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On defining partition entropy by inequalities
Partition entropy is the numerical metric of uncertainty within
a partition of a finite set, while conditional entropy measures the degree of
difficulty in predicting a decision partition when a condition partition is
provided. Since two direct methods exist for defining conditional entropy
based on its partition entropy, the inequality postulates of monotonicity,
which conditional entropy satisfies, are actually additional constraints on
its entropy. Thus, in this paper partition entropy is defined as a function
of probability distribution, satisfying all the inequalities of not only partition
entropy itself but also its conditional counterpart. These inequality
postulates formalize the intuitive understandings of uncertainty contained
in partitions of finite sets.We study the relationships between these inequalities,
and reduce the redundancies among them. According to two different
definitions of conditional entropy from its partition entropy, the convenient
and unified checking conditions for any partition entropy are presented, respectively.
These properties generalize and illuminate the common nature
of all partition entropies
Critical and Non-Critical Einstein-Weyl Supergravity
We construct N=1 supersymmetrisations of some recently-proposed theories of
critical gravity, conformal gravity, and extensions of critical gravity in four
dimensions. The total action consists of the sum of three separately off-shell
supersymmetric actions containing Einstein gravity, a cosmological term and the
square of the Weyl tensor. For generic choices of the coefficients for these
terms, the excitations of the resulting theory around an AdS_4 background
describe massive spin-2 and massless spin-2 modes coming from the metric;
massive spin-1 modes coming from a vector field in the theory; and massless and
massive spin-3/2 modes (with two unequal masses) coming from the gravitino.
These assemble into a massless and a massive N=1 spin-2 multiplet. In critical
supergravity, the coefficients are tuned so that the spin-2 mode in the massive
multiplet becomes massless. In the supersymmetrised extensions of critical
gravity, the coefficients are chosen so that the massive modes lie in a
"window" of lowest energies E_0 such that these ghostlike fields can be
truncated by imposing appropriate boundary conditions at infinity, thus leaving
just positive-norm massless supergravity modes.Comment: 29 page
Massive Three-Dimensional Supergravity From R+R^2 Action in Six Dimensions
We obtain a three-parameter family of massive N=1 supergravities in three
dimensions from the 3-sphere reduction of an off-shell N=(1,0) six-dimensional
Poincare supergravity that includes a curvature squared invariant. The
three-dimensional theory contains an off-shell supergravity multiplet and an
on-shell scalar matter multiplet. We then generalise this in three dimensions
to an eight-parameter family of supergravities. We also find a duality
relationship between the six-dimensional theory and the N=(1,0) six-dimensional
theory obtained through a T^4 reduction of the heterotic string effective
action that includes the higher-order terms associated with the
supersymmetrisation of the anomaly-cancelling \tr(R\wedge R) term.Comment: Latex, 32 Pages, an equation is corrected, a few new equations and a
number of clarifying remarks are adde
Supersymmetry of the Schrodinger and PP Wave Solutions in Einstein-Weyl Supergravities
We obtain the Schrodinger and general pp-wave solutions with or without the
massive vector in Einstein-Weyl supergravity. The vector is an auxiliary field
in the off-shell supermultiplet and it acquires a kinetic term in the
Weyl-squared super invariant. We study the supersymmetry of these solutions and
find that turning on the massive vector has a consequence of breaking all the
supersymmetry. The Schrodinger and also the pp-wave solutions with the massive
vector turned off on the other hand preserve 1/4 of the supersymmetry.Comment: 13 pages, no figur
Study of color suppressed modes
The color suppressed modes are
analyzed in perturbative QCD approach. We find that the dominant contribution
is from the non-factorizable diagrams. The branching ratios calculated in our
approach for agree with current experiments. By
neglecting the gluonic contribution, we predict the branching ratios of are at the comparable size of , but smaller than that of .Comment: revtex, 5 pages, axodraw.st
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Long-term stability of GaAs/AlAs terahertz quantum-cascade lasers
We have investigated high-performance GaAs/AlAs terahertz (THz) quantum-cascade lasers (QCLs) with respect to the long-term stability of their operating parameters. The output power of lasers that contain an additional, thick AlAs refractive-index contrast layer underneath the cascade structure decreases after three months by about 35%. The deterioration of these lasers is attributed to the oxidation processes in this contrast layer starting from the facets. However, GaAs/AlAs THz QCLs with an Al0.9Ga0.1As refractive-index contrast layer exhibit long-term stability of the operating parameters over many years even when they are exposed to atmospheric conditions. Therefore, these lasers are promising high-power radiation sources in the terahertz spectral region for commercial applications
Toda p-brane black holes and polynomials related to Lie algebras
Black hole generalized p-brane solutions for a wide class of intersection
rules are obtained. The solutions are defined on a manifold that contains a
product of n - 1 Ricci-flat internal spaces. They are defined up to a set of
functions H_s obeying non-linear differential equations equivalent to Toda-type
equations with certain boundary conditions imposed. A conjecture on polynomial
structure of governing functions H_s for intersections related to semisimple
Lie algebras is suggested. This conjecture is proved for Lie algebras: A_m,
C_{m+1}, m > 0. For simple Lie algebras the powers of polynomials coincide with
the components of twice the dual Weyl vector in the basis of simple coroots.
The coefficients of polynomials depend upon the extremality parameter \mu >0.
In the extremal case \mu = 0 such polynomials were considered previously by H.
L\"u, J. Maharana, S. Mukherji and C.N. Pope. Explicit formulas for
A_2-solution are obtained. Two examples of A_2-dyon solutions, i.e. dyon in D =
11 supergravity with M2 and M5 branes intersecting at a point and Kaluza-Klein
dyon, are considered.Comment: 24 pages, Latex, typos are eliminated, a correct relation on
parameters of special block-orthogonal solution is added in third line after
eq. (4.10
Qualitative Analysis of Isotropic Curvature String Cosmologies
A complete qualitative study of the dynamics of string cosmologies is
presented for the class of isotopic curvature universes. These models are of
Bianchi types I, V and IX and reduce to the general class of
Friedmann-Robertson-Walker universes in the limit of vanishing shear isotropy.
A non-trivial two-form potential and cosmological constant terms are included
in the system. In general, the two-form potential and spatial curvature terms
are only dynamically important at intermediate stages of the evolution. In many
of the models, the cosmological constant is important asymptotically and
anisotropy becomes dynamically negligible. There also exist bouncing
cosmologies.Comment: Accepted to Classical and Quantum Gravity, 40 pages, 12 figures (uses
"graphicx" package for figures
Branching ratio and CP asymmetry of decays in the perturbative QCD approach
In this paper, we calculate the decay rate and CP asymmetry of the decay in perturbative QCD approach with Sudakov resummation. Since
none of the quarks in final states is the same as those of the initial
meson, this decay can occur only via annihilation diagrams in the standard
model. Besides the current-current operators, the contributions from the QCD
and electroweak penguin operators are also taken into account. We find that (a)
the branching ratio is about ; (b) the penguin diagrams
dominate the total contribution; and (c) the direct CP asymmetry is small in
size: no more than ; but the mixing-induced CP asymmetry can be as large
as ten percent testable in the near future LHC-b experiments.Comment: 12 pages, 4 figures included, RevTe
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