2-(5-Amino-2H-tetra­zol-2-yl)acetic acid

In the title mol­ecule, C3H5N5O2, the tetra­zole ring and carboxyl group form a dihedral angle of 82.25 (14)°. In the crystal, adjacent mol­ecules are linked through O—H⋯N, N—H⋯O and N—H⋯N hydrogen bonds into layers parallel to the bc plane

Applying a Heuristic Approach for a Minimum-cost Operating Strategy for Tap Water

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchive

Weighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges

An $n$-by-$n$ ($n\ge 3$) weighted shift matrix $A$ is one of the form [{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & & 0{array}], where the $a_j$'s, called the weights of $A$, are complex numbers. Assume that all $a_j$'s are nonzero and $B$ is an $n$-by-$n$ weighted shift matrix with weights $b_1,..., b_n$. We show that $B$ is unitarily equivalent to $A$ if and only if $b_1... b_n=a_1...a_n$ and, for some fixed $k$, $1\le k \le n$, $|b_j| = |a_{k+j}|$ ($a_{n+j}\equiv a_j$) for all $j$. Next, we show that $A$ is reducible if and only if $A$ has periodic weights, that is, for some fixed $k$, $1\le k \le \lfloor n/2\rfloor$, $n$ is divisible by $k$, and $|a_j|=|a_{k+j}|$ for all $1\le j\le n-k$. Finally, we prove that $A$ and $B$ have the same numerical range if and only if $a_1...a_n=b_1...b_n$ and $S_r(|a_1|^2,..., |a_n|^2)=S_r(|b_1|^2,..., |b_n|^2)$ for all $1\le r\le \lfloor n/2\rfloor$, where $S_r$'s are the circularly symmetric functions.Comment: 27 page

A Global Method for a Two-Dimensional Cutting Stock Problem in the Manufacturing Industry

A two-dimensional cutting stock problem (2DCSP) needs to cut a set of given rectangular items from standard-sized rectangular materials with the objective of minimizing the number of materials used. This problem frequently arises in different manufacturing industries such as glass, wood, paper, plastic, etc. However, the current literatures lack a deterministic method for solving the 2DCSP. However, this study proposes a global method to solve the 2DCSP. It aims to reduce the number of binary variables for the proposed model to speed up the solving time and obtain the optimal solution. Our experiments demonstrate that the proposed method is superior to current reference methods for solving the 2DCSP

What is Needed for Future 3D Printing from Maker’S Viewpoints

This study focused on investigating makers’ opinions about current 3D printing technology to foster the development and use of 3D printing technologies in Taiwan. 3D printing has revolutionized the manufacturing industries as it provided a highly flexible, customizable way of small-quantity production at low cost. Its popularity among general users, however, encountered difficulties such as high requirements in skills, less user-friendliness, lack of practicality, low reliability, etc. Makers, a special group of customers of 3D printers are familiar with problems of this technology as they shared experience on the Internet, started collaborative manufacturing with open sources and turned their DIY activities into E-business. The study utilized questionnaires in the makers’ space to obtain the background of this special group of customers, their viewpoints regarding important features to consider for purchasing a 3D printer, and difficulties and solutions in propagation of 3D printing. The results demonstrated that makers were a group of extrovert and intuitive thinkers in terms of MBTI personalities and treasured printing precision (surface quality), stability (long tuning period) and easy maintenance as most attractive factors to customers. From their viewpoints, difficulties in use, customers’ low interests, and lack of practicality of its products were rated top 3 problems for 3D printing. However, school education, propagation of makers’ space and development of ease-to-use 3D software may help its popularity. The results of this study may help 3D printer manufacturers and 3D printing service providers to better understand their customers’ behaviors, based on which better 3D printing services and 3D printers can be developed to improve their business

Birman-Wenzl-Murakami Algebra and the Topological Basis

In this paper, we use entangled states to construct 9x9-matrix representations of Temperley-Lieb algebra (TLA), then a family of 9x9-matrix representations of Birman-Wenzl-Murakami algebra (BWMA) have been presented. Based on which, three topological basis states have been found. And we apply topological basis states to recast nine-dimensional BWMA into its three-dimensional counterpart. Finally, we find the topological basis states are spin singlet states in special case.Comment: 11pages, 1 figur

Hexaaqua­magnesium(II) bis­{5-[3-(1H-tetra­zol-5-yl)phen­yl]tetra­zolide} tetra­hydrate

The asymmetric unit of the title compound, [Mg(H2O)6](C8H5N8)2·4H2O, contains one half of the centrosymmetric dication, one anion and two water mol­ecules. The MgII ion is coordinated by six water mol­ecules in a slightly distorted octa­hedral geometry. In the anion, the two five-membered heterocycles are twisted from the central benzene ring by 4.34 (11) and 3.20 (10)°. In the crystal, O—H⋯N, O—H⋯O and N—H⋯O hydrogen bonds generate a three-dimensional network