CONSTRUCTION AND PROPERTIES OF QUASI RICCI FLAT SPACES

1986 ◽  
Vol 01 (04) ◽  
pp. 997-1007 ◽  
Author(s):  
GUY BONNEAU ◽  
FRANÇOIS DELDUC
Keyword(s):  
String Theory ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Real ◽  
Ricci Flat ◽  
Compact Case ◽  
Flat Manifolds ◽  
Necessary And Sufficient ◽  
Lagrangian Densities ◽  
Torsion Free

We look for the necessary and sufficient conditions for a generalized torsion-free nonlinear σ-model to be one-loop finite. The corresponding metrics are not only Ricci flat ones, but also a larger class we call “quasi Ricci flat” spaces. We give expressions for the corresponding Lagrangian densities in the real and Kähler cases. In the latter, the manifold is shown to be proper, complete and nonhomogeneous. Unfortunately, in the compact case, relevant for string theory, these quasi Ricci flat manifolds become Ricci flat ones.

Characterizations of symmetric cones by means of the basic relative invariants of homogeneous cones

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Hideto Nakashima
Keyword(s):  
Sufficient Conditions ◽  
Rational Functions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Symmetric Cones ◽  
The Real ◽  
Tube Domains ◽  
Homogeneous Cone ◽  
Necessary And Sufficient ◽  
Relative Invariants

AbstractIn this paper, we give necessary and sufficient conditions for a homogeneous cone Ω to be symmetric in two ways. One is by using the multiplier matrix of Ω, and the other is in terms of the basic relative invariants of Ω. In the latter approach, we need to show that the real parts of certain meromorphic rational functions obtained by the basic relative invariants are always positive on the tube domains over Ω. This is a generalization of a result of Ishi and Nomura [Math. Z. 259 (2008), 604–674].

A Subnormal Operator and its Dual

1996 ◽  
Vol 48 (2) ◽  
pp. 381-396
Author(s):  
Robert F. Olin ◽  
Liming Yang
Keyword(s):  
Unit Circle ◽  
Essential Spectrum ◽  
Real Axis ◽  
Additional Assumption ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Subnormal Operator ◽  
The Real ◽  
Necessary And Sufficient

AbstractIt is shown that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric with respect to the real axis. The study of the structure of a cyclic, irreducible, self-dual, subnormal operator is reduced to the operator Sμ with bpeμ = D. Necessary and sufficient conditions for a cyclic subnormal operator Sμ with bpeμ = D to be self-dual are obtained under the additional assumption that the measure on the unit circle is log-integrable. Finally, an approach to a general cyclic, self-dual, subnormal operator is discussed.

On a Geometrical Theorem in Exterior Algebra

1967 ◽  
Vol 19 ◽  
pp. 1187-1191
Author(s):  
Daniel Pedoe
Keyword(s):  
Euclidean Plane ◽  
Sufficient Conditions ◽  
Exterior Algebra ◽  
Necessary And Sufficient Conditions ◽  
The Real ◽  
Necessary And Sufficient

In this paper we shall give necessary and sufficient conditions for three lines, passing respectively through the vertices of a proper triangle PQR in the real Euclidean plane, to be concurrent. Of course, the theorem of Ceva deals with this problem, but it is useful to have a criterion which involves only vectors localized at a point O of the plane, and the exterior products of these vectors. Applications are made to theorems which are not easily proved by other methods.

scholarly journals On the Solutions of Some Linear Complex Quaternionic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Cennet Bolat ◽  
Ahmet İpek
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sylvester Equation ◽  
Real Matrix ◽  
Matrix Representations ◽  
Linear Complex ◽  
The Real ◽  
Special Cases ◽  
Necessary And Sufficient

Some complex quaternionic equations in the typeAX-XB=Care investigated. For convenience, these equations were called generalized Sylvester-quaternion equations, which include the Sylvester equation as special cases. By the real matrix representations of complex quaternions, the necessary and sufficient conditions for the solvability and the general expressions of the solutions are obtained.

scholarly journals Mean Value theorems for multiplicative functions bounded in mean α-power, α >1

1980 ◽  
Vol 29 (2) ◽  
pp. 177-205 ◽  
Author(s):  
P. D. T. A. Elliott
Keyword(s):  
Real Line ◽  
Sufficient Conditions ◽  
Mean Value ◽  
Necessary And Sufficient Conditions ◽  
Multiplicative Functions ◽  
The Real ◽  
Mean Value Theorems ◽  
Necessary And Sufficient

AbstractOn analogy with functions if Lebesuge class Lα on the real line the author considers those multiplicative arthmetic functions which are bounded in mean α>1. Necessary and sufficient conditions are obtained in order that they should have a mean-value, zero or non-zero. An application is made to Ramanujan's τ-function.

scholarly journals The semicentre of a group algebra

1999 ◽  
Vol 42 (1) ◽  
pp. 95-111 ◽  
Author(s):  
Paul Wauters
Keyword(s):  
Finite Group ◽  
Group Algebra ◽  
Characteristic Zero ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Normal Element ◽  
Necessary And Sufficient ◽  
Torsion Free

We study the semicentre of a group algebra K[G] where K is a field of characteristic zero and G is a polycyclic-by-finite group suchthat Δ(G) is torsion-free abelian. Several properties about the structure of this ring are proved, in particular as to when is the semicentre a UFD. Examples are constructed when this is not the case. We also prove necessary and sufficient conditions for every normal element of K[G] which belongs to K[Δ(G)] to be the product of a unit and a semi-invariant.

scholarly journals The ordering on permutations induced by continuous maps of the real line

1987 ◽  
Vol 7 (2) ◽  
pp. 155-160 ◽  
Author(s):  
Chris Bernhardt
Keyword(s):  
Real Line ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Partial Ordering ◽  
The Real ◽  
Continuous Maps ◽  
Necessary And Sufficient ◽  
Natural Way

AbstractContinuous maps from the real line to itself give, in a natural way, a partial ordering of permutations. This ordering restricted to cycles is studied.Necessary and sufficient conditions are given for a cycle to have an immediate predecessor. When a cycle has an immediate predecessor it is unique; it is shown how to construct it. Every cycle has immediate successors; it is shown how to construct them.

scholarly journals On the Modulus of Continuity of Mappings Between Euclidean Spaces

2013 ◽  
Vol 112 (1) ◽  
pp. 147
Author(s):  
Dieudonné Agbor ◽  
Jan Boman
Keyword(s):  
Modulus Of Continuity ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Euclidean Spaces ◽  
The Real ◽  
Lipschitz Continuous ◽  
Finite Set ◽  
Necessary And Sufficient

Let $f$ be a function from $\mathbf{R}^p$ to $\mathbf{R}^q$ and let $\Lambda$ be a finite set of pairs $(\theta, \eta) \in \mathbf{R}^p \times \mathbf{R}^q$. Assume that the real-valued function $\langle\eta, f(x)\rangle$ is Lipschitz continuous in the direction $\theta$ for every $(\theta, \eta) \in \Lambda$. Necessary and sufficient conditions on $\Lambda$ are given for this assumption to imply each of the following: (1) that $f$ is Lipschitz continuous, and (2) that $f$ is continuous with modulus of continuity $\le C\epsilon |{\log \epsilon}|$.

scholarly journals SURFACE FAMILY WITH COMMON LINE OF CURVATURE IN 3-DIMENSIONAL GALILEAN SPACE

2021 ◽  
pp. 1315
Author(s):  
Mustafa Altin ◽  
İnan Ünal
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
3 Dimensional ◽  
Common Line ◽  
Galilean Space ◽  
Necessary And Sufficient ◽  
Torsion Free ◽  
Line Of Curvature

In this paper we study to find parametric presentation of a surface family with common line of curvature in 3-dimensional Galilean space. We obtain necessary and sufficient conditions for the curve to be a common line of curvature on this surface. We state examples to visualize our results and we obtain some results for a torsion free curve.

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