Carlsson-Gelatt-Ehrenreich technique and the Möbius inversion theorem

1992 ◽  
Vol 45 (14) ◽  
pp. 8177-8180 ◽  
Author(s):  
Nan-xian Chen ◽  
Guang-bao Ren
Keyword(s):  
Inversion Theorem ◽  
Möbius Inversion

Erratum: Carlsson-Gelatt-Ehrenreich technique and the Möbius inversion theorem

1993 ◽  
Vol 47 (1) ◽  
pp. 593-593 ◽  
Author(s):  
Nan-xian Chen ◽  
Guang-bao Ren
Keyword(s):  
Inversion Theorem ◽  
Möbius Inversion

Extension of Chromatic Polynomials by Utilizing Mobius Inversion Theorem

2013 ◽  
Author(s):  
R.V.N. SrinivasaRao ◽  
J. VenkateswaraRao ◽  
Haftamu Menker GebreYohannes
Keyword(s):  
Chromatic Polynomials ◽  
Inversion Theorem ◽  
Möbius Inversion

scholarly journals On an inversion theorem of Möbius

1980 ◽  
Vol 30 (1) ◽  
pp. 15-32 ◽  
Author(s):  
J. H. Loxton ◽  
J. W. Sanders
Keyword(s):  
Nineteenth Century ◽  
Numerical Integration ◽  
Inversion Theorem ◽  
Möbius Inversion ◽  
Inversion Principle ◽  
Infinite Sums

AbstractThe theme of the paper is a Möbius inversion principle for infinite sums. We deal with the origins and unprincipled use of this idea in the nineteenth century, its rigorous justification under minimal hypotheses and some applications to a problem in numerical integration.

Some Characterizations of the Systems Represented by Choquet and Multi-Linear Functionals through the use of Möbius Inversion

1997 ◽  
Vol 05 (05) ◽  
pp. 547-561 ◽  
Author(s):  
Katsushige Fujimoto ◽  
Toshiaki Murofushi
Keyword(s):  
Structural Analysis ◽  
Fuzzy Measure ◽  
Fuzzy Integral ◽  
Linear Functionals ◽  
Inversion Theorem ◽  
Möbius Inversion ◽  
Integral Systems

The systems represented by the Choquet or the multi-linear fuzzy integral with respect to fuzzy measure is equivalently decomposable into hierarchically sub-systems through the use of Inclusion-Exclusion Covering (IEC) (Theorem 4.1,4.2). Hence, IEC is one of very useful concepts/indexes for structural analysis of the fuzzy integral systems (short for: the systems represented by the Choquet or the multi-linear fuzzy integral) However, it is quite difficult to identify all IEC's. This paper shows a method for identifying it easily, through the use of Möbius inversion (Theorem 5.1).

scholarly journals Classification of Algebraic Properties of Chromatic Polynomials

2013 ◽  
Vol 5 (3) ◽  
pp. 469-477 ◽  
Author(s):  
R. V. N. S. Rao ◽  
J. V. Rao
Keyword(s):  
Chromatic Polynomial ◽  
Möbius Function ◽  
Chromatic Polynomials ◽  
Inversion Theorem ◽  
Mobius Function ◽  
Möbius Inversion ◽  
Algebraic Properties

This manuscript attempts to introduce the concept of chromatic polynomials of total graphs using Mobius inversion theorem. In fact it studies various algebraic properties of chromatic polynomial using Mobius inversion theorem. Keywords: Bond lattice; Chromatic polynomial; Mobius function; Poset.  © 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.  doi: http://dx.doi.org/10.3329/jsr.v5i3.11634 J. Sci. Res. 5 (3), 469-477 (2013)

scholarly journals An inversion theorem in Fermi surface theory

2000 ◽  
Vol 53 (11) ◽  
pp. 1350-1384 ◽  
Author(s):  
Joel Feldman ◽  
Manfred Salmhofer ◽  
Eugene Trubowitz
Keyword(s):  
Fermi Surface ◽  
Surface Theory ◽  
Inversion Theorem

scholarly journals On the existence and uniqueness of solution to Volterra equation on a time scale

2019 ◽  
Vol 27 (3) ◽  
pp. 177-194
Author(s):  
Bartłomiej Kluczyński
Keyword(s):  
Integral Equation ◽  
Sobolev Space ◽  
Time Scale ◽  
Existence And Uniqueness ◽  
Nonlinear Term ◽  
Volterra Equation ◽  
Uniqueness Of Solution ◽  
Inversion Theorem ◽  
T Tau

AbstractUsing a global inversion theorem we investigate properties of the following operator\matrix{\matrix{ V(x)( \cdot ): = {x^\Delta }( \cdot ) + \int_0^ \cdot {v\left( { \cdot ,\tau ,x,\left( \tau \right)} \right)} \Delta \tau , \hfill \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x(0) = 0, \hfill \cr}\cr {} \cr }in a time scale setting. Under some assumptions on the nonlinear term v we then show that there exists exactly one solution {x_y} \in W_{\Delta ,0}^{1,p}\left( {{{[0,1]}_\mathbb{T}},{\mathbb{R}^N}} \right) to the associated integral equation\left\{ {\matrix{{{x^\Delta }(t) + \int_0^t {v\left( {t,\tau ,x\left( \tau \right)} \right)} \Delta \tau = y(t)\,\,\,for\,\Delta - a.e.\,\,\,t \in {{[0.1]}_\mathbb{T}},} \cr {x(0) = 0,} \cr } } \right.which is considered on a suitable Sobolev space.

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