6,627 research outputs found
Gravitational waves from cosmic bubble collisions
Cosmic bubbles are nucleated through the quantum tunneling process. After
nucleation they would expand and undergo collisions with each other. In this
paper, we focus in particular on collisions of two equal-sized bubbles and
compute gravitational waves emitted from the collisions. First, we study the
mechanism of the collisions by means of a real scalar field and its quartic
potential. Then, using this model, we compute gravitational waves from the
collisions in a straightforward manner. In the quadrupole approximation,
time-domain gravitational waveforms are directly obtained by integrating the
energy-momentum tensors over the volume of the wave sources, where the
energy-momentum tensors are expressed in terms of the scalar field, the local
geometry and the potential. We present gravitational waveforms emitted during
(i) the initial-to-intermediate stage of strong collisions and (ii) the final
stage of weak collisions: the former is obtained numerically, in \textit{full
General Relativity} and the latter analytically, in the flat spacetime
approximation. We gain qualitative insights into the time-domain gravitational
waveforms from bubble collisions: during (i), the waveforms show the
non-linearity of the collisions, characterized by a modulating frequency and
cusp-like bumps, whereas during (ii), the waveforms exhibit the linearity of
the collisions, featured by smooth monochromatic oscillations.Comment: 17 pages, 5 figure
Security Analysis of the Unrestricted Identity-Based Aggregate Signature Scheme
Aggregate signatures allow anyone to combine different signatures signed by
different signers on different messages into a single short signature. An ideal
aggregate signature scheme is an identity-based aggregate signature (IBAS)
scheme that supports full aggregation since it can reduce the total transmitted
data by using an identity string as a public key and anyone can freely
aggregate different signatures. Constructing a secure IBAS scheme that supports
full aggregation in bilinear maps is an important open problem. Recently, Yuan
{\it et al.} proposed an IBAS scheme with full aggregation in bilinear maps and
claimed its security in the random oracle model under the computational
Diffie-Hellman assumption. In this paper, we show that there exists an
efficient forgery attacker on their IBAS scheme and their security proof has a
serious flaw.Comment: 9 page
Bishop-Phelps-Bolloba's theorem on bounded closed convex sets
This paper deals with the \emph{Bishop-Phelps-Bollob\'as property}
(\emph{BPBp} for short) on bounded closed convex subsets of a Banach space ,
not just on its closed unit ball . We firstly prove that the \emph{BPBp}
holds for bounded linear functionals on arbitrary bounded closed convex subsets
of a real Banach space. We show that for all finite dimensional Banach spaces
and the pair has the \emph{BPBp} on every bounded closed convex
subset of , and also that for a Banach space with property
the pair has the \emph{BPBp} on every bounded closed absolutely convex
subset of an arbitrary Banach space . For a bounded closed absorbing
convex subset of with positive modulus convexity we get that the pair
has the \emph{BPBp} on for every Banach space . We further
obtain that for an Asplund space and for a locally compact Hausdorff ,
the pair has the \emph{BPBp} on every bounded closed absolutely
convex subset of . Finally we study the stability of the \emph{BPBp} on
a bounded closed convex set for the -sum or -sum of a
family of Banach spaces
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