Descent c-Wilf Equivalence

Let $S_n$ denote the symmetric group. For any $\sigma \in S_n$, we let $\mathrm{des}(\sigma)$ denote the number of descents of $\sigma$, $\mathrm{inv}(\sigma)$ denote the number of inversions of $\sigma$, and $\mathrm{LRmin}(\sigma)$ denote the number of left-to-right minima of $\sigma$. For any sequence of statistics $\mathrm{stat}_1, \ldots \mathrm{stat}_k$ on permutations, we say two permutations $\alpha$ and $\beta$ in $S_j$ are $(\mathrm{stat}_1, \ldots \mathrm{stat}_k)$-c-Wilf equivalent if the generating function of $\prod_{i=1}^k x_i^{\mathrm{stat}_i}$ over all permutations which have no consecutive occurrences of $\alpha$ equals the generating function of $\prod_{i=1}^k x_i^{\mathrm{stat}_i}$ over all permutations which have no consecutive occurrences of $\beta$. We give many examples of pairs of permutations $\alpha$ and $\beta$ in $S_j$ which are $\mathrm{des}$-c-Wilf equivalent, $(\mathrm{des},\mathrm{inv})$-c-Wilf equivalent, and $(\mathrm{des},\mathrm{inv},\mathrm{LRmin})$-c-Wilf equivalent. For example, we will show that if $\alpha$ and $\beta$ are minimally overlapping permutations in $S_j$ which start with 1 and end with the same element and $\mathrm{des}(\alpha) = \mathrm{des}(\beta)$ and $\mathrm{inv}(\alpha) = \mathrm{inv}(\beta)$, then $\alpha$ and $\beta$ are $(\mathrm{des},\mathrm{inv})$-c-Wilf equivalent.Comment: arXiv admin note: text overlap with arXiv:1510.0431

The Impact of Increased Import Competition from the People’s Republic of China on Income Inequality and Household Welfare in Viet Nam

This paper examines the surge of imports from the PRC to Viet Nam from 2000 to 2014 in order to evaluate the effects of increased exposure to trade with the PRC on income inequality and household welfare in Viet Nam. Using household level data from the Viet Nam Household Living Standard Survey and combining it with measures of trade exposure, we find that increased imports led to a fall in inequality at the provincial and district level. We distinguish between intermediate and final goods and find similar results. In order to better understand the relative gains and losses across income groups, we apply a quantile regression approach. Our results indicate that increased imports were more often positively correlated with household income for households located in the lower quantiles. In contrast, for households in the upper quantiles the correlation is either negative or less pronounced

Microstructure and strength of metals processed by severe plastic deformation

The microstructure of f.c.c. metals (Al, Cu, Ni) and alloys (Al-Mg) processed by severe plastic deformation (SPD) methods is studied by X-ray diffraction line profile analysis. It is shown that the crystallite size and the dislocation density saturate with increasing strain. Furthermore, the Mg addition promotes efficiently a reduction of the crystallite size and an increase of the dislocation density in Al during the SPD process. The yield strength correlates well with that calculated from the dislocation density using the Taylor equation, thereby indicating that the main strengthening mechanism in both pure metals and alloys is the interaction between dislocations

Energy harvesting over Rician fading channel: A performance analysis for half-duplex bidirectional sensor networks under hardware impairments

In this paper, a rigorous analysis of the performance of time-switching energy harvesting strategy that is applied for a half-duplex bidirectional wireless sensor network with intermediate relay over a Rician fading channel is presented to provide the exact-form expressions of the outage probability, achievable throughput and the symbol-error-rate (SER) of the system under the hardware impairment condition. Using the proposed probabilistic models for wireless channels between mobile nodes as well as for the hardware noises, we derive the outage probability of the system, and then the throughput and SER can be obtained as a result. Both exact analysis and asymptotic analysis at high signal-power-to-noise-ratio regime are provided. Monte Carlo simulation is also conducted to verify the analysis. This work confirms the effectiveness of energy harvesting applied in wireless sensor networks over a Rician fading channel, and can provide an insightful understanding about the effect of various parameters on the system performance.Web of Science186art. no. 1781

Two-way half duplex decode and forward relaying network with hardware impairment over Rician fading channel: system performance analysis

In this paper, the system performance analysis of a two-way decode and forward (DF) relaying network over the Rician fading environment under hardware impairment effect is proposed, analyzed and demonstrated. In this analysis, the analytical mathematical expressions of the achievable throughput, the outage probability, and ergodic capacity were proposed, analyzed and demonstrated. After that, the effect of various system parameters on the system performance is deeply studied with closed-form expressions for the system performance. Finally, the analytical results are also demonstrated by Monte-Carlo simulation in comparison with the closed-form expressions. The numerical results demonstrated and convinced the effect of the system parameters on the system performance of the two-way DF relaying network. The results show that the analytical mathematical and simulated results match for all possible parameter values.Web of Science242787