scholarly journals Asymptotic curvature bounds for conformally flat metrics on the plane

Filomat ◽  
2010 ◽  
Vol 24 (2) ◽  
pp. 93-100
Author(s):  
Miodrag Mateljevic ◽  
Ivan Anic ◽  
Stephen Taylor
Keyword(s):  
Decay Rate ◽  
Finite Order ◽  
Negative Curvature ◽  
Conformal Factor ◽  
Gauss Curvature ◽  
Conformally Flat ◽  
Curvature Bounds ◽  
Subject Classifications ◽  
Mathematics Subject Classifications ◽  
Conformally Flat Metrics

The decay rate of the Gauss curvature of conformally flat planer surfaces of strictly negative curvature is studied. It is show that generically there is an asymptotic sequence that decays faster than quadratically in the distance from the origin. In the case that the conformal factor is of finite order, it is shown that one can improve this decay rate. 2010 Mathematics Subject Classifications. 53C21, 31A05. .

scholarly journals Common fixed point theorems for occasionally converse commuting mappings in symmetric spaces

1970 ◽  
Vol 7 (1) ◽  
pp. 56-62
Author(s):  
HK Pathak ◽  
RK Verma
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Symmetric Spaces ◽  
The Other ◽  
Implicit Relation ◽  
Subject Classifications ◽  
Keywords And Phrases ◽  
Mathematics Subject Classifications ◽  
Common Fixed Point Theorems ◽  
Commuting Mappings

In this paper, we introduce the notion of occasionally converse commuting (occ) mappings. Every converse commuting mappings ([1]) are (occ) but the converse need not be true (see, Ex.1.1-1.3). By using this concept, we prove two common fixed point results for a quadruple of self-mappings which satisfy an implicit relation. In first result one pair is (owc) [5] and the other is (occ), while in second result both the pairs are (occ). We illustrate our theorems by suitable examples. Since, there may exist mappings which are (occ) but not conversely commuting, the Theorems 1.1[2], 1.2[2] and 1.3[3] fails to handle those mapping pairs which are only (occ) but not conversely commuting (like Ex.1.4). On the other hand, since every conversely commuting mappings are (occ), so our Theorem 3.1 and 3.2 generalizes these theorems and the main results of Pathak and Verma [6]-[7]   Mathematics Subject Classifications: 47H10; 54H25. Keywords and Phrases: commuting mappings; conversely commuting mappings; occasionally converse commuting (occ) mappings; set of commuting mappings; fixed point. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5422 KUSET 2011; 7(1): 56-62  

scholarly journals Lorentz violation with a universal minimum speed as foundation of de Sitter relativity

2018 ◽  
Vol 27 (02) ◽  
pp. 1850011 ◽  
Author(s):  
Cláudio Nassif Cruz ◽  
Rodrigo Francisco dos Santos ◽  
A. C. Amaro de Faria
Keyword(s):  
Cosmological Constant ◽  
Extra Dimension ◽  
Negative Curvature ◽  
Lorentz Violation ◽  
Conformal Factor ◽  
De Sitter ◽  
Minkowski Metric ◽  
Minimum Speed ◽  
New Space ◽  
Cosmological Constants

We aim to investigate the theory of Lorentz violation with an invariant minimum speed called Symmetrical Special Relativity (SSR) from the viewpoint of its metric. Thus, we should explore the nature of SSR-metric in order to understand the origin of the conformal factor that appears in the metric by deforming Minkowski metric by means of an invariant minimum speed that breaks down Lorentz symmetry. So, we are able to realize that there is a similarity between SSR and a new space with variable negative curvature ([Formula: see text]) connected to a set of infinite cosmological constants ([Formula: see text]), working like an extended de Sitter (dS) relativity, so that such extended dS-relativity has curvature and cosmological “constant” varying in time. We obtain a scenario that is more similar to dS-relativity given in the approximation of a slightly negative curvature for representing the current universe having a tiny cosmological constant. Finally, we show that the invariant minimum speed provides the foundation for understanding the kinematics origin of the extra dimension considered in dS-relativity in order to represent the dS-length.

Conformally convex functions and conformally flat metrics of nonnegative curvature

2015 ◽  
Vol 91 (3) ◽  
pp. 287-289 ◽  
Author(s):  
M. V. Kurkina ◽  
E. D. Rodionov ◽  
V. V. Slavskii
Keyword(s):  
Convex Functions ◽  
Nonnegative Curvature ◽  
Conformally Flat ◽  
Conformally Flat Metrics

scholarly journals Dreibein as Prepotential for Three-Dimensional Yang-Mills Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Indrajit Mitra ◽  
H. S. Sharatchandra
Keyword(s):  
Boundary Condition ◽  
Gauge Transformation ◽  
Three Dimensional ◽  
Scalar Fields ◽  
Gauge Potential ◽  
Conformally Flat ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Conformally Flat Metrics

We advocate and develop the use of the dreibein (and the metric) as prepotential for three-dimensional SO(3) Yang-Mills theory. Since the dreibein transforms homogeneously under gauge transformation, the metric is gauge invariant. For a generic gauge potential, there is a unique dreibein on fixing the boundary condition. Topologically nontrivial monopole configurations are given by conformally flat metrics, with scalar fields capturing the monopole centres. Our approach also provides an ansatz for the gauge potential covering the topological aspects.

scholarly journals Detour index of a class of unicyclic graphs

Filomat ◽  
2010 ◽  
Vol 24 (1) ◽  
pp. 29-40 ◽  
Author(s):  
Qi Xuli ◽  
Bo Zhou
Keyword(s):  
Connected Graph ◽  
Unicyclic Graphs ◽  
The Third ◽  
Subject Classifications ◽  
Mathematics Subject Classifications

The detour index of a connected graph is defined as the sum of detour distances between all unordered pairs of vertices. We determine the n-vertex unicyclic graphs whose vertices on its unique cycle all have degree at least three with the first, the second and the third smallest and largest detour indices respectively for n ? 7. 2010 Mathematics Subject Classifications. 05C12, 05C35, 05C90. .

scholarly journals New bounds for the Cebysev functional of two functions of selfadjoint operators in Hilbert spaces

Filomat ◽  
2010 ◽  
Vol 24 (2) ◽  
pp. 27-39 ◽  
Author(s):  
S.S. Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Selfadjoint Operators ◽  
Čebyšev Functional ◽  
Subject Classifications ◽  
Mathematics Subject Classifications ◽  
New Inequalities

Some new inequalities for the Cebysev functional of two functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and operators, are given. 2010 Mathematics Subject Classifications. 47A63; 47A99. .

scholarly journals Global approximation properties of modified SMK operators

Filomat ◽  
2010 ◽  
Vol 24 (1) ◽  
pp. 47-61 ◽  
Author(s):  
Ali Özarslan ◽  
Oktay Duman
Keyword(s):  
Approximation Properties ◽  
Global Approximation ◽  
Subject Classifications ◽  
Special Cases ◽  
Mathematics Subject Classifications

In this paper, introducing a general modification of the classical Sz?sz-Mirakjan-Kantorovich (SMK) operators, we study their global approximation behavior. Some special cases are also presented. 2010 Mathematics Subject Classifications. 41A25, 41A36. .

scholarly journals Subordination and superordination results for the family of Jung-Kim-Srivastava integral operators

Filomat ◽  
2010 ◽  
Vol 24 (1) ◽  
pp. 69-85 ◽  
Author(s):  
Yong Sun ◽  
Wei-Ping Kuang ◽  
Zhi-Hong Liu
Keyword(s):  
Meromorphic Functions ◽  
Primary 30C45 ◽  
Integral Operators ◽  
Secondary 30C80 ◽  
Subject Classifications ◽  
The Family ◽  
Sandwich Type ◽  
Space Of Meromorphic Functions ◽  
Mathematics Subject Classifications

In this paper, we derive some subordination and superordination results associated with the family of Jung-Kim-Srivastava integral operators defined on the space of meromorphic functions. Several sandwich-type results are also obtained. 2010 Mathematics Subject Classifications. Primary 30C45; Secondary 30C80. .

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