-
Class Number Formula for Certain Imaginary Quadratic Fields
Issue:
Volume 4, Issue 2-1, March 2015
Pages:
1-6
Received:
26 October 2014
Accepted:
6 November 2014
Published:
29 November 2014
Abstract: In this note we shall show how Carlitz in 1954 could have reached an analogue of the Voronoi congruence in the more difficult case of p≡1(mod4): h(-4p) ≡B(p+1)/2(x4)(mod p), where B(p+1)/2(x4) is the generalized Bernoulli number with x4 being the Kronecker symbol associated to the Gaussian field Q(√-4).
-
Descartes’ Dream: Cartesian Products
Keiichi Takahashi,
Takayasu Kaida
Issue:
Volume 4, Issue 2-1, March 2015
Pages:
7-13
Received:
22 November 2014
Accepted:
2 December 2014
Published:
27 December 2014
Abstract: In the last century, especially in the last half of the century, there was the paradigm of sectionalism prevailing and sciences and engineering were divided into very small parts which are mutually independent. It was like in Babel where there was no common language to communicate. The purpose of this paper is to present one of the possible glues—the notion of Cartesian product—to stick some remotely separated parts of science and engineering together. This concept appears in various places and it will turn out that it can unify the scattered notions quite well. Our two main objectives are the interpretation of cyclic codes as polynomials and nested PSO. We make clear the meaning of polynomials through Cartesian product or rather as terminating formal power series. The latter, formal power series, is not touched in engineering disciplines but is quite useful in unifying and interpreting various notions. In particular, it will make clear the meaning of addition of polynomials. This reminds us of topologization of adéles. PSO (Particle Swarm Optimization), a developed form of genetic algorithm, has come to our attention through the papers [4], [23] and [24]. In [4], the PSO is used to find optimal choice of parameters in the FOPID. In other two papers, PSO algorithm is used in cell balancing in the Lithium-ion battery pack for EV’s. Motivated by the passage on [3] that the stability is preserved by the Cartesian product of many copies of the attractor, we may conceive of the nested PSO.
Abstract: In the last century, especially in the last half of the century, there was the paradigm of sectionalism prevailing and sciences and engineering were divided into very small parts which are mutually independent. It was like in Babel where there was no common language to communicate. The purpose of this paper is to present one of the possible glues—t...
Show More
-
Tychonoff’s Theorem as a Direct Application of Zorn’s Lemma
Issue:
Volume 4, Issue 2-1, March 2015
Pages:
14-17
Received:
25 November 2014
Accepted:
11 December 2014
Published:
27 December 2014
Abstract: A simple proof of Tychonoff’s theorem (the compactness of the product of compact spaces) as a direct application of Zorn’s lemma is given. In contrast to the classical Cartan-Bourbaki proof which uses Zorn’s lemma twice, our proof uses it only once.
-
Dielectric Properties of Au/C60 (OH) 24-26/Au Structure
Y. Sun,
S. Kanemitsu,
K. Kirimoto
Issue:
Volume 4, Issue 2-1, March 2015
Pages:
18-24
Received:
26 November 2014
Accepted:
1 December 2014
Published:
27 December 2014
Abstract: Dielectric properties of the Au/C60 (OH)24-26/Au structure were studied by measuring a.c. impedance and d.c. current in a wide temperature range. Three dielectric response characteristics were identified from Cole-Cole plots of a.c. impedance and dielectric dissipation factor of the structure. First, the bulk resistance and capacitance of the structure were observed at frequencies below 10 Hz, regardless of preparation condition of the Au electrode. Secondly, an interfacial characteristic of the Au foil/C60 (OH)24-26 contact was observed as a peak of dielectric dissipation factor at frequency of 200 Hz. Thirdly, an interfacial characteristic of the Au paste/C60 (OH)24-26 contact was also observed as a peak of dielectric dissipation factor at frequency of 1.7×〖10〗^5 Hz.
Abstract: Dielectric properties of the Au/C60 (OH)24-26/Au structure were studied by measuring a.c. impedance and d.c. current in a wide temperature range. Three dielectric response characteristics were identified from Cole-Cole plots of a.c. impedance and dielectric dissipation factor of the structure. First, the bulk resistance and capacitance of the struc...
Show More
-
Codons and Codes
Kalyan Chakraborty,
Shigeru Kanemitsu,
Y. Sun
Issue:
Volume 4, Issue 2-1, March 2015
Pages:
25-29
Received:
11 December 2014
Accepted:
13 December 2014
Published:
27 December 2014
Abstract: In this paper we assemble a few ingredients that are remotely connected to each other, but governed by the rule of coding theory ([1], [12]) and formal language theory, i.e. cyclic codes and DNA codes. Our interest arose from the remark that there exist both linear and circular DNAs in higher living organisms. We state the theory of codes in a wide sense due to [1] in order to understand the circular DNAs while we state rudiments of formal language theory as a means to interpret genes. We hope this will be a starter for unifying two approaches depending on the theory of codes and that of formal language.
Abstract: In this paper we assemble a few ingredients that are remotely connected to each other, but governed by the rule of coding theory ([1], [12]) and formal language theory, i.e. cyclic codes and DNA codes. Our interest arose from the remark that there exist both linear and circular DNAs in higher living organisms. We state the theory of codes in a wide...
Show More
-
Applications of the Hurwitz-Lerch Zeta-Function
Tomihiro Arai,
Kalyan Chakraborty,
Jing Ma
Issue:
Volume 4, Issue 2-1, March 2015
Pages:
30-35
Received:
5 November 2014
Accepted:
14 November 2014
Published:
27 December 2014
Abstract: In this paper, we shall exhibit the use of two principles, “principle of decomposition into residue classes” and “binomial principle of analytic continuation” due to Ram Murty and Sinha and indicate a certain distribution property and the functional equation for the Lipschitz-Lerch transcendent at integral arguments ofs. By considering the limiting cases ,we can also deduce new striking identities for Lipschizt-Lerch transcendent, among which is the Gauss second formula for the digamma function, Lipschitz-Lerch transcendent
Abstract: In this paper, we shall exhibit the use of two principles, “principle of decomposition into residue classes” and “binomial principle of analytic continuation” due to Ram Murty and Sinha and indicate a certain distribution property and the functional equation for the Lipschitz-Lerch transcendent at integral arguments ofs. By considering the limiting...
Show More
-
A Note on the Rank Bounded Distance and Its Algorithms for Cyclic Codes
Takayasu Kaida,
Junru Zheng
Issue:
Volume 4, Issue 2-1, March 2015
Pages:
36-41
Received:
22 December 2014
Accepted:
30 January 2015
Published:
11 February 2015
Abstract: The minimum distance for linear codes is one of the important parameters. The shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. It is necessary to construct the maximum value of the independent set for the calculation of the shift bound. However, its computational complexity is very large, because the construction of the independent set is not unique. The authors proposed an algorithm for calculation of the independent set using the discrete Fourier transform in 2010. In this paper we give simple modification and new recurrent algorithms to improve the original algorithm.
Abstract: The minimum distance for linear codes is one of the important parameters. The shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. It is necessary to construct the maximum value of the independent set for the calculation of the shift bound. However, its computational complexity is ...
Show More
-
On Some Point Groups
Y. Sun,
S. Kanemitsu,
H. Kitajima
Issue:
Volume 4, Issue 2-1, March 2015
Pages:
42-46
Received:
1 February 2015
Accepted:
1 February 2015
Published:
12 February 2015
Abstract: In this note, we indicate the coincidence as abstract groups of some point groups which belong to different molecular orbitals. This elucidates somewhat vague presentation in many existing textbooks on molecular orbitals, thus abridging between group theory and quantum chemistry.
-
An Adaptation Method for Removing Arsenate Species from Water Solution
Sainyam Galhotra,
Shigeru Kanemitsu,
Hiroyuki Kondo
Issue:
Volume 4, Issue 2-1, March 2015
Pages:
47-54
Received:
28 October 2014
Accepted:
2 March 2015
Published:
6 March 2015
Abstract: This paper is based on the idea of adaptation under which we mean the replacement of one element in a system with another with similar aspects. The first adaptation comes from the replacement of orthophospheric acid H3PO4 by arsenious acid H3AsO4. There is a close relation between calcium-sulfate and calcium carbonate-arsenate species. The main objective of this note is to give an explicit formula for the ratio of each arsenal species to the total and to make an adaptation of the former by the latter to develop a new adsorption material of arsenic acid which spends almost no energy. Some recently proposed methods of using calcium sulphate or other material has ambivalent aspects regarding energy spending as well as the treatment after adsorption.
Abstract: This paper is based on the idea of adaptation under which we mean the replacement of one element in a system with another with similar aspects. The first adaptation comes from the replacement of orthophospheric acid H3PO4 by arsenious acid H3AsO4. There is a close relation between calcium-sulfate and calcium carbonate-arsenate species. The main obj...
Show More
