Meromorphic solutions of algebraic differential equations by A. E. Eremenko Some questions in spe... more Meromorphic solutions of algebraic differential equations by A. E. Eremenko Some questions in spectral theory for the operator Sturm-Liouville equation on the half-line by M. L. Gorbachuk and V. A. Kutovoi On the connection between spectral and oscillatory properties of the matrix Jacobi problem by V. S. Bondarchuk On the numerical solution of the Cauchy problem for ordinary linear homogeneous differential equations on large intervals of integration by S. F. Zaletkin On the solutions of a uniformly elliptic complex equation of first order connected with the convergence of analytic functions by S. A. Akhmedov On the behavior of solutions of the equations of plane elasticity theory in the neighborhood of irregular boundary points and at infinity by O. A. Oleinik, G. A. Iosifyan, and I. N. Tavkhelidze The Dirichlet problem for the Laplace operator in the exterior of a thin body of revolution by M. V. Fedoryuk Variational methods in a mixed problem of thermal equilibrium with a free boundary by B. V. Bazalii and V. Yu. Shelepov On an estimate of $N^\ast(\lambda)$ for the series of quasimodes of the Laplace operator by V. F. Lazutkin On the selfadjointness and maximal dissipativity of differential operators for functions of an infinite-dimensional argument by Yu. L. Daletskii Selfadjoint differential operators acting in spaces of functions of infinitely many variables by Yu. M. Berezanskii.
In previous articles [1-7] a wide class of geometric figures-"Generalized Twisting and Rotat... more In previous articles [1-7] a wide class of geometric figures-"Generalized Twisting and Rotated" bodies (sometimes called "surface of Revolution" see [11])-shortly n m GTR-was defined through their analytic representation. In particular cases, this analytic representation gives back many classical objects (torus, helicoid, helix, Möbius strip ... etc.). Aim of this article is to consider some geometric properties of a wide subclass of the already defined surfaces, by using their analytical representation. In previous articles [1-7] a set of the Generalized Möbius Listing's bodies-shortly n m GML , which are a particular case of the n m GTR bodies, have been defined. In the present paper we show some geometric properties of Generalized Twisting and Rotated-surfaces and relationships between the set n GML 2 and the sets of Knots and Links.
Natural forms affect all of us, not only for their beauty, but also for their diversity (see e.g.... more Natural forms affect all of us, not only for their beauty, but also for their diversity (see e.g. Fig. 1). It is still not known whether forms define the essence of the phenomena associated with them, or vice versa - that is, forms are natural consequences of the phenomena. The essence of one “unexpected” phenomenon is as follows: Usually after one “full cutting”, an object is split into two parts. The Mobius strip is a well-known exception, however, which still remains whole after cutting. The first author discovered a class of surfaces, which have following properties - after full cutting more than two surfaces appear, but this is a result for specific class of pure mathematical surfaces [1, 2]. It turns out that three-dimensional Mobius Listing bodies, \(GML_m^n\), which is a wide subclass of the Generalized Twisting and Rotated figures - shortly \(GTR_m^n\) - which, through their analytic representation, could yield more than two objects after only single cutting ([3] or [2]). These are not only theoretical results, as can be proved by real-life examples. Many classical objects (torus with different forms of radial cross sections, helicoid, helix, Mobius strip,... etc.) are elements of this wide class of \(GTR_m^n\) figures, so it is important to study the similarity and difference between these figures and surfaces. In this chapter we study some questions of similarity and difference in the cases of the “cut” of Generalized Mobius–Listing’s figures.
Since implementing the strategy of "going global"in 1990s, after decades of endeavor an... more Since implementing the strategy of "going global"in 1990s, after decades of endeavor and hard working, Jiangsu Provincial Construction Group Co., Ltd (JPC) has developed into a first-class company for contracting project in overseas market and AAA qualification company recognized by China International Contractors
In the present paper, we consider the “bulky knots” and “bulky links” that appear after cutting o... more In the present paper, we consider the “bulky knots” and “bulky links” that appear after cutting of generalized Möbius–Listing GML4n bodies (with corresponding radial cross sections square) along different generalized Möbius–Listing surfaces GML2n situated in it. The aim of this article is to examine the number and geometric structure of independent objects that appear after such a cutting process of GML4n bodies. In most cases, we are able to count the indices of the resulting mathematical objects according to the known tabulation for knots and links of small complexity.
Abstract. Aim of this article is the analytical representation of a class of geometric figures, s... more Abstract. Aim of this article is the analytical representation of a class of geometric figures, surfaces and lines. This class of surfaces includes the sur-faces appearing in some problems of Shell Theory or problems of spreading of smoke-rings; furthermore, the lines of this class can be used for describ-ing the complicated orbit of some celestial objects. In previous articles [1-5] sets of Generalized Möbius Listing’s bodies, which are a particular case of this class in static case, have been already defined. In particular cases, this analytic representation gives back many classical objects (torus, helicoid, helix, Möbius strip... etc.). In present paper was studied some relations between set of GMLn2 (Generalized Möbius-Listing’s surfases) and sets of Knots and Links. Also, here was defined classes of DMLn2 (Degenerated
We will present 2 different analytical representations of only one general idea—this is the repre... more We will present 2 different analytical representations of only one general idea—this is the representation of complex movements using the superposition of certain elementary displacements! Despite of the analytical and structural similarity of these representations, they describe fundamentally different geometric figures (in statics) and trajectories of motion (in dynamics). In previous articles [1, 2, 3, 4, 5, 6, 7, 8, 9] a wide class of geometric figures—“Generalized Twisting and Rotated” bodies \(GRT^n_m\) in short—was defined through their analytic representation. In particular cases, this analytic representation gives back many classical objects (torus, helicoid, helix, Mobius strip ... etc.). The aim of this article is to consider some geometric properties of a wide subclass of the generally defined surfaces. We show some geometric properties of GRT and GML—surfaces.
Meromorphic solutions of algebraic differential equations by A. E. Eremenko Some questions in spe... more Meromorphic solutions of algebraic differential equations by A. E. Eremenko Some questions in spectral theory for the operator Sturm-Liouville equation on the half-line by M. L. Gorbachuk and V. A. Kutovoi On the connection between spectral and oscillatory properties of the matrix Jacobi problem by V. S. Bondarchuk On the numerical solution of the Cauchy problem for ordinary linear homogeneous differential equations on large intervals of integration by S. F. Zaletkin On the solutions of a uniformly elliptic complex equation of first order connected with the convergence of analytic functions by S. A. Akhmedov On the behavior of solutions of the equations of plane elasticity theory in the neighborhood of irregular boundary points and at infinity by O. A. Oleinik, G. A. Iosifyan, and I. N. Tavkhelidze The Dirichlet problem for the Laplace operator in the exterior of a thin body of revolution by M. V. Fedoryuk Variational methods in a mixed problem of thermal equilibrium with a free boundary by B. V. Bazalii and V. Yu. Shelepov On an estimate of $N^\ast(\lambda)$ for the series of quasimodes of the Laplace operator by V. F. Lazutkin On the selfadjointness and maximal dissipativity of differential operators for functions of an infinite-dimensional argument by Yu. L. Daletskii Selfadjoint differential operators acting in spaces of functions of infinitely many variables by Yu. M. Berezanskii.
In previous articles [1-7] a wide class of geometric figures-"Generalized Twisting and Rotat... more In previous articles [1-7] a wide class of geometric figures-"Generalized Twisting and Rotated" bodies (sometimes called "surface of Revolution" see [11])-shortly n m GTR-was defined through their analytic representation. In particular cases, this analytic representation gives back many classical objects (torus, helicoid, helix, Möbius strip ... etc.). Aim of this article is to consider some geometric properties of a wide subclass of the already defined surfaces, by using their analytical representation. In previous articles [1-7] a set of the Generalized Möbius Listing's bodies-shortly n m GML , which are a particular case of the n m GTR bodies, have been defined. In the present paper we show some geometric properties of Generalized Twisting and Rotated-surfaces and relationships between the set n GML 2 and the sets of Knots and Links.
Natural forms affect all of us, not only for their beauty, but also for their diversity (see e.g.... more Natural forms affect all of us, not only for their beauty, but also for their diversity (see e.g. Fig. 1). It is still not known whether forms define the essence of the phenomena associated with them, or vice versa - that is, forms are natural consequences of the phenomena. The essence of one “unexpected” phenomenon is as follows: Usually after one “full cutting”, an object is split into two parts. The Mobius strip is a well-known exception, however, which still remains whole after cutting. The first author discovered a class of surfaces, which have following properties - after full cutting more than two surfaces appear, but this is a result for specific class of pure mathematical surfaces [1, 2]. It turns out that three-dimensional Mobius Listing bodies, \(GML_m^n\), which is a wide subclass of the Generalized Twisting and Rotated figures - shortly \(GTR_m^n\) - which, through their analytic representation, could yield more than two objects after only single cutting ([3] or [2]). These are not only theoretical results, as can be proved by real-life examples. Many classical objects (torus with different forms of radial cross sections, helicoid, helix, Mobius strip,... etc.) are elements of this wide class of \(GTR_m^n\) figures, so it is important to study the similarity and difference between these figures and surfaces. In this chapter we study some questions of similarity and difference in the cases of the “cut” of Generalized Mobius–Listing’s figures.
Since implementing the strategy of "going global"in 1990s, after decades of endeavor an... more Since implementing the strategy of "going global"in 1990s, after decades of endeavor and hard working, Jiangsu Provincial Construction Group Co., Ltd (JPC) has developed into a first-class company for contracting project in overseas market and AAA qualification company recognized by China International Contractors
In the present paper, we consider the “bulky knots” and “bulky links” that appear after cutting o... more In the present paper, we consider the “bulky knots” and “bulky links” that appear after cutting of generalized Möbius–Listing GML4n bodies (with corresponding radial cross sections square) along different generalized Möbius–Listing surfaces GML2n situated in it. The aim of this article is to examine the number and geometric structure of independent objects that appear after such a cutting process of GML4n bodies. In most cases, we are able to count the indices of the resulting mathematical objects according to the known tabulation for knots and links of small complexity.
Abstract. Aim of this article is the analytical representation of a class of geometric figures, s... more Abstract. Aim of this article is the analytical representation of a class of geometric figures, surfaces and lines. This class of surfaces includes the sur-faces appearing in some problems of Shell Theory or problems of spreading of smoke-rings; furthermore, the lines of this class can be used for describ-ing the complicated orbit of some celestial objects. In previous articles [1-5] sets of Generalized Möbius Listing’s bodies, which are a particular case of this class in static case, have been already defined. In particular cases, this analytic representation gives back many classical objects (torus, helicoid, helix, Möbius strip... etc.). In present paper was studied some relations between set of GMLn2 (Generalized Möbius-Listing’s surfases) and sets of Knots and Links. Also, here was defined classes of DMLn2 (Degenerated
We will present 2 different analytical representations of only one general idea—this is the repre... more We will present 2 different analytical representations of only one general idea—this is the representation of complex movements using the superposition of certain elementary displacements! Despite of the analytical and structural similarity of these representations, they describe fundamentally different geometric figures (in statics) and trajectories of motion (in dynamics). In previous articles [1, 2, 3, 4, 5, 6, 7, 8, 9] a wide class of geometric figures—“Generalized Twisting and Rotated” bodies \(GRT^n_m\) in short—was defined through their analytic representation. In particular cases, this analytic representation gives back many classical objects (torus, helicoid, helix, Mobius strip ... etc.). The aim of this article is to consider some geometric properties of a wide subclass of the generally defined surfaces. We show some geometric properties of GRT and GML—surfaces.
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Papers by Ilia Tavkhelidze