PROBLEM S5 FOR THE THIRD-ORDER HYPERBOLIC EGUATION IN A THREE-DIMENSIONAL SPACE

2020 ◽  
Author(s):  
Irina Nikolaevna Rodionova ◽  
◽  
S.A. Sevastyanova ◽  
Keyword(s):  
Special Class ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Hyperbolic Type ◽  
Darboux Problem ◽  
Third Order ◽  
The Third ◽  
Class Of Functions ◽  
Three Dimensional Space

The article presents a method for solving the boundary value for the complete equation of the thirdorder hyperbolic type with variable coefficients. The solution to the problem posed is based on the solution of the Darboux problem in a special class of functions obtained by the authors. The problem is reduced to a set of uniquely solvable Volterra integral equations, by virtue of which its solution can be obtained in explicit form.

scholarly journals On conditions of solvability of three-dimensional integralsystem in quadratures

2017 ◽  
Vol 21 (10) ◽  
pp. 40-46
Author(s):  
E.A. Sozontova
Keyword(s):  
Differential Equations ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Original System ◽  
Goursat Problem ◽  
System Of Differential Equations ◽  
Third Order ◽  
First Order ◽  
Three Dimensional Space

In this paper we consider the system of equations with partial integrals in three-dimensional space. The purpose is to find sufficient conditions of solvability of this system in quadratures. The proposed method is based on the reduction of the original system, first, to the Goursat problem for a system of differential equations of the first order, and after that to the three Goursat problems for differential equations of the third order. As a result, the sufficient conditions of solvability of the considering system in explicit form were obtained. The total number of cases discussing solvability is 16.

The Greek Neoplatonist Commentators on Aristotle

2018 ◽  
pp. 894-920
Author(s):  
Michael Griffin
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
The Third ◽  
Natural Place ◽  
Biological Reproduction ◽  
Three Dimensional Space

Greek Neoplatonist commentators on Aristotle practiced philosophy and science in the third through seventh centuries ce by performing innovative exegesis of Aristotle’s works. To investigate nature is, for the commentators, to read with understanding Aristotle’s treatises in a set curriculum, with a commentary and teacher. Therefore, a mature philosopher would often prove to be a capable commentator, or interpreter, who could foster the reading of the primary texts with charity and objectivity, eliciting the author’s meaning through paraphrase, lemmatized discussion, and a critically evaluated doxography of the puzzles presented by the text. On the Neoplatonist account, the system expounded in Aristotle’s treatises is uniform and consistent, and is harmonious with the philosophy expounded in Plato’s dialogues. This chapter surveys concepts in the commentators including nature (phusis), biological reproduction, the five or four elements, dynamics and Philoponus’ impetus, natural place and three-dimensional space, modes of causation, teleology, time, cosmogony, and cosmology.

The Content of Descriptive Geometry Course For High Educational Institution’s In the Third Industrial Revolution’s Era

2018 ◽  
Vol 6 (3) ◽  
pp. 49-55 ◽  
Author(s):  
Юрий Поликарпов ◽  
Yuriy Polikarpov
Keyword(s):  
Industrial Revolution ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Descriptive Geometry ◽  
Cad Systems ◽  
Course Content ◽  
The Third ◽  
Stage Of Development ◽  
High Educational ◽  
Three Dimensional Space

A brief journey into the history of industrial revolutions has been presented. It is noted that our society has entered the third industrial revolution’s era. In this regard, the main consequences of the third industrial revolution have been noted. The stages of development for design methods and the basic science providing the design process have been considered. The historical necessity and significance of Gaspar Monge’s descriptive geometry appearance has been considered as well. Modern products design approaches using CAD systems are described. It is stated that design has again returned to three-dimensional space, in fact prior to the Monge’s era, but at a new stage of development. The conclusion is drawn that, taking into account the realities and needs of modern production, it is necessary to modernize the descriptive geometry course for technical high educational institutions. The author's suggestions on course content changing are presented related to extension of one sections and reducing of another ones, taking into account the fact that in real design practice the designer solves geometric problems in three-dimensional space, rather than in a complex drawing. It is noted that in connection with the extensive use of CAD systems, the design stages and the composition of design documentation developed at each stage are changed. Such concepts as "electronic model" and "electronic document" have appeared and are widely used, that is confirmed by adoption of new USDD standards. In such a case the role and significance of some types of drawings may change in the near future, since modern CAD systems allow transfer to production not 2D drawings, but electronic models and product drawings.

Determination of the modulated structure of Sr14/11CoO3 through a (3 + 1)-dimensional space description and using non-harmonic ADPs

1999 ◽  
Vol 55 (6) ◽  
pp. 841-848 ◽  
Author(s):  
O. Gourdon ◽  
V. Petricek ◽  
M. Dusek ◽  
P. Bezdicka ◽  
S.  Durovic ◽  
...  
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Atomic Displacement ◽  
Atomic Displacement Parameter ◽  
Third Order ◽  
Modulated Structure ◽  
New Phase ◽  
Space Description ◽  
Three Dimensional Space

Sr14/11CoO3 (i.e. Sr14Co11O33, tetradecastrontium undecacobalt tritriacontaoxide), a new phase in the hexagonal perovskite Sr x CoO3 system, has been prepared and its structure solved from single-crystal X-ray data within the (3 + 1)-dimensional formalism. Sr14/11CoO3 crystallizes in the trigonal symmetry, R3¯m(00γ)0s superspace group with the following lattice parameters: as = 9.508 (2), cs = 2.5343 (7) Å, q = 0.63646 (11)c * and Vs = 198.40 (13) Å3. With the commensurate versus incommensurate test not being conclusive, the structure was considered as commensurate (P32 three-dimensional space group), but refined within the (3 + 1)-dimensional formalism to a residual factor R = 0.0351 for 47 parameters and 1169 independent reflections. Crenel functions were used for the oxygen and cobalt description and a Gram–Charlier expansion up to the third order of the atomic displacement parameter was employed for one Co atom. The structure is similar to that of Sr6/5CoO3, but with a different sequence of the octahedra and trigonal prism polyhedra along the [CoO3] chains. An interesting feature evidenced by the non-harmonic expansion is the displacement of the prismatic Co atoms from the site center, towards the prism rectangular faces.

scholarly journals The Third Dimention in a Landscape

Secreta Artis ◽  
2021 ◽  
pp. 74-82
Author(s):  
Daria Vladimirovna Fomicheva
Keyword(s):  
Land Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The Other ◽  
Landscape Painting ◽  
The Third ◽  
Soviet Art ◽  
Other Hand ◽  
Third Dimension ◽  
Three Dimensional Space

The present study examines the principles of conveying the third dimension in landscape painting. The author analyzes the recommendations provided in J. Littlejohns’ manual entitled “The Composition of a Landscape” [London, 1931]. J. Littlejohns describes four methods of showing depth in a landscape painting, each illustrated with pictorial composition schemes: 1) portrayal of long roads, which allows one to unveil the plasticity of the land surface; 2) creation of a “route” for the viewer by means of a well-thought-out arrangement of natural landforms; 3) introduction of vertically and horizontally flowing streams of water on different picture planes; 4) depiction of cloud shadows on a distinctly hilly landscape. The author of the article compares the schemes contained in the manual of J. Littlejohns with the works of G. G. Nissky, which enables readers to comprehend and reflect on the compositions of the masterpieces created by a prominent figure in Soviet art; on the other hand, Nissky’s landscape paintings open for a deeper understanding of the meaning and effectiveness of the methods proposed by J. Littlejohns. The outlined composition techniques are certainly relevant for contemporary artists (painters, graphic artists, animators, designers, etc.) as they make it possible to achieve the plastic expressiveness of a three-dimensional space in a twodimensional image.

scholarly journals УНІФІКАЦІЯ ТА ГАРМОНІЗАЦІЯ ІНФОРМАЦІЇ В АРТРОЛОГІЇ ДЛЯ СТВОРЕННЯ СИСТЕМИ ПРОГНОЗУВАННЯ РЕЗУЛЬТАТІВ ОПЕРАТИВНОГО ВТРУЧАННЯ

2014 ◽  
Author(s):  
M. M. Ryhan
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Automated Diagnosis ◽  
Information Base ◽  
The Third ◽  
Class 1 ◽  
The Creation ◽  
Three Dimensional Space

<p class="1">This article discusses the possibility of establishing an information base for automated diagnosis and predicting the outcomes of surgery in gonarthrosis. The unified information document provides the creation of three-dimensional space for decision­making system. Recorded on the same plane the primary symptoms of the disease, the second - the results of pre­processing the information obtained using internationally accepted questionnaires. Finally, the third presents the results of “voting” for final conclusions decision.</p>

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

A Peptoid with Extended Shape in Water

2019 ◽  
Author(s):  
Jumpei Morimoto ◽  
Yasuhiro Fukuda ◽  
Takumu Watanabe ◽  
Daisuke Kuroda ◽  
Kouhei Tsumoto ◽  
...  
Keyword(s):  
Spectroscopic Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Biomolecular Recognition ◽  
Biological Application ◽  
New Class ◽  
Proteolytic Resistance ◽  
Pharmacokinetic Properties ◽  
Optically Pure ◽  
Three Dimensional Space

<div> <div> <div> <p>“Peptoids” was proposed, over decades ago, as a term describing analogs of peptides that exhibit better physicochemical and pharmacokinetic properties than peptides. Oligo-(N-substituted glycines) (oligo-NSG) was previously proposed as a peptoid due to its high proteolytic resistance and membrane permeability. However, oligo-NSG is conformationally flexible and is difficult to achieve a defined shape in water. This conformational flexibility is severely limiting biological application of oligo-NSG. Here, we propose oligo-(N-substituted alanines) (oligo-NSA) as a new peptoid that forms a defined shape in water. A synthetic method established in this study enabled the first isolation and conformational study of optically pure oligo-NSA. Computational simulations, crystallographic studies and spectroscopic analysis demonstrated the well-defined extended shape of oligo-NSA realized by backbone steric effects. The new class of peptoid achieves the constrained conformation without any assistance of N-substituents and serves as an ideal scaffold for displaying functional groups in well-defined three-dimensional space, which leads to effective biomolecular recognition. </p> </div> </div> </div>

Sign in / Sign up

Export Citation Format

Share Document