Sustainability and long-term strategies in the modeling of biological processes

In this article, we intend to explore the role of using an”infinite time horizon” framework to address the issues of sustainability and long-term strategies in the control of biological processes. We use two case study models to explain why considering a fixed or moving endpoint does not lead to the desired long-term effects. The first biological model considered concerns the spread of an infectious disease and its treatment as an infinite horizon optimal control problem. The second one deals with the metronomic chemotherapy cancer treatment over the remaining lifetime horizon of the patient. The latter is consistent with the conception of cancer as a chronic disease. Both models show structural differences in the choice of the objective functional, the first one uses a stabilization functional containing a weight function, the second one contains a damage functional which involves a density function

Study of dry pellets of blood plasma using THz spectroscopy

This work is devoted to the development of a suitable phantom of a biological object for measurements in the THz frequency range and for approbation with various diagnostic methods developed in different THz laboratories. The phantoms were represented as a pellet of human and a laboratory rat blood plasma in the diabetic and the control groups. These objects were analyzed in various laboratories, using THz pulsed spectroscopy and a high-resolution THz spectrometer based on a backward wave oscillator. The components of the dry blood plasma were identified by the detected spectral lines

On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems

This paper deals with infinite horizon optimal control problems, which are formulated in weighted Sobolev spaces ... [wzór] and weighted Lp-spaces ... [wzór]. We ask for the consequences of the interpretation of the integral within the objective as a Lebesgue or an improper Riemann integral. In order to justify the use of both types of integrals, various applications of infinite horizon problems are presented. We provide examples showing that lower semicontinuity may fail for objectives involving Lebesgue as well as improper Riemann integrals. Further we prove a lower semicontinuity theorem for an objective with Lebesgue integral under more restrictive growth conditions on the integrand

Necessity and Use of a Multilayer Test Object Based on an Anonymous 19th Century Copy of a Painting by Ivan Konstantinovich Aivazovsky (1817–1900)

The emergence of new research methods in the field of heritage science always raises a large number of questions related to their applicability, reproducibility of results on similar objects, complementarity with other methods, and development of new research methods. To solve such problems, it is necessary to have a test object with the required structure. A multilayer test object based on a fragment of a copy of a 19th century painting by I.K. Aivazovsky was created and described. Analytical studies of the colourful layers were carried out on a Fourier-transform infrared (FT-IR) spectrometer with an attenuated total reflectance (ATR) attachment in single-reflection mode with a diamond crystal. As part of the use of one research method, differences between painting layers of the 19th and 20th centuries were revealed. Results are presented in the IR graphs. The aim of the work was to identify the characteristics of the pictorial layers inherent in the copy of the painting by I.K. Aivazovsky. This will improve the methodology of technological expertise of the I.K. Aivazovsky’s artworks

Necessity and Use of a Multilayer Test Object Based on an Anonymous 19th Century Copy of a Painting by Ivan Konstantinovich Aivazovsky (1817–1900)

The emergence of new research methods in the field of heritage science always raises a large number of questions related to their applicability, reproducibility of results on similar objects, complementarity with other methods, and development of new research methods. To solve such problems, it is necessary to have a test object with the required structure. A multilayer test object based on a fragment of a copy of a 19th century painting by I.K. Aivazovsky was created and described. Analytical studies of the colourful layers were carried out on a Fourier-transform infrared (FT-IR) spectrometer with an attenuated total reflectance (ATR) attachment in single-reflection mode with a diamond crystal. As part of the use of one research method, differences between painting layers of the 19th and 20th centuries were revealed. Results are presented in the IR graphs. The aim of the work was to identify the characteristics of the pictorial layers inherent in the copy of the painting by I.K. Aivazovsky. This will improve the methodology of technological expertise of the I.K. Aivazovsky’s artworks