Elements Of Theory Research Articles

Multi-disciplinary design optimisation considered fluid-structure interaction and life prediction applied in the lightweight carbody structure

Multi-disciplinary design optimisation based on rigid-flexible multi-body system (MBS) is presented to solve the multi-object design optimisation problems of lightweight carbody structure by considering the fluid-structure interactions at different typical load cases. A mathematical model is developed to simulate structure interactions based on the theory of finite elements. The model is integrated with a multi-object optimisation approach which utilises the Non-Sort Genetic Algorithm method. The MBS was used to understand complex vehicle system dynamics performance and obtain the structure load time histories. Through performing structural quasi-static stress analysis method, the structure dynamic stress/strain histories were obtained for fatigue life evaluation. The obtained results demonstrate the effectiveness of the proposed approach in simultaneously considering the structural vibration and the aerodynamic pressure at several vehicle speeds by proper lightweight design. This method has the advantage which can be used to understand the interaction mechanism between the vehicle dynamics characteristic and lightweight structural fatigue damage.

Spectral theory of B-Weyl elements and the generalized Weyl's theorem in primitive C*-algebra

Let $\mathcal{A}$ be a unital primitive C*-algebra. This paper studies the spectral theories of B-Weyl elements and B-Browder elements in $\mathcal{A}$, including the spectral mapping theorem and a characterization of B-Weyl spectrum. In addition, we characterize the generalized Weyl's theorem and the generalized Browder's theorem for an element $a\in\mathcal{A}$ and $f(a)$, where $f$ is a complex-valued function analytic on a neighborhood of $\sigma(a)$. What's more, the perturbations of the generalized Weyl's theorem under the socle of $\mathcal{A}$ and quasinilpotent element are illustrated.

$\mathbb{Z}$-graded identities on the infinite-dimensional Grassmann algebra and arithmetic tools: revisited

The main purpose of this paper is to provide a survey of results concerning the $\mathbb{Z}$-gradings on the infinite-dimensional Grassmann algebra $E$ over a field of characteristic zero. First, we provide graded identities and central polynomials for $E$ equipped with fine gradings on $E$ by the semigroup $(\mathbb{Z}^\ast,\times)$. We also describe briefly techniques in order to illustrate some important methods to exhibit graded identities and central polynomials of $E$ for other abelian groups. In particular, over a field of characteristic zero, so-called $2$-induced gradings of full support were considered. In order to obtain these descriptions, we strongly use elementary number theory as a tool, providing an interesting connection between this area and PI-Theory.

Joint ergodicity of fractional powers of primes

Abstract We establish the mean convergence for multiple ergodic averages with iterates given by distinct fractional powers of primes and related multiple recurrence results. A consequence of our main result is that every set of integers with positive upper density contains patterns of the form $\{m,m+[p_n^a], m+[p_n^b]\}$ , where $a,b$ are positive nonintegers and $p_n$ denotes the nth prime, a property that fails if a or b is a natural number. Our approach is based on a recent criterion for joint ergodicity of collections of sequences, and the bulk of the proof is devoted to obtaining good seminorm estimates for the related multiple ergodic averages. The input needed from number theory are upper bounds for the number of prime k-tuples that follow from elementary sieve theory estimates and equidistribution results of fractional powers of primes in the circle.

Subsonic and Supersonic Gas Flows to Condensation Surface

Intense heat-mass transfer in a gas flow to a condensation surface is studied with the consistent atomistic and kinetic theory methods. The simple moment method is utilized for solving the Boltzmann kinetic equation (BKE) for the nonequilibrium gas flow and its condensation, while molecular dynamics (MD) simulation of a similar flow is used for verification of BKE results. We demonstrate that BKE can provide the steady flow profiles close to those obtained from MD simulations in both subsonic and supersonic regimes of steady gas flows. Surprisingly, the elementary theory of condensation is shown with BKE results to have a good accuracy in a wide range of gas flow parameters. MD confirms that a steady supersonic gas flow condensates on a surface at the distinctive temperature after formation of a standing shock front in reference to this surface, which can be interpreted as a permeable condensating piston. The last produces the shock compression but completely absorbs incoming gas flow in contrast to a common impermeable piston. The shock front divides the vapor flow on the supersonic and subsonic zones, and condensation of compressed gas happens in the subsonic regime. The complete and partial condensation regimes are discussed. It is shown that above the certain surface temperatures determined by the shock Hugoniot the runaway shock front stops an inflow gas and condensation is ceased.

Intersection Cographs and Aesthetics

Cographs are complete graphs with colored lines (edges); in an intersection cograph, the points (vertices) and lines (edges) are labeled by sets, and the line between each pair of points is (or represents) their intersection. This article first presents the elementary theory of intersection cographs: 15 are possible on 4 points; constraints on the triangles and quadrilaterals; some forbidden configurations; and how, under suitable constraints, to generate the points from the lines alone. The mathematical theory is then applied to aesthetics, using set cographs to describe the experience of a person enjoying a picture (Mu Qi), poem (Dickinson), play (Shakespeare), or piece of music (Anna Magdalena Bach).

Fungsi Dan Makna Point Of Interest Dalam Unsur Grafis Pada Label Makanan Tradisional Getuk Goreng Di Sokaraja

Point of Interest (center of attention) becomes important for identity on product labels for Sokaraja fried getuk packaging. On each label, Sokaraja fried getuk uses a different center of attention from one label to another. This study aims to determine the role of the center of interest in the fried getuk label. The research method used is descriptive qualitative research by extracting data from primary and secondary sources such as interviews and literature studies. Through the perspective of the theory of graphic elements and design principles as the unit of analysis for the label of getuk goreng Sukaraja. Based on data analysis, it was concluded that the Sokaraja Fried Getuk Label has the characteristics of traditional visual elements and is dominated by red. Aspects of typography tend to be serif, sans serif, and script, using symmetrical and asymmetrical compositions. Design principles such as unity, proportion, balance, rhythm, and emphasis are visual elements that are composed quite well.

MUSIC-THEORETICAL TRAINING OF FUTURE TEACHERS ON THE BASIS OF MODULAR TEACHING

The article substantiates the views on the training of future teachers on the basis of modular learning. Changing educational priorities, emphasis on training a modern specialist who can adapt to the professional field and quickly solve the problems facing them, lead to the emergence of new views on the organization of the educational process in higher education and the possibility of individual trajectory of formation and functioning of future teachers. Such a search for the realization of personal needs in education contributed to the birth of the idea of modular learning.
 Traditionally, the teaching of music theory is taught through separate disciplines, including elementary music theory, harmony, polyphony, analysis of musical works, instrumentation, as well as solfeggio as a special discipline. The integrated nature of the content determines the application of a modular approach to teaching the discipline "Music Theory and Solfeggio", which is subject to one cross-cutting goal of the course, provides general and concretized approaches to determining expected learning outcomes in accordance with forms, content, principles, methods of teaching. Modules as academic disciplines have a cross-cutting structure in the form of content modules and can be used while training of music teachers in institutions of higher pedagogical education. Qualification characteristics of the music teacher in institutions of general secondary education and out-of-school education institution provide a variety of functions of the team leader, artistic, music director, who must understand and implement the complex task of music education of the younger generation.

On elementary complex variable theory applied to generalised sinc(p) and related integrals

The elementary application of complex variable theory in an earlier paper [Hey, J.D. 2020. On elementary complex variable theory applied to sinc and related integrals. Transactions of the Royal Society of South Africa 75(3): 295–306] is extended by use of the generalised sinc(p) function defined below, in order to provide some interesting, additional insight into the behaviour of the Borwein integrals, which arise as simple consequences of Jordan’s lemma applied to Cauchy’s theorem. The present treatment is of physical interest in relation to the analysis of spectral line broadening by the electric fields of ion perturbers in laboratory and astrophysical plasmas. Finally, a result, stated as a student problem in the well-known treatise [Whittaker, E.T. & Watson, G.N. 1927. A Course of Modern Analysis, Ch. VI (4th ed.). Cambridge University Press], is formulated in more general terms with the aid of the sinc(p) function. The simplicity of application of the present analytical results is extensively illustrated by numerical tables.

Complexity in Young's lattice

We investigate the complexity of the partial order relation of Young's lattice. The definable relations are characterized by establishing the maximal definability property modulo the single automorphism given by conjugation; consequently, as an ordered set Young's lattice has an undecidable elementary theory and is non-finitely axiomatizable but every ideal generates a finitely axiomatizable universal class of equivalence relations. We show the class of equivalence relations has positive definability and is second-order capable in the finite. We end with conjectures concerning the complexities of the Σ1 and Σ2-theories of Young's lattice.

The Axiomatics of Free Group Rings

In [FGRS1,FGRS2] the relationship between the universal and elementary theory of a group ring $R[G]$ and the corresponding universal and elementary theory of the associated group $G$ and ring $R$ was examined. Here we assume that $R$ is a commutative ring with identity $1 \ne 0$. Of course, these are relative to an appropriate logical language $L_0,L_1,L_2$ for groups, rings and group rings respectively. Axiom systems for these were provided in [FGRS1]. In [FGRS1] it was proved that if $R[G]$ is elementarily equivalent to $S[H]$ with respect to $L_{2}$, then simultaneously the group $G$ is elementarily equivalent to the group $H$ with respect to $L_{0}$, and the ring $R$ is elementarily equivalent to the ring $S$ with respect to $L_{1}$. We then let $F$ be a rank $2$ free group and $\mathbb{Z}$ be the ring of integers. Examining the universal theory of the free group ring ${\mathbb Z}[F]$ the hazy conjecture was made that the universal sentences true in ${\mathbb Z}[F]$ are precisely the universal sentences true in $F$ modified appropriately for group ring theory and the converse that the universal sentences true in $F$ are the universal sentences true in ${\mathbb Z}[F]$ modified appropriately for group theory. In this paper we show this conjecture to be true in terms of axiom systems for ${\mathbb Z}[F]$.

A STUDY OF URBAN MORPHOLOGY AND URBAN DESIGN ELEMENTS: PEKAN REMBAU, NEGERI SEMBILAN

Urban design is part of the planning process that covers aspects of the physical quality of the environment and urban development relationships. Urban design is formed gradually along with the development of an area. Meanwhile, urban morphology is the expansion and shape of urban change, structure, and function of a city's fabric. Therefore, the purpose of this study conducted is to overview the urban morphology pattern and to determine the urban design elements that are being implemented in the Pekan Rembau. This study is conducted to identify the pattern of urban morphology and all the elements of urban design. The methodology applied for this paper is exploratory research in Rembau District, which consists of field observation and case study or field research of urban design and morphology toward creating sustainable development has been identified. The findings of this study are the urban morphology of Rembau City centre pattern as linear patterns were successfully built as planned to reveal their various functions. Then, according to Lynch’s theories of urban design elements, Pekan Rembau has identified five urban design elements. It locates urban morphology and urban design as products and processes within a framework based on the distinction between a few elements of urban. The paper concludes with suggestions of potential development and strategies.

Third quantization of the electromagnetic field

We consider an approach in which the usual wave function in the quadrature representation of mode j of the electromagnetic field is further quantized to produce a field operator. Since the electromagnetic field is already second quantized, this corresponds to an additional or third quantization. The third-quantization approach can be used to perform certain quantum optics calculations in the Heisenberg picture that could only be performed in the Schrodinger picture when using the conventional second-quantized theory. This approach also allows an interesting generalization of quantum optics and quantum electrodynamics that is analogous to symmetry breaking in elementary particle theory. The predictions of the generalized theory could be tested using a proposed photon scattering experiment.

The contribution of Theodore von Kármán to the development of metal forming technology and the controversy with Erich Siebel

AbstractIn 1925, Theodore von Kármán publishes an article in [1] where he presents a simple method for calculating strip rolling. This procedure (later called elementary theory), can today be regarded as the starting point for the theoretical treatment of many metal forming technology problems. Von Kármán pursues two objectives: On the one hand, he illuminates the rolling process from the point of view of a mechanic and wants to make this comprehensible to the practical engineer. On the other hand, he wants to create the basis for further investigations. For describing the state in the rolling gap, he introduces a number of simplifying assumptions, which lead to the fact that the compressive stresses in the rolled material can be represented directly as the solution of a statically determinate problem. Although this work is published in German, it received rapid acceptance, particularly in the English‐speaking world.

A literature review of questionnaires for the assessment of online learning with a specific focus on the factors and items employed

Studies measuring online learning have adopted different perspectives, resulting in different approaches to their assessment of online learning. However, when we consider the literature from a wider angle, there may be complimentary or contrasting relationships. This study performed content analysis on a total of 44 studies that used questionnaires with good reliability and validity from the database of the Social Science Citation Index. Through encoding the 241 factors and 1,171 items used in the questionnaires, we found relationships among them that could be supported by classical theoretical frameworks or our general knowledge of instruction. The content measured by these questionnaires can be divided into five categories according to Li’s (2001) theory of instructional elements: (1) learning environment, (2) learner, (3) teacher, (4) learning content, and (5) learning interaction. Following the initial analysis, this study used the unified theory of acceptance and use of technology (UTAUT) (Oye et al., 2014) to classify 58 factors that reflect the learning environment. In addition, the combination of Marzano and Kendall’s (2007) new taxonomy of educational objectives and learning outcomes provides useful information for 111 factors used to assess learners. Implications for policy and practice: An online learning questionnaire database was established with a good structure based on the classification of the factors and items of these questionnaires. Based on the results, teachers can more accurately design online teaching without feeling lost or taking detours.

A closer look at the multilinear cryptography using nilpotent groups

In Kahrobaei et al. [Multilinear cryptography using nilpotent groups, Proceedings of Elementary Theory of Groups and Group Rings, and Related Topics conference. Conference held at Fairfield University and at the Graduate Center, CUNY, New York, NY, USA, November 1–2, 2018, De Gruyter, 2020, pp. 127–133] we generalized the definition of a multilinear map to arbitrary groups and introduced two multiparty key-exchange protocols using nilpotent groups. In this paper we have a closer look at the protocols and will address some incorrect cryptanalysis which has been proposed in Roman'kov [Discrete logarithm for nilpotent groups and cryptanalysis of polylinear cryptographic system, Prikl. Diskretn. Mat. Suppl. (12), (2019), pp. 154–160].

Geometry and dynamics link form, function, and evolution of finch beaks

Darwin's finches are a classic example of adaptive radiation, exemplified by their adaptive and functional beak morphologies. To quantify their form, we carry out a morphometric analysis of the three-dimensional beak shapes of all of Darwin's finches and find that they can be fit by a transverse parabolic shape with a curvature that increases linearly from the base toward the tip of the beak. The morphological variation of beak orientation, aspect ratios, and curvatures allows us to quantify beak function in terms of the elementary theory of machines, consistent with the dietary variations across finches. Finally, to explain the origin of the evolutionary morphometry and the developmental morphogenesis of the finch beak, we propose an experimentally motivated growth law at the cellular level that simplifies to a variant of curvature-driven flow at the tissue level and captures the range of observed beak shapes in terms of a simple morphospace. Altogether, our study illuminates how a minimal combination of geometry and dynamics allows for functional form to develop and evolve.

The atomic structure of chemical elements in the theory of compressible oscillating ether

Previously, the basic laws and equations of electrodynamics, atomic nuclei, elementary particles theory and gravitation theory were derived from the equations of compressible oscillating ether. In this work, the theory of atomic structure for all chemical elements is constructed. A formula for the values of the energy levels of the electrons of an atom, which are the values of the energies of binding of electrons with the nucleus of an atom in the ground unexcited state, is derived from the equations of the ether. Based on experimental data on the ionization energies of atoms and ions, it is shown that the sequence of values of the energy levels of electrons has jumps, exactly corresponding to the periods of the table of chemical elements. It is concluded that it is precisely these jumps, and not quantum-mechanical rules, prohibitions and postulates that determine the periodicity of the properties of chemical elements. Ethereal correction of the table of chemical elements is presented which returns it to the form proposed by D.I. Mendeleev.

Ventilation of roadways using kinetic energy of air flows

The article presents the studies into effectiveness of ventilation by local sources of draught installed in the brattice-free roadways. The relevance of this topic is defined by the need to improve mine ventilation, prevent leaks in the conditions of insufficient fresh air, as well as to remove harmful impurities from faces. The efficiency of ejector units is analyzed versus the aerodynamic drag of a ventilation section and a cross section area of a mixing chamber. On this basis, the optimal parameters for the ejector unit to reach the maximum performance are determined. The numerical simulation of the ejection effect in large crosssection roadways has found that a part of the kinetic energy of the jet is spent for the formation of an air vortex which plays the role of a mixing chamber. The problem connected with insufficient airing is eliminated by means of series arrangement of fans, which reduces air circulation and leakage in minedout voids, and ensures air feed to work spaces. The variants of application of air curtains to reduce air leaks via roadways which cannot be shut by brattices are discussed. It is shown that this method is costeffective when pressure drops are under 2 daPa and is ineffective in prevention of leaks via installations above ground. In ventilation of dead-end roadways, the increase in the distance between the end of the vent pipe and the face surface prevents the damage of the vent pipe by blasted rock chips and reduces the labor input of installation and dismantling. The analytical estimation of the permissible spacing for the face surface–vent pipe is carried out as function of excess flow rate as against the required air flow. The ventilation simulation was carried out using the theory of turbulent jets and elements of numerical simulation in specialized software products for the verification of analytical dependences.The study was supported by the Russian Foundation for Basic Research and by the Perm Krai Government within the framework of R&D Project No. 20-45-596021 r_NOTS_Permskii krai.

Extension of the Freiberg Layer Model by Means of Elastic–Plastic Material Behavior

Finite element method simulations offer deep and detailed modeling of complex processes, but with high effort of computation power and time. For the special purpose of flat rolling, a layer model was developed by Schmidtchen before based on the classic elementary theory of plasticity with the purpose to model inhomogeneous behavior with significant lower effort at computation. This model considered the layers only as rigid or in plastic deformation state. Herein, the model is extended by elastic material behavior to get closer to the depth of finite elements method (FEM) models. The results are first compared with a FEM simulation and measurements from the literature. The current model is found to fit well the FEM results as well as the measurements. Second, the results are compared with classic elementary theory and the layer model of Schmidtchen. From these comparisons is found, that the main elastic influences on the stress curve shape are due to the full elastic zones. Elastic deformations in the plastic regions are found to be smaller, but growing on transition from block rolling to thin sheet rolling.