Toward a Unique Representation for AVL and Red-Black Trees

2019 ◽  
Vol 23 (2) ◽  
Author(s):  
Lynda Bounif ◽  
Djamel Eddine Zegour
Keyword(s):  
Unique Representation

‘Who is Sir Curtis Seretse?’: A Re evaluation of Black Representation in Sixties British Television

2014 ◽  
Vol 7 (3) ◽  
Author(s):  
Michael Ahmed
Keyword(s):  
The Other ◽  
Prime Time ◽  
Black Representation ◽  
Unique Representation ◽  
Prime Ministers ◽  
Highly Educated ◽  
Crime Dramas ◽  
The Media ◽  
The 1960S ◽  
Head Of Department

This paper re-evaluates the significance of Sir Curtis Seretse, a black character from the 1960s television series Department S (ITV 1969-70) which has largely been ignored. While earlier critical and academic discourse of Department S has primarily centred on the flamboyant Jason King, the importance of Seretse’s character has been overlooked. Seretse, as the head of Department S, is in a position of authority and power over the other (white) characters of the show. Furthermore, he represents a highly educated character that converses on equal terms with Prime Ministers and Presidents, a unique representation of a black character on British television at that time. Seretse’s appearance on prime time television, at a period when black performers in the media were invariably confined to little more than token characters, is therefore worthy of further attention. This paper examines how Seretse represents a different type of black character not previously seen on British television, when compared to the representations of racial problems on other television crime dramas.

scholarly journals A New Algorithm for Unique Representation and Isomorphism Detection of Planar Kinematic Chains with Simple and Multiple Joints

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 601
Author(s):  
Mahmoud Helal ◽  
Jong Wan Hu ◽  
Hasan Eleashy
Keyword(s):  
Degree Of Freedom ◽  
Synthesis Process ◽  
Structural Synthesis ◽  
Joint Configuration ◽  
Unique Representation ◽  
Kinematic Chains

In this work, a new algorithm is proposed for a unique representation for simple and multiple joint planar kinematic chains (KCs) having any degree of freedom (DOF). This unique representation of KCs enhances the isomorphism detection during the structural synthesis process of KCs. First, a new concept of joint degree is generated for all joints of a given KC based on joint configuration. Then, a unified loop array (ULA) is obtained for each independent loop. Finally, a unified chain matrix (UCM) is established as a unique representation for a KC. Three examples are presented to illustrate the proposed algorithm procedures and to test its validity. The algorithm is applied to get a UCM for planar KCs having 7–10 links. As a result, a complete atlas database is introduced for 7–10-link non-isomorphic KCs with simple or/and multiple joints and their corresponding unified chain matrix.

On Nilpotent Products of Cyclic Groups. II

1961 ◽  
Vol 13 ◽  
pp. 557-568 ◽  
Author(s):  
Ruth Rebekka Struik
Keyword(s):  
Normal Subgroup ◽  
Finite Number ◽  
Free Product ◽  
Multiplication Table ◽  
Unique Representation ◽  
Cyclic Groups ◽  
Positive Integers

In a previous paper (18), G = F/Fn was studied for F a free product of a finite number of cyclic groups, and Fn the normal subgroup generated by commutators of weight n. In that paper the following cases were completely treated:(a) F a free product of cyclic groups of order pαi, p a prime, αi positive integers, and n = 4, 5, … , p + 1.(b) F a free product of cyclic groups of order 2αi, and n = 4.In this paper, the following case is completely treated:(c) F a free product of cyclic groups of order pαi p a prime, αi positive integers, and n = p + 2.(Note that n = 2 is well known, and n — 3 was studied by Golovin (2).) By ‘'completely treated” is meant: a unique representation of elements of the group is given, and the order of the group is indicated. In the case of n = 4, a multiplication table was given.

scholarly journals Equivalence among orbital equations of polynomial maps

2018 ◽  
Vol 29 (09) ◽  
pp. 1850082 ◽  
Author(s):  
Jason A. C. Gallas
Keyword(s):  
Equations Of Motion ◽  
Algebraic Equations ◽  
Nonlinear Transformations ◽  
Unique Representation ◽  
Real Roots ◽  
Polynomial Maps ◽  
Infinite Sequences

This paper shows that orbital equations generated by iteration of polynomial maps do not necessarily have a unique representation. Remarkably, they may be represented in an infinity of ways, all interconnected by certain nonlinear transformations. Five direct and five inverse transformations are established explicitly between a pair of orbits defined by cyclic quintic polynomials with real roots and minimum discriminant. In addition, infinite sequences of transformations generated recursively are introduced and shown to produce unlimited supplies of equivalent orbital equations. Such transformations are generic and valid for arbitrary dynamics governed by algebraic equations of motion.

scholarly journals A basal aïstopod from the earliest Pennsylvanian of Canada, and the antiquity of the first limbless tetrapod lineage

2018 ◽  
Vol 5 (12) ◽  
pp. 181056 ◽  
Author(s):  
Jason D. Pardo ◽  
Arjan Mann
Keyword(s):  
Nova Scotia ◽  
New Genus ◽  
Taxonomic Diversity ◽  
Unique Representation ◽  
Vertebrate Fauna ◽  
Lower Jaw ◽  
Anterior Half ◽  
True Diversity ◽  
Fossil Assemblages

Earliest Pennsylvanian (Bashkirian) vertebrate fossil assemblages of the Joggins Formation (Cumberland Group) of Nova Scotia, Canada, have long been noted for the unique representation of the earliest known crown amniotes, but the overall vertebrate fauna remains poorly understood. The vast majority of Joggins vertebrates have historically been assigned to the Microsauria, a group originally established by Dawson specifically to accommodate the abundant, diminutive fossils of the Joggins Formation. As the Microsauria concept has evolved, some Joggins taxa (e.g. the eureptile Hylonomus lyelli ) have been removed from the group, but many of the Joggins ‘microsaurs’ remain unrevised, obscuring the true diversity of the earliest Pennsylvanian tetrapod fauna. Here we amend part of this problem by revisiting the morphology of Dawson's ‘microsaur’ Hylerpeton longidentatum . This taxon, represented by the anterior half of a left hemimandible, is here reinterpreted as a plesiomorphic aïstopod and assigned to a new genus, Andersonerpeton . A. longidentatum shows a surprisingly primitive anatomy of the lower jaw, retaining a parasymphyseal fang pair on the dentary, an adsymphyseal bone bearing a denticle field, fangs on all coronoids and parasymphyseal foramina, as well as a prearticular which extends far anterior along the coronoid series. However, several aïstopod characters can also be seen, including a lack of sculpturing on the dentary and a reduced number of recurved, weakly socketed teeth. The anatomy of A. longidentatum corroborates recent phylogenetic work which has placed the origin of aïstopods within the Devonian fin-to-limb transition but preserves a mosaic of characteristics suggesting an even earlier divergence. The presence of an aïstopod in the Joggins fauna expands the taxonomic diversity of the Joggins fauna and suggests that Joggins may preserve a more typical Carboniferous fauna than previously thought.

A UNIQUE REPRESENTATION BI-BASIS FOR THE INTEGERS. II

2016 ◽  
Vol 94 (1) ◽  
pp. 1-6
Author(s):  
MIN TANG
Keyword(s):  
Unique Representation

For$n\in \mathbb{Z}$and$A\subseteq \mathbb{Z}$, define$r_{A}(n)$and${\it\delta}_{A}(n)$by$r_{A}(n)=\#\{(a_{1},a_{2})\in A^{2}:n=a_{1}+a_{2},a_{1}\leq a_{2}\}$and${\it\delta}_{A}(n)=\#\{(a_{1},a_{2})\in A^{2}:n=a_{1}-a_{2}\}$. We call$A$a unique representation bi-basis if$r_{A}(n)=1$for all$n\in \mathbb{Z}$and${\it\delta}_{A}(n)=1$for all$n\in \mathbb{Z}\setminus \{0\}$. In this paper, we prove that there exists a unique representation bi-basis$A$such that$\limsup _{x\rightarrow \infty }A(-x,x)/\sqrt{x}\geq 1/\sqrt{2}$.

The Joint Interface of RT Components for Mobile Robots: The Activity Report Inform the Mobile Robot Working Group of the NEDO Intelligent RT Software Project

2010 ◽  
Vol 22 (6) ◽  
pp. 767-776 ◽  
Author(s):  
Masaharu Shimizu ◽  
◽  
Nobuyuki Kita ◽  
Toshihisa Saito ◽  
Eijiro Takeuchi ◽  
...  
Keyword(s):  
Research And Development ◽  
Mobile Robot ◽  
Mobile Robots ◽  
Working Group ◽  
Joint Interface ◽  
Software Project ◽  
Robotic Technology ◽  
Description Language ◽  
Unique Representation ◽  
Activity Report

RT-middleware enables an interface between RT components by means of interface description language IDL, but it does not prescribe any specific format. If a unique representation format is used, it leads to a reduction in the reusability of a Robotic Technology Component (RTC). A working group of three research bodies engaged in the research and development of mobile robots was organized in the NEDO Intelligent RT Software Project, and this working group is involved in activities aimed at the jointing of RTCs for mobile robots. This paper describes specific this working group’s attempts enhance the sustainability and reusability of common RT components for mobile robots by achieving the jointing of RTCs for mobile robots.

Sign in / Sign up

Export Citation Format

Share Document