scholarly journals Enumeration of Dumont permutations avoiding certain four-letter patterns

2021 ◽  
Vol vol. 22 no. 2, Permutation... (Special issues) ◽  
Author(s):  
Alexander Burstein ◽  
Opel Jones
Keyword(s):  
Dumont Permutations ◽  
Wilf Equivalence ◽  
Fourth Kind

In this paper, we enumerate Dumont permutations of the fourth kind avoiding or containing certain permutations of length 4. We also conjecture a Wilf-equivalence of two 4-letter patterns on Dumont permutations of the first kind.

Vier Arten von Römern unter den Franken im 6. bis 8. Jh.

2016 ◽  
Vol 133 (1) ◽  
pp. 459-468
Author(s):  
Detlef Liebs
Keyword(s):  
Criminal Law ◽  
Civil Law ◽  
Roman Law ◽  
Procedural Law ◽  
The Status ◽  
The Difference ◽  
Law Texts ◽  
Fourth Kind

Abstract Four kinds of Romans in the Frankish kingdoms in the 6th to 8th centuries. Roman law texts from Merowingian Gaul make a difference between cives Romani, Latini and dediticii, all considered as Romans. This difference mattered only to slaves who had been freed. The status of Latin and dediticius was hereditary, whereas the descendants of one who had been freed as civis Romanus were free born Romans, who should be classified as a proper, a fourth kind of beeing Roman; it was the standard kind. The difference was important in civil law, procedural law and criminal law, especially in wergeld, the sum to be payed for expiation when somebody had been killed: Who had killed a Roman, had to pay different sums according to the status of the killed.

scholarly journals Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Yun Wu ◽  
Zhengrong Liu
Keyword(s):  
Solitary Waves ◽  
Nonlinear Waves ◽  
Blow Up ◽  
Periodic Waves ◽  
The Third ◽  
Bifurcation Phenomena ◽  
Kink Waves ◽  
Fourth Kind

We study the bifurcation phenomena of nonlinear waves described by a generalized Zakharov-Kuznetsov equationut+au2+bu4ux+γuxxx+δuxyy=0. We reveal four kinds of interesting bifurcation phenomena. The first kind is that the low-kink waves can be bifurcated from the symmetric solitary waves, the 1-blow-up waves, the tall-kink waves, and the antisymmetric solitary waves. The second kind is that the 1-blow-up waves can be bifurcated from the periodic-blow-up waves, the symmetric solitary waves, and the 2-blow-up waves. The third kind is that the periodic-blow-up waves can be bifurcated from the symmetric periodic waves. The fourth kind is that the tall-kink waves can be bifurcated from the symmetric periodic waves.

New Operational Matrix for Solving Multiterm Variable Order Fractional Differential Equations

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
A. M. Nagy ◽  
N. H. Sweilam ◽  
Adel A. El-Sayed
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Algebraic System ◽  
Order Differential Equation ◽  
Fundamental Problem ◽  
Operational Matrix ◽  
Variable Order ◽  
Engineering Problems ◽  
Fractional Differential ◽  
Fourth Kind

The multiterm fractional variable-order differential equation has a massive application in physics and engineering problems. Therefore, a numerical method is presented to solve a class of variable order fractional differential equations (FDEs) based on an operational matrix of shifted Chebyshev polynomials of the fourth kind. Utilizing the constructed operational matrix, the fundamental problem is reduced to an algebraic system of equations which can be solved numerically. The error estimate of the proposed method is studied. Finally, the accuracy, applicability, and validity of the suggested method are illustrated through several examples.

MATHEMATICAL MODELING OF CONCRETE STRUCTURE CORROSION IN BIOLOGICALLY AGGRESSIVE ENVIRONMENTS

2021 ◽  
Vol 3 (102) ◽  
pp. 55-67
Author(s):  
VARVARA E. RUMYANTSEVA ◽  
SVETLANA A. LOGINOVA ◽  
NATALIA E. KARTSEVA
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Parabolic Type ◽  
Cement Concrete ◽  
Mass Conductivity ◽  
Kinetics And Dynamics ◽  
Biological Corrosion ◽  
First Time ◽  
Fourth Kind

In the aquatic environment, biocorrosion is an important factor affecting the reliability and durability of concrete structures. The destruction of cement concretes during biological corrosion is determined by the processes of mass transfer. The article presents the development of a calculated mathematical model of liquid corrosion in cement concrete, taking into account the biogenic factor. For the first time, a model of mass transfer in an unbounded two-layer plate is considered in the form of differential equations of parabolic type in partial derivatives with boundary conditions of the second kind at the interface between concrete and liquid and of the fourth kind at the interface between concrete and biofilm. The results of a numerical experiment are presented to study the influence of the coefficients of mass conductivity and mass transfer on the kinetics and dynamics of the process.

scholarly journals A General Theory of Wilf-Equivalence for Catalan Structures

10.37236/5629 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Michael Albert ◽  
Mathilde Bouvel
Keyword(s):  
General Theory ◽  
Equivalence Relation ◽  
Generating Functions ◽  
Asymptotic Estimate ◽  
Equivalence Classes ◽  
Catalan Number ◽  
Combinatorial Structures ◽  
Dyck Paths ◽  
Significant Interest ◽  
Wilf Equivalence

The existence of apparently coincidental equalities (also called Wilf-equivalences) between the enumeration sequences or generating functions of various hereditary classes of combinatorial structures has attracted significant interest. We investigate such coincidences among non-crossing matchings and a variety of other Catalan structures including Dyck paths, 231-avoiding permutations and plane forests. In particular we consider principal subclasses defined by not containing an occurrence of a single given structure. An easily computed equivalence relation among structures is described such that if two structures are equivalent then the associated principal subclasses have the same enumeration sequence. We give an asymptotic estimate of the number of equivalence classes of this relation among structures of size $n$ and show that it is exponentially smaller than the $n^{th}$ Catalan number. In other words these "coincidental" equalities are in fact very common among principal subclasses. Our results also allow us to prove in a unified and bijective manner several known Wilf-equivalences from the literature.

Linguistic Encounters of the Fourth Kind

1996 ◽  
Vol 1 (1) ◽  
pp. 54-75 ◽  
Author(s):  
Carolyn Steedman
Keyword(s):  
Fourth Kind

scholarly journals Wilf equivalence relations for consecutive patterns

2018 ◽  
Vol 99 ◽  
pp. 134-157 ◽  
Author(s):  
Tim Dwyer ◽  
Sergi Elizalde
Keyword(s):  
Equivalence Relations ◽  
Wilf Equivalence

Olatunde Osunsanmi and Living the Transatlantic Apocalypse

2018 ◽  
pp. 151-182
Author(s):  
Alexis Brooks de Vita
Keyword(s):  
Alien Invasion ◽  
Human Trade ◽  
Fourth Kind

This chapter explores Nigerian American Olatunde Osunsanmi’s commercially successful film The Fourth Kind as African sf immersing the audience in an empathic experience of the Transatlantic Human Trade as described in Olaudah Equiano’s Interesting Narrative, and alien invasion and colonization as depicted in Okot p’Bitek’s Song of Lawino. Analysis includes excavation of traditional pre-Christian Ifá symbolism in the film, such as the use of the owl to represent the quest for wisdom and humility of the god/dess Obatala, and situates Osunsanmi’s experiential achievement in relation to the legacy of H. G. Wells’s War of the Worlds.

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