We prove an extension of Choquet's theorem to the framework of compact metric spaces with a global nonpositive curvature. Together with Sturm's extension K.T. Sturm, Probability measures on metric ...spaces of nonpositive curvature, in: Pascal Auscher, et al. (Eds.), Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces, Lecture Notes from a Quarter Program on Heat Kernels, Random Walks, and Analysis on Manifolds and Graphs April 16–July 13, 2002, Paris, France, in: Contemp. Math., vol. 338, Amer. Math. Soc., Providence, RI, 2003, pp. 357–390 of Jensen's inequality, this provides a full analogue of the Hermite–Hadamard inequality for the convex functions defined on such spaces.
T. Popoviciu (1965)
13 has proved an interesting characterization of the convex functions of one real variable, based on an inequality relating the values at any three points
x
1
,
x
2
,
x
3
, with ...the values at their means of different orders:
(
x
1
+
x
2
)
/
2
,
(
x
2
+
x
3
)
/
2
,
(
x
3
+
x
1
)
/
2
and
(
x
1
+
x
2
+
x
3
)
/
3
. The aim of our paper is to develop a higher dimensional analogue of the usual convexity based on his characterization.
We discuss a rather general condition under which the inequality of Jensen works for certain convex combinations of points not all in the domain of convexity of the function under attention. Based on ...this fact, an extension of the Hardy–Littlewood–Pólya theorem of majorization is proved and a new insight is given into the problem of risk aversion in mathematical finance.
Quantum Gates to Other Universes Bachas, Constantin; Lavdas, Ioannis
Fortschritte der Physik,
February 2018, Letnik:
66, Številka:
2
Journal Article
Recenzirano
Odprti dostop
We present a microscopic model of a bridge connecting two large Anti‐de‐Sitter Universes. The Universes admit a holographic description as three‐dimensional N=4 supersymmetric gauge theories based on ...large linear quivers, and the bridge is a small rank‐n gauge group that acts as a messenger. On the gravity side, the bridge is a piece of a highly‐curved AdS5 × S5 throat carrying n units of five‐form flux. We derive a universal expression for the mixing of the two massless gravitons: M2≃3n2(κ42+κ4′2)/16π2, where M is the mass splitting of the gravitons, κ42,κ4′2 are the effective gravitational couplings of the AdS4 Universes, and n is the quantized charge of the gate. This agrees with earlier results based on double‐trace deformations, with the important difference that the effective coupling is quantized. We argue that the apparent non‐localities of holographic double‐trace theories are resolved by integrating‐in the (scarce) degrees of freedom of the gate.
A microscopic model of a bridge connecting two large Anti‐de‐Sitter Universes is presented. The Universes admit a holographic description as three‐dimensional N=4 supersymmetric gauge theories based on large linear quivers, and the bridge is a small rank‐n gauge group that acts as a messenger. On the gravity side, the bridge is a piece of a highly‐curved AdS5 × S5 throat carrying n units of five‐form flux. A universal expression for the mixing of the two massless gravitons is derived. The results agree with earlier findings based on double‐trace deformations, with the important difference that the effective coupling is quantized. The apparent non‐localities of holographic double‐trace theories are resolved by integrating‐in the (scarce) degrees of freedom of the gate.
Fan’s inequality in geodesic spaces Niculescu, Constantin P.; Rovenţa, Ionel
Applied mathematics letters,
10/2009, Letnik:
22, Številka:
10
Journal Article
Recenzirano
Odprti dostop
Fan’s minimax inequality is extended to the context of metric spaces with global nonpositive curvature. As a consequence, a much more general result on the existence of a Nash equilibrium is obtained.
Using chaos game representation we introduce a novel and straightforward method for identifying similarities/dissimilarities between DNA sequences of the same type, from different organisms. A matrix ...is associated to each CGR pattern and the similarities result from the comparison between the matrices of the sequences of interest. Three different methods of analysis of the resulting difference matrix are considered: a 3-dimensional representation giving both local and global information, a numerical characterization by defining an
n-letter word similarity measure and a statistical evaluation. The method is illustrated by implementation to the study of albumin nucleotides sequences from eight mammal species taking as reference the human albumin.
A
bstract
We study top-down embeddings of massive Anti-de Sitter (AdS) gravity in type-IIB string theory. The supergravity solutions have a AdS
4
fiber warped over a manifold M
6
whose shape ...resembles that of scottish bagpipes: the ‘bag’ is a conventional AdS
4
compactification manifold, while the ‘pipes’ are highly-curved semi-infinite Janus throats. Besides streamlining previous discussions of the problem, our main new result is a formula for the graviton mass which only depends on the effective gravitational coupling of the bag, and on the D3-brane charges and dilaton jumps of the Janus throats. We compare these embeddings to the Karch-Randall model and to other bottom-up proposals for massive AdS gravity, and we comment on their holographic interpretation. This is a companion paper to
1
, where some closely-related bimetric models with pure AdS
5
×S
5
throats were analyzed.
In this paper we study a class of nonlinearities for which a nonlocal parabolic equation with Neumann–Robin boundary conditions, for
p
-Laplacian, has finite time blow-up solutions.
We present a novel method for the parameter oriented analysis of mutual correlation between independent time series or between equivalent structures such as ordered data sets. The proposed method is ...based on the sliding window technique, defines a new type of correlation measure and can be applied to time series from all domains of science and technology, experimental or simulated. A specific parameter that can characterize the time series is computed for each window and a cross correlation analysis is carried out on the set of values obtained for the time series under investigation. We apply this method to the study of some currency daily exchange rates from the point of view of the Hurst exponent and the intermittency parameter. Interesting correlation relationships are revealed and a tentative crisis prediction is presented.
► Object oriented analysis of correlation of time series or equivalent structures. ► Sliding window technique applied to time series or ordered data sets. ► A new type of correlation measure is defined. ► Study of currency exchange rates using Hurst exponent and intermittency parameter.
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