scholarly journals On Ternary Inclusion-Exclusion Polynomials

Integers ◽  
2010 ◽  
Vol 10 (5) ◽  
Author(s):  
Gennady Bachman
Keyword(s):  
Point Of View ◽  
Cyclotomic Polynomials ◽  
Basic Properties ◽  
Combinatorial Point

AbstractTaking a combinatorial point of view on cyclotomic polynomials leads to a larger class of polynomials we shall call the inclusion-exclusion polynomials. This gives a more appropriate setting for certain types of questions about the coefficients of these polynomials. After establishing some basic properties of inclusion-exclusion polynomials we turn to a detailed study of the structure of ternary inclusion-exclusion polynomials. The latter subclass is exemplified by cyclotomic polynomials Φ

PURE-INJECTIVITY FROM A DIFFERENT PERSPECTIVE

2017 ◽  
Vol 60 (1) ◽  
pp. 135-151 ◽  
Author(s):  
S. R. LÓPEZ-PERMOUTH ◽  
J. MASTROMATTEO ◽  
Y. TOLOOEI ◽  
B. UNGOR
Keyword(s):  
Point Of View ◽  
Endomorphism Rings ◽  
Von Neumann ◽  
Basic Properties ◽  
Injective Modules ◽  
Von Neumann Regular Rings ◽  
Von Neumann Regular ◽  
Pure Extension ◽  
Regular Rings

AbstractThe study of pure-injectivity is accessed from an alternative point of view. A module M is called pure-subinjective relative to a module N if for every pure extension K of N, every homomorphism N → M can be extended to a homomorphism K → M. The pure-subinjectivity domain of the module M is defined to be the class of modules N such that M is N-pure-subinjective. Basic properties of the notion of pure-subinjectivity are investigated. We obtain characterizations for various types of rings and modules, including absolutely pure (or, FP-injective) modules, von Neumann regular rings and (pure-) semisimple rings in terms of pure-subinjectivity domains. We also consider cotorsion modules, endomorphism rings of certain modules, and, for a module N, (pure) quotients of N-pure-subinjective modules.

scholarly journals Graphs and complete intersection toric ideals

2015 ◽  
Vol 14 (09) ◽  
pp. 1540011 ◽  
Author(s):  
I. Bermejo ◽  
I. García-Marco ◽  
E. Reyes
Keyword(s):  
Complete Intersection ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Point Of View ◽  
Toric Ideals ◽  
Induced Subgraphs ◽  
Toric Ideal ◽  
Vertex Set ◽  
Combinatorial Point ◽  
Ring Graph

Our purpose is to study the family of simple undirected graphs whose toric ideal is a complete intersection from both an algorithmic and a combinatorial point of view. We obtain a polynomial time algorithm that, given a graph G, checks whether its toric ideal PG is a complete intersection or not. Whenever PG is a complete intersection, the algorithm also returns a minimal set of generators of PG. Moreover, we prove that if G is a connected graph and PG is a complete intersection, then there exist two induced subgraphs R and C of G such that the vertex set V(G) of G is the disjoint union of V(R) and V(C), where R is a bipartite ring graph and C is either the empty graph, an odd primitive cycle, or consists of two odd primitive cycles properly connected. Finally, if R is 2-connected and C is connected, we list the families of graphs whose toric ideals are complete intersection.

Ruggiero Boscovich and “the Forces Existing in Nature”

2017 ◽  
Vol 30 (4) ◽  
pp. 385-422
Author(s):  
Luca Guzzardi
Keyword(s):  
Natural Philosophy ◽  
Point Of View ◽  
Active Force ◽  
Crucial Aspect ◽  
Basic Properties ◽  
Primary Element ◽  
Definition Of

ArgumentAccording to a long-standing interpretation which traces back to Max Jammer'sConcepts of Force(1957), Ruggiero G. Boscovich would have developed a concept of force in the tradition of Leibniz's dynamics. In his variation on the theme, basic properties of matter such as solidity or impenetrability would be derived from an interplay of some “active” force of attraction and repulsion that any primary element of nature (“point of matter” in Boscovich's theory) would possess. In the present paper I discuss many flaws of this interpretation and argue for an alternative point of view, according to which the crucial aspect in the development of Boscovich's natural philosophy is his early definition of forces as “mathematical determinations” to have a certain state of motion. This is consistent with a Newtonian background and has as its epistemological consequence a certain agnosticism about the nature of forces and a “mathematical neutralism” (mathematics as a neutral tool, allowing for a plurality of interpretations).

scholarly journals Developmental Systems with Fragmentation

1974 ◽  
Vol 3 (36) ◽  
Author(s):  
Grzegorz Rozenberg ◽  
K. Rouhonen ◽  
Arto Salomaa
Keyword(s):  
Formal Language ◽  
Point Of View ◽  
Formal Language Theory ◽  
Language Theory ◽  
Developmental Systems ◽  
Basic Properties ◽  
New Class ◽  
Theory Point ◽  
L Systems ◽  
Context Free

The paper introduces a new class of L systems, where it is possible to continue derivations from certain specified subwords of the words obtained. Such L systems (called L systems with fragmentation or just JL systems) are of interest both from biological and formal language theory point of view. The paper deals with JL systems without interactions, discusses the basic properties of the language families obtained, as well as their position in the L hierarchy. Finalhy, two infinite hierarchies of language families are obtained by limited fragmentation, the notions being analogous to those of ultralinearity and finiteness of index for context-free languages.

86.30 Number Theory from a Combinatorial Point of View

2002 ◽  
Vol 86 (506) ◽  
pp. 266 ◽  
Author(s):  
Shinji Tanimoto
Keyword(s):  
Number Theory ◽  
Point Of View ◽  
Combinatorial Point

Living-Time and Lived Time: Rereading St. Augustine

KronoScope ◽  
2004 ◽  
Vol 4 (1) ◽  
pp. 39-68
Author(s):  
Hervé Barreau
Keyword(s):  
Point Of View ◽  
Clear Understanding ◽  
Basic Properties ◽  
Mctaggart's Paradox ◽  
Point Of Departure ◽  
Lived Time

AbstractA rereading of St. Augustine's treatise about time (Confessions, chap. 13-28) is useful to interpret the phenomenology of time espoused by authors such Husserl, Heidegger, and Merleau-Ponty. But it is also useful to recall McTaggart's paradox which stems from the same point that characterizes Augustinian analyses: the distinction of past, present, future. Only with a clear understanding of the insufficiency of this point of departure to capture the basic properties of time as a structure of becoming or change can an analysis be justified to go from the point of view of lived time (in the sense of consciously experienced time) to the point of view of living-time.

scholarly journals Complex surface singularities from the combinatorial point of view

1995 ◽  
Vol 66 (3) ◽  
pp. 251-265 ◽  
Author(s):  
Francisco Larrión ◽  
José Seade
Keyword(s):  
Complex Surface ◽  
Point Of View ◽  
Surface Singularities ◽  
Combinatorial Point

scholarly journals The combinatorics of minimal unsatisfiability: connecting to graph theory

2021 ◽  
Author(s):  
◽  
Hoda Abbasizanjani
Keyword(s):  
Graph Theory ◽  
Building Blocks ◽  
Point Of View ◽  
New Class ◽  
Strongly Connected ◽  
Combinatorial Point ◽  
Minimal Unsatisfiability ◽  
Full Classification ◽  
New Framework

Minimally Unsatisfiable CNFs (MUs) are unsatisfiable CNFs where removing any clause destroys unsatisfiability. MUs are the building blocks of unsatisfia-bility, and our understanding of them can be very helpful in answering various algorithmic and structural questions relating to unsatisfiability. In this thesis we study MUs from a combinatorial point of view, with the aim of extending the understanding of the structure of MUs. We show that some important classes of MUs are very closely related to known classes of digraphs, and using arguments from logic and graph theory we characterise these MUs.Two main concepts in this thesis are isomorphism of CNFs and the implica-tion digraph of 2-CNFs (at most two literals per disjunction). Isomorphism of CNFs involves renaming the variables, and flipping the literals. The implication digraph of a 2-CNF F has both arcs (¬a → b) and (¬b → a) for every binary clause (a ∨ b) in F .In the first part we introduce a novel connection between MUs and Minimal Strong Digraphs (MSDs), strongly connected digraphs, where removing any arc destroys the strong connectedness. We introduce the new class DFM of special MUs, which are in close correspondence to MSDs. The known relation between 2-CNFs and implication digraphs is used, but in a simpler and more direct way, namely that we have a canonical choice of one of the two arcs. As an application of this new framework we provide short and intuitive new proofs for two im-portant but isolated characterisations for nonsingular MUs (every literal occurs at least twice), both with ingenious but complicated proofs: Characterising 2-MUs (minimally unsatisfiable 2-CNFs), and characterising MUs with deficiency 2 (two more clauses than variables).In the second part, we provide a fundamental addition to the study of 2-CNFs which have efficient algorithms for many interesting problems, namely that we provide a full classification of 2-MUs and a polytime isomorphism de-cision of this class. We show that implication digraphs of 2-MUs are “Weak Double Cycles” (WDCs), big cycles of small cycles (with possible overlaps). Combining logical and graph-theoretical methods, we prove that WDCs have at most one skew-symmetry (a self-inverse fixed-point free anti-symmetry, re-versing the direction of arcs). It follows that the isomorphisms between 2-MUs are exactly the isomorphisms between their implication digraphs (since digraphs with given skew-symmetry are the same as 2-CNFs). This reduces the classifi-cation of 2-MUs to the classification of a nice class of digraphs.Finally in the outlook we discuss further applications, including an alter-native framework for enumerating some special Minimally Unsatisfiable Sub-clause-sets (MUSs).

scholarly journals Dual Pairs of Matroids with Coefficients in Finitary Fuzzy Rings of Arbitrary Rank

2021 ◽  
Vol 27_NS1 (1) ◽  
pp. 48-60
Author(s):  
Walter Wenzel
Keyword(s):  
Point Of View ◽  
The Other ◽  
Finite Intersection ◽  
Dual Pairs ◽  
Arbitrary Rank ◽  
Other Hand ◽  
Combinatorial Point ◽  
Fuzzy Ring

Infinite matroids have been defined by Reinhard Diestel and coauthors in such a way that this class is (together with the finite matroids) closed under dualization and taking minors. On the other hand, Andreas Dress introduced a theory of matroids with coefficients in a fuzzy ring which is – from a combinatorial point of view – less general, because within this theory every circuit has a finite intersection with every cocircuit. Within the present paper, we extend the theory of matroids with coefficients to more general classes of matroids, if the underlying fuzzy ring has certain properties to be specified.

scholarly journals Padé Approximants, Their Properties, and Applications to Hydrodynamic Problems

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1869
Author(s):  
Igor Andrianov ◽  
Anatoly Shatrov
Keyword(s):  
Power Series ◽  
Asymptotic Analysis ◽  
Original Problem ◽  
Asymptotic Methods ◽  
Padé Approximation ◽  
Padé Approximants ◽  
Point Of View ◽  
Pade Approximation ◽  
Pade Approximants ◽  
Basic Properties

This paper is devoted to an overview of the basic properties of the Padé transformation and its generalizations. The merits and limitations of the described approaches are discussed. Particular attention is paid to the application of Padé approximants in the mechanics of liquids and gases. One of the disadvantages of asymptotic methods is that the standard ansatz in the form of a power series in some parameter usually does not reflect the symmetry of the original problem. The search for asymptotic ansatzes that adequately take into account this symmetry has become one of the most important problems of asymptotic analysis. The most developed technique from this point of view is the Padé approximation.

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