160,274 research outputs found

### Diffusion multi-rate LMS algorithm for acoustic sensor networks

In this paper, we present a diffusion multi-rate least-mean-square (LMS)
algorithm, named DMLMS, which is an effective solution for distributed
estimation when two or more observation sequences are available with different
sampling rates. Then, we focus on a more practical application in the wireless
acoustic sensor networks (ASN). The filtered-x LMS (FxLMS) algorithm is
extended to the distributed multi-rate system and it introduces collaboration
between nodes following a diffusion strategy. Simulation results show that the
effectiveness of the proposed algorithms

### Frozen Gaussian approximation for general linear strictly hyperbolic system: formulation and Eulerian methods

The frozen Gaussian approximation, proposed in [Lu and Yang, [15]], is an
efficient computational tool for high frequency wave propagation. We continue
in this paper the development of frozen Gaussian approximation. The frozen
Gaussian approximation is extended to general linear strictly hyperbolic
systems. Eulerian methods based on frozen Gaussian approximation are developed
to overcome the divergence problem of Lagrangian methods. The proposed Eulerian
methods can also be used for the Herman-Kluk propagator in quantum mechanics.
Numerical examples verify the performance of the proposed methods

### Hardy-Sobolev-Maz'ya inequalities for higher order derivatives on half spaces

By using, among other things, the Fourier analysis techniques on hyperbolic
and symmetric spaces, we establish the Hardy-Sobolev-Maz'ya inequalities for
higher order derivatives on half spaces. The proof relies on a
Hardy-Littlewood-Sobolev inequality on hyperbolic spaces which is of its
independent interest. We also give an alternative proof of Benguria, Frank and
Loss' work concerning the sharp constant in the Hardy-Sobolev-Maz'ya inequality
in the three dimensional upper half space. Finally, we show the sharp constant
in the Hardy-Sobolev-Maz'ya inequality for bi-Laplacian in the upper half space
of dimension five coincides with the Sobolev constant.Comment: 32 page

### The electromagnetic form factors of $\Lambda$ hyperon in $e^+e^-\rightarrow \bar\Lambda\Lambda$

We study the electromagnetic form factors of $\Lambda$ hyperon in the
timelike region using the recent experimental data in the exclusive production
of $\bar{\Lambda} \Lambda$ pair in electron-position annihilation. We present a
pQCD inspired parametrization of $G_E(s)$ and $G_M(s)$ with only two
parameters, and we consider a suppression mechanism of the electric form factor
$G_E(s)$ compared to the magnetic form factor $G_M(s)$. The parameters are
determined through fitting our parametrization to the effective form factor
data in the reaction $e^+e^-\rightarrow \bar\Lambda\Lambda$. Except the
threshold region, our parametrization can reproduce satisfactorily the known
behavior of the existing data from the BarBar, DM2 and BESIII Collaborations.
We also predict the double spin polarization observables $A_{xx}$, $A_{yy}$ and
$A_{zz}$ in $e^+e^-\rightarrow \bar\Lambda\Lambda$.Comment: 5 pages, 3 figure

### Phase Space Sketching for Crystal Image Analysis based on Synchrosqueezed Transforms

Recent developments of imaging techniques enable researchers to visualize
materials at the atomic resolution to better understand the microscopic
structures of materials. This paper aims at automatic and quantitative
characterization of potentially complicated microscopic crystal images,
providing feedback to tweak theories and improve synthesis in materials
science. As such, an efficient phase-space sketching method is proposed to
encode microscopic crystal images in a translation, rotation, illumination, and
scale invariant representation, which is also stable with respect to small
deformations. Based on the phase-space sketching, we generalize our previous
analysis framework for crystal images with simple structures to those with
complicated geometry

### Analytic Constructions of General n-Qubit Controlled Gates

In this Letter, we present two analytic expressions that most generally
simulate $n$-qubit controlled-$U$ gates with standard one-qubit gates and CNOT
gates using exponential and polynomial complexity respectively. Explicit
circuits and general expressions of decomposition are derived. The exact
numbers of basic operations in these two schemes are given using gate counting
technique.Comment: 4 pages 7 figure

### A sharp Trudinger-Moser inequality on any bounded and convex planar domain

Wang and Ye conjectured in [22]:
Let $\Omega$ be a regular, bounded and convex domain in $\mathbb{R}^{2}$.
There exists a finite constant $C({\Omega})>0$ such that $\int_{\Omega}e^{\frac{4\pi u^{2}}{H_{d}(u)}}dxdy\le C(\Omega),\;\;\forall u\in
C^{\infty}_{0}(\Omega),$ where $H_{d}=\int_{\Omega}|\nabla
u|^{2}dxdy-\frac{1}{4}\int_{\Omega}\frac{u^{2}}{d(z,\partial\Omega)^{2}}dxdy$
and $d(z,\partial\Omega)=\min\limits_{z_{1}\in\partial\Omega}|z-z_{1}|$.}
The main purpose of this paper is to confirm that this conjecture indeed
holds for any bounded and convex domain in $\mathbb{R}^{2}$ via the Riemann
mapping theorem (the smoothness of the boundary of the domain is thus
irrelevant).
We also give a rearrangement-free argument for the following Trudinger-Moser
inequality on the hyperbolic space
$\mathbb{B}=\{z=x+iy:|z|=\sqrt{x^{2}+y^{2}}<1\}$: $\sup_{\|u\|_{\mathcal{H}}\leq 1} \int_{\mathbb{B}}(e^{4\pi u^{2}}-1-4\pi
u^{2})dV=\sup_{\|u\|_{\mathcal{H}}\leq 1}\int_{\mathbb{B}}\frac{(e^{4\pi
u^{2}}-1-4\pi u^{2})}{(1-|z|^{2})^{2}}dxdy< \infty,$ by using the method
employed earlier by Lam and the first author [9, 10], where $\mathcal{H}$
denotes the closure of $C^{\infty}_{0}(\mathbb{B})$ with respect to the norm
$\|u\|_{\mathcal{H}}=\int_{\mathbb{B}}|\nabla
u|^{2}dxdy-\int_{\mathbb{B}}\frac{u^{2}}{(1-|z|^{2})^{2}}dxdy.$ Using this
strengthened Trudinger-Moser inequality, we also give a simpler proof of the
Hardy-Moser-Trudinger inequality obtained by Wang and Ye [22]

### Distributed economic control of dynamically coupled networks

This paper investigates the synthesis of distributed economic control
algorithms under which dynamically coupled physical systems are regulated to a
variational equilibrium of a constrained convex game. We study two
complementary cases: (i) each subsystem is linear and controllable; and (ii)
each subsystem is nonlinear and in the strict-feedback form. The convergence of
the proposed algorithms is guaranteed using Lyapunov analysis. Their
performance is verified by two case studies on a multi-zone building
temperature regulation problem and an optimal power flow problem, respectively.Comment: 14 pages, 4 figures, journa

### SL(n,R)-Toda Black Holes

We consider D-dimensional Einstein gravity coupled to (n-1) U(1) vector
fields and (n-2) dilatonic scalars. We find that for some appropriate
exponential dilaton couplings of the field strengths, the equations of motion
for the static charged ansatz can be reduced to a set of one-dimensional
SL(n,R) Toda equations. This allows us to obtain a general class of explicit
black holes with mass and (n-1) independent charges. The near-horizon geometry
in the extremal limit is AdS_2 x S^{D-2}. The n=2 case gives the
Reissner-Nordstrom solution, and the n=3 example includes the Kaluza-Klein
dyon. We study the global structure and the black hole thermodynamics and
obtain the universal entropy product formula. We also discuss the
characteristics of extremal multi-charge black holes that have positive, zero
or negative binding energies.Comment: Latex, 20 page

### Green's functions of Paneitz and GJMS operators on hyperbolic spaces and sharp Hardy-Sobolev-Maz'ya inequalities on half spaces

Using the Fourier analysis techniques on hyperbolic spaces and Green's
function estimates, we confirm in this paper the conjecture given by the same
authors in [43]. Namely, we prove that the sharp constant in the
$\frac{n-1}{2}$-th order Hardy-Sobolev-Maz'ya inequality in the upper half
space of dimension $n$ coincides with the best $\frac{n-1}{2}$-th order Sobolev
constant when $n$ is odd and $n\geq9$ (See Theorem 1.6). We will also establish
a lower bound of the coefficient of the Hardy term for the $k-$th order
Hardy-Sobolev-Maz'ya inequality in upper half space in the remaining cases of
dimension $n$ and $k$-th order derivatives (see Theorem 1.7). Precise
expressions and optimal bounds for Green's functions of the operator $-\Delta_{\mathbb{H}}-\frac{(n-1)^{2}}{4}$ on the hyperbolic space
$\mathbb{B}^n$ and operators of the product form are given, where
$\frac{(n-1)^{2}}{4}$ is the spectral gap for the Laplacian
$-\Delta_{\mathbb{H}}$ on $\mathbb{B}^n$. Finally, we give the precise
expression and optimal pointwise bound of Green's function of the Paneitz and
GJMS operators on hyperbolic space, which are of their independent interest
(see Theorem 1.10).Comment: 33 page

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