In-situ Measurements of Blast Seismic Waves and Their Safety Distance

Empirical formulae and their applications are given after systematically analysing the seismic wave data as measured in various blasting operations. The computed results are ln close agreement with the field measured dat

Q∖Z\mathbb Q\setminus\mathbb Z is diophantine over Q\mathbb Q with 32 unknowns

In 2016 J. Koenigsmann refined a celebrated theorem of J. Robinson by proving that $\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$, i.e., there is a polynomial $P(t,x_1,\ldots,x_{n})\in\mathbb Z[t,x_1,\ldots,x_{n}]$ such that for any rational number $t$ we have $$t\not\in\mathbb Z\iff \exists x_1\cdots\exists x_{n}[P(t,x_1,\ldots,x_{n})=0]$$ where variables range over $\mathbb Q$, equivalently $$t\in\mathbb Z\iff \forall x_1\cdots\forall x_{n}[P(t,x_1,\ldots,x_{n})\not=0].$$ In this paper we prove further that we may even take $n=32$ and require deg$\,P<6\times10^{11}$, which provides the best record in this direction. Combining this with a result of Sun, we get that there is no algorithm to decide for any $f(x_1,\ldots,x_{41})\in\mathbb Z[x_1,\ldots,x_{41}]$ whether $$\forall x_1\cdots\forall x_9\exists y_1\cdots\exists y_{32}[f(x_1,\ldots,x_9,y_1,\ldots,y_{32})=0],$$ where variables range over $\mathbb Q$.Comment: 13 pages. Correct few typo

Beamforming Designs and Performance Evaluations for Intelligent Reflecting Surface Enhanced Wireless Communication System with Hardware Impairments

Intelligent reflecting surface (IRS) can effectively control the wavefront of the impinging signals, and has emerged as a promising way to improve the energy and spectrum efficiency of wireless communication systems. Most existing studies were conducted with an assumption that the hardware operations are perfect without any impairment. However, both physical transceiver and IRS suffer from non-negligible hardware impairments in practice, which will bring some major challenges, e.g., increasing the difficulty and complexity of the beamforming designs, and degrading the system performance. In this paper, by taking hardware impairments into consideration, we make the transmit and reflect beamforming designs and evaluate the system performance. First, we utilize the linear minimum mean square error estimator to make the channel estimations, and analyze the factors that affect estimation accuracy. Then, we derive the optimal transmit beamforming vector, and propose a gradient descent method-based algorithm to obtain a sub-optimal reflect beamforming solution. Next, we analyze the asymptotic channel capacities by considering two types of asymptotics with respect to the transmit power and the numbers of antennas and reflecting elements. Finally, we analyze the power scaling law and the energy efficiency. By comparing the performance of our proposed algorithm with the upper bound on the performance of global optimal reflect beamforming solution, the simulation results demonstrate that our proposed algorithm can offer an outstanding performance with low computational complexity. The simulation results also show that there is no need to cost a lot on expensive antennas to achieve both high spectral efficiency and energy efficiency when the communication system is assisted by an IRS and suffer from hardware impairments.Comment: arXiv admin note: text overlap with arXiv:2004.09804, arXiv:2004.0976