Parametric analysis of static bending of the pipeline

2016 ◽  
Vol 11 (1) ◽  
pp. 24-29 ◽  
Author(s):  
A.A. Yulmukhametov
Keyword(s):  
Inverse Problem ◽  
Pressure Drop ◽  
Inverse Problems ◽  
Internal Pressure ◽  
Parametric Analysis ◽  
Direct And Inverse Problems ◽  
Relative Stiffness

Consideration is given to the direct and inverse problems for pipeline bending both by gravity and transported fluid. The effect of internal pressure drop and the velocity of a fluid are taken into account. The influence of point fixing of “pipeline-capacity” constructions for the deflection is also taken into account. The inverse problem is to determine the relative stiffness of distributed support under the instrument determining pipeline deflection or deformation of its outer fibers. The method of loading pipeline by the concentrated power and determination of appropriate instrument deflection or deformation is applied. In particular, loading and corresponding measurements are carried out at the midpoint of the pipeline span.

scholarly journals Analysis of direct and inverse problems for a fractional elastoplasticity model

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 699-708 ◽  
Author(s):  
Salih Tatar ◽  
Süleyman Ulusoy
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Unique Solution ◽  
Continuous Dependence ◽  
Direct Problem ◽  
Direct And Inverse Problems

This study is devoted to a nonlinear time fractional inverse coeficient problem. The unknown coeffecient depends on the gradient of the solution and belongs to a set of admissible coeffecients. First we prove that the direct problem has a unique solution. Afterwards we show the continuous dependence of the solution of the corresponding direct problem on the coeffecient, the existence of a quasi-solution of the inverse problem is obtained in the appropriate class of admissible coeffecients.

scholarly journals Mathematical models of centers of equal pressure in stellar systems

2021 ◽  
pp. 25-30
Author(s):  
Garold Gurevich ◽  
◽  
Sergey Lutmanov ◽  
Oleg Penskiy ◽  
◽  
...  
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Mathematical Models ◽  
Stellar Systems ◽  
Direct And Inverse Problems ◽  
Radiation Sources ◽  
Material Substance

Mathematical models are proposed that allow calculating the coordinates of the centers of equal pressure in stellar systems and solving the inverse problem of determining the radiation sources of a material substance during the formation of macro-bodies. It is shown that the solutions of direct and inverse problems are not unique.

Imaginary Straight Lines in Cartesian Coordinate System

2020 ◽  
Vol 7 (4) ◽  
pp. 5-17
Author(s):  
Viktor Korotkiy
Keyword(s):  
Inverse Problems ◽  
Geometric Model ◽  
Conic Section ◽  
Direct And Inverse Problems ◽  
Geometric Problems ◽  
Geometric Representations ◽  
One To One ◽  
Cartesian Coordinate ◽  
Straight Lines

A geometric model of imaginary conjugate straight lines a~b, allowing symbolic representation of these lines on the real coordinate plane xy is considered. In order to connect the algebraic and geometric representations of imaginary straight lines, it is proposed to use the “mark” formed by orthogonal d1 ⊥ d2 and main g1~g2 directions of the elliptic involution σ in the pencil V. The specification of two pairs of pulling apart each other real straight lines d1~d2, g1~g2 passing through V, uniquely defines the elliptic involution σ in the pencil V, therefore, the V(d1 ⊥ d2, g1~g2) mark completely defines a pair of imaginary double straight lines a~b of elliptic involution σ(V), that allows consider the mark as an “image” of these imaginary straight lines. When using a mark, it is required to establish a one-to-one correspondence between complex coefficients of imaginary double straight lines equations and a graphically given mark. The direct and inverse problems are solved in this paper. The direct one is creation a mark representing imaginary straight lines, given by its own equations. The inverse one is determination of coefficients for the equations of imaginary lines defined by the mark. The essence of the direct and inverse problems consists in establishing a oneto-one correspondence between the equations of imaginary double straight elliptic involutions σ in the pencil V, and a graphically given mark containing the orthogonal and main directions of this involution. To solve both the direct and inverse problems, the Hirsch theorem (A.G. Hirsch) is used, which establishes a one-to-one correspondence between the complex Cartesian coordinates for a pair of imaginary conjugated points and real coordinates of a special “marker” symbolically representing these points. Have been considered examples of solution for geometric problems involving imaginary lines. In particular, has been solved the problem of constructing a circle passing through a given point and touching imaginary lines defined by its mark V(d1 ⊥ d2, g1~g2). Has been proposed a graphical and analytical algorithm for determining the coefficients of equations of imaginary tangents, traced to a conic section from its inner point.

scholarly journals INVERSE HEAT TRANSPORT PROBLEMS FOR COEFFICIENTS IN TWO‐LAYER DOMAINS AND METHODS FOR THEIR SOLUTION

2002 ◽  
Vol 7 (2) ◽  
pp. 217-228 ◽  
Author(s):  
S. Guseinov ◽  
A. Buikis
Keyword(s):  
Inverse Problem ◽  
Thermal Diffusivity ◽  
Inverse Problems ◽  
Heat Transport ◽  
Transport Process ◽  
Direct Problem ◽  
Piecewise Constant Function ◽  
Algebraic Equations ◽  
Heat Transport Process

In various fields of science and technology it is often necessary to solve inverse problems, where from measurements of state of the system or process it is required to determine a certain typesetting of the causal characteristics. It is known that infringement of the natural causal relationships can entail incorrectness of the mathematical stating of inverse problems. Therefore the development of efficient methods for solving such problems allows one to considerably simplify experimental research and to increase the accuracy and reliability of the obtained results due to certain complication of algorithms for processing the experimental data. The problem of determination of thermal diffusivity coefficients considering other known characteristics of heat transport process is among incorrect inverse problems. These inverse problems for coefficients are quite difficult even in the case of homogeneous media. In this paper it is supposed that the heat transport equation is non‐homogeneous and an algorithm for determination of the thermal diffusivity coefficients for both the media is proposed. At the first step, the non‐homogeneous inverse problem with piecewise‐constant function of non‐homogeneity is solved. For this auxiliary inverse problem, the proposed method allows one to determine both the coefficients of thermal diffusivity and to restore the heat transport process without any additional information, i.e. the algorithm also solves the direct problem. Then the initial non‐homogeneous inverse problem with a piecewise‐continuous function of non‐homogeneity is solved. The proposed method reduces the non‐homogeneous inverse problem for coefficients to a set of two transcendent algebraic equations. Finally, the analytical solution to direct problem is obtained using Green's function.

scholarly journals Direct and Inverse Problems for Sturm-Liouville Operator Which Has Discontinuity Conditions and Coulomb Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yalçın Güldü ◽  
Merve Arslantaş
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Unique Solvability ◽  
Coulomb Potential ◽  
Liouville Operator ◽  
Direct And Inverse Problems ◽  
Main Equation ◽  
Sturm Liouville ◽  
Discontinuity Conditions

We give a derivation of the main equation for Sturm-Liouville operator with Coulomb potential and prove its unique solvability. Using the solution of the main equation, we get an algorithm for the solution of the inverse problem.

On the determination of differential pencils with nonlocal conditions

2018 ◽  
Vol 26 (5) ◽  
pp. 577-588
Author(s):  
Chuan-Fu Yang ◽  
Vjacheslav Yurko
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Nonlocal Conditions ◽  
Weyl Function ◽  
Uniqueness Theorems ◽  
Type Function ◽  
Sturm Liouville ◽  
Differential Pencils ◽  
Liouville Operators

Abstract Inverse problems for differential pencils with nonlocal conditions are considered. Uniqueness theorems of inverse problems from the Weyl-type function and spectra are proved, which are generalizations of the well-known Weyl function and Borg’s inverse problem for the classical Sturm–Liouville operators.

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