Artistic architectonics of human behavioral models in boundary situations and conditions

The article is devoted to one aspect of the problem of reproduction of boundaries and states in a literary text, in particular the study of artistic architecture of human behavioral models in boundary situations and states. On the basis of philosophical and psychological works, the structural elements of such a model were identified. In invariant form, it consists of three main constructs, which are topos of limited rationality, compensatory satisfaction, awareness of potential meaning. Variant forms of architectonics of behavioral models in boundary situations and states may lose their individual components or differ in certain artistic and semantic nuances. The artistic architecture of the behavioral models of the characters in the article is studied on the material of the novels Dan Brown «Angels and Demons» and M. Kidruk «Where there is no God». There are similar approaches of the authors to the structuring of images-characters who are in borderline situations, and in both works revealed both invariant and variant forms of these structures. The invariant behavioral models of the characters in D. Brown's novel «Angels and Demons» are mostly represented by images of lonely, individual figures (Carlo Ventresca, Pope Francis and Maximilian Kohler)

Geometry and kinematics induced by biquaternionic and twistor structures

The algebra of biquaternions possess a manifestly Lorentz invariant form and induces an extended space-time geometry. We consider the links between this complex pre-geometry and real geometry of the Minkowski space-time. Twistor structures naturally arise in the framework of biquaternionic analysis. Both together, algebraic and twistor structures impose rigid restriction on the transport of singular points of biquaternion-valued fields identified with particle-like formations.

O(25, 25) symmetry of bosonic string theory at order $$\alpha '^2$$

It has been recently observed that the imposition of the O(1, 1) symmetry on the circle reduction of the classical effective action of string theory, can fix the effective action of the bosonic string theory at order $$\alpha '^2$$ α ′ 2 , up to an overall factor. In this paper, we use the cosmological reduction on the action and show that, up to one-dimensional field redefinitions and total derivative terms, it can be written in the O(25, 25)-invariant form proposed by Hohm and Zwiebach.

O(n, n) invariance and Wald entropy formula in the Heterotic Superstring effective action at first order in α′

We perform the toroidal compactification of the full Bergshoeff-de Roo version of the Heterotic Superstring effective action to first order in α′. The dimensionally-reduced action is given in a manifestly-O(n, n)-invariant form which we use to derive a manifestly-O(n, n)-invariant Wald entropy formula which we then use to compute the entropy of α′-corrected, 4-dimensional, 4-charge, static, extremal, supersymmetric black holes.

Higher order functions and Brouwer’s thesis

Extending Martín Escardó’s effectful forcing technique, we give a new proof of a well-known result: Brouwer’s monotone bar theorem holds for any bar that can be realized by a functional of type (ℕ→ℕ)→ℕ in Gödel’s System T. Effectful forcing is an elementary alternative to standard sheaf-theoretic forcing arguments, using ideas from programming languages, including computational effects, monads, the algebra interpretation of call-by-name λ-calculus, and logical relations. Our argument proceeds by interpreting System T programs as well-founded dialogue trees whose nodes branch on a query to an oracle of type ℕ→ℕ, lifted to higher type along a call-by-name translation. To connect this interpretation to the bar theorem, we then show that Brouwer’s famous “mental constructions” of barhood constitute an invariant form of these dialogue trees in which queries to the oracle are made maximally and in order.

DGLA Dg and BV formalism

Differrential Graded Lie Algebra Dg was previously introduced in the context of current algebras. We show that under some conditions, the problem of constructing equivariantly closed form from closed invariant form is reduces to construction of a representation of Dg. This includes equivariant BV formalism. In particular, an analogue of intertwiner between Weil and Cartan models allows to clarify the general relation between integrated and unintegrated operators in string worldsheet theory.

Some Properties of Blow up Solutions in the Cauchy Problem for 3D Navier–Stokes Equations

Up to now, it is unknown an existence of blow up solutions in the Cauchy problem for Navier–Stokes equations in space. The first important property of hypothetical blow up solutions was found by J. Leray in 1934. It is connected with norms in Lp(R3),p>3. However, there are important solutions in L2(R3) because the second power of this norm can be interpreted as a kinetic energy of the fluid flow. It gives a new possibility to study an influence of kinetic energy changing on solution properties. There are offered new tools in this way. In particular, inequalities with an invariant form are considered as elements of latent symmetry.