Home – Home – Jornals – Advanced Search

The paper deals with a numerical solution of the wave equation. The solution algorithm uses optimal parameters which are obtained by using Laguerre transform in time for the wave equation. Additional parameters are introduced into a difference scheme of 2nd-order approximation for the equation. The optimal values of these parameters are obtained by minimizing the error of a difference approximation of the Helmholtz equation. Applying the inverse Laguerre transform in the equation for harmonics, a differential-difference wave equation with the optimal parameters is obtained. This equation is difference in the spatial variables and differential in time. An iterative algorithm for solving the differential-difference wave equation with the optimal parameters is proposed. 2-dimensional and 1-dimensional equations are considered. The results of numerical calculations of the differential-difference equations are presented. It is shown that the difference schemes with the optimal parameters give an increase in the accuracy of solving the equations.

In this paper, we provide a new a posteriori error analysis for a linear finite element approximation of a parabolic integro-differential optimal control problem. The state and co-state are approximated by piecewise linear functions, while the control variable is discretized by a variational discretization method. We first define elliptic reconstructions of numerical solutions and then discuss a posteriori error estimates for all variables.

A problem of variational data assimilation for a sea thermodynamics model is considered, with the aim to reconstruct sea surface heat fluxes taking into account the covariance matrices of input data errors. The sensitivity of some solution functionals to input data in this problem of variational assimilation is studied, and the results of numerical experiments for a model of dynamics of the Baltic Sea are presented.

An inverse problem of reconstructing a coefficient in the differential equation of a model of development for a homogeneous biological population of organisms structured by age is considered. The model takes into account the impact of migration flows on population size changes. Conditions are established to ensure the uniqueness of the solution of the inverse problem. A brief overview of algorithms for the numerical solution of the inverse problem is provided.

The article considers assumptions used by R. Descartes, of which he declares he does not recognize them as true. He declares them as such, since he uses them not guided by biblical texts, but on the basis of experimental data. Nevertheless, he recognizes them as significant “for life”. First of all, Descartes here considers the corporeal world in the making, but not as created by God wholly-formed. Also, here he not only demonstrates a distraction from the idea of God as the ruler of the processes occurring in nature, but also notes that such a distraction is justifiable. All this gives grounds to recognize the presence of a materialistic component in the considered constituent of his teaching. And since before this, Descartes formulated the basic laws of mechanics, his contribution to the development of modern science is also appreciated. The conclusion is made that although the main part of what Descartes states here is not proclaimed by him as true, nevertheless, by publishing his considerations he contributed a lot to strengthening the emerging tendencies to overcome adherence to a religious worldview

The paper analyses the studies of philosophers and psychologists, and also the ideas of futurologists and biologists, which allows us to conclude that not only the present affects the future, but vice versa as well. The shift of the viewpoint beyond the limits of the usual meanings contributes to a change in the understanding of the relationship of temporal modes and the strengthening of the indeterminist position regarding the ontology of the future.

Quantum physics radically changes the worldview, destroys the usual picture of the world and related philosophical concepts. Science is increasingly reminiscent of science fiction, in which the impossible becomes possible: time flows in different directions, matter dissolves in a vacuum, communications beyond the speed of light take place, and a lot more. The phenomenal nature of the results of physical experiments at the micro- and macrolevel of cognition is inevitably suggestive of the possible virtuality of the surrounding reality. The simulation hypothesis is one of the most consistent models of the universe, the singularity point of which becomes the point of a phase shift to a new interpretation of reality

The advance of QBism over other interpretations of quantum mechanics is that it introduces the first-person perspective and treats quantum theory, including the Born rule, as a norm. The problematic nature of this position (subjectivism, relativism, residual dualism, etc.) stems from the fact that it remains within the assumptions and prejudices of modern philosophy, including when it is interpreted phenomenologically. Cubism, however, can be transformed into contextual quantum realism (CQR) - a consistent and genuinely realistic position - by reinterpreting its basic notions, particularly the notions of reality, experience, agent, quantum norm, quantum probability, and others

The article deals with the problem of describing reality in the language of mathematics and logic with regard to the intellectual intuition corresponding to a certain stage in the development of knowledge. The question is raised of how the basic requirements for mathematical theory and logic will change if we take some of the multiverse models of modern physics as a basis. Mathematics is considered in the context of various historical approaches; mutual criticism of intuitionism, logicism and formalism is analyzed. It is shown that some of the well-known requirements for a formal theory (such as consistency) may begin to play a different role if the multiverse hypothesis is accepted. Under the theories based on the idea of the plurality of worlds, disputes related to logical consequence, the law of Duns Scotus, the law of the excluded middle and other well-known facts of classical logic, due to intuitive unacceptability, become resolved. An approach based on paraconsistent logics is considered; such logics can be treated as the first to conform to the multiverse theories. The problem of the universality of the mathematical language and the accompanying intellectual intuition is proposed for discussion. Can mathematics describe any of the physically possible worlds and therefore become the basis for the “theory of everything” (not so much in the sense of the quantum gravity theory, but as describing all possible worlds) and in what epistemological consequences this can result? It is shown that in a unified theory that claims to describe multiverse models, the classical intuitive requirement of consistency becomes restrictive and serving the purpose of an approximate description of a particular world, rather than the whole of all possible worlds. This requires a change in the general methodology in describing the world by such a theory and a revision of current standards

The article proves in a fundamentally new way the reasons for the unidirectionality and asymmetry of the arrow of objective time, which are considered from the perspective of the functional concept of time developed by the author. According to the functional concept, the arrow of time, like objective time, is formed by a successive change in qualitatively new states of a material object or process. Since objective time is formed only by concrete and finite objects, it is always local. The arrow of time, like objective time, is non-substantial, is not a physical entity, and therefore is irreversible. Since the arrow of objective time is irreversible, it is directed only forward. Therefore, the arrow of objective time is unidirectional. In nature, only the present exists, while the past and the future do not exist in nature, but appear only in the observer’s mind. And so, the arrow of time, like objective time, moves from the present to the next present, and not from the past to the future, as is it generally believed in science. Accordingly, the arrow of objective time is asymmetric. Objective time is formed only by concrete and finite objects or processes, while the Universe is uncreatable and indestructible and exists eternally. For this reason, the concept of time and the concept of the arrow of time do not apply to it. The concepts of objective time and the arrow of objective time would apply to the Universe, if it pulsed and the cycles of its expansion and compression completely repeated all its inherent possibilities to change. The article also discusses the possibilities of using the concept of objective, functional time in practice.