The regions of special cycle of division of Agapanthus chromosomes

Chromosoma ◽  
1953 ◽  
Vol 6 (1) ◽  
pp. 33-44 ◽  
Author(s):  
A. Lima-de-Faria
Keyword(s):  
Special Cycle

scholarly journals A New Bound on the Domination Number of Graphs with Minimum Degree Two

10.37236/499 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Michael A. Henning ◽  
Ingo Schiermeyer ◽  
Anders Yeo
Keyword(s):  
Connected Graph ◽  
Minimum Degree ◽  
Domination Number ◽  
Degree Condition ◽  
Cut Vertex ◽  
Delta G ◽  
Vertex Disjoint ◽  
Special Cycle

For a graph $G$, let $\gamma(G)$ denote the domination number of $G$ and let $\delta(G)$ denote the minimum degree among the vertices of $G$. A vertex $x$ is called a bad-cut-vertex of $G$ if $G-x$ contains a component, $C_x$, which is an induced $4$-cycle and $x$ is adjacent to at least one but at most three vertices on $C_x$. A cycle $C$ is called a special-cycle if $C$ is a $5$-cycle in $G$ such that if $u$ and $v$ are consecutive vertices on $C$, then at least one of $u$ and $v$ has degree $2$ in $G$. We let ${\rm bc}(G)$ denote the number of bad-cut-vertices in $G$, and ${\rm sc}(G)$ the maximum number of vertex disjoint special-cycles in $G$ that contain no bad-cut-vertices. We say that a graph is $(C_4,C_5)$-free if it has no induced $4$-cycle or $5$-cycle. Bruce Reed [Paths, stars and the number three. Combin. Probab. Comput. 5 (1996), 277–295] showed that if $G$ is a graph of order $n$ with $\delta(G) \ge 3$, then $\gamma(G) \le 3n/8$. In this paper, we relax the minimum degree condition from three to two. Let $G$ be a connected graph of order $n \ge 14$ with $\delta(G) \ge 2$. As an application of Reed's result, we show that $\gamma(G) \le \frac{1}{8} ( 3n + {\rm sc}(G) + {\rm bc}(G))$. As a consequence of this result, we have that (i) $\gamma(G) \le 2n/5$; (ii) if $G$ contains no special-cycle and no bad-cut-vertex, then $\gamma(G) \le 3n/8$; (iii) if $G$ is $(C_4,C_5)$-free, then $\gamma(G) \le 3n/8$; (iv) if $G$ is $2$-connected and $d_G(u) + d_G(v) \ge 5$ for every two adjacent vertices $u$ and $v$, then $\gamma(G) \le 3n/8$. All bounds are sharp.

scholarly journals AN INVARIANT OF LEGENDRIAN AND TRANSVERSE LINKS FROM OPEN BOOK DECOMPOSITIONS OF CONTACT 3-MANIFOLDS

2020 ◽  
pp. 1-33
Author(s):  
ALBERTO CAVALLO
Keyword(s):  
Chain Complex ◽  
Open Book ◽  
Rational Homology ◽  
Open Book Decompositions ◽  
Chain Complexes ◽  
Legendrian Links ◽  
Sum Formula ◽  
A Chain ◽  
Special Cycle ◽  
Rational Homology Sphere

Abstract We introduce a generalization of the Lisca–Ozsváth–Stipsicz–Szabó Legendrian invariant ${\mathfrak L}$ to links in every rational homology sphere, using the collapsed version of link Floer homology. We represent a Legendrian link L in a contact 3-manifold ${(M,\xi)}$ with a diagram D, given by an open book decomposition of ${(M,\xi)}$ adapted to L, and we construct a chain complex ${cCFL^-(D)}$ with a special cycle in it denoted by ${\mathfrak L(D)}$ . Then, given two diagrams ${D_1}$ and ${D_2}$ which represent Legendrian isotopic links, we prove that there is a map between the corresponding chain complexes that induces an isomorphism in homology and sends ${\mathfrak L(D_1)}$ into ${\mathfrak L(D_2)}$ . Moreover, a connected sum formula is also proved and we use it to give some applications about non-loose Legendrian links; that are links such that the restriction of ${\xi}$ on their complement is tight.

scholarly journals Research on the Development Mode of Slow Traffic System in Cities Based on Low-carbon Concept

2011 ◽  
Vol 2 (1) ◽  
pp. 33
Author(s):  
Zhang Hang ◽  
Wan Jun
Keyword(s):  
Low Cost ◽  
Urban Traffic ◽  
Bus Rapid Transit ◽  
System Construction ◽  
Low Carbon ◽  
Development Mode ◽  
Sustained Development ◽  
Traffic System ◽  
Bus Transit ◽  
Special Cycle

The slow traffic system, which has a series of advantages including low cost of traveling, green environment protection and fewer resource-consuming, indicates its important role in the urban traffic system. This paper, through the research on the slow traffic system and based on current slow traffic system construction, puts forward new urban traffic mode including connection of “BRT (bus rapid transit) and PBFR (public bike free rental), integration of NBT (Normal Bus Transit) and TBB (take bicycle on bus), and planning of SCF (special cycle facilities) and SFW (special foot way) and NBT(normal bus transit).Finally, the paper Prouides a reference for exploring urban green and sustained development.

scholarly journals A Lot-Size Model for Deteriorating Items under Conditions of a One-Time Only Extended Credit Period

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Nita H. Shah
Keyword(s):  
Mathematical Model ◽  
Cycle Time ◽  
Deteriorating Items ◽  
Special Period ◽  
Lot Size ◽  
Credit Period ◽  
Size Model ◽  
The Mathematical Model ◽  
Special Cycle ◽  
Theoretical Results

Now-a-days, the offer of credit period to the customer for settling the account for the units purchased by the supplier is considered to be the most beneficial policy. In this article, an attempt is made to formulate the mathematical model for a customer to determine optimal special cycle time when the supplier offers the special extended credit period for one time only during a special period. A decision policy for a retailer is developed to find optimal special cycle time. The theoretical results and effects of various parameters are studied by appropriate dataset.

Constructing de Bruijn Sequences Based on a New Necessary Condition

2020 ◽  
Vol 31 (03) ◽  
pp. 301-312
Author(s):  
Zhongxiao Wang ◽  
Xiangyu Wang ◽  
Tian Tian
Keyword(s):  
Necessary Condition ◽  
State Graph ◽  
Nonlinear Feedback ◽  
Conjugate State ◽  
De Bruijn Sequences ◽  
State Formula ◽  
Nonlinear Feedback Shift Register ◽  
Feedback Shift Register ◽  
De Bruijn ◽  
Special Cycle

In this paper, we propose a new necessary condition for feedback functions of de Bruijn sequences and discuss its application in constructing de Bruijn sequences. It is shown that a large number of de Bruijn sequences could be easily constructed by precomputing an [Formula: see text]-stage nonlinear feedback shift register (NFSR) with a special cycle structure—that is, if a state [Formula: see text] is on a cycle generated by this NFSR, then all the states with the same Hamming weight as [Formula: see text] are also on this cycle. Moreover, if there are [Formula: see text] different cycles in the state graph of the precomputed NFSR, then we can construct [Formula: see text] de Bruijn sequences by the different choices of conjugate state pairs, where [Formula: see text].

scholarly journals On Graphs whose Orientations are Determined by their Hermitian Spectra

10.37236/9640 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Yi Wang ◽  
Bo-Jun Yuan
Keyword(s):  
Upper Bound ◽  
Connected Graph ◽  
Simple Graph ◽  
Equivalence Classes ◽  
Cycle Space ◽  
Mixed Graph ◽  
Cycle Basis ◽  
Underlying Graph ◽  
Mixed Graphs ◽  
Special Cycle

A mixed graph $D$ is obtained from a simple graph $G$, the underlying graph of $D$, by orienting some edges of $G$. A simple graph $G$ is said to be ODHS (all orientations of $G$ are determined by their $H$-spectra) if every two $H$-cospectral graphs in $\mathcal{D}(G)$ are switching equivalent to each other, where $\mathcal{D}(G)$ is the set of all mixed graphs with $G$ as their underlying graph. In this paper, we characterize all bicyclic ODHS graphs and construct infinitely many ODHS graphs whose cycle spaces are of dimension $k$. For a  connected graph $G$ whose cycle space is of dimension $k$, we also obtain an achievable upper bound $2^{2k-1} + 2^{k-1}$ for the number of switching equivalence classes in $\mathcal{D}(G)$, which naturally is an upper bound of the number of  cospectral classes in $\mathcal{D}(G)$. To achieve these, we propose a valid method to estimate the number of switching equivalence classes in $\mathcal{D}(G)$ based on the strong cycle basis, a special cycle basis  introduced in this paper.

CNC Routine for Manufacturing Spur Gear

2014 ◽  
Vol 598 ◽  
pp. 539-545
Author(s):  
Omar Monir Koura
Keyword(s):  
Spur Gear ◽  
Cnc Machining ◽  
Spur Gears ◽  
Part Program ◽  
Wire Cutting ◽  
Gear Profile ◽  
Special Cycle

Manufacturing of spur gears on CNC machining centers and CNC wire cutting is randomly used due to the difficulty in producing the perfect gear profile. The present paper faces this problem by developing a special cycle that can be used on both types of machines. A code for this cycles is designed to read the part program of any product and if detects the code nominated for this cycle (G77) which indicates that a gear needs to be cut, it develops the geometrical statements of the gear profile and the motion statements. It follows by writing the full code of the cycle. The validity of the designed model was verified on a CNC simulator.

scholarly journals On the Global Structure of Special Cycles on Unitary Shimura Varieties

2013 ◽  
Vol 65 (5) ◽  
pp. 1125-1163
Author(s):  
Nicolas Vandenbergen
Keyword(s):  
Global Structure ◽  
Shimura Varieties ◽  
Shimura Variety ◽  
Local Models ◽  
Irreducible Components ◽  
Special Cycle

AbstractIn this paper, we study the reduced loci of special cycles on local models of the Shimura variety for GU(1; n − 1). Those special cycles are defined by Kudla and Rapoport. We explicitly compute the irreducible components of the reduced locus of a single special cycle, as well as of an arbitrary intersection of special cycles, and their intersection behaviour in terms of Bruhat–Tits theory. Furthermore, as an application of our results, we prove the connectedness of arbitrary intersections of special cycles, as conjectured by Kudla and Rapoport.

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