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Universes in explicit mathematics

Gerhard Jäger, Reinhard Kahle, Thomas Studer
2001 Annals of Pure and Applied Logic  
This paper deals with universes in explicit mathematics. After introducing some basic definitions, the limit axiom and possible ordering principles for universes are discussed.  ...  Special emphasis is put on theories for explicit mathematics with universes which are proof-theoretically equivalent to Feferman's T 0 .  ...  Explicit mathematics Explicit mathematics has been introduced in Feferman [5] as a framework for Bishop style constructive mathematics.  ... 
doi:10.1016/s0168-0072(00)00057-9 fatcat:7alxn3zpknapnp4ok4hnmzu3bu

On integration of special types of differential inequalities in explicit form

2019 Vestnik of Saint Petersburg University Mathematics Mechanics Astronomy  
Keywords: differential inequality, comparison theorems, integration in explicit form, general solution, method of variations, continuation of solution, nonuniqueness points.  ... 
doi:10.21638/11701/spbu01.2019.202 fatcat:gsmsj7tckze7hnce2qntvr2bja

General problems of integration of differential inequalities in explicit form

Yuriy A. Iljin, St. Petersburg State University
2017 Vestnik of Saint Petersburg University Mathematics Mechanics Astronomy  
This article examines the problem of finding in explicit form all solutions of the first-order nonstrict differential inequality.  ...  Вып. 4 случае a 1 < b 1 выполнялось Литература GENERAL PROBLEMS OF INTEGRATION OF DIFFERENTIAL INEQUALITIES IN EXPLICIT FORM Yuriy A. Iljin St.  ... 
doi:10.21638/11701/spbu01.2017.408 fatcat:hr4li65mavappngtf6uiadnivq

Explicit model for surface waves in a pre-stressed, compressible elastic half-space

D. A. Prikazchikov, School of Computing and Mathematics, Keele University, Staffordshire, UK
2020 International Journal of Mathematics and Physics  
The paper is concerned with the derivation of the hyperbolic-elliptic asymptotic model for surface wave in a pre-stressed, compressible, elastic half-space, within the framework of plane-strain assumption  ...  As a result, the vector problem of elasticity is reduced to a scalar one for the scaled Laplace equation in terms of the auxiliary function, with the boundary condition is formulated as a hyperbolic equation  ...  Explicit model for surface wave field Following the procedure in [18], the following ansatz for displacement components may be adopted i i i u u u i       . (2.11) The leading order problem is then  ... 
doi:10.26577/ijmph.2020.v11.i1.02 fatcat:th65viqc6nc6bc2rylzikh5wiu

Explicit Models for Flexural Edge Waves in Thin Orthotropic Plates
Явные модели распространения изгибных краевых волн в тонких полубесконечных ортотропных пластинах

Elena Leonidovna Kossovich, Saratov State University named after N. G. Chernyshevsky
2013 Izvestiya of Saratov University New Series Series Mathematics Mechanics Informatics  
Analysis of flexural edge wave propagation in thin plates is presented. Several problems of semi-infinite plates vibrations are solved. These plates are assumed to be orthotropic.  ...  Some basic features of flexural edge wave propagation are found using the constructed explicit parabolic-elliptic models. They extract the localized wave contribution into the overall solution.  ...  на торце w in (x, 0) = w e (x), D y ∂ 2 w in ∂y 2 = −D 1 ∂ 2 w e ∂x 2 .  ... 
doi:10.18500/1816-9791-2013-13-1-1-64-69 fatcat:3tmtukqj25bdrj2kv3saavf5xe

Explicit integral representations of implicit functions

L. P. CASTRO, CENTER FOR R&D IN MATHEMATICS AND APPLICATIONS DEPARTMENT OF MATHEMATICS, UNIVERSITY OF AVEIRO 3810-193 AVEIRO, PORTUGAL E-mail address: castro@ua.pt, K. MURATA, S. SAITOH, M. YAMADA, THE OPEN UNIVERSITY OF JAPAN 2-11 WAKABA, MIHAMA-KU, 261-8586 CHIBA, JAPAN E-mail address: k-murata@hb.tp1.jp, CENTER FOR R&D IN MATHEMATICS AND APPLICATIONS DEPARTMENT OF MATHEMATICS, UNIVERSITY OF AVEIRO 3810-193 AVEIRO, PORTUGAL E-mail address: saburou.saitoh@gmail.com, UNIVERSITY EDUCATION CENTER GUNMA UNIVERSITY 4-2, ARAMAKI-MACHI, MAEBASHI CITY, GUNMA, 371-8510, JAPAN E-mail address: yamadama@cap.ocn.ne.jp
2013 Carpathian Journal of Mathematics  
We derive the mentioned representation formulas of inverse functions within a very general framework on general domains in several dimensions.  ...  The main goal of the paper is to obtain explicit integral representations of implicit functions whose existence is guaranteed by the implicit function theory.  ...  THE OPEN UNIVERSITY OF JAPAN 2-11 WAKABA, MIHAMA-KU, 261-8586 CHIBA, JAPAN E-mail address: k-murata@hb.tp1.jp CENTER FOR R&D IN MATHEMATICS AND APPLICATIONS DEPARTMENT OF MATHEMATICS, UNIVERSITY OF AVEIRO  ... 
doi:10.37193/cjm.2013.02.16 fatcat:yxs4vxzkk5adnhohlcze5g2jny

Explicit Models for Flexural Edge and Interfacial Waves in Thin Isotropic Plates
Явные модели распространения изгибных краевых и интерфейсных волн в тонких изотропных пластинах

Julius Davidovich Kaplunov, Brunel University, Elena Leonidovna Kossovich, Rinat Ravilyevich Mukhomodyarov, Olga Valentinovna Sorokina, Saratov State University named after N. G. Chernyshevsky, Saratov State University named after N. G. Chernyshevsky, Saratov State University named after N. G. Chernyshevsky
2013 Izvestiya of Saratov University New Series Series Mathematics Mechanics Informatics  
These waves do not appear in an explicit form in the original equations of motion within the framework of the classical Kirchhoff plate theory.  ...  In the thesis explicit dual parabolic-elliptic models are constructed for the Konenkov flexural edge wave and the Stoneley-type flexural interfacial wave in case of thin linearly elastic plates.  ...  This is the lower limit of the universal expression for r in all problems solved in the thesis.  ... 
doi:10.18500/1816-9791-2013-13-1-1-56-63 fatcat:kfvsd42ktvea3e3olvsqhxatum

A Case of an Explicit Solutions for the Three-element Problem of Carleman Type for Analytic Functions in a Circle
ОБ ОДНОМ СЛУЧАЕ ЯВНОГО РЕШЕНИЯ ТРЕХЭЛЕМЕНТНОЙ ЗАДАЧИ ТИПА КАРЛЕМАНА ДЛЯ АНАЛИТИЧЕСКИХ ФУНКЦИЙ В КРУГЕ

N. R. Perelman
2016 Izvestiya of Saratov University New Series Series Mathematics Mechanics Informatics  
A Case of an Explicit Solutions for the Three-element Problem of Carleman Type for Analytic Functions in a Circle The article investigates the three-element Carleman boundary value problem in the class  ...  Then it is proved that if the boundary condition coefficients are rational functions , and shift a linear-fractional function, then the boundary value problem is solved in an explicit form (in quadrature  ... 
doi:10.18500/1816-9791-2016-16-2-159-165 fatcat:wsr3jvwtpjflfhzlktzgakvfua

Explicit Representation of the Euler and Navier – Stokes Equations of Incompressible Fluid with Reduced Dimensionality in Integral Form
Явное представление сокращенных в размерности уравнений Эйлера и Навье – Стокса несжимаемой жидкости в интегральной форме

Maksim Zaytsev, Business, Vyacheslav Akkerman, West Virginia University
2022 Mathematical Physics and Computer Simulation  
The peculiarity of this work lies in the fact that all the equations reduced in dimension are obtained in an explicit form, in contrast to the previous works of the authors, where up to 200–300 equations  ...  , to track vortex activity at a distance from this object in real time.  ...  The peculiarity of this work lies in the fact that all the equations reduced in dimension are obtained in an explicit form, in contrast to the previous works of the authors, where up to 200-300 equations  ... 
doi:10.15688/mpcm.jvolsu.2022.1.1 fatcat:2bu5ofrslvbn5c7vkl6nsjexki

An explicit representation and enumeration for negacyclic codes of length \begin{document}$ 2^kn $\end{document} over \begin{document}$ \mathbb{Z}_4+u\mathbb{Z}_4 $\end{document}

Yuan Cao, ,School of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong 255091, China, Yonglin Cao, Hai Q. Dinh, Ramakrishna Bandi, Fang-Wei Fu, ,Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China, ,School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan 410114, China, ,Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam, ,Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam, ,Department of Mathematics, Dr. SPM IIIT Naya Raipur, Atal Nagar 493661, India, ,Chern Institute of Mathematics and LPMC, Nankai University, Tianjin Key Laboratory of Network and Data Security Technology, Tianjin 300071, China
2019 Advances in Mathematics of Communications  
In this paper, we give an explicit representation and enumeration for negacyclic codes of length 2 k n over the local non-principal ideal ring R = Z 4 + uZ 4 (u 2 = 0), where k, n are arbitrary positive  ...  Moreover, we provide an exact mass formula for the number of negacyclic codes of length 2 k n over R and correct several mistakes in some literatures. 2010 Mathematics Subject Classification: Primary:  ...  Acknowledgments Part of this work was done when Yonglin Cao was visiting Chern Institute of Mathematics, Nankai University, Tianjin, China.  ... 
doi:10.3934/amc.2020067 fatcat:b5ck6zmzoja6vcny35o4vk23vq

Explicit investment setting in a Kaldor macroeconomic model with macro shock

Zhenzhen Wang, ,School of Mathematics, South China University of Technology, Guangzhou, 510640, China, Zhenghui Li, Shuanglian Chen, Zhehao Huang, ,Guangzhou International Institute of Finance and Guangzhou University, Guangzhou, 510405, China
2018 Discrete and Continuous Dynamical Systems. Series S  
In reality, externally macro shocks are essential attributes in a macroeconomic system.  ...  In the former cycles are generated due to the nonlinear investment function. Nevertheless, the investment lag is addressed in the latter.  ...  In practice, a completely explicit investment setting is more preferred and could be executed more expediently.  ... 
doi:10.3934/dcdss.2020093 fatcat:obeeyn5f7rcshd2kysqg4qlzu4

Reflections on reflections in explicit mathematics

Gerhard Jäger, Thomas Strahm
2005 Annals of Pure and Applied Logic  
We give a broad discussion of reflection principles in explicit mathematics, thereby addressing various kinds of universe existence principles.  ...  The proof-theoretic strength of the relevant systems of explicit mathematics is couched in terms of suitable extensions of Kripke-Platek set theory.  ...  The next step is to introduce the concept of a universe in explicit mathematics.  ... 
doi:10.1016/j.apal.2005.05.008 fatcat:yxyzm4djkncf7f42u6hb2rbeby

Homogenized equations of the linear elasticity in two-dimensional domains with very rough interfaces

Pham Chi Vinh, Do Xuan Tung
2010 Mechanics research communications  
Since these equations are in explicit form, they are significant in practical applications.  ...  The main purpose of the present paper is to find homogenized equations in explicit form of the linear elasticity theory in a two-dimensional domain with a very rough interface.  ...  Since these equations are in explicit form, they are significant in practical applications. © 2010 Elsevier Ltd. All rights reserved.  ... 
doi:10.1016/j.mechrescom.2010.02.006 fatcat:ij5vekat5bfm5illqvav7i6a4q

Page 72 of Mathematics Teacher Vol. 28, Issue 2 [page]

1935 Mathematics Teacher  
72 THE MATHEMATICS TEACHER importance of mathematics in the college curriculum are refuted by existing tendencies to remove explicit mention of more than a bare minimum of mathematics from the college  ...  in secondary mathematics.  ... 

Page 102 of The Annals of Mathematical Statistics Vol. 6, Issue 2 [page]

1935 The Annals of Mathematical Statistics  
Kullback,® in his thesis, has made further extensions and has applied them successfully to the distribution problem in statistics. 1 Presented to the American Mathematical Society, February 23, 1935. 2  ...  In this paper we present the following results: (1) We have obtained an explicit expression for the distribution of means of samples of n; (2) we have obtained an explicit expression for the distribution  ... 
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