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We continue studying systems whose state depends on time and whose resources are renewably based on functional operators with shift. In previous articles, we considered the term which described results of reproductive processes as a linear expression or as a shift summand. In this work, the reproductive term is represented using an integral with a degenerate kernel. A cyclic model of evolution of the system with a renewable resource is developed. We propose a method for solving the balance equation and we determine an equilibrium state of the system. Having applied this model, we can investigate problems of natural systems and their resource production.

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In this report, we give an overview of the proceedings from the online Imperial College London Neurotechnology Symposium 2020. The first part deals with the fundamentals of how artificial intelligence (AI) can be used to inform research frameworks used in the field of neurotechnology. The second part goes a level higher and shows how AI can be used in cutting-edge cellular and molecular methodologies and their applications. The final part focuses on the efforts to ''decode'' neural systems in brain-computer interfaces to advance neuroprosthetics.

We describe unconditional bases of the form {k(z, λ n ) : λ n ∈ Λ}, Λ ∩ R = ∅, in de Branges spaces, where k is the reproducing kernel.We extend the method of integral norm estimates for resolvents [1] to a class of model operators in de Branges spaces of entire functions [2]. The results are stated in the form of theorems on completeness and the basis property of function families constructed from the reproducing kernel of a de Branges space.

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