Closure properties of bonded sequential insertion-deletion systems

Through the years, formal language theory has evolved through continual interdisciplinary work in theoretical computer science, discrete mathematics and molecular biology. The combination of these areas resulted in the birth of DNA computing. Here, language generating devices that usually considered any set of letters have taken on extra restrictions or modified constructs to simulate the behavior of recombinant DNA. A type of these devices is an insertion-deletion system, where the operations of insertion and deletion of a word have been combined in a single construct. Upon appending integers to both sides of the letters in a word, bonded insertion-deletion systems were introduced to accurately depict chemical bonds in chemical compounds. Previously, it has been shown that bonded sequential insertion-deletion systems could generate up to recursively enumerable languages. However, the closure properties of these systems have yet to be determined. In this paper, it is shown that bonded sequential insertion-deletion systems are closed under union, concatenation, concatenation closure, λ-free concatenation closure, substitution and intersection with regular languages. Hence, the family of languages generated by bonded sequential insertion-deletion systems is shown to be a full abstract family of languages

The nonabelian tensor square of a Bieberbach group with symmetric point group of order six

Bieberbach groups are torsion free crystallographic groups. In this paper, our focus is given on the Bieberbach groups with symmetric point group of order six. The nonabelian tensor square of a group is a well known homological functor which can reveal the properties of a group. With the method developed for polycyclic groups, the nonabelian tensor square of one of the Bieberbach groups of dimension four with symmetric point group of order six is computed. The nonabelian tensor square of this group is found to be not abelian and its presentation is constructed

The exterior square of a Bieberbach group with quaternion point group of order eight

A Bieberbach group is defined to be a torsion free crystallographic group which is an extension of a free abelian lattice group by a finite point group. This paper aims to determine a mathematical representation of a Bieberbach group with quaternion point group of order eight. Such mathematical representation is the exterior square. Mathematical method from representation theory is used to find the exterior square of this group. The exterior square of this group is found to be nonabelian

Microalgae microbial fuel cell (MMFC) using Chlorella vulgaris and “batik” wastewater as bioelectricity

Nowadays, Indonesia is faced with an increase in human growth, and followed by increasing electricity demand. One of the environmental friendly alternative energy that can solve this problem is microbial fuel cell, which utilizes organic matter as a substrate of bacteria in carrying out its metabolic activities to produce electricity. In this study, investigated the electrical energy produced by Microalgae Microbial Fuel Cell (MMFC) using Chlorella vulgaris and "Batik"wastewater. This study aims to assess the performance of the MMFC system based on the influence of yeast (8 g L-1 and 4 g L-1), "Batik wastewater"concentration (50 % and 100 %), and graphite electrodes (1:1 and 2:2). The MMFC system was carried out by filling anode chamber with "Batik"wastewater and the cathode with C. vulgaris. MMFC simulation was operated for 7 d. Concentration of 100 % "Batik"wastewater and 2:2 number of electrodes gave the best result in MMFC with voltage 0.115 Volt, algae absorbance 0.666. The COD decreased from 824 mg L-1 to 752 mg L-1 after the MMFC. The addition of 8 g L-1 yeast gave the optimum of bioelectricity production reached 0.322 Volt and the microalgae grew until the absorbance reached 1.031

Recent updates on homological invariants of bieberbach groups

Homological invariants or homological functors of groups have their roots in algebraic K-theory and homotopy theory. They were first used in algebraic topology, but are common in many areas of mathematics. The homological invariants are also used in group cohomology to classify abelian group extensions. Researches on homological invariants have grown intensively over the years. In this paper, recent updates of the homological invariants of Bieberbach groups with certain point groups will be presented. Furthermore, some of the homological invariants of a Bieberbach group of dimension six with quaternion point group of order eight are computed