The methods for the formation of optimal acoustic conditions for the transmission of speech content in small rooms

The subject of research in the article is the methodology for the examination of small-volume premises with a predominance of speech content. The aim of the work is to analyze all stages of acoustic expertise for meeting rooms, conference rooms, press centers, to determine the volume and sequence of the stages, taking into account the specific restrictions and conditions that arise in small rooms. All stages of acoustic expertise are considered in the work on examples of real premises of meeting rooms, conference halls, press centers. The sequence of stages of the examination, when it was carried out for premises of small volumes, did not undergo any changes, compared to the sequence that is used for spectator halls. The main distinctive feature of the first stage of acoustic examination in small rooms with a predominance of speech content is the analysis of the structures of the reverberation process in listening places in order to identify the drawbacks of the formation of a diffuse field, instead of checking the geometry of the wall and ceiling panel walls using geometric theory. A feature of the second stage is the development of recommendations for improving the sound-absorbing properties of enclosing surfaces and eliminating the effect of multiple re-reflections of sound energy between parallel surfaces through the use of partial replacement of surface geometry, work with suspended ceiling structures and the use of sound-absorbing curtains (to correct the properties of glass surfaces). The third and fourth stages of the examination remained unchanged.

Gauge Symmetries in Physical Fields (Review)

Gauge invariance is one of the fundamental symmetries in theoretical physics. In this paper, the gauge symmetry is reviewed to see how it is working in fundamental physical fields: Electromagnetism, Quantum Electro Dynamics and Geometric Theory of Gravity. In the 19th century, the gauge invariance was recognized as a mathematical non-uniqueness of the electromagnetic potentials. Real recognition of the gauge symmetry and its physical significance required two new fields developed in the 20th century: the relativity theory for physics of the world structure of linked 4d-spacetime and the quantum mechanics for the new dimension of a phase factor in complex representation of wave function. Finally the gauge theory was formulated on the basis of the gauge principle which played a role of guiding principle in the study of physicalfields such as Quantum Electrodynamics, Particle Physics and Theory of Gravitation. Fluid mechanics of a perfect fluid can join in this circles, which is another motivation of the present review. There is a hint of fluid gauge theory in the general representation of rotational flows of an ideal compressible fluid satisfying the Euler’s equation, found in 2013 by the author. In fact, law of mass conservation can be deduced from the gauge symmetry equipped in the new system of fluid-flow field combined with a gauge field, rather than given a priori.

Completely geometric theory I: gravitation

In order to describe motions in arbitrary physical systems, a geometric approach is proposed, in which the goal is not to find the Lagrangian, but to find the geometry of space that models the experimental space. The requirement that the observed trajectory coincides with the geodesic makes it possible to use geometric identity to find the equation for the metric. As a result, it is possible to give an interpretation of a number of observations that do not have such in the existing theories.

Completely geometric theory II: basics of quantum mechanics

The geometrical approach suggested earlier, makes it possible to investigate the regions both in mega-and micro worlds that cannot be accessed by the direct observation. This makes it possible not only to interpret the basic experiments of quantum mechanics in a new way but also to escape the paradoxes stemming from the wave function introduction. It also gives perspectives to adjust the quantum mechanics and the relativity theory.

Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems

Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium processes in terms of a (dimensionless) distance by quantifying how information unfolds over time as a probability density function (PDF) evolves in time. Here, we discuss some recent developments in information geometric theory focusing on time-dependent dynamic aspects of non-equilibrium processes (e.g., time-varying mean value, time-varying variance, or temperature, etc.) and their thermodynamic and physical/biological implications. We compare different distances between two given PDFs and highlight the importance of a path-dependent distance for a time-dependent PDF. We then discuss the role of the information rate Γ=dLdt and relative entropy in non-equilibrium thermodynamic relations (entropy production rate, heat flux, dissipated work, non-equilibrium free energy, etc.), and various inequalities among them. Here, L is the information length representing the total number of statistically distinguishable states a PDF evolves through over time. We explore the implications of a geodesic solution in information geometry for self-organization and control.

Scientific and Practical Approaches to Improving Noise Muffler Designs of Piston Internal Combustion Engines Based on Theory of Numbers

A methodological method based on the use of the theory of preferred numbers has been proposed in order to improve the most important parameters of the working bodies of noise mufflers. As a result of many years of scientific research, the authors have established a previously unknown theoretical relationship between the main series of preferred numbers, golden ratio and Fibonacci series numbers. A new direction in the development of number theory has been considered in the paper, its classification has been compiled, including the geometric theory of numbers, preferred numbers, containing a new basic series of preferred numbers using the Fibonacci sequence. New formulas have been obtained to determine the denominators of geometric progressions for the series of preferred numbers and the area of a circle. Determining the area of a circle using the new formula allows to get more accurate values. A new formula for determining the circumference of a circle has also been derived. The designs of perforated partitions have been developed, in which the laws of the new basic series of preferred numbers are used. Determining the area of a circle using the new formula allows you to get more accurate values. A new formula for determining the circumference of a circle is also obtained. The designs of perforated partitions have been developed, in which the regularities of the new basic series of preferred numbers have been used. A calculated substantiation of the main geometric and structural dimensions of noise mufflers is given using a mathematical model of a perforated golden partition and new basic series of preferred numbers, which allow to obtain a noise muffler design that has the lowest possible aerodynamic resistance with the maximum possible reduction in the noise level of exhaust gases from internal combustion engines. An innovative model of a noise muffler for reciprocating internal combustion engines with improved hydraulic and acoustic characteristics based on the theory of numbers is proposed in the paper. The theory of preferred numbers applies to any technical device.

Geometric theory of non-regular separation of variables and the bi-Helmholtz equation

The geometric theory of additive separation of variables is applied to the search for multiplicative separated solutions of the bi-Helmholtz equation. It is shown that the equation does not admit regular separation in any coordinate system in any pseudo-Riemannian space. The equation is studied in the four coordinate systems in the Euclidean plane where the Helmholtz equation and hence the bi-Helmholtz equation is separable. It is shown that the bi-Helmoltz equation admits non-trivial non-regular separation in both Cartesian and polar coordinates, while it possesses only trivial separability in parabolic and elliptic–hyperbolic coordinates. The results are applied to the study of small vibrations of a thin solid circular plate of uniform density which is governed by the bi-Helmholtz equation.

FRACTIONAL APPROXIMATIONS OF THERMOELASTIC PLATE SYSTEMS

Let $\Omega$ be a bounded domain in $\mathbb{R}^N$ with $N\geqslant 2$, which boundary $\partial\Omega$ is assumed to be a $\mathcal{C}^4$-hypersurface. In this paper we consider the initial-boundary value problem associated with the following thermoelastic plate system \[ \begin{cases} \partial_t^2u +\Delta^2 u+\Delta\theta=f(u),\ & x\in\Omega,\ t>0, \\ \partial_t\theta-\Delta \theta-\Delta \partial_tu=0,\ & x\in\Omega,\ t>0, \end{cases} \] subject to boundary conditions \[ \begin{cases} u=\Delta u=0,\ & x\in\partial\Omega,\ t>0,\\ \theta=0,\ & x\in\partial\Omega,\ t>0, \end{cases} \] and initial conditions \[ u(x,0)=u_0(x),\ \partial_tu(x,0)=v_0(x)\ \mbox{and}\ \theta(x,0)=\theta_0(x),\ x\in\Omega. \] We calculate explicit the fractional powers of the thermoelastic plate operator associated with this system via Balakrishnan integral formula and we present a fractional approximated system. We obtain a result of local well-posedness of the thermoelastic plate system and of its fractional approximations via geometric theory of semilinear parabolic systems.

GEOMETRIC MODELING OF ADAPTIVE ALGEBRAIC CURVES PASSING THROUGH PREDETERMINED POINTS

In this paper, the geometric theory of multidimensional interpolation was further developed in terms of modeling and using adaptive curves passing through predetermined points. A feature of the proposed approach to modeling curved lines is the ability to adapt to any initial data for high-quality interpolation, which excludes unplanned oscillations, due to the uneven distribution of parameter values, the source of which are the initial data. This is the improvement of the previously proposed method for constructing and analytically describing arcs of algebraic curves passing through predetermined points, obtained on the basis of Bezier curves, which are compiled taking into account the expansion coefficients of the Newton binomial. The paper gives an example of using adaptive algebraic curves passing through predetermined points for geometric modeling of the stress-strain state of membrane coatings cylindrical shells using two-dimensional interpolation. The given example an illustrative showed the advantages of the proposed adaptation of algebraic curves passing through predetermined points and obtained on the basis of Bezier curves for geometric modeling of multifactor processes and phenomena. The use of such adaptation allows not only to avoid unplanned oscillations, but also self-intersection of geometric objects when generalized to a multidimensional space. Adaptive algebraic curves can also be effectively used as formative elements for constructing geometric objects of multidimensional space, both as guide lines and as generatrix’s.

Affine connection representation of gauge fields

There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincar{\'{e}} gauge theory and metric-affine gauge theory adopt the first approach. This paper adopts the second. In this approach:(i) Gauge field and gravitational field can both be represented by affine connection; they can be described by a unified spatial frame.(ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space and external coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as a geometric theory of distribution of gradient directions. Hence, gauge theory, gravitational theory and quantum theory obtain the same geometric foundation and a unified description of evolution.(iii) Coupling constants, chiral asymmetry, PMNS mixing and CKM mixing arise spontaneously as geometric properties in affine connection representation, so they are not necessary to be regarded as direct postulates in the Lagrangian anymore.(iv) The unification theory of gauge fields that are represented by affine connection can avoid the problem that a proton decays into a lepton in theories such as $SU(5)$.(v) There exists a geometric interpretation to the color confinement of quarks.In the affine connection representation, we can get better interpretations to the above physical properties, therefore, to represent gauge fields by affine connection is probably a necessary step towards the ultimate theory of physics.