Acta Universitatis Lodziensis. Folia Mathematica vol. 18/2013http://hdl.handle.net/11089/41412020-08-12T19:46:16Z2020-08-12T19:46:16ZSpatial and age-dependent population dynamics model with an additional structure: can there be a unique solution?Tchuenche, Jean M.http://hdl.handle.net/11089/181592018-02-01T11:20:38Z2013-01-01T00:00:00ZSpatial and age-dependent population dynamics model with an additional structure: can there be a unique solution?
Tchuenche, Jean M.
A simple age-dependent population dynamics model with an additional structure or physiological variable is presented in its variational formulation. Although the model is well-posed, the closed form solution with space variable is difficult to obtain explicitly, we prove the uniqueness of its solutions using the fundamental Green’s formula. The space variable is taken into account in the extended model with the assumption that the coefficient of diffusivity is unity.
2013-01-01T00:00:00ZStability of the Volterra Integrodifferential EquationJanfada, MohammadSadeghi, Gh.http://hdl.handle.net/11089/181532018-02-01T11:20:37Z2013-01-01T00:00:00ZStability of the Volterra Integrodifferential Equation
Janfada, Mohammad; Sadeghi, Gh.
In this paper, the Hyers-Ulam stability of the Volterra integrodifferential equation and the Volterra equation on the finite interval [0, T], T > 0, are studied, where the state x(t) take values in a Banach space X.
2013-01-01T00:00:00ZIntegrable Functions Versus a Generalization of Lebesgue Points in Locally Compact GroupsBasu, Sanjihttp://hdl.handle.net/11089/169662018-02-01T11:20:37Z2013-01-01T00:00:00ZIntegrable Functions Versus a Generalization of Lebesgue Points in Locally Compact Groups
Basu, Sanji
Here in this paper we intend to deal with two questions: How large is a “Lebesgue Class” in the topology of Lebesgue integrable functions, and also what can be said regarding the topological size of a “Lebesgue set” in R?, where by a Lebesgue class (corresponding to some x in R) is meant the collection of all Lebesgue integrable functions for each of which the point x acts as a common Lebesgue point, and, by a Lebesgue set (corresponding to some Lebesgue integrable function f ) we mean the collection of all ebesgue points of f.
However, we answer these two questions in a more general setting where in place of Lebesgue integration we use abstract integration in locally compact Hausdorff topological groups.
The author is thankful to the referee for his valuable
comments and suggestions that led to an improvement of the paper.
He also owes to Prof. M. N. Mukherjee of the Deptt. of Pure Mathematics,
Calcutta University, for the present linguistically improved version.
2013-01-01T00:00:00ZFamilies of Increasing Sequences Possessing the Harmonic Series PropertyWituła, RomanHetmaniok, EdytaSłota, Damianhttp://hdl.handle.net/11089/64492018-02-01T11:17:33Z2013-01-01T00:00:00ZFamilies of Increasing Sequences Possessing the Harmonic Series Property
Wituła, Roman; Hetmaniok, Edyta; Słota, Damian
We prove in this paper that any maximal, with respect to inclusion, subset of N – the family of all increasing sequences of positive integers –
possessing the harmonic series property has the cardinality of the continuum.
Moreover, we prove that for any countable (infinite) set
exists an "orthogonal" family such that it hold some facts. All facts are proved constructively, by using the modified version of the classical Sierpiński family of increasing sequences having the cardinality of the continuum.
2013-01-01T00:00:00Z