The author elucidates the ontological basis of elementary mathematical theories and thereby assesses their certainty as a foundation for the more complex theories of modern mathematics, such as mathematical analysis and set theory. He adduces arguments in favor of the position of Frege, who held that geometry can provide a sufficiently broad and certain foundation for mathematics.

Many biosystems are complex mixtures of disparate biofluids. To study contact and transport phenomena in these mixtures, one has to apply much information on the biofluids which are components of the mixtures. A lot of the corresponding data can be extracted by means of experiments. However, it is not always easy to obtain experimental results on rather deep physical characteristics of biofluids, especially if the bioparticles are complicated systems and the fluid coexists in the mixture with a large number of (...) other fluids. In these cases, the necessary data can, in principle, be extracted from those results which are easier to obtain experimentally. The present work proposes a method to evaluate the biofluid equilibrium pressure and electrochemical potential from common experimental values of the fluid concentration and absolute temperature as well as the fluid-particle mass, volume and spin. In so doing, the nonzero values of the particle volume are accounted for. The procedure is illustrated with a numerical example on the fluid of red blood cells (or erythrocytes) in human blood. The pressure values obtained are 49.1 and 38.8 micropascals for men and women respectively whereas the electrochemical-potential values are –2.124 and –2.130 electronvolts for men and women respectively. (shrink)

Oncogenic hyperplasia is the first and inevitable stage of formation of a (solid) tumor. This stage is also the core of many other proliferative diseases. The present work proposes the first minimal model that combines homeorhesis with oncogenic hyperplasia where the latter is regarded as a genotoxically activated homeorhetic dysfunction. This dysfunction is specified as the transitions of the fluid of cells from a fluid, homeorhetic state to a solid, hyperplastic-tumor state, and back. The key part of the model is (...) a nonlinear reaction-diffusion equation (RDE) where the biochemical-reaction rate is generalized to the one in the well-known Schlögl physical theory of the non-equilibrium phase transitions. A rigorous analysis of the stability and qualitative aspects of the model, where possible, are presented in detail. This is related to the spatially homogeneous case, i.e. when the above RDE is reduced to a nonlinear ordinary differential equation. The mentioned genotoxic activation is treated as a prevention of the quiescent G0-stage of the cell cycle implemented with the threshold mechanism that employs the critical concentration of the cellular fluid and the nonquiescent-cell-duplication time. The continuous tumor morphogeny is described by a time-space-dependent cellular-fluid concentration. There are no sharp boundaries (i.e. no concentration jumps exist) between the domains of the homeorhesis- and tumor-cell populations. No presumption on the shape of a tumor is used. To estimate a tumor in specific quantities, the model provides the time-dependent tumor locus, volume, and boundary that also points out the tumor shape and size. The above features are indispensable in the quantitative development of antiproliferative drugs or therapies and strategies to prevent oncogenic hyperplasia in cancer and other proliferative diseases. The work proposes an analytical-numerical method for solving the aforementioned RDE. A few topics for future research are suggested. (shrink)

t. 1. Problemy vospitanii︠a︡ vsestoronne razvitoĭ lichnosti. Dukhovnyĭ mir shkolʹnika. Metodika vospitanii︠a︡ kollektiva.--t. 2. Formirovanie Kommunisticheskikh ubezhdeniĭ molodogo pokolenii︠a︡. Kak vospitat nastoi︠a︡shchego cheloveka. Sto sovetov uchiteli︠u︡.--t. 3. Serdt︠s︡e otdai︠u︡ deti︠a︡m. Rozhdenie grazhdanina. Pisʹma k synu.--t. 4. Pavlyshskai︠a︡ sredni︠a︡i︠a︡ shkola. Razgovor s molodym direktorom shkoly.--t. 5. Statʹi.

t. 1. Serdt︠s︡e otdai︠u︡ deti︠a︡m. Rozhdenie grazhdanina.--t. 2. Pavlyshskai︠a︡ sredni︠a︡i︠a︡ shkola.

t. 1. Problemy vykhovanni︠a︡ vsebichno rozvynenoï osobystosti. Dukhovnyĭ svit shkoli︠a︡ra. Metodika vykhovanni︠a︡ kolektyvu -- t. 2. Formuvanni︠a︡ komunistychnykh perekonanʹ molodoho pokolinni︠a︡. I︠A︡k vykhovaty spravz︠h︡ni︠u︡ li︠u︡dynu. Sto porad uchytelevi -- t. 3. Sert︠s︡e viddai︠u︡ diti︠a︡m. Narodz︠h︡enni︠a︡ hromadi︠a︡nyna. Lysty do syna -- t. 4. Pavlysʹka seredni︠a︡ shkola. Rozmova z molodym dyrektorom -- t. 5. Statti.