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A method for identification of material parameters of the constitutive relations of elastoplastic and viscoelastic deformation of isotropic and composite materials is developed. The method is based on minimizing the functional of the residue of results of numerical and experimental analysis of unsteady deformation of structural elements made of examined materials. The method is tested, and prospects of its application for determining material parameters of viscoelastic and elastoplastic models of nonlinear deformation of cylindrical metal-plastic shells under explosive loading are demonstrated.

Results of an experimental study of properties of joints obtained by using different regimes of laser welding of the 1424 alloy (Al-Mg-Li) are reported. The strength and structure of the welded joints are determined. The influence of various types of welded joint straining on its strength is studied. It is demonstrated that the joint strength increases in the case of plastic straining.

A method of the numerical solution of nonlinear unsteady problems of axisymmetric elastoplastic straining of shells of revolution with allowance for torque loading at high strains is proposed. The method is based on the geometrically nonlinear theory of the Timoshenko shells and the plasticity theory with due allowance for combined isotropic and kinematic hardening. The problem is solved with the use of the variational difference method. Results of numerical and experimental investigations of elastoplastic straining of cylindrical shells under proportional and sequential kinematic tensile and torque loading are reported.

A mixed boundary-value problem for a parabolic equation of heat distribution in a layer is considered. Ggradient is specified in one region of the boundary, and temperature in the other. It is assumed that away from the initial conditions, the process is established in time and the temperature decreases slowly and exponentially and then increases. We study temperature localization in one of the regions, and the conditions and consequences of localization in the other region at various stages of temperature change. An analogy is drawn between the temperature distribution pattern in the layer and some climatic events.

An axisymmetric problem of high strains in a spherical lead shell enclosed into an aluminum ``spacesuit" under the action of pulsed loading is considered. The shell straining is described with the use of equations of mechanics of elastoviscoplastic media in Lagrangian variables, and the kinematic relations are determined in the current state metrics. Equations of state are taken in the form of equations of the flow theory with isotropic hardening. The problem is solved numerically by using the variational difference method and the ``cross" explicit scheme of integration with respect to time. The influence of the yield stress as a function of the strain rate on changes in the shell shape is studied for different values of loading. The calculated final shape and residual strains are demonstrated to be in good agreement with experimental data.

Results of a series of inverted laboratory experiments on the normal impact of spherical bodies onto targets made of wet sand (with humidity of 10$\%$) and water-saturated sand (with humidity of 18-20$\%$) placed into cylindrical metallic containers are reported. Experimental data are compared with results calculated by a modified Godunov difference method. Changes in the forces of resistance to penetration at different stages of the impact interaction process are analyzed, and the influence of humidity and granulometric composition of sand on the maximum values of forces at different impact velocities is studied. The maximum force of resistance for sand with 20$\%$ humidity is found to be smaller by a factor of 1.5-2 than that for dry sand.

Awareness of self-awareness is a fundamental cognitive property of human beings. This means that awareness of self-awareness could be naturalized as specific functional mental state of human brain. Nature of reflection as real mental state is social one. Evolution of reflective forms of mind could be explained through evolution epistemological standpoint as a result of social reflective games. Organisms have an ability to grasp opponent’s reflective range and to detect epistemic lie by their behavior and external physiological data. Probably this is possible due the evolution of empathy phenomena caused by mirror neurons.

The concept of consciousness is considered through its relation to unconscious mental processes, brain activity, and behavioral automatisms. Impossibility of consciousness ontology construction with consciousness being detached from unconscious work of the mind is shown though fallacy of some reductive and nonproductive views on consciousness.

A curious instance of utilization of algebraic terminology in Hippolytus’ ( Elenchos I 2, 9-10: dynamis, cubus, dynamocubus , etc.) indicates that a relatively advanced arithmetic originated in works of such mathematicians as Heron and Diophantus, for some reason, aroused interest in Platonic and Pythagorean circles. Indeed, if we were to look for an example of an “ideal” Pythagorean, Diophantus would certainly qualify: he wrote a book on such a popular Pythagorean subject as polygonal numbers, transformed traditional arithmetic, and created a new theory of number; in a word, he did things a Pythagorean is supposed to do. It is no secret that Pythagorean numerology is not very useful from a mathematical point of view. What if an unknown Pythagorean (Hippolytus’ source) decided to translate the standard Pythagorean theory into the language of higher mathematics of his time? It is as if asked to define number I were to indulge in axiomatic set theory. Besides, the text has clear implications for the dating of Diophantus. Textual observations allow us to entertain the idea that Diophantus as the philosophus Pythagoricus was known and used in the Neopythagorean and Platonic sources from the second, and, possibly, the first century AD. Moreover, if he, as it seems, authored an introductory work on arithmetic, he may be set in a series with such persons as Eudorus, Cleomedes, Moderatus, Nicomachus, and Theon of Smyrna as a fully fledged contributor to the development of the Neopythagorean movement, perhaps to be placed somewhere between Eudorus and Nicomachus.

The review of approaches to the problem of unity of knowledge in the history of philosophical thought made. Performances philosophers from antiquity to modern times and the varieties of reductionist and synthetic models of the unity of knowledge since the philosophy of positivism are considered. Based on the review is concluded that there are several basic approaches to the problem of the unity of knowledge. The approaches can be classified by the ontological (the possibility of the unity of the world) and epistemological (the possibility of reducing / combining elements of the world) grounds.