相关论文: Shrinking parallelepiped targets in beta-dynamical…

We develop the Mass Transference Principle for rectangles of Wang \& Wu (Math. Ann. 2021) to incorporate the `unbounded' setup; that is, when along some direction the lower order (at infinity) of the side lengths of the rectangles under…

Radio frequency (RF) wireless power transfer (WPT) is a promising technology for future wireless systems. However, the low power transfer efficiency (PTE) is a critical challenge for practical implementations. One of the main inefficiency…

Consider the Maximum Weight Independent Set problem for rectangles: given a family of weighted axis-parallel rectangles in the plane, find a maximum-weight subset of non-overlapping rectangles. The problem is notoriously hard both in the…

To achieve efficient long-range wireless power transfer (WPT), large antenna systems are necessary spanning lengths of tens to thousands of meters in one dimension. This creates an array in the order of at least hundreds of thousands to…

For some special window functions $\psi_{\beta} \in H^2(\mathbb{C}^+),$ we prove that, over all sets $\Delta \subset \mathbb{C}^+$ of fixed hyperbolic measure $\nu(\Delta),$ the ones over which the Wavelet transform…

We consider the two dimensional shrinking target problem in the beta dynamical system for general $\beta>1$ and with the general error of approximations. Let $f, g$ be two positive continuous functions. For any $x_0,y_0\in[0,1]$, define the…

In this note, we use the mass transference principle for rectangles, recently obtained by Wang and Wu (Math. Ann., 2021), to study the Hausdorff dimension of sets of "weighted $\Psi$-well-approximable" points in certain self-similar sets in…

Let $\beta>1$ be a real number and define the $\beta$-transformation on $[0,1]$ by $T_\beta:x\mapsto \beta x\bmod 1$. Further, define $$W_y(T_{\beta},\Psi):=\{x\in [0, 1]:|T_\beta^nx-y|<\Psi(n) \mbox{ for infinitely many $n$}\}$$ and…

We consider the distribution of the orbits of the number 1 under the $\beta$-transformations $T_\beta$ as $\beta$ varies. Mainly, the size of the set of $\beta>1$ for which a given point can be well approximated by the orbit of 1 is…

We develop a new metric for quantifying end-to-end throughput in multihop wireless networks, which we term random access transport capacity, since the interference model presumes uncoordinated transmissions. The metric quantifies the…

This paper derives a lower bound to the per-node throughput achievable by a wireless network when n source-destination pairs are randomly distributed throughout a disk of radius $n^\gamma$, $ \gamma \geq 0$, propagation is modeled by…

This paper presents a rigorous optimization technique for wireless power transfer (WPT) systems enhanced by passive elements, ranging from simple reflectors and intermedi- ate relays all the way to general electromagnetic guiding and…

The extremely low efficiency is regarded as the bottleneck of Wireless Power Transfer (WPT) technology. To tackle this problem, either enlarging the transfer power or changing the infrastructure of WPT system could be an intuitively…

We have optimized the zero frequency first hyperpolarizability \beta of a one-dimensional piecewise linear potential well containing a single electron by adjusting the shape of that potential. With increasing numbers of parameters in the…

Wireless power transfer (WPT) is a promising technology that provides the network a way to replenish the batteries of the remote devices by utilizing RF transmissions. We study a class of harvest-first-transmit-later type of WPT policy,…

Extending results of Linial (1984) and Aigner (1985), we prove a uniform lower bound on the balance constant of a poset $P$ of width $2$. This constant is defined as $\delta(P) = \max_{(x, y)\in P^2}\min\{\mathbb{P}(x\prec y),…

The resonant transmission of a moving particle which interacts with an one-dimensional array of N delta-function potentials is investigated. A suitable transfer matrix formulation is used to obtain the particle transmission. We give the…

Wireless power transfer (WPT) prolongs the lifetime of wireless sensor network by providing sustainable power supply to the distributed sensor nodes (SNs) via electromagnetic waves. To improve the energy transfer efficiency in a large WPT…

The beta polytope $P_{n,d}^\beta$ is the convex hull of $n$ i.i.d. random points distributed in the unit ball of $\mathbb{R}^d$ according to a density proportional to $(1-\lVert{x}\rVert^2)^{\beta}$ if $\beta>-1$ (in particular, $\beta=0$…

While measuring returns to scale in data envelopment analysis (DEA), the occurrence of multiple supporting hyperplanes has been perceived as a crucial issue. To deal effectively with this in weigh restrictions (WR) framework, we first…