Univalence of a complex linear combination of two extremal parallel slit mappings

Analysis ◽  
2007 ◽  
Vol 27 (2-3) ◽  
Author(s):  
Masakazu Shiba
Keyword(s):  
Linear Combination ◽  
Present Article ◽  
Convex Combination ◽  
Plane Domain ◽  
Partial Answer ◽  
Vertical Slit ◽  
Complete Answer ◽  
Conformal Welding ◽  
Parallel Slit ◽  
Complex Linear

Any convex combination of the so-called extremal horizontal and vertical slit mappings of a plane domain is known to be univalent. In his study on the conformal welding of annuli F. Maitani needed to know when a complex linear combination is univalent and he gave a partial answer to this problem. In the present article we give a complete answer to his and to generalized problems.

Two open problems in the fixed point theory of contractive type mappings on quasimetric spaces

2017 ◽  
Vol 33 (2) ◽  
pp. 169-180
Author(s):  
MITROFAN M. CHOBAN ◽  
◽  
VASILE BERINDE ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Answer ◽  
Open Problems ◽  
Complete Answer ◽  
Contractive Type ◽  
Generalized Distances

Two open problems in the fixed point theory of quasi metric spaces posed in [Berinde, V. and Choban, M. M., Generalized distances and their associate metrics. Impact on fixed point theory, Creat. Math. Inform., 22 (2013), No. 1, 23–32] are considered. We give a complete answer to the first problem, a partial answer to the second one, and also illustrate the complexity and relevance of these problems by means of four very interesting and comprehensive examples.

scholarly journals Invariance groups of finite functions and orbit equivalence of permutation groups

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Eszter K. Horváth ◽  
Géza Makay ◽  
Reinhard Pöschel ◽  
Tamás Waldhauser
Keyword(s):  
Symmetric Group ◽  
Partial Answer ◽  
Permutation Groups ◽  
Computational Results ◽  
Orbit Equivalence ◽  
Alternating Groups ◽  
Primitive Groups ◽  
Complete Answer ◽  
The Difference ◽  
Invariance Groups

AbstractWhich subgroups of the symmetric group Sn arise as invariance groups of n-variable functions defined on a k-element domain? It appears that the higher the difference n-k, the more difficult it is to answer this question. For k ≤ n, the answer is easy: all subgroups of Sn are invariance groups. We give a complete answer in the cases k = n-1 and k = n-2, and we also give a partial answer in the general case: we describe invariance groups when n is much larger than n-k. The proof utilizes Galois connections and the corresponding closure operators on Sn, which turn out to provide a generalization of orbit equivalence of permutation groups. We also present some computational results, which show that all primitive groups except for the alternating groups arise as invariance groups of functions defined on a three-element domain.

scholarly journals A note on cycle times in tree-like queueing networks

1984 ◽  
Vol 16 (01) ◽  
pp. 216-219 ◽  
Author(s):  
P. G. Harrison
Keyword(s):  
Linear Combination ◽  
Cycle Time ◽  
Queueing Networks ◽  
Time Distribution ◽  
Queueing Network ◽  
Density Functions ◽  
Cycle Times ◽  
Complex Linear

Cycle-time distribution is shown to take the form of a linear combination of M Erlang-N density functions in a cyclic queueing network of M servers and N customers. For paths of m servers in tree-like networks, the components in the more complex linear combination are convolutions of Erlang-N with at most m − 1 negative exponentials.

scholarly journals Concentration of Product Spaces

2021 ◽  
Vol 9 (1) ◽  
pp. 186-218
Author(s):  
Daisuke Kazukawa
Keyword(s):  
Partial Answer ◽  
Natural Question ◽  
Metric Measure Spaces ◽  
Product Spaces ◽  
Complete Answer ◽  
Measure Spaces

Abstract We investigate the relation between the concentration and the product of metric measure spaces. We have the natural question whether, for two concentrating sequences of metric measure spaces, the sequence of their product spaces also concentrates. A partial answer is mentioned in Gromov’s book [4]. We obtain a complete answer for this question.

Some Steiner concepts on lexicographic products of graphs

2014 ◽  
Vol 06 (04) ◽  
pp. 1450060 ◽  
Author(s):  
Bijo S. Anand ◽  
Manoj Changat ◽  
Iztok Peterin ◽  
Prasanth G. Narasimha-Shenoi
Keyword(s):  
Steiner Tree ◽  
Steiner Trees ◽  
Partial Answer ◽  
Lexicographic Product ◽  
Complete Answer ◽  
Radon Number ◽  
Minimum Number ◽  
Carathéodory Number ◽  
Product Of Graphs

Let G be a graph and W a subset of V(G). A subtree with the minimum number of edges that contains all vertices of W is a Steiner tree for W. The number of edges of such a tree is the Steiner distance of W and union of all vertices belonging to Steiner trees for W form a Steiner interval. We describe both of these for the lexicographic product of graphs. We also give a complete answer for the following invariants with respect to the Steiner convexity: the Steiner number, the rank, the hull number, and the Carathéodory number, and a partial answer for the Radon number.

scholarly journals A note on cycle times in tree-like queueing networks

1984 ◽  
Vol 16 (1) ◽  
pp. 216-219 ◽  
Author(s):  
P. G. Harrison
Keyword(s):  
Linear Combination ◽  
Cycle Time ◽  
Queueing Networks ◽  
Time Distribution ◽  
Queueing Network ◽  
Density Functions ◽  
Cycle Times ◽  
Complex Linear

Cycle-time distribution is shown to take the form of a linear combination of M Erlang-N density functions in a cyclic queueing network of M servers and N customers. For paths of m servers in tree-like networks, the components in the more complex linear combination are convolutions of Erlang-N with at most m − 1 negative exponentials.

Named Testimonia to the Gospel of Thomas: An Expanded Inventory and Analysis

2011 ◽  
Vol 105 (1) ◽  
pp. 53-89 ◽  
Author(s):  
Simon Gathercole
Keyword(s):  
Present Article ◽  
Middle Ages ◽  
Gospel Of Thomas ◽  
Nag Hammadi ◽  
Complete Answer ◽  
Explicit Reference ◽  
Apocryphal Gospels ◽  
Christian Origins ◽  
The Middle Ages

The question of how much apocryphal Gospels were rebutted, suppressed or even destroyed in antiquity is a question of perennial interest, both popular and scholarly. The present article makes no attempt at any sort of complete answer to this question, but has the rather more modest aim of analyzing the various testimonia—from antiquity into the middle ages—that make explicit reference to a “Gospel of Thomas.” This article will not touch on the numerous allusions to, or quotations of, the contents of this Gospel, but will be confined to treatments of the title (hence “named testimonia”). The impetus for this particular investigation is of course the presence, at the end of the second tractate of Nag Hammadi Codex II, of a colophon reading “The Gospel according to Thomas.”1 Given the controversial contents of this Gospel, and the equally controversial place that it occupies in scholarly reconstructions of Christian origins, Thomas's reception in antiquity has been widely discussed since the discovery of the Nag Hammadi Codices (see n. 2 below).

The Zimba and the Lundu State in the Late Sixteenth and Early Seventeenth Centuries

1987 ◽  
Vol 28 (3) ◽  
pp. 337-355 ◽  
Author(s):  
Matthew Schoffeleers
Keyword(s):  
Seventeenth Century ◽  
Sixteenth Century ◽  
Present Article ◽  
Lake Malawi ◽  
State System ◽  
Partial Answer ◽  
The South ◽  
Strong State ◽  
Orthodox View

This article is a partial answer to M. D. D. Newitt, who proposed that settled Maravi states were established only as a result of the rise of Muzura in the first half of the seventeenth century (cf. J. Afr. Hist., 1982, ii). Newitt thereby challenged the more orthodox view that a formal Maravi state system existed already by the middle of the sixteenth century, if not earlier. It is argued here that the orthodox view is still valid in the case of the Lundu state in the lower Shire valley, and perhaps also in the case of some of the neighbouring states. It is shown that around 1590 the then Lundu incumbent embarked on a course of strong state centralisation during which he appropriated the power of the traditional rain priests and thus became both the secular and the ritual leader of the country. It is also argued that this unusual degree of centralisation was achieved and could for a time be maintained with the help of the Zimba, an army of fugitives from the south bank of the Zambezi. However, the present article challenges Malawian historiographical orthodoxy on a very different point, by maintaining that Muzura is not to be identified with the Kalonga dynasty on the south-western shores of Lake Malawi, but with a separate state system in the western Shire Highlands, which gained prominence well before the Kalongas came to the fore.

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