Timelessness of C.G. Jung and Super-Temporality of N.O. Lossky: Comparative Analysis

The article compares views of C.G. Jung and N.O. Lossky on the nature of time, including in the context of contemporary to them physical theories - quantum mechanics by W. Pauli and relativistic physics by A. Einstein. In particular, the author points to the similarity of ideas of both thinkers that the psyche relativizes time not only subjectively, but also objectively. Jung and Lossky provide this statement with a similar empirical basis, for example, the researches of T. Flournoy, as well as similar theoretical arguments by postulating a fundamental acausal principle of the connection of all things, which is better suited for describing psychic and some physical phenomena than the classical causal explanation. In analytical psychology, such a principle is synchronicity, in hierarchical personalism - gnoseological coordination. Both concepts are genetically related to the G.W. Leibniz idea of pre-established harmony, which was reinterpreted by Jung and Lossky through different worldview foundations. Jung in his reasoning relied on the transcendental idealism of I. Kant, the principle of complementarity and the discoveries of quantum mechanics, Lossky - on intuitivism, the principle of subordination and on his own interpretation of Einsteins theories. Jung comes to the conclusion that the psyche has a timeless character, and Lossky comes to the conclusion that it has a super-temporal character. Jungs timelessness indicates the transcendental nature of psyche and the strive to get away from the classical causal explanation, saving it according to the principle of complementarity only to consider the phenomenal side of being and mainly physical processes. One of the pioneers of quantum mechanics Pauli was of the same opinion in general. Because of there is nothing transcendent in hierarchical personalism, Losskys super-temporality is of a strive to find a deeper basis for occurring in time processes, and, according to the principle of subordination, to include time in the hierarchical structure of the universe, prescribing for it a role of one of the two key forms of psychic and psycho-material processes characteristic of a certain stage of being.

A Subclass of Multivalent Janowski Type q-Starlike Functions and Its Consequences

In this article, by utilizing the theory of quantum (or q-) calculus, we define a new subclass of analytic and multivalent (or p-valent) functions class Ap, where class Ap is invariant (or symmetric) under rotations. The well-known class of Janowski functions are used with the help of the principle of subordination between analytic functions in order to define this subclass of analytic and p-valent functions. This function class generalizes various other subclasses of analytic functions, not only in classical Geometric Function Theory setting, but also some q-analogue of analytic multivalent function classes. We study and investigate some interesting properties such as sufficiency criteria, coefficient bounds, distortion problem, growth theorem, radii of starlikeness and convexity for this newly-defined class. Other properties such as those involving convex combination are also discussed for these functions. In the concluding part of the article, we have finally given the well-demonstrated fact that the results presented in this article can be obtained for the (p,q)-variations, by making some straightforward simplification and will be an inconsequential exercise simply because the additional parameter p is obviously unnecessary.

Metaphor as an object of the synergy paradigm study

The article investigates the ontognoseological properties of metaphor from the point of view of the synergetic paradigm. By the principles of synergetic science, metaphor is considered as a nonlinear system category that performs a system-forming, heuristic, generalizing function. With the help of the principle of subordination, complex systems are described through a limited number of order parameters, as a result of which information is compressed without loss. The metaphor has its origins in the economy: as a method of abstraction, the transition from the infinite to the finite, and the reduction of lexical means. Metaphor is a way of transmitting an idea that has a methodological significance, i.e. one theoretical system is translated into another and one system is investigated through another, simpler system. Metaphor as a dynamic formation establishes connections between objects of different orders and processes in their development in space and time, which allows you to explore metaphors using the principles of synergetics.

Faber Polynomial for Holomorphic Functions Involving Differential Operator

The purpose of this paper, is to present differential operator for the univalent functions employ a Faber Polynomial . In addition, we will introduce some inclusion properties of the operator that were obtained employ the principle of subordination between holomorphic functions.

SUBCLASSES OF MULTIVALENT NON-BAZILEVIC FUNCTIONS DEFINED WITH HIGHER ORDER DERIVATIVES

By making use of the principle of subordination, we introduce a certain class of multivalent non-Bazilevic functions with higher order. Also, we obtain subordination property, inclusion result, and inequality properties of this class. The results presented here would provide extensions of those given in earlier works.

FORMATION OF CELLULAR-TYPE STRUCTURES DURING PLASTIC DEFORMATION

A theoretical study of patterns of the evolution and formation of dislocation structures during the plastic deformation of crystals is carried out. A nonlinear theory of the formation of cellular dislocation structures in an ensemble of screw dislocations has been developed. The nonlinear dynamics of an ensemble of dislocations is investigated in a two-dimensional domain, taking into account periodic boundary conditions of the Born - Karman type imposed on the initial equation. The local kinetics of dislocations is chosen in the form of multiplication of dislocations by means of their double transverse sliding and annihilation. A homogeneous stationary solution of the system (thermodynamic branch) is found. It is established that at a critical deviation from the thermodynamic branch, an instability of the homogeneous state occurs in the system due to the correlation interaction of dislocations. To obtain solutions in the domain of instability, the system of evolutionary equations is transformed to a system of equations for collective (mode ) variables. The expediency of such transformation lies in the fact that the system can be divided into subsystems of unstable and damped modes and it makes possible to apply the principle of adiabatic exclusion of unstable variables (the principle of subordination). Using the smallness of the values characterizing the increments of unstable modes, the principle of subordination is applied for the system of collective variables. In this case, it is shown that the system can be reduced to solving differential equations for a relatively small number of variables (order parameters). In the vicinity of the bifurcation point, two stable solutions are obtained for the order parameters. The first one is a consequence of the competition of modes and it leads, in the soft excitation regime, to a periodic one-dimensional structure for the dislocation density, the second parameter is a result of the cooperation of unstable modes and it leads to the formation of a hexagonal structure in the hard regime of emergence. The question is solved, which of these two structures is implemented, when the system reaches the bifurcation point. The equations for the order parameters are written in the variational form and the corresponding potential function is determined. Its analysis at the points of minima showed that the hexagonal configuration is more likely at the moment of instability occurrence. As the bifurcation parameter increases, the single-mode structure becomes more likely. Thus, the formation of a dissipative cellular structure serves as an indicator of the attaining of non-equilibrium critical conditions in a local volume, when a deformable crystal begins to change its defective structure minimizing its elastic energy.

Некоторые результаты о подчинении для одного функционального класса, определяемого $q$-разностным оператором типа Салагина

The theory of the basic quantum calculus (that is, the basic q-calculus) plays important roles in many diverse areas of the engineering, physical and mathematical science. Making use of the basic definitions and concept details of the q-calculus, Govindaraj and Sivasubramanian [10] defined the Salagean type q-difference (q-derivative) operator. In this paper, we introduce a certain subclass of analytic functions with complex order in the open unit disk by applying the Salagean type q-derivative operator in conjunction with the familiar principle of subordination between analytic functions. Also, we derive some geometric properties such as sufficient condition and several subordination results for functions belonging to this subclass. The results presented here would provide extensions of those given in earlier works.

On Certain Class of Bazilevič Functions Associated with the Lemniscate of Bernoulli

Making use of the principle of subordination, we introduce a certain class of multivalently Bazilevi c ˘ functions involving the Lemniscate of Bernoulli. Also, we obtain subordination properties, inclusion relationship, convolution result, coefficients estimate, and Fekete–Szegö problem for this class.

Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization Rq(h) of the class R(h) of analytic functions, which are associated with the leaf-like domain in the open unit disk U, is given. Then, the coefficient estimates, the Fekete–Szegö problem, and the second-order Hankel determinant H2(1) for functions belonging to this class Rq(h) are investigated. Furthermore, similar results are examined and presented for the functions zf(z) and f−1(z). For the validity of our results, relevant connections with those in earlier works are also pointed out.

Just Hierarchy between Humans and Animals

This chapter considers human relations with the animal kingdom. Throughout much of human history, most cultural and religious traditions—with some notable exceptions, such as Daoism—have valued humans over animals. The chapter presents the argument that it is morally justifiable to posit a moral hierarchy with humans on top, but only if accompanied by the principle that humans should not be cruel to animals. But the principle of “subordination without cruelty” is not sufficient to spell out the kinds of obligations we owe to animals. Humans have different kinds of relations with different animals, and the strongest obligations of care are owed to animals with human-like traits and that contribute most to human well-being. In the case of animals bred for human consumption, the chapter argues that such subordination is only justified if the animals are bred in humane conditions that are exceptionally rare in the modern world. Furthermore, the chapter states that we owe least to ugly animals that harm humans, but the principle of subordination without cruelty applies even in the case of the nastiest animals.