Mechanical proof of planimetric theorems of rational type

2014 ◽  
Vol 40 (2) ◽  
pp. 71-78
Author(s):  
N. N. Osipov
Keyword(s):  
Mechanical Proof ◽  
Rational Type

scholarly journals Fixed point results for rational contraction in function weighted dislocated quasi-metric spaces with an application

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdullah Shoaib ◽  
Qasim Mahmood ◽  
Aqeel Shahzad ◽  
Mohd Salmi Md Noorani ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Multivalued Mapping ◽  
Metric Spaces ◽  
Nonlinear Integral Equations ◽  
Rational Contraction ◽  
Rational Type

AbstractThe objective of this article is to introduce function weighted L-R-complete dislocated quasi-metric spaces and to present fixed point results fulfilling generalized rational type F-contraction for a multivalued mapping in these spaces. A suitable example confirms our results. We also present an application for a generalized class of nonlinear integral equations. Our results generalize and extend the results of Karapınar et al. (IEEE Access 7:89026–89032, 2019).

scholarly journals Fixed Point Results for the Family of Multivalued F-Contractive Mappings on Closed Ball in Complete Dislocated b-Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 56 ◽  
Author(s):  
Qasim Mahmood ◽  
Abdullah Shoaib ◽  
Tahair Rasham ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Closed Ball ◽  
Multivalued Mappings ◽  
System Of Integral Equations ◽  
Contractive Mappings ◽  
The Family ◽  
Rational Type

The purpose of this paper is to find out fixed point results for the family of multivalued mappings fulfilling a generalized rational type F-contractive conditions on a closed ball in complete dislocated b-metric space. An application to the system of integral equations is presented to show the novelty of our results. Our results extend several comparable results in the existing literature.

A rational type of checker for regenerators of glass furnaces

1962 ◽  
Vol 18 (12) ◽  
pp. 597-600
Author(s):  
A. A. Sukhov
Keyword(s):  
Glass Furnaces ◽  
Rational Type

scholarly journals CORROSION OF GALVANIZED STEEL AND ALUMINUM ALLOYS IN THE INDUSTRIAL ENVIRONMENT OF CHAMPIGNON

2019 ◽  
Vol 4 (5) ◽  
pp. 50-55
Author(s):  
С. Иконников ◽  
S. Ikonnikov ◽  
А. Блажнов ◽  
A. Blazhnov
Keyword(s):  
Aluminum Alloys ◽  
Penetration Rate ◽  
Galvanized Steel ◽  
Layer By Layer ◽  
Test Results ◽  
Structural Scheme ◽  
Construction Design ◽  
Alloys Of The Al ◽  
Rational Type ◽  
Selection Of

Generalization the experience building for the cultivation of champignons shows the diversity of construction solutions. The method of layer-by-layer assembly with galvanized steel and aluminum alloy coverings is economically feasible to use in champignons of frame structural scheme, enclosing structures of industrial premises. However, the technologically required wet air conditions of the premises and aggressive gases during construction design complicate the selection of a rational type of outer layers of enclosing structures. To reveal the rational material of coverings in the production premises of champignons, corrosion tests are carried out on samples of aluminum alloys of the Al-Mg, Al-Mn, Al-Mg-Si systems, technical aluminum, galvanized steel and galvanized steel with a protective coating. The type and corrosion penetration rate are set for the exposed samples. According to the test results, suitable covering materials for various types of champignon production premises are determined

scholarly journals Mechanical Proof of the Maxwell-Boltzmann Speed Distribution With Analytical Integration

2021 ◽  
Vol 10 (3) ◽  
pp. 135
Author(s):  
Hejie Lin ◽  
Tsung-Wu Lin
Keyword(s):  
Integral Form ◽  
Point Of View ◽  
Speed Ratio ◽  
Mass Ratio ◽  
Exact Integration ◽  
Speed Distribution ◽  
Ideal Gases ◽  
Mechanical Proof ◽  
Theoretical Limitation ◽  
New Distribution

The Maxwell-Boltzmann speed distribution is the probability distribution that describes the speeds of the particles of ideal gases. The Maxwell-Boltzmann speed distribution is valid for both un-mixed particles (one type of particle) and mixed particles (two types of particles). For mixed particles, both types of particles follow the Maxwell-Boltzmann speed distribution. Also, the most probable speed is inversely proportional to the square root of the mass. The Maxwell-Boltzmann speed distribution of mixed particles is based on kinetic theory; however, it has never been derived from a mechanical point of view. This paper proves the Maxwell-Boltzmann speed distribution and the speed ratio of mixed particles based on probability analysis and Newton’s law of motion. This paper requires the probability density function (PDF) ψ^ab(u_a; v_a, v_b) of the speed u_a  of the particle with mass M_a  after the collision of two particles with mass M_a  in speed v_a  and mass M_b  in speed v_b . The PDF ψ^ab(u_a; v_a, v_b)  in integral form has been obtained before. This paper further performs the exact integration from the integral form to obtain the PDF ψ^ab(u_a; v_a, v_b)  in an evaluated form, which is used in the following equation to get new distribution P_new^a(u_a)  from old distributions P_old^a(v_a) and P_old^b(v_b). When P_old^a(v_a) and P_old^b(v_b)  are the Maxwell-Boltzmann speed distributions, the integration P_new^a(u_a)  obtained analytically is exactly the Maxwell-Boltzmann speed distribution. P_new^a(u_a)=∫_0^∞ ∫_0^∞ ψ^ab(u_a;v_a,v_b) P_old^a(v_a) P_old^b(v_b) dv_a dv_b,    a,b = 1 or 2 The mechanical proof of the Maxwell-Boltzmann speed distribution presented in this paper reveals the unsolved mechanical mystery of the Maxwell-Boltzmann speed distribution since it was proposed by Maxwell in 1860. Also, since the validation is carried out in an analytical approach, it proves that there is no theoretical limitation of mass ratio to the Maxwell-Boltzmann speed distribution. This provides a foundation and methodology for analyzing the interaction between particles with an extreme mass ratio, such as gases and neutrinos.

scholarly journals A Formalism for Primitive Logic and Mechanical Proof-Checking

1966 ◽  
Vol 26 ◽  
pp. 195-203 ◽  
Author(s):  
Katuzi Ono
Keyword(s):  
Simple Form ◽  
Predicate Logic ◽  
View Point ◽  
Proof Checking ◽  
Mechanical Proof ◽  
Classical Predicate

The universal character of the primitive logic LO in the sense that popular logics such as the lower classical predicate logic LK, the intuitionistic predicate logic LJ, Johansson’s minimal predicate logic LM, etc. can be faithfully interpreted in LO is very remarkable even from the view point of mechanical proof-checking. Since LO is very simple, deductions in LO could be mechanized in a simple form if a suitable formalism for LO is found out. Main purpose of this paper is to introduce a practical formalism for LO, practical in the sense that it is suitable at least for mechanical proof-checking business.

Best approximation and fixed points for rational-type contraction mappings

2019 ◽  
Vol 25 (2) ◽  
pp. 205-209
Author(s):  
Sumit Chandok
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Best Approximation ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Invariant Approximation ◽  
Frame Work ◽  
Rational Type ◽  
Type Contraction

AbstractIn this paper, we prove a fixed point theorem for a rational type contraction mapping in the frame work of metric spaces. Also, we extend Brosowski–Meinardus type results on invariant approximation for such class of contraction mappings. The results proved extend some of the known results existing in the literature.

scholarly journals Note relating to M. Foucault’s new mechanical proof of the rotation of the Earth

1854 ◽  
Vol 6 ◽  
pp. 65-68
Keyword(s):  
The Earth ◽  
Rotation Of The Earth ◽  
Mechanical Proof

The experiment which led M. Foucault to his ingenious and interesting researches relating to the rotation of the earth, is stated by him thus:—"Having fixed on the arbor of a lathe and in the direction of the axis, a round and flexible steel rod, it was put in vibration by deflecting it from its position of equilibrium and leaving it to itself. A plane of oscillation is thus determined, which, from the persistence of the visual impressions, is clearly delineated in space; now it was remarked that, on turning by the hand the arbor which serves as a support to this vibrating rod, the plane of oscillation is not carried with it."

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