scholarly journals Optimal Two Parameter Bounds for the Seiffert Mean

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Hui Sun ◽  
Ying-Qing Song ◽  
Yu-Ming Chu
Keyword(s):  
Parameter Family ◽  
Sharp Bounds ◽  
Seiffert Mean ◽  
Two Parameter ◽  
Parameter Bounds

We obtain sharp bounds for the Seiffert mean in terms of a two parameter family of means. Our results generalize and extend the recent bounds presented in the Journal of Inequalities and Applications (2012) and Abstract and Applied Analysis (2012).

scholarly journals The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Bobev ◽  
Friðrik Freyr Gautason ◽  
Jesse van Muiden
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Parameter Family ◽  
Global Symmetry ◽  
Maximal Supergravity ◽  
All Solutions ◽  
Operator Spectrum ◽  
Type Iib String Theory ◽  
Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

Dynamics of a two-parameter family of maps of the interval

1986 ◽  
Vol 10 (5) ◽  
pp. 415-423 ◽  
Author(s):  
J.R. Pounder ◽  
Thomas D. Rogers
Keyword(s):  
Parameter Family ◽  
Two Parameter

CONTINUITY OF ENTROPY FOR A TWO-PARAMETER FAMILY OF BIMODAL MAPS

1995 ◽  
pp. 101-116
Author(s):  
LOUIS BLOCK ◽  
ROZA GALEEVA ◽  
JAMES KEESLING
Keyword(s):  
Parameter Family ◽  
Two Parameter

scholarly journals Moffatt-type flows in a trihedral cone

2013 ◽  
Vol 725 ◽  
pp. 446-461 ◽  
Author(s):  
Julian F. Scott
Keyword(s):  
Linear Combination ◽  
Particle Motion ◽  
Particle Trajectory ◽  
Three Dimensional ◽  
Parameter Family ◽  
The Other ◽  
Transient Phase ◽  
Primary Flow ◽  
Special Cases ◽  
Two Parameter

AbstractThe three-dimensional analogue of Moffatt eddies is derived for a corner formed by the intersection of three orthogonal planes. The complex exponents of the first few modes are determined and the flows resulting from the primary modes (those which decay least rapidly as the apex is approached and, hence, should dominate the near-apex flow) examined in detail. There are two independent primary modes, one symmetric, the other antisymmetric, with respect to reflection in one of the symmetry planes of the cone. Any linear combination of these modes yields a possible primary flow. Thus, there is not one, but a two-parameter family of such flows. The particle-trajectory equations are integrated numerically to determine the streamlines of primary flows. Three special cases in which the flow is antisymmetric under reflection lead to closed streamlines. However, for all other cases, the streamlines are not closed and quasi-periodic limiting trajectories are approached when the trajectory equations are integrated either forwards or backwards in time. A generic streamline follows the backward-time trajectory in from infinity, undergoes a transient phase in which particle motion is no longer quasi-periodic, before being thrown back out to infinity along the forward-time trajectory.

scholarly journals Sharp Bounds for Seiffert Mean in Terms of Contraharmonic Mean

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Yu-Ming Chu ◽  
Shou-Wei Hou
Keyword(s):  
Sharp Bounds ◽  
Double Inequality ◽  
Seiffert Mean ◽  
Contraharmonic Mean

We find the greatest valueαand the least valueβin(1/2,1)such that the double inequalityC(αa+(1-α)b,αb+(1-α)a)<T(a,b)<Cβa+1-βb,βb+(1-βa)holds for alla,b>0witha≠b. Here,T(a,b)=(a-b)/[2 arctan((a-b)/(a+b))]andCa,b=(a2+b2)/(a+b)are the Seiffert and contraharmonic means ofaandb, respectively.

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