scholarly journals The Square of a Directed Graph

2019 ◽  
Vol 8 (4) ◽  
pp. 8331-8335

The square of an oriented graph is an oriented graph such that if and only if for some , both and exist. According to the square of oriented graph conjecture (SOGC), there exists a vertex such that . It is a special case of a more general Seymour’s second neighborhood conjecture (SSNC) which states for every oriented graph , there exists a vertex such that . In this study, the methods to square a directed graph and verify its correctness were introduced. Moreover, some lemmas were introduced to prove some classes of oriented graph including regular oriented graph, directed cycle graph and directed path graphs are satisfied the SOGC. Besides that, the relationship between SOGC and SSNC are also proved in this study. As a result, the verification of the SOGC in turn implies partial results for SSNC.

10.37236/270 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Bryan Shader ◽  
Wasin So

An oriented graph $G^{\sigma}$ is a simple undirected graph $G$ with an orientation $\sigma$, which assigns to each edge a direction so that $G^{\sigma}$ becomes a directed graph. $G$ is called the underlying graph of $G^{\sigma}$, and we denote by $Sp(G)$ the adjacency spectrum of $G$. Skew-adjacency matrix $S( G^{\sigma} )$ of $G^{\sigma}$ is introduced, and its spectrum $Sp_S( G^{\sigma} )$ is called the skew-spectrum of $G^{\sigma}$. The relationship between $Sp_S( G^{\sigma} )$ and $Sp(G)$ is studied. In particular, we prove that (i) $Sp_S( G^{\sigma} ) = {\bf i} Sp(G)$ for some orientation $\sigma$ if and only if $G$ is bipartite, (ii) $Sp_S(G^{\sigma}) = {\bf i} Sp(G)$ for any orientation $\sigma$ if and only if $G$ is a forest, where ${\bf i}=\sqrt{-1}$.


1977 ◽  
Vol 9 (1) ◽  
pp. 191-195 ◽  
Author(s):  
Thomas L. Sporleder ◽  
Robert A. Skinner

Several definitions of diversification exist. Typically, the concept is dynamic and refers to the relationship among various activities or enterprises in which the firm is engaged. As new activities are acquired by a firm from some existing base of activities, complementarity of the newly acquired activity relative to the existing base is subjectively determined. Judgment is rendered on whether the result represents diversification or conglomeration.Conventional wisdom has not succinctly differentiated between diversification and conglomeration. Some writers have considered conglomeration a special case of diversification [2, 7]. For purposes of this paper, this taxonomic argument need not be settled.


2021 ◽  
Vol 18 (180) ◽  
pp. 20210334
Author(s):  
Liane Gabora ◽  
Mike Steel

Natural selection successfully explains how organisms accumulate adaptive change despite that traits acquired over a lifetime are eliminated at the end of each generation. However, in some domains that exhibit cumulative, adaptive change—e.g. cultural evolution, and earliest life—acquired traits are retained; these domains do not face the problem that Darwin’s theory was designed to solve. Lack of transmission of acquired traits occurs when germ cells are protected from environmental change, due to a self-assembly code used in two distinct ways: (i) actively interpreted during development to generate a soma, and (ii) passively copied without interpretation during reproduction to generate germ cells. Early life and cultural evolution appear not to involve a self-assembly code used in these two ways. We suggest that cumulative, adaptive change in these domains is due to a lower-fidelity evolutionary process, and model it using reflexively autocatalytic and foodset-generated networks. We refer to this more primitive evolutionary process as self–other reorganization (SOR) because it involves internal self-organizing and self-maintaining processes within entities, as well as interaction between entities. SOR encompasses learning but in general operates across groups. We discuss the relationship between SOR and Lamarckism, and illustrate a special case of SOR without variation.


2021 ◽  
pp. 54-77
Author(s):  
Daniel Greco

This chapter defends the possible worlds framework for modeling the contents of belief. Both the threats against which the chapter defends it—the problems of coarse grain—and the ‘fragmentationist’ response it offers are familiar. At least as a sociological matter, the fragmentationist response has been unpersuasive, likely because it can look like an ad hoc patch—an unmotivated epicycle aimed at saving a flailing theory from decisive refutation. The chapter offers two responses to this charge. First, the problems of coarse grain aren’t unique to the possible worlds framework and indeed arise for anyone who accepts certain very attractive views about the relationship between beliefs, desires, and action. Second, the fragmentationist response to these problems is in fact a special case of an independently motivated, ‘modest’ approach to model-building in philosophy.


Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 766-770 ◽  
Author(s):  
F. E. M. Lilley

Observed magnetotelluric data are often transformed to the frequency domain and expressed as the relationship [Formula: see text]where [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] represent electric and magnetic components measured along two orthogonal axes (in this paper, for simplicity, to be north and east, respectively). The elements [Formula: see text] comprise the magnetotelluric impedance tensor, and they are generally complex due to phase differences between the electric and magnetic fields. All quantities in equation (1) are frequency dependent. For the special case of “two‐dimensional” geology (where structure can be described as having a certain strike direction along which it does not vary), [Formula: see text] with [Formula: see text]. For the special case of “one‐dimensional” geology (where structure varies with depth only, as if horizontally layered), [Formula: see text] and [Formula: see text].


Author(s):  
Chaufah Nilrat ◽  
Cheryl E. Praeger

AbstractA balanced directed cycle design with parameters (υ, k, 1), sometimes called a (υ, k, 1)-design, is a decomposition of the complete directed graph into edge disjoint directed cycles of length k. A complete classification is given of (υ, k, 1)-designs admitting the holomorph {øa, b: x ↦ ax + b∣ a, b ∈ Zυ, (a, υ1) = 1} of the cyclic group Zυ as a group of automorphisms. In particular it is shown that such a design exists if and ony if one of (a) k = 2, (b) p ≡ 1 (mod k) for each prime p dividing υ, or (c) k is the least prime dividing υ, k2 does not divide υ, and p ≡ 1 (mod k) for each prime p < k dividing υ.


2014 ◽  
Vol 8 (2) ◽  
Author(s):  
Simone Elisabeth Lang

AbstractIn describing the position of the narrator, research in literary studies generally follows Gérard Genette’s pioneering theory of narrative in distinguishing between the homo- and heterodiegetic type of narrator. This categorization is not sufficient to allow the position of the narrator to be described properly. The different ways in which the terms are used in literary studies reveal a shortcoming in the distinction behind them. Even in Genette’s work, there is a contradiction between the definition and the names of the two categories: Genette defines homo- and heterodiegesis with reference to the narrator’s presence in the narrated story, whereas he elsewhere states that the diegesis (in the sense of FrenchThe present article aims to do just that, starting from a theoretical standpoint. Thus, the different types of narrator that are possible are sketched in outline, and then explained with the help of examples.I begin by exposing the problems that result from using the terms in Genette’s manner (1), in order then to develop a list of possible narratorial standpoints based on the one hand on the involvement of the narratorial instance in the narrated world and on the other on its involvement in the story. By establishing separation of the two aspects as a ground rule in this way, a number of misunderstandings that are due to the varied ways in which the terminology has been used to date can be overcome.There follows a description of those cases that are unambiguously hetero- and homodiegetic (2), after which the problematic cases are considered (3), yielding the different types of homodiegetic narration that are possible. This latter set of distinctions will, like the others, shed light on the contours of the different narratorial positions and thus be capable of being put profitably into practice in textual interpretation. Accordingly, what is suggested is a way of using the terms that is first unambiguous and second beneficial to the interpretation of works, thus doing justice to the heuristic importance of narratology (see Kindt/Müller 2003; Stanzel 2002, 19).Thus, whereas the concept of diegesis provides the foundation for a distinction based on an ontological criterion that divides homo- and heterodiegesis from each other, the relationship between story and narrator is used to describe various types of homodiegetic narration. In the process, there come to light two types that are distinguished from each other by involvement in events (›homodiegetic, in the story‹ and ›homodiegetic, not in the story‹ narrators). If the narrator is not involved in events, the question arises of whether it would in principle have been possible for him to be involved in events, which is the norm with ›homodiegetic, not in the story‹ narrators, or whether a physical impossibility is the reason for his lack of involvement in the story. A special case of the ›homodiegetic, not in the story‹ narrator can be derived from this: peridiegetic narration: whereas narratorial instances of the ›homodiegetic, in the story‹ and ›homodiegetic, not in the story‹ types could in principle have been involved in the action and those of the ›homodiegetic, in the story‹ type actually were, peridiegetic narrators are marked by the fact that they cannot have been involved in the events.In summary, it will be shown that the concept of homodiegesis – in particular in the form in which it has previously been used, where links with the action and appearance in the story were not kept distinct – is in effect an umbrella term that brings together a number of possible forms. There is a prominent distinction between the ›homodiegetic, in the story‹ and the ›homodiegetic, not in the story‹ types of narrator (these types are represented in the present article by the old lawyer in Leo Perutz’s »The Beaming Moon« and the narrator who is a friend of Nathanael in E. T. A. Hoffmann’s »Sandman« respectively). The different degrees of homodiegetic narrator, which have often been mentioned in previous research and are defined by the strength of the character’s presence in the narrated world (from an uninvolved witness to an autodiegetic protagonist), are also to be situated between these two poles.It will also be shown in the process that the case of the narrator who is, for reasons of physical difference, not involved in events (the peridiegetic narrator) should be treated as a form of homodiegesis (for instance the schoolmaster in Theodor Storm’s


2017 ◽  
Author(s):  
D. Diwyacitta ◽  
A. P. Putra ◽  
K. A. Sugeng ◽  
S. Utama
Keyword(s):  

1999 ◽  
Vol 11 (4) ◽  
pp. 274-282 ◽  
Author(s):  
Takayoshi Yamada ◽  
◽  
Sushanta Kumar Saha ◽  
Nobuharu Mimura ◽  
Yasuyuki Funahashi ◽  
...  

We analyze stability of planar grasp using a 2D virtual spring model. A 2D virtual spring model is widely used to explore frictionless grasp, but the direction of contact force has not been studied for a grasped object displaced by external disturbance. Finger displacement is restricted to the normal at initial contact. We introduce a 2D spring model for a frictionless case. The direction of contact force is explicitly formulated. Using potential energy, we analyze stability of frictionless grasp and show that the 1D-spring model is a special case of our proposed 2D-spring model. Frictional grasp stability is also studied using rolling contact. Numerical examples of 2-fingered grasp demonstrate the effects of parameters such as spring stiffness and contact force. It is shown that an optimum force exists for stabilizing frictionless grasp. It is proved that friction enhances grasp stability from the relationship between frictionless and frictional stiffness matrices. Stiffness conditions for stabilizing 3-fingered grasp is clarified.


Sign in / Sign up

Export Citation Format

Share Document