Characterization of graphs whose a small power of their edge ideals has a linear free resolution

Let $I(G)$ be the edge ideal of a simple graph $G$. We prove that $I(G)^2$ has a linear free resolution if and only if $G$ is gap-free and reg$I(G) \le 3$. Similarly, we show that $I(G)^3$ has a linear free resolution if and only if $G$ is gap-free and reg$I(G) \le 4$. We deduce these characterizations from a general formula for the regularity of powers of edge ideals of gap-free graphs $${\rm reg}(I(G)^s) = \max({\rm reg} I(G) + s-1,2s),$$ for $s =2,3$.Comment: 14 pages. Update a proof of Theorem 2.13 with a statement for a squarefree monomial ideal. arXiv admin note: text overlap with arXiv:2109.0639

General Rank Multiuser Downlink Beamforming With Shaping Constraints Using Real-valued OSTBC

In this paper we consider optimal multiuser downlink beamforming in the presence of a massive number of arbitrary quadratic shaping constraints. We combine beamforming with full-rate high dimensional real-valued orthogonal space time block coding (OSTBC) to increase the number of beamforming weight vectors and associated degrees of freedom in the beamformer design. The original multi-constraint beamforming problem is converted into a convex optimization problem using semidefinite relaxation (SDR) which can be solved efficiently. In contrast to conventional (rank-one) beamforming approaches in which an optimal beamforming solution can be obtained only when the SDR solution (after rank reduction) exhibits the rank-one property, in our approach optimality is guaranteed when a rank of eight is not exceeded. We show that our approach can incorporate up to 79 additional shaping constraints for which an optimal beamforming solution is guaranteed as compared to a maximum of two additional constraints that bound the conventional rank-one downlink beamforming designs. Simulation results demonstrate the flexibility of our proposed beamformer design

Entity Resolution in Big Data

Today, with the rapid development of technology, human entered a new era of Information Technology. Data is being transfer from paper to digital second by second. Therefore, the demand of data storage is increasing quickly. Human need a new technique to handle Big Data, that’s why Hadoop was born. However, the conflicts and duplicates of data is still happen in many cases. In this report, we will illustrate a new technique for entity resolution in big data which uses Hadoop\u27s Map-Reduce framework

Suitability assessment and recommendations for Urban agricultural development: A case study in Cai Rang District, Can Tho City, Viet Nam

This study aimed to assess the contributing aspects and design decentralized adaptive models for urban agriculture. The research techniques included data collection, surveying and interviewing farmers, statistical analysis and FAO land suitability assessment techniques. The results show that the model of growing green vegetables, fruits and vegetables outside, together with decorative plants, orchids and raising cattle, is the most effective. Moreover, job-creating models boost income, calm down people, spread joy, supply clean food right away, provide room for greenery, recycle agricultural waste and reduce environmental pollution. The outcome is the foundation for selecting the best foreign investment model for future growth. According to the study's findings, sustainable agricultural options for the area assist people in living better, protecting the environment, and earning more money in the future

STUDY ON THE PROPERTIES OF SILVER PLATING ON A6061 ALUMINUM ALLOY

This article presents the properties of the silver plating on A6061 aluminum alloy. The structure, chemical composition, phase composition, thickness and corrosion durability of the plating are determined by scanning electron microscopy-energy dispersive X-ray spectroscopy (SEM-EDS), X-ray diffraction, corrosion current measurement, frost acceleration and hygrothermal test. The results show that the silver plating has good corrosion resistance, is not blistered, remains white, light, no appearance of rust and other abnormalities. These parameters meet the technical requirements laid out for resonator of ultra - high frequency filter

A Prototype of Automated Chayote Peeling Machine

Fruit peeling seems a simple performance, but it is the consist of many elements such as the peeler, the way we grasp and move the blade and cutting speed, etc. - all these factors play a role, and interact with each other. This paper describes the prototype of a chayote peeling machine. The machine has been designed with a simple and low-cost approach. To improve chayote peeling rate and ensure pulp quality, a proposed structure was designed, manufactured and tested in laboratory. The experimental results are examined to demonstrate the efficiency of the peeling machine. It proves that the proposed machine could be widely applied in the fruit peeling technology

Depth of powers of edge ideals of cycles and trees

Let $I$ be the edge ideal of a cycle of length $n \ge 5$ over a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_n]$. We prove that for $2 \le t < \lceil (n+1)/2 \rceil$, $$\operatorname{depth} (S/I^t) = \lceil \frac{n -t + 1}{3} \rceil.$$ When $G = T_{\mathbf{a}}$ is a starlike tree which is the join of $k$ paths of length $a_1, \ldots, a_k$ at a common root $1$, we give a formula for the depth of powers of $I(T_{\mathbf{a}})$