Bäcklund Transformations for Liouville Equations with Exponential Nonlinearity

This work aims to obtain new transformations and auto-Bäcklund transformations for generalized Liouville equations with exponential nonlinearity having a factor depending on the first derivatives. This paper discusses the construction of Bäcklund transformations for nonlinear partial second-order derivatives of the soliton type with logarithmic nonlinearity and hyperbolic linear parts. The construction of transformations is based on the method proposed by Clairin for second-order equations of the Monge–Ampere type. For the equations studied in the article, using the Bäcklund transformations, new equations are found, which make it possible to find solutions to the original nonlinear equations and reveal the internal connections between various integrable equations.

Social orientation of postmodern choreographic performance in a post-pandemic society

Today, in a post-pandemic space, all types of art, comprehending, due to their figurative specificity, certain spheres of objective reality, already as a result of this, circumstances have their own, only inherent laws. Using the inexhaustible possibilities of the plasticity of the human body, choreography has refined and developed expressive dance movements for many centuries. As a result of this complex process, a system of choreographic movements arose, that is, a special artistic and expressive speech of plastics, constitutes the creative material of dance imagery. Choreographic art includes various types of arts: music, choreography itself, drama, painting. Each of them, changing in accordance with the requirements of this type of art, becomes a necessary component of choreographic figurative thinking. Each type of art is achieved thanks to its own figurative specificity, patterns and certain pictorial and expressive means. Choreographic activity dictates its own laws of reflection of reality, is based not on the correspondence of life and artistic material, but on the degree of devotion to the metaphorical reflection of life. A comprehensive study of social constituting dance art in today's post-pandemic space is a complex and versatile task, it mainly involves the study of all its components. Moreover, each of them should be considered not in isolation, but in the general system of their internal connections - in the aspect of their rhythmic and metric, that is, motor organization.

Jordan eliminations in bar system analysis with changes in design model

The article discusses the use of the Jordan elimination method for solving the system of resolvent equations when analyzing the bar systems. The use of the Jordan elimination method makes it possible to determine the forces in cross-sections of bars and displacements of the system units in the case of changes in the design model of the system without the solution of new resolvent equations at each change. Changes in the design model indicate the introduction or removal of the support or internal connections, changes in the stiffness parameters of elements of statically indeterminate systems, and others. The Jordan elimination method is used for a simple statically indeterminate beam, which is a special case of the bar system.

FLEXIBLE ARCHITECTURAL ENVIRONMENT. SYSTEM ANALYSIS. PROCESS ASPECT

This article examines a flexible architectural environment as a system that can change itsnparameters under the influence of various factors. These changes are motivated by the development or adaptation of the system to external environmental factors. A flexible architectural environment is considered as a system from the point of view of the procedural aspect, which determines changes in the system at various levels, as well as changes in the connections between the internal elements of the system. In this aspect, the internal elements of the system can be identified, with the help of which the flexibility of the architectural environment is achieved. Three levels of change and development of the system are considered in detail: material, functional, and aesthetic. The material and functional level involves changes in the system, which are achieved by structural elements and equipment. The aesthetic level implies changes in the system with elements such as color and light, materials, textures and decor. These groups of elements of the system undergo changes in internal connections, which are formal and aesthetic in nature.

Internal hexagon versus conical implant–abutment connections: evaluation of 3-year postloading outcomes

Different types of internal implant–abutment connections, namely hexagon and conical, have been used for implant restoration. However, data regarding the benefits of these internal connections in terms of clinical outcomes are scarce. Accordingly, the aim of this study was to compare radiographic marginal bone loss (RMBL) and associated implant complications between implants with internal hexagon (IH) connections and those with internal conical (IC) connections. Forty-nine patients with 98 implants (two per patient) placed in the posterior mandible were recruited. All implants were inserted in pairs in solid D2 bone according to a randomized sequence; the first patient received an IH connection implant on the mesial side while the second patient received an IC connection implant on the mesial side. Each patient received one implant with an IH connection and one with an IC connection, placed side-by-side. Four months after placement, all implants were loaded with single screw-retained ceramic restorations with internal hexagon or conical connections. RMBL and complications, including implant/prosthesis failure, were recorded at the time of implant loading (baseline) and 6, 12, and 36 months after loading. The results revealed no significant between-group differences in RMBL (P = .74), gingival bleeding on probing (P = .29), and complications (P = .32). Thus, the type of internal implant–abutment connection did not affect clinical outcomes, including RMBL and implant/prosthesis failure. Future studies should additionally evaluate long-term prosthesis-related complications such as screw loosening and fracture between the two types of internal connections.