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162. Nested matrices and inverse M-matrices

Creator:
Stuart, Jeffrey L
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, nested matrix, tridiagonal matrix, inverse M-matrix, principal minor, determinant, QR-factorization, 13, and 51
Language:
English
Description:
Given a sequence of real or complex numbers, we construct a sequence of nested, symmetric matrices. We determine the LU- and QR-factorizations, the determinant and the principal minors for such a matrix. When the sequence is real, positive and strictly increasing, the matrices are strictly positive, inverse M-matrices with symmetric, irreducible, tridiagonal inverses., Jeffrey L. Stuart., and Obsahuje seznam literatury
Rights:
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163. Neutral set differential equations

Creator:
Abbas, Umber, Lupulescu, Vasile, O’Regan, Donald, and Younus, Awais
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, neutral type, existence, uniqueness, continous dependence, 13, and 51
Language:
English
Description:
The aim of this paper is to establish an existence and uniqueness result for a class of the set functional differential equations of neutral type \left\{ {\begin{array}{*{20}c} {D_H X(t) = F(t,X_t ,D_H X_t ),} // {\left. X \right|_{\left[ { - r,0} \right]} = \Psi ,} // \end{array} } \right. where F: [0, b]× C_{0}x L_{0}^{1}\rightarrow K_{c}(E)) is a given function, Kc(E) is the family of all nonempty compact and convex subsets of a separable Banach space E, C0 denotes the space of all continuous set-valued functions X from [−r, 0] into Kc(E), L_{0}^{1} is the space of all integrally bounded set-valued functions X: [−r, 0] → Kc(E), Ψ \in C_{0} and D_{H} is the Hukuhara derivative. The continuous dependence of solutions on initial data and parameters is also studied., Umber Abbas, Vasile Lupulescu, Donald O’Regan, Awais Younus., and Obsahuje seznam literatury
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164. New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces

Creator:
Guo, Xin-Cui and Zhou, Ze-Hua
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, weighted composition operator, Zygmund type space, Bloch type space, essential norm, 13, and 51
Language:
English
Description:
Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk D in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators uCφ from Zygmund type spaces to Bloch type spaces in D in terms of u, φ, their derivatives, and φn, the n-th power of φ. Moreover, we obtain some similar estimates for the essential norms of the operators uCφ, from which sufficient and necessary conditions of compactness of uCφ follows immediately., Xin-Cui Guo, Ze-Hua Zhou., and Obsahuje seznam literatury
Rights:
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165. New results about semi-positive matrices

Creator:
Dorsey, Jonathan, Gannon, Tom, Charles R Johnson, and Turnansky, Morrison
Format:
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Type:
model:article and TEXT
Subject:
Matematika, matematika, mathematics, sign semipositivity, semipositive matrix, M-matrix, spectrum, equivalence, 13, and 51
Language:
English
Description:
Our purpose is to present a number of new facts about the structure of semipositive matrices, involving patterns, spectra and Jordon form, sums and products, and matrix equivalence, etc. Techniques used to obtain the results may be of independent interest. Examples include: any matrix with at least two columns is a sum, and any matrix with at least two rows, a product, of semipositive matrices. Any spectrum of a real matrix with at least 2 elements is the spectrum of a square semipositive matrix, and any real matrix, except for a negative scalar matrix, is similar to a semipositive matrix. M-matrices are generalized to the non-square case and sign patterns that require semipositivity are characterized., Jonathan Dorsey, Tom Gannon, Charles R. Johnson, Morrison Turnansky., and Obsahuje seznam literatury
Rights:
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166. Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra

Creator:
Makai Jr., Endre and Jaroslav Zemánek
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, Banach algebra, C*-algebra, (self-adjoint) idempotent, (local) pathwise connectedness, connected component of (self-adjoint) algebraic elements, similarity, analytic path, polynomial path, polygonal path, centre of a Banach algebra, distance of connected components, 13, and 51
Language:
English
Description:
Generalizing earlier results about the set of idempotents in a Banach algebra, or of self-adjoint idempotents in a C*-algebra, we announce constructions of nice connecting paths in the connected components of the set of elements in a Banach algebra, or of self-adjoint elements in a C*-algebra, that satisfy a given polynomial equation, without multiple roots. In particular, we prove that in the Banach algebra case every such non-central element lies on a complex line, all of whose points satisfy the given equation. We also formulate open questions., Endre Makai Jr., Jaroslav Zemánek., and Obsahuje seznam literatury
Rights:
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167. Non supercyclic subsets of linear isometries on Banach spaces of analytic functions

Creator:
Moradi, Abbas, Hedayatian, Karim, Robati, Bahram Khani, and Ansari, Mohammad
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, supercyclicity, hypercyclic operator, semigroup, isometry, 13, and 51
Language:
English
Description:
Let X be a Banach space of analytic functions on the open unit disk and Γ a subset of linear isometries on X. Sufficient conditions are given for non-supercyclicity of Γ. In particular, we show that the semigroup of linear isometries on the spaces S^{p} (p>1), the little Bloch space, and the group of surjective linear isometries on the big Bloch space are not supercyclic. Also, we observe that the groups of all surjective linear isometries on the Hardy space H^{p} or the Bergman space L_{a}^{p} (1< p< ∞,p\neq 2) are not supercyclic., Abbas Moradi, Karim Hedayatian, Bahram Khani Robati, Mohammad Ansari., and Obsahuje seznam literatury
Rights:
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168. O počítačových důkazech matematických vět

Creator:
Hora, Jaroslav
Format:
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Type:
model:article and TEXT
Subject:
počítačová věda, matematika, teorie grafů, computer science, mathematics, graph theory, 6, and 53
Language:
Czech
Description:
Postačí čtyři barvy na obarvení každé rovinné mapy obsahující jistý počet států? Tato zdánlivě nevinná otázka napadla Francise Guthrieho při barvení mapy anglických hrabství. Jeho bratr Frederick položil dne 23. 10. 1852 stejnou otázku svému profesoru Augustu de Morganovi. Tak vznikl slavný "problém čtyř barev“. Po nezbytných upřesněních pojmu rovinná mapa atd. se zdařilo daný problém "přeložit“ do rozvíjející se matematické disciplíny - teorie grafů. Následovala dlouhá historie řešení, která trvala přes sto let a byla provázena i mnoha omyly (více viz [1,3]). Nakonec, již v sedmdesátých letech minulého století, bylo zapotřebí prověřit dlouhý seznam "map“, tzv. nevyhnutelnou množinu ireducibilních konfigurací, obsahující 1 936 prvků. K tomu přistoupili Apell, Haken a Koch - využili hned tři počítače firmy IBM. Příprava metod a programu jim zabrala tři a půl roku a další půlrok si vyžádala práce s počítači. Dílo bylo dokončeno 21. června 1976. Závěr zněl: čtyři barvy stačí!, Jaroslav Hora., and Obsahuje seznam literatury
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169. On a characterization of k-trees

Creator:
Zeng, De-Yan and Yin, Jian-Hua
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, characterization, k-tree, K_{t} -minor, 13, and 51
Language:
English
Description:
A graph G is a k-tree if either G is the complete graph on k + 1 vertices, or G has a vertex v whose neighborhood is a clique of order k and the graph obtained by removing v from G is also a k-tree. Clearly, a k-tree has at least k + 1 vertices, and G is a 1-tree (usual tree) if and only if it is a 1-connected graph and has no K_{3} -minor. In this paper, motivated by some properties of 2-trees, we obtain a characterization of k-trees as follows: if G is a graph with at least k + 1 vertices, then G is a k-tree if and only if G has no K_{k+2} -minor, G does not contain any chordless cycle of length at least 4 and G is k-connected., De-Yan Zeng, Jian-Hua Yin., and Obsahuje seznam literatury
Rights:
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170. On a generalization of a theorem of Burnside

Creator:
Shi, Jiangtao
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, non-cyclic p-subgroup, p-nilpotent, self-normalizing subgroup, normal sub-group, 13, and 51
Language:
English
Description:
A theorem of Burnside asserts that a finite group G is p-nilpotent if for some prime p a Sylow p-subgroup of G lies in the center of its normalizer. In this paper, let G be a finite group and p the smallest prime divisor of |G|, the order of G. Let P \in Syl_{p} (G). As a generalization of Burnside’s theorem, it is shown that if every non-cyclic p-subgroup of G is self-normalizing or normal in G then G is solvable. In particular, if P \not\cong \left\langle {a,b;{a^{{p^{n - 1}}}} = 1,{b^2} = 1,{b^{ - 1}}ab = {a^{1 + {p^{n - 2}}}}} \right\rangle, where n\geq 3 for p > 2 and n\geq 4 for p = 2, then G is p-nilpotent or p-closed., Jiangtao Shi., and Obsahuje seznam literatury
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