On the Johnson–Tzitzeica Theorem, Graph Theory, and Yang–Baxter Equations

This paper presents several types of Johnson–Tzitzeica theorems. Graph diagrams are used in this analysis. A symmetric scheme is derived, and new results are obtained and open problems stated. We also present results relating the graphs and the Yang–Baxter equation. This equation has certain symmetries, which are used in finding solutions for it. All these constructions are related to integrable systems.

A Table-Top Pilot Experiment for Narrow Mass Range Light Cold Dark Matter Particle Searches

This report presents the detection framework and a proposal for a pilot table-top experiment (supported by simulations and preliminary test results) for adoption into narrow mass range light Cold Dark Matter (CDM) searches, specifically for axions or Axion-Like Particles (ALPs) in a resonant cavity-based scheme. The novelty of this proposal lies in an attempt to concentrate searches corresponding to specific axion masses of interest (coinciding with recent proposals), using multiple cavities in a symmetric scheme, instead of using noisy and complicated tuning mechanisms, and in reduction of associated hardware by employing simpler underlying instrumentation instead of heterodyne mode of detection, by means of a low-noise ac amplification and dc phase-sensitive detection scheme, in order to make a viable and compact table-top experiment possible. These simplifications could possibly be valuable in substantially reducing detection hardware, experiment complexities (and associated noise) and long run-times, while maintaining low noise similar to conventional axion searches. The feasibility of proposed scheme and the experiment design are demonstrated with some calculations, simulations and preliminary tests with artificial axion signals injected into the cavities. The technique and ideas reported here have significant potential to be developed into a small-scale table-top, narrow-range, dark matter axion/ALP spectroscopy experiment, in addition to aiding in the on-going resonant cavity-based and broadband experiments.

Music and choreography interaction in the stage dances of musical theater productions of the 17th – the first half of the 18th century

Background. One of the typical trends of modern musicology is the increasing interest in the problem of components dialogue in the synthetic forms of art. In the context of this global topic, the issue of music and choreography interaction in the stage dances of musical theater productions of the 17th – the first half of the 18th century is of particular interest. The connection of music and choreography in the art of stage dance of the 17th – the first half of the 18th century appears as a kind of continuation of the syncretic unity of ancient art seen through the prism of the professional experience of the creators of court musical and stage productions in the French classicism style. In the court operas, ballets and other types of performances such of the composers, as A. Kampra, J.-B. Lully, J. F. Rameau, the spirit of the antique art was reviving in its own special way representing the “ensemble of arts” in a miniature. The research objective is to identify the features of the combination and interaction of musical and choreographic arts in the stage dances of French musical and theatre productions of the 17th – the first half of the 18th century. The article uses the method of comparative analysis. This method allows to analyze the features and the ways of interaction between the elements of dance and musical syntax. Results. The art of choreography is a rhythm and plastic form of thinking and self-expression, which can reflect reality not only in its eventual plot related manifestations, but also to rise to the broad abstract generalizations. In view of its rather conditional nature, dance requires, to one degree or another, the interpretation of its content. In the 17th and early 18th centuries, the need for such an explanation increases significantly because of the great role of emblems and encoded content in various aesthetic and artistic phenomena. In the dance, the close relation to the court ceremonial, which did not allow the expression of emotions, initiated this feature additionally. For example, at that time one was believed that stepping a minuet means “drawing up secret signs of love”, which were recognized in movements, poses, facial expressions and gestures. In the Baroque Epoch the audience easily was recognizing the content of such dances, whereas for the modern observer and researcher it remains unknown. The dance moves and their combinations in stage dances of the 17th and early 18th century receive a specific meaning in the context of poetic, musical and dance phrases. However, first, the moves of dancers-performers were consistent with the music. As a rule, the result of making a choreographic production depended on the composer’s choice of the musical form. Most of the dances within the researched period were set to music in a two-part form. Less often we can find the samples in the form of a couplet rondo and ostinato variations. When making the dance productions, French choreographers took into account the features of other popular musical forms of the 17th –18th centuries. In some cases they emphasized or combined with their own author’s decision the symmetric basis laid down in the musical structure (the form of rondo), in others – they disclosed the effect of the continuity principle. An example of the embodiment of a choreographic idea set to music in the form of a rondo is the passepied production (fr. passé-pied) “La Gouastalla” realized by R. A. Feye to the music of the unknown composer. The choreographic composition consists of five dance periods corresponding to five sections of the musical form. A slightly different choreography scheme – ABCBC is combined with the symmetric scheme in the musical variation– ABACA. In this production the combination of the musical form and the choreographic composition is somewhat changed, however, this does not mean the complete neglect of the musical form regularities in the construction of the dance general plan. One of the aspects of the musical and choreographic arts combination in French stage dances of the 17th and 18th centuries is the connection with of the choreographic component of the latter with the tonal plan of the musical work. The tonal coloring of the music was reflecting in the formation of a choreographic drawing of dance, in the process of expressing in the movements of various emotions and feelings. Changes of tonalities, the most used of which, as a rule, a certain circle of images and affects, their own “character” carried along at that time, were associated with a variety of transitions in the emotional coloring of the dance. It is from such, emotional, the perception of tonality, the versions of the tonal plans of French dances follows, which are unusual for later canons of Viennese Classicism, in particular, with the violation of the harmonic sequence of T-D-S-T. Conclusions. Thus, the stage dance of the 17th and early 18th century is a peculiar form of embodiment of the “miniature ensemble of arts”, where dance moves and their combinations receive a specific coloring in the context of poetic, musical and dance phrases and certain allegorical meanings. Nevertheless, first and foremost, the moves of dancers-performers were consistent with the music. Obvious is the great dependence of the choreographic production on the musical form and its components – the rhythm as well as the tonal and harmonic plan, which combined with the choreographic elements, prompt the feelings transmitted in the dance, which give to it the life and inspiration.

Numerical Solution of the Stefan's Problem

All of the most well-known numerical methods for solving the Stefan’s problem, as well as a new method developed by the author are considered for the purpose of choosing the most efficient of them from a perspective of accuracy and computational speed. A comparison is carried out on the results of solving the problem for the boundary motion of “ice-water” phase transition around the vertical well passing through the thickness of permafrost. The conclusions, which are distributed to other multidimensional and multi-front statements of the Stefan’s problem, are made. The mathematical model, the brief description of the considered numerical methods and the boundaries of their applicability are presented. The comparison shows the advantages and disadvantages of different methods. It is demonstrated that the use of the explicit scheme leads to a marked increase in computation time, the six-point symmetric scheme may have oscillating solution; therefore, the implicit scheme is the most preferred. It is concluded that the most efficient method for one-dimensional and one front Stefan’s problems is the method of catching the front in the grid node using the implicit scheme, and the most efficient method for multi-dimensional and multi-front Stefan’s problems is the enthalpy method using the implicit scheme, which has been developed by the author.