5,700 research outputs found

### On the Number of Nonnegative Solutions to the Inequality a1 +....ar < n

In this paper, we present a simple and fast method for counting the number of nonnegative integer solutions to the equality a1x1+a2x2+: : :+arxr = n where a1; a2; :::; ar and n are positive integers. As an application, we use the method for finding the number of solutions of a Diophantine inequality

### Improved Energy Detector for Wideband Spectrum Sensing in Cognitive Radio Networks

In this paper, an improved energy detector for a wideband spectrum sensing is proposed. For a better detection of the spectrum holes the overall band is divided into equal non-overlapping sub-bands. The main objective is to determine the detection thresholds for each of these subbands jointly. By defining the problem as an optimization problem, we aim to find the maximum aggregated opportunistic throughput of cognitive radio networks. Introducing practical constraints to this optimization problem will change the problem into a convex and solvable one. The results of this paper show that the proposed improved energy detector will increase the aggregated throughput considerably

### Canonical decomposition of linear differential operators with selected differential Galois groups

We revisit an order-six linear differential operator having a solution which
is a diagonal of a rational function of three variables. Its exterior square
has a rational solution, indicating that it has a selected differential Galois
group, and is actually homomorphic to its adjoint. We obtain the two
corresponding intertwiners giving this homomorphism to the adjoint. We show
that these intertwiners are also homomorphic to their adjoint and have a simple
decomposition, already underlined in a previous paper, in terms of order-two
self-adjoint operators. From these results, we deduce a new form of
decomposition of operators for this selected order-six linear differential
operator in terms of three order-two self-adjoint operators. We then generalize
the previous decomposition to decompositions in terms of an arbitrary number of
self-adjoint operators of the same parity order. This yields an infinite family
of linear differential operators homomorphic to their adjoint, and, thus, with
a selected differential Galois group. We show that the equivalence of such
operators is compatible with these canonical decompositions. The rational
solutions of the symmetric, or exterior, squares of these selected operators
are, noticeably, seen to depend only on the rightmost self-adjoint operator in
the decomposition. These results, and tools, are applied on operators of large
orders. For instance, it is seen that a large set of (quite massive) operators,
associated with reflexive 4-polytopes defining Calabi-Yau 3-folds, obtained
recently by P. Lairez, correspond to a particular form of the decomposition
detailed in this paper.Comment: 40 page

### In vitro inhibition of Helicobacter pylori urease with non and semi fermented Camellia sinensis

Purpose: Helicobacter pylori is the etiological agent in duodenal and peptic ulcers. The growing problem of antibiotic resistance by the organism demands the search for novel compounds, especially from natural sources. This study was conducted to evaluate the effect of Camellia sinensis extracts on the urease enzyme that is a major colonization factor for H. pylori. Methods: Minimum inhibitory concentrations of nonfermented and semifermented C. sinensis methanol: water extracts were assessed by broth dilution method. Examination of the urease function was performed by Mc Laren method, and urease production was detected on 12% SDS polyacrylamide gel electrophoresis from whole cell and membrane bound proteins. Results: Both extracts had inhibitory effects against H. pylori and urease production. At a concentration of 2.5 mg/ml of nonfermented extract and 3.5 mg/ml of semifermented extract the production of Ure A and Ure B subunits of the urease enzyme were inhibited completely. A concentration of 4 mg/ml of nonfermented and 5.5 mg/ml of semifermented extract were bactericidal for H. pylori. Conclusions: C. sinensis extracts, especially the nonfermented, could reduce H. pylori population and inhibit urease production at lower concentrations. The superior effect of nonfermented extract is due to its rich polyphenolic compounds and catechin contents

### Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity

We show that the n-fold integrals $\chi^{(n)}$ of the magnetic susceptibility
of the Ising model, as well as various other n-fold integrals of the "Ising
class", or n-fold integrals from enumerative combinatorics, like lattice Green
functions, are actually diagonals of rational functions. As a consequence, the
power series expansions of these solutions of linear differential equations
"Derived From Geometry" are globally bounded, which means that, after just one
rescaling of the expansion variable, they can be cast into series expansions
with integer coefficients. Besides, in a more enumerative combinatorics
context, we show that generating functions whose coefficients are expressed in
terms of nested sums of products of binomial terms can also be shown to be
diagonals of rational functions. We give a large set of results illustrating
the fact that the unique analytical solution of Calabi-Yau ODEs, and more
generally of MUM ODEs, is, almost always, diagonal of rational functions. We
revisit Christol's conjecture that globally bounded series of G-operators are
necessarily diagonals of rational functions. We provide a large set of examples
of globally bounded series, or series with integer coefficients, associated
with modular forms, or Hadamard product of modular forms, or associated with
Calabi-Yau ODEs, underlying the concept of modularity. We finally address the
question of the relations between the notion of integrality (series with
integer coefficients, or, more generally, globally bounded series) and the
modularity (in particular integrality of the Taylor coefficients of mirror
map), introducing new representations of Yukawa couplings.Comment: 100 page

### Ising n-fold integrals as diagonals of rational functions and integrality of series expansions

We show that the n-fold integrals $\chi^{(n)}$ of the magnetic susceptibility
of the Ising model, as well as various other n-fold integrals of the "Ising
class", or n-fold integrals from enumerative combinatorics, like lattice Green
functions, correspond to a distinguished class of function generalising
algebraic functions: they are actually diagonals of rational functions. As a
consequence, the power series expansions of the, analytic at x=0, solutions of
these linear differential equations "Derived From Geometry" are globally
bounded, which means that, after just one rescaling of the expansion variable,
they can be cast into series expansions with integer coefficients. We also give
several results showing that the unique analytical solution of Calabi-Yau ODEs,
and, more generally, Picard-Fuchs linear ODEs, with solutions of maximal
weights, are always diagonal of rational functions. Besides, in a more
enumerative combinatorics context, generating functions whose coefficients are
expressed in terms of nested sums of products of binomial terms can also be
shown to be diagonals of rational functions. We finally address the question of
the relations between the notion of integrality (series with integer
coefficients, or, more generally, globally bounded series) and the modularity
of ODEs.Comment: This paper is the short version of the larger (100 pages) version,
available as arXiv:1211.6031 , where all the detailed proofs are given and
where a much larger set of examples is displaye

### Globally nilpotent differential operators and the square Ising model

We recall various multiple integrals related to the isotropic square Ising
model, and corresponding, respectively, to the n-particle contributions of the
magnetic susceptibility, to the (lattice) form factors, to the two-point
correlation functions and to their lambda-extensions. These integrals are
holonomic and even G-functions: they satisfy Fuchsian linear differential
equations with polynomial coefficients and have some arithmetic properties. We
recall the explicit forms, found in previous work, of these Fuchsian equations.
These differential operators are very selected Fuchsian linear differential
operators, and their remarkable properties have a deep geometrical origin: they
are all globally nilpotent, or, sometimes, even have zero p-curvature. Focusing
on the factorised parts of all these operators, we find out that the global
nilpotence of the factors corresponds to a set of selected structures of
algebraic geometry: elliptic curves, modular curves, and even a remarkable
weight-1 modular form emerging in the three-particle contribution $\chi^{(3)}$
of the magnetic susceptibility of the square Ising model. In the case where we
do not have G-functions, but Hamburger functions (one irregular singularity at
0 or $\infty$) that correspond to the confluence of singularities in the
scaling limit, the p-curvature is also found to verify new structures
associated with simple deformations of the nilpotent property.Comment: 55 page

### Renormalization, isogenies and rational symmetries of differential equations

We give an example of infinite order rational transformation that leaves a
linear differential equation covariant. This example can be seen as a
non-trivial but still simple illustration of an exact representation of the
renormalization group.Comment: 36 page

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