scholarly journals The Covered Components Polynomial: A New Representation of the Edge Elimination Polynomial

10.37236/2072 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Martin Trinks
Keyword(s):  
Recurrence Relation ◽  
Graph Polynomials ◽  
Number Of Components ◽  
Spanning Subgraphs ◽  
Definition Of

Motivated by the definition of the edge elimination polynomial of a graph we define the covered components polynomial counting spanning subgraphs with respect to their number of components, edges and covered components. We prove a recurrence relation, which shows that both graph polynomials are substitution instances of each other. We give some properties of the covered components polynomial and some results concerning relations to other graph polynomials.

scholarly journals Some remarks on incomplete gamma type function γ*(α, x_)

Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 125-131 ◽  
Author(s):  
Emin Özcağ ◽  
İnci Egeb
Keyword(s):  
Recurrence Relation ◽  
Real Line ◽  
Summable Function ◽  
Type Function ◽  
The Real ◽  
Definition Of ◽  
Derivatives Of

The incomplete gamma type function ?*(?, x_) is defined as locally summable function on the real line for ?>0 by ?*(?,x_) = {?x0 |u|?-1 e-u du, x?0; 0, x > 0 = ?-x_0 |u|?-1 e-u du the integral divergining ? ? 0 and by using the recurrence relation ?*(? + 1,x_) = -??*(?,x_) - x?_ e-x the definition of ?*(?, x_) can be extended to the negative non-integer values of ?. Recently the authors [8] defined ?*(-m, x_) for m = 0, 1, 2,... . In this paper we define the derivatives of the incomplete gamma type function ?*(?, x_) as a distribution for all ? < 0.

On associated and co-recursive d-orthogonal polynomials

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
A. Sadek Saib ◽  
Ebtissem Zerouki
Keyword(s):  
Orthogonal Polynomials ◽  
Recurrence Relation ◽  
Explicit Form ◽  
Stieltjes Function ◽  
Stieltjes Functions ◽  
Definition Of ◽  
Dual Sequence

AbstractThe associated sequence of order r for a given d-OPS (i.e. a sequence of orthogonal polynomials satisfying a (d + 1)-order recurrence relation), is again a d-OPS. In this paper we are interested in the determination of the corresponding dual sequence. The explicit form of the dual sequence of the first associated sequence and the corresponding formal Stieltjes function are given. Indeed, we construct by recurrence the dual sequence of the r-associated sequence and we give some properties of the corresponding Stieltjes function. Second, we give the definition of co-recursive polynomials of dimension d and some relations in the particular cases d = 3 and d = 4. Some properties of the dual sequence as well as of the corresponding Stieltjes functions are given.

New Graph Polynomials from the Bethe Approximation of the Ising Partition Function

2010 ◽  
Vol 20 (2) ◽  
pp. 299-320 ◽  
Author(s):  
Y. WATANABE ◽  
K. FUKUMIZU
Keyword(s):  
Performance Analysis ◽  
Partition Function ◽  
The Other ◽  
Cambridge Philos ◽  
Graph Polynomials ◽  
Bethe Approximation ◽  
Special Values ◽  
Spanning Subgraphs

We introduce two graph polynomials and discuss their properties. One is a polynomial of two variables whose investigation is motivated by the performance analysis of the Bethe approximation of the Ising partition function. The other is a polynomial of one variable that is obtained by the specialization of the first one. It is shown that these polynomials satisfy deletion–contraction relations and are new examples of the V-function, which was introduced by Tutte (Proc. Cambridge Philos. Soc.43, 1947, p. 26). For these polynomials, we discuss the interpretations of special values and then obtain the bound on the number of sub-coregraphs,i.e., spanning subgraphs with no vertices of degree one. It is proved that the polynomial of one variable is equal to the monomer–dimer partition function with weights parametrized by that variable. The properties of the coefficients and the possible region of zeros are also discussed for this polynomial.

scholarly journals The Equivalence of Two Graph Polynomials and a Symmetric Function

2009 ◽  
Vol 18 (4) ◽  
pp. 601-615 ◽  
Author(s):  
CRIEL MERINO ◽  
STEVEN D. NOBLE
Keyword(s):  
Symmetric Function ◽  
Tutte Polynomial ◽  
Graph Polynomials ◽  
Definition Of ◽  
Natural Way

The U-polynomial, the polychromate and the symmetric function generalization of the Tutte polynomial, due to Stanley, are known to be equivalent in the sense that the coefficients of any one of them can be obtained as a function of the coefficients of any other. The definition of each of these functions suggests a natural way in which to strengthen them, which also captures Tutte's universal V-function as a specialization. We show that the equivalence remains true for the strong functions, thus answering a question raised by Dominic Welsh.

Rhotic variation in Spanish codas

2018 ◽  
pp. 21-47
Author(s):  
Beatriz Blecua ◽  
Jordi Cicres
Keyword(s):  
Contextual Factors ◽  
Spontaneous Speech ◽  
Temporal Characteristics ◽  
Number Of Components ◽  
Peninsular Spanish ◽  
Definition Of ◽  
As Stress ◽  
Manner Of Articulation ◽  
Main Effects ◽  
Opening Phase

The present study describes the variation that syllable-final rhotics (preconsonantal and prepausal) exhibit in spontaneous speech in Central Peninsular Spanish. First, a detailed description of the acoustic and temporal characteristics of each variant is provided. At the same time, the effects of contextual factors are analyzed for the different acoustic realizations. The proportion of more relaxed variants (elision and one-component, without a vocalic fragment) is higher in spontaneous speech than in read speech, while only 6.7% of the tokens are trilled. Furthermore, realizations with a fricative opening phase, as opposed to the usual vocalic element, were also obtained. Results indicate that the most important factor in the acoustic definition of rhotics is their position (before a consonant or before a pause). Finally, main effects were found for the place and manner of articulation of the following gesture as well as stress on the number of components of coda rhotics.

6 Culture History of the Site

1970 ◽  
Vol 24 ◽  
pp. 72-78
Author(s):  
Lewis R. Binford ◽  
Sally R. Binford ◽  
Robert Whallon ◽  
Margaret Ann Hardin
Keyword(s):  
Projectile Points ◽  
Number Of Components ◽  
Chipped Stone ◽  
Rigorous Definition ◽  
Stone Materials ◽  
Culture History ◽  
History Of ◽  
Cursory Examination ◽  
Definition Of ◽  
Range Of Variation

In this section we move from the analysis of various formal classes of data defined by non-historical criteria to an anlysis of categories of artifacts treated historically, i.e., their spatial and formal characteristics within the remains of single communities.The discussion of these occupations, although suspected of being rather numerous, must by virtue of the nature of the data be very skimpy. The relevant data are amost exclusively obtained from the surface collections. Their manner of clustering suggests that there was some range of variation in the activities carried out.Even a cursory examination of the projectile points recovered in the surface collection indicates the presence of multiple preceramic occupations. Types represented include Dalton points, Modoc Expanding Stem points, Faulkner Side-Notched points, and points of the Saratoga and Boaz type clusters. The detailed typological analysis of these points, as well as of other chipped stone materials, should make possible a more rigorous definition of the number of components. At present our understanding is limited by the nature of the data thus far analyzed.

scholarly journals IN REGARDS TO CONSTANT AND INTERPRETATIVE CRITERIA OF CONCEPT IN A LANGUAGE

2014 ◽  
pp. 232-238
Author(s):  
M. N. Fedulova
Keyword(s):  
Space Time ◽  
Emotional States ◽  
Clear Definition ◽  
Linguistic Development ◽  
Number Of Components ◽  
Language Discourse ◽  
Thinking Process ◽  
Concept Logic ◽  
Definition Of ◽  
Objective Side

The article is devoted to the research about the criteria for defining the "concept" in the modern linguistics. The existence of a number of concepts and terms doesn't allow the scientists to agree on its clear definition. The author points out that the base of concept emergence is founded on the processes of conceptualization, these processes are supported by the basic types of metaphorical judgment. In this article, the analysis of different approaches in order to define the structure of the concept indicates that the concept structure consists of a number of components, and for the most part they are permanent and the rest are interpretative. Until recently the linguistic development of "concept" was mainly limited by the framework of subject-thematic criteria. Along with this the scientists focused on and are still focusing on non-contradictory construction of concept logic in a language discourse. The author of the article states that the forming of the notions and perceptions about space, time, life is based on the conceptualization processes and reflected in the language and concepts. The understanding of concept is being achieved through the number of notions revealed during the speaking process, i.e. discursively, as well as through images, symbols, expression of feelings, and different emotional states. The evaluation of different occurrences, emerged within a certain situation is considered the beginning of the concept emergence. Thus, the author is inclining, that the concept is transsituational; its status is cognitive because the thinking process plays an important role in the cognition of the concept. It is particularly interesting to note the author's conclusion that it is incorrect to mix this important philosophical and linguistic notion with the notion/definition of "word". 'Word' is an objective side of conceptualization and it can not be considered a 'concept'. With all that the processes of conceptualization in the language can be considered in two ways: semasiologically and onomosemasiologically.

scholarly journals REDUPLICATION IN LITERARY PROSE (BASED ON THE WORKS OF BRITISH AND AMERICAN WRITERS)

2020 ◽  
Vol 23 (4) ◽  
pp. 142-150
Author(s):  
Elena V. Shliakhtina ◽  
Keyword(s):  
Sampling Method ◽  
Continuous Sampling ◽  
Number Of Components ◽  
Part Of Speech ◽  
Definition Of ◽  
Research Show ◽  
Linguistic Means ◽  
The Way

The article deals with the question of studying such linguistic means as reduplication in English literary prose. The paper contains a definition of the phenomenon as well as several classifications of reduplicatives based on formalstructural, compositional and some other principles. The article states that reduplication can be found in texts of different genres, for instance, in poetic, advertising and journalistic ones. However, it emphasizes that reduplication is significant when a piece of literary prose is created because it allows to highlight contextually important information and to show the shades of meaning. With the help of a continuous sampling method the examples of reduplicatives were picked from the works of british and american writers of XIX–XXI centuries. They were chosen on the basis of the principle: two or more units of content correspond to one unit of expression. The study contains the analysis of the following: a number of full, partial and divergent reduplicatives, a number of components in a reduplicative, its part of speech and topic, the way it is spelt and if it has any connotation. The results of the research show that in most cases the reduplicatives are nouns that contain two components. Many of them are pejorative. The majority of the reduplicatives are hyphenated as this is the most codified way of their spelling. The topics of the examples under study are quite various. Special attention is paid to author-individual reduplicatives. They make a piece of literary prose unique and help the writer to creatively implement his or her idea. The data prove that reduplication is a popular linguistic means when creating literary prose in English.

Instantaneous polarization attributes and directional filtering

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 872-881 ◽  
Author(s):  
Igor B. Morozov ◽  
Scott B. Smithson
Keyword(s):  
Effective Means ◽  
Polarization Vector ◽  
Seismic Signal ◽  
Natural Generalization ◽  
Number Of Components ◽  
Instantaneous Phase ◽  
Directional Filtering ◽  
Multicomponent Seismic ◽  
Definition Of ◽  
Phase Amplitude

We introduce a systematic definition of instantaneous attributes for an arbitrary multicomponent seismic signal. The definition is a natural generalization of known complex trace attributes of a one‐component signal. Instantaneous amplitude and all polarization parameters are defined as invariants of “instantaneous phase rotation.” The principal feature of our approach is the unique definition of the instantaneous phase for a signal with any number of components. Plots of subtle polarization parameters of multicomponent seismic data are easily obtained using conventional seismic plotting routines. We illustrate our approach on a synthetic example and apply it to real 3‐component, wide‐angle crustal data. Plots of polarization attributes provide evidence for shear‐wave splitting in an [Formula: see text] arrival. Having determined the instantaneous polarization vector, we design a new type of time‐domain spatial directional filter. The filter enhances linearly polarized events with specified instantaneous polarization. The filter can work with any number of components in the data, has no user‐specified parameters, and is controlled only by the signal. We conclude that rigorously defined instantaneous phase, amplitude, and polarization attributes provide new effective means for the visualization, analysis, and processing of multicomponent signal.

scholarly journals The stability of harrod's growth model of an economy

1965 ◽  
Vol 5 (2) ◽  
pp. 207-215
Author(s):  
P. E. Lush
Keyword(s):  
Recurrence Relation ◽  
Growth Model ◽  
National Income ◽  
Proper Choice ◽  
Linear Recurrence ◽  
Non Linear ◽  
The Stability ◽  
Definition Of ◽  
Image Position ◽  
Linear Recurrence Relation

Nevile [2] has shown that if Rt is a certain measure of the rate of growth of the national income in Harrod's growth model of an economy, then Rt satisfies the non-linear recurrence relation , where 0 < k < and −1 < c < 1. The definition of Rt ([2] p. 369) is such that Rt > 0 for all t. Nevile has pointed out features of the model that indicate that it may be unstable. In this paper I propose to show that the model is, in general. unstable, but that proper choice of the initial values R0R1 apparently leads to stability. In order to do this, we require the conditions (if any) under which Rt converges.

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