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Lower Bounds on Boundary Slope Diameters for Montesinos Knots
Ichihara, Kazuhiro,Mizushima, Shigeru Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.2
In this paper, we give two lower bounds on the diameter of the boundary slope set of a Montesinos knot. One is described in terms of the minimal crossing numbers of the knots, and the other is related to the Euler characteristics of essential surfaces with the maximal/minimal boundary slopes.
KNOTS WITH ARBITRARILY HIGH DISTANCE BRIDGE DECOMPOSITIONS
Ichihara, Kazuhiro,Saito, Toshio Korean Mathematical Society 2013 대한수학회보 Vol.50 No.6
We show that for any given closed orientable 3-manifold M with a Heegaard surface of genus g, any positive integers b and n, there exists a knot K in M which admits a (g, b)-bridge splitting of distance greater than n with respect to the Heegaard surface except for (g, b) = (0, 1), (0, 2).
Knots in homology lens spaces determined by their complements
Kazuhiro Ichihara,Toshio Saito 대한수학회 2022 대한수학회보 Vol.59 No.4
In this paper, we consider the knot complement problem for not null-homologous knots in homology lens spaces. Let $M$ be a homology lens space with $H_1(M; \mathbb{Z}) \cong \mathbb{Z}_p$ and $K$ a not null-homologous knot in $M$. We show that, $K$ is determined by its complement if $M$ is non-hyperbolic, $K$ is hyperbolic, and $p$ is a prime greater than 7, or, if $M$ is actually a lens space $L(p,q)$ and $K$ represents a generator of $H_1(L(p,q))$.
COLORING LINKS BY THE SYMMETRIC GROUP OF DEGREE THREE
Kazuhiro Ichihara,Eri Matsudo Korean Mathematical Society 2023 대한수학회논문집 Vol.38 No.3
We consider the number of colors for colorings of links by the symmetric group S<sub>3</sub> of degree 3. For knots, such a coloring corresponds to a Fox 3-coloring, and thus the number of colors must be 1 or 3. However, for links, there are colorings by S<sub>3</sub> with 4 or 5 colors. In this paper, we show that if a 2-bridge link admits a coloring by S<sub>3</sub> with 5 colors, then the link also admits such a coloring with only 4 colors.
MULTIFUNCTIONAL POWER LINE COMPENSATOR FOR DISTRIBUTION POWER LINES
M.Ichihara,T Akiyama,H.Nara,K.Tamura,F.Ichikawa 전력전자학회 1998 ICPE(ISPE)논문집 Vol.- No.-
We propose a multifunctional power line compensator (PLC) which can individually compensate multiple impediments at the same time The PLC has the flexibility to share power to each compensation according to commands, this improving the working rate We constructed a 100 kVA PLC model including a controller with digital signal processor (DSP) to realize a multifunctional compensation The PLC was connected to a power receiving facility, and experimental results of multifunctional compensation were obtained.
Finite-Time Control for Linear Systems with Impulse Control
Hiroyuki Ichihara,Hitoshi Katayama 제어로봇시스템학회 2009 제어로봇시스템학회 국제학술대회 논문집 Vol.2009 No.8
This paper deals with finite-time stabilization and finite-time boundedness control problems for continuoustime linear time-varying systems with impulse control, which control is governed by discrete-time linear time-varying systems. Sufficient conditions are given for the existence of observer-based output feedback controllers that make a system finite-time stable and finite-time bounded, in terms of differential-difference linear matrix inequalities (DDLMIs). Assuming periodic solutions of the DDLMIs, numerically tractable design conditions for impulse control are given by LMIs. Numerical examples illustrate the design methods of observer-based output control as well as state feedback control.
Computational Approach to Input-to-State Stability Analysis of a Class of Nonlinear Systems
Hiroyuki Ichihara 제어로봇시스템학회 2009 제어로봇시스템학회 국제학술대회 논문집 Vol.2009 No.8
Numerically tractable conditions for input-to-state stability(ISS) analysis are given for a class of nonlinear systems. The seconditions originate from ISS inequalities for the cascade connection of the systems and the feedback interconnected system. If class of the systems is restricted such as polynomial ones, then it is possible to avail recent developed sum of squares relaxation of positive polynomials for ISS analysis. One of the keys of these formulations is to realize class K∞ functions, which has inverse map on real nonnegative region, by polynomials.