonconvex case. We prove apriori estimates showing that any surface with positive mean curvature at the initial time becomes asymptotically convex near a singularity. Similar estimates also hold for the mean curvature flow; for the flow considered here they admit a simpler proof based only on the maximum principle.     

Statistical simulation methods for a nonhomogeneous Poisson ensemble

Some Monte Carlo methods for modeling homogeneous and nonhomogeneous Poisson ensembles are proposed. A generalization of the maximum cross-section method is constructed and proved to be valid for modeling nonhomogeneous Poisson ensembles of points.     

Multiplicity of solutions for a fourth-order quasilinear nonhomogeneous equation

We consider a fourth-order quasilinear nonhomogeneous equation which is equivalent to a nonhomogeneous Hamiltonian system. The purpose of this work is to prove the existence of at least two solutions for such equation when a certain parameter is small enough. Furthermore, under an additional hypothesis on positiveness of the nonhomogeneous part we prove that our solutions are positive.     

On a nonhomogeneous,nonlinear Dirichlet eigenvalue problem

We consider a nonlinear eigenvalue problem for the Dirichlet $(p,q)$-Laplacian with a sign-changing Carath$\acute{\mathrm{e}}$odory reaction. Using variational tools, truncation and comparison techniques, and critical groups, we prove an existence and multiplicity result which is global in the parameter $\lambda >0$ (bifurcation-type theorem). Our work here complements the recent one by Papageorgiou–Qin–Rădulescu, Bull. Sci. Math. 172 (2021).     

On p-superlinear equations with a nonhomogeneous differential operator

We consider a nonlinear elliptic equation driven by a nonhomogeneous differential operator and with a (p?1)-superlinear Carathéodory reaction. Our formulation incorporates as a special case equations monitored by the p-Laplacian. Using variational methods coupled with truncation techniques and comparison principles, we show that the problem has at least five nontrivial smooth solutions.     

Schwarz-type problem of nonhomogeneous Cauchy-Riemann equation on a triangle

We consider the Schwarz-type boundary-value problem (BVP) of the nonhomogeneous Cauchy-Riemann equation on an isosceles orthogonal triangle. By the technique of plane parqueting and the Cauchy-Pompeiu formula on the triangle, the Schwarz-Poisson formula is obtained. We also investigate boundary behaviors of the Schwarz-type operator and the Pompeiu-type operator. Especially, boundary-values at the corners are proved to exist. Finally, the solution of the Schwarz-type BVP is explicitly obtained.     

Selecting a portfolio of nonhomogeneous R&D proposals

This article reports a procedure developed to assist the U.S. Department of Energy in the selection of a portfolio of proposals addressing the design and manufacture of components of solar photovoltaic arrays, and complete photovoltaic systems. Considerations such as the relative importance of the different components in the overall effort, compatibility of the proposed designs, and budgetary and programmatic issues were complicating factors. The technical quality of each proposal was represented by multiple evaluation measures. These were combined into a single index through the use of multi attributeutility function. Indices representing the relative importance of the various components were then developed, and results in measurable value theory were applied to derive an index of technical quality of a portfolio of proposals. The problem was then formulated as an integer program. It was solved by using an interactive branch and bound code that allowed for sensitivity analysis before selecting the portfolio of proposals for funding.The procedure was successfully applied to funding a portfolio of proposals aimed at reducing the cost of producing photovoltaic arrays, and to several other government-sponsored procurements.     

Continuous spectrum for a class of nonhomogeneous differential operators

We study the boundary value problem in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in with smooth boundary, λ is a positive real number, and the continuous functions p ₁, p ₂, and q satisfy 1 < p ₂(x) < q(x) < p ₁(x) < N and for any . The main result of this paper establishes the existence of two positive constants λ₀ and λ₁ with λ₀ ≤ λ₁ such that any is an eigenvalue, while any is not an eigenvalue of the above problem.     

Modeling the field of a cable in a two-dimensional nonhomogeneous medium

In this article we model the electromagnetic field of a cable on the surface of a two-dimensional nonhomogeneous medium used for electromagnetic sounding. The model of the medium represents the sea. Calculations are reported describing the coast effect on the electromagnetic field. An iterative field calculation method is proposed, which reduces the computing effort. The effect of sub-seafloor nonhomogeneities on the electromagnetic field measured at the seafloor is investigated numerically.     

A note on life expectancy in a nonhomogeneous population

This note offers a simple mathematical model for life expectancy in a nonhomogeneous population. It is a function of life expectancy at birth and age of the population. The method is illustrated using Australian males (1961) data.