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Concept Equations

R. Belohlavek
2004 Journal of Logic and Computation  
Studied in the paper are systems of equations which naturally arise in the formalization of the Port-Royal theory of concepts. The unknown quantity is a relation between objects and attributes.  ...  For the above reasons, we call such equations concept equations.  ...  Returning to our problem, we ask for the most economical change of logical precision such that the system of concept equations has a solution.  ... 
doi:10.1093/logcom/14.3.395 fatcat:xvmykxvuwvdotbw74mugeuzej4

Some considerations of matrix equations using the concept of reproductivity [article]

Branko Malesevic, Biljana Radicic
2012 arXiv   pre-print
We determine reproductive and non-reproductive general solutions of analysed matrix equation and analysed matrix systems.  ...  In this paper we analyse Cline's matrix equation, generalized Penrose's matrix system and a matrix system for k-commutative 1-inverses.  ...  The concept of reproductive equations was introduced by S.B. Prešić [2] in 1968. Let S be a given non-empty set and J be a given unary relation of S.  ... 
arXiv:1110.3519v5 fatcat:qzxnxjm5prh5zn3cixa5q3lway

Classical and Quantum Electrodynamics Concept Based on Maxwell Equations' Symmetry [article]

Dmitri Yerchuck, Alla Dovlatova, Andrey Alexandrov
2011 arXiv   pre-print
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field.  ...  Generalized Maxwell equations for quaternion four-component EM-field are obtained. Invariants for EM-field, consisting of dually symmetric parts are found.  ...  Similar conclusion concerns the conception of complex characteristics of EM-field in the matter. Given conception agrees well with all practice of electric circuits' calculations.  ... 
arXiv:1101.1886v4 fatcat:dk6pmxzxlvbs7owwuq4yvu4dsq

Classical and Quantum Electrodynamics Concept Based on Maxwell Equations' Symmetry [article]

Dmitri Yerchuck, Alla Dovlatova, Andrey Alexandrov
2013 arXiv   pre-print
Generalized Maxwell equations for quaternion four-component EM-field are obtained. Invariants for EM-field, consisting of dually symmetric parts are found.  ...  There exists physical conserving quantity, which is simultaneously invariant under both Rainich dual and additional hyperbolic dual symmetry transformation of Maxwell equations.  ...  Similar conclusion concerns the conception of complex characteristics of EM-field in the matter. Given conception agrees well with all practice of electric circuits' calculations.  ... 
arXiv:1102.2619v4 fatcat:atimjhqvyfcxnjprbpjeuah6tq

Rearranging equations: (concepts – misconceptions) × peer discussion

Maryna Lishchynska, Catherine Palmer, Julie Crowley
2020 MSOR Connections  
lesson plans that emphasise conceptual understanding while also dispelling the relevant misconceptions, using a peer discussion teaching model as a vehicle for consolidating and propagating the right concepts  ...  Transposition of formulae (also known as rearranging equations and changing the subject) is a skill vital for professionals in many fields of science and engineering.  ...  With regard to rearranging equations, we believe, a successful intervention must firstly focus on building up a solid understanding of the concepts of equality and equations.  ... 
doi:10.21100/msor.v18i3.1053 fatcat:5ut25m5sqvfrhmmi5xmxyr5yvy

Integral Equations: The Concept Of Integrals

Mr. Chetan Ambekar
2012 IOSR Journal of Mathematics  
Also the equation of the curve formed when the double integral is converted to a single in integral is mentioned.  ...  The paper deals with the question that if the double integral is solved and it is converted to single integral then what is ment by it, also the equation of the curve formed of that single integral function  ...  This concept is applied in the various fields of mechanics and fluid mechanics.  ... 
doi:10.9790/5728-0353538 fatcat:gv5o6rosw5eg5je4vpqkxolozu

Distributional solution concepts for the Euler-Bernoulli beam equation with discontinuous coefficients [article]

Guenther Hoermann, Ljubica Oparnica
2007 arXiv   pre-print
We study existence and uniqueness of distributional solutions to the differential equation of the Euler-Bernoulli rod with discontinuous coefficients and right-hand side.  ...  Curiously, the choice of the distributional product concept is thus incompatible with the possibility of having a discontinuous displacement function as a solution.  ...  the solution concept itself.  ... 
arXiv:math/0606058v4 fatcat:6hqjlwzj6vdftbhirk5b4lbwdy

A concept of Dirac-type tensor equations [article]

Nikolai Marchuk
2002 arXiv   pre-print
Considering a four dimensional parallelisable manifold, we develop a concept of Dirac-type tensor equations with wave functions that belong to left ideals of the set of nonhomogeneous complex valued differential  ...  Now we develop a concept of Dirac-type tensor equations with wave functions that belong to left ideals of Λ C .  ...  This concept gives us possibility to find an SU(3) invariant Dirac-type tensor equation with 12 complex valued components of wave function.  ... 
arXiv:math-ph/0212006v1 fatcat:4hh2ztbos5ay7ar35p3xfiicle

Concept of semi-velocity and related wave equation [article]

Robert M.Yamaleev
2017 arXiv   pre-print
A kinematical wave equation related with the Fermat principle and the concept of the semi-velocity is derived.  ...  This concept leads to new kind of wave equation which can be interpreted as wave equation of the relativistic kinematics. The paper is presented by the following sections.  ...  Section 2 we introduce a concept of the semi-velocity and give its geometrical interpretation.  ... 
arXiv:1712.08495v1 fatcat:w5zleedmafh7tfuwjtmjao2rky

Generalized regularity and solution concepts for differential equations [article]

Simon Haller
2008 arXiv   pre-print
As the title "Generalized regularity and solution concepts for differential equations" suggests, the main topic of my thesis is the investigation of generalized solution concepts for differential equations  ...  Another topic is the comparsion of Colombeau techniques for solving ordinary and partial differential equations to other generalized solution concepts, which has led to a joint article with G\"unther H  ...  As the title "Generalized regularity and solution concepts for differential equations" suggests, the main topic of my thesis is the investigation of generalized solution concepts for differential equations  ... 
arXiv:0806.1451v1 fatcat:lw2xasfyqnee5ar5ei3sakzjpy

Solving systems of phaseless equations via Kaczmarz methods: A proof of concept study [article]

Ke Wei
2015 arXiv   pre-print
We study the Kaczmarz methods for solving systems of quadratic equations, i.e., the generalized phase retrieval problem.  ...  The methods extend the Kaczmarz methods for solving systems of linear equations by integrating a phase selection heuristic in each iteration and overall have the same per iteration computational complexity  ...  for solving a system of linear equations Ax = y.  ... 
arXiv:1502.01822v3 fatcat:bsll64xe4nevhpe6wdyaz7wsqa

Lax Integrability of the Modified Camassa-Holm Equation and the Concept of Peakons [article]

Xiangke Chang, Jacek Szmigielski
2017 arXiv   pre-print
In this Letter we propose that for Lax integrable nonlinear partial differential equations the natural concept of weak solutions is implied by the compatibility condition for the respective distributional  ...  We illustrate our proposal by comparing two concepts of weak solutions of the modified Camassa-Holm equation pointing out that in the peakon sector (a family of non-smooth solitons) only one of them, namely  ...  Lax integrability and the preservation of the H 1 norm The following theorem supports the idea of building the concept of weak solutions to (1) based on the multiplication formula (12) .  ... 
arXiv:1610.06537v3 fatcat:3cjqe3shkrchblfpfd24omrol4

New concepts of Hahn calculus and impulsive Hahn difference equations

Jessada Tariboon, Sotiris K Ntouyas, Weerawat Sudsutad
2016 Advances in Difference Equations  
In this paper, we introduce new concepts of Hahn difference operator, the q k , ω k -Hahn difference operator.  ...  As applications, we establish existence and uniqueness results for first-and second-order impulsive q k , ω k -Hahn difference equations.  ...  The aim of this paper is to introduce new concepts of Hahn's difference operator, the q k , ω k -Hahn difference operator, to establish a calculus based on this operator and to construct the associated  ... 
doi:10.1186/s13662-016-0982-4 fatcat:5yqxk34lurgbvfgyqrresfxixe

An extension of the well-posedness concept for fractional differential equations of Caputo's type

Kai Diethelm
2014 Applicable Analysis  
It is well known that, under standard assumptions, initial value problems for fractional ordinary differential equations involving Caputo-type derivatives are well posed in the sense that a unique solution  ...  Here we extend this well-posedness concept to the extent that we also allow the location of the starting point of the differential operator to be changed, and we prove that the solution depends on this  ...  Most notably, while the initial value problems discussed in Section 2 were equivalent to integral equations of Volterra's type, cf. eq. (6), the natural integral equation formulation of the terminal value  ... 
doi:10.1080/00036811.2013.872776 fatcat:6rzpsx3c2zav7pidprsbdbzlpa

Point Equation, Line Equation, Plane Equation Etc And Point Solution, Line Solution, Plane Solution Etc. - Expanding Concepts Of Equation And Solution With Neutrosophy And Quad-Stage Method

Yuhua Fu
2016 Zenodo  
The concepts of equations and solutions are constantly developed and expanded.  ...  With Neutrosophy and Quad-stage method, this paper attempts to expand the concepts of equations and solutions in the way of referring to the concepts of domain of function, the geometry elements included  ...  into the concepts of point equation, line equation, plane equation, solid equation, sub-domain equation, whole-domain equation, and the like; and the concept of solution can be expanded into the concepts  ... 
doi:10.5281/zenodo.571573 fatcat:vl6n7mnfvzda7llvyomg72bh7a
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