# Makoto Sakamoto

## Publications

##### 3 Stress Distribution in Axisymmetric Indentation of an Elastic Layer-Substrate Body

**Authors:**
Makoto Sakamoto,
Kotaro Miura,
Yuji Tanabe

**Abstract:**

We focus on internal stress and displacement of an elastic axisymmetric contact problem for indentation of a layer-substrate body. An elastic layer is assumed to be perfectly bonded to an elastic semi-infinite substrate. The elastic layer is smoothly indented with a flat-ended cylindrical indenter. The analytical and exact solutions were obtained by solving an infinite system of simultaneous equations using the method to express a normal contact stress at the upper surface of the elastic layer as an appropriate series. This paper presented the numerical results of internal stress and displacement distributions for hard-coating system with constant values of Poisson’s ratio and the thickness of elastic layer.

**Keywords:**
Coating Materials,
indentation,
contact problem,
stress distribution,
layer-substrate body

##### 2 k-Neighborhood Template A-Type Three-Dimensional Bounded Cellular Acceptor

**Authors:**
Yasuo Uchida,
Makoto Sakamoto,
Makoto Nagatomo,
Takao Ito,
Tsunehiro Yoshinaga,
Satoshi Ikeda,
Masahiro Yokomichi,
Hiroshi Furutani,
Tuo Zhang,
Tatsuma Kurogi

**Abstract:**

**Keywords:**
Turing Machine,
converter,
four-dimension,
Cellular acceptor,
configuration-reader,
finite automaton,
on-line tessellation acceptor,
parallel/sequential array acceptor

##### 1 Hierarchies Based On the Number of Cooperating Systems of Finite Automata on Four-Dimensional Input Tapes

**Authors:**
Yasuo Uchida,
Makoto Sakamoto,
Makoto Nagatomo,
Takao Ito,
Tsunehiro Yoshinaga,
Satoshi Ikeda,
Masahiro Yokomichi,
Hiroshi Furutani

**Abstract:**

In theoretical computer science, the Turing machine has played a number of important roles in understanding and exploiting basic concepts and mechanisms in computing and information processing [20]. It is a simple mathematical model of computers [9]. After that, M.Blum and C.Hewitt first proposed two-dimensional automata as a computational model of two-dimensional pattern processing, and investigated their pattern recognition abilities in 1967 [7]. Since then, a lot of researchers in this field have been investigating many properties about automata on a two- or three-dimensional tape. On the other hand, the question of whether processing fourdimensional digital patterns is much more difficult than two- or threedimensional ones is of great interest from the theoretical and practical standpoints. Thus, the study of four-dimensional automata as a computasional model of four-dimensional pattern processing has been meaningful [8]-[19],[21]. This paper introduces a cooperating system of four-dimensional finite automata as one model of four-dimensional automata. A cooperating system of four-dimensional finite automata consists of a finite number of four-dimensional finite automata and a four-dimensional input tape where these finite automata work independently (in parallel). Those finite automata whose input heads scan the same cell of the input tape can communicate with each other, that is, every finite automaton is allowed to know the internal states of other finite automata on the same cell it is scanning at the moment. In this paper, we mainly investigate some accepting powers of a cooperating system of eight- or seven-way four-dimensional finite automata. The seven-way four-dimensional finite automaton is an eight-way four-dimensional finite automaton whose input head can move east, west, south, north, up, down, or in the fu-ture, but not in the past on a four-dimensional input tape.

**Keywords:**
Computational complexity,
Hierarchy,
cooperating system,
finite
automaton,
four-dimension,
multihead

## Abstracts

##### 1 Stress Distribution in Axisymmetric Indentation of an Elastic Layer-Substrate Body

**Authors:**
Makoto Sakamoto,
Kotaro Miura,
Yuji Tanabe

**Abstract:**

**Keywords:**
Coating Materials,
indentation,
contact problem,
stress distribution,
layer-substrate body