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Norihiro Someyama

Publications and source records attributed to Norihiro Someyama.

7 recordsLinked to original sources
arXiv2021

Bulging Triangles: Generalization of Reuleaux Triangles

We introduce a bulging triangle like the generalization of the Reuleaux triangle. We may be able to propose various ways to bulge a triangle, but this paper presents the way so that its vertices are the same as them of the original triangle. We find some properties and theorems of our bulging triangles. In particular, we investigate, via calculus, whether basic facts such as triangle inequalities and Pythagorean theorem hold for bulging triangles.

math.GM↗
arXiv2021

Type-2 Fuzzy Initial Value Problems for Second-order T2FDEs

Type-2 fuzzy differential equations (T2FDEs) of order 1 are already known and the solution method of type-2 fuzzy initial value problems (T2FIVPs) for them was given by M. Mazandarani and M. Najariyan \cite{MN} in 2014. We give the solution method of second-order T2FIVPs in this paper. Furthermore, we would like to propose new notations for type-2 fuzzy theory where symbols tend to be complicated and misleading. In particular, the Hukuhara differential symbols introduced experimentally in this paper will give us clearler meanings and expressions.

math.GM↗
arXiv2020

Another Application of Dilation Analytic Method for Complex Lieb--Thirring Type Estimates

We consider non-self-adjoint Schrödinger operators $H_{\rm c}=-Δ+V_{\rm c}$ (resp. $H_{\rm r}=-Δ+V_{\rm r}$) acting in $L^2(\mathbb R^d)$, $d\ge 1$, with dilation analytic complex (resp. real) potentials. We were able to find out perhaps a new application of dilation analytic method in \cite{So1} (N. Someyama, "Number of Eigenvalues of Non-self-adjoint Schrödinger Operators with Dilation Analytic Complex Potentials," Reports on Mathematical Physics, Volume 83, Issue 2, pp.163-174 (2019).). We give a Lieb--Thirring type estimate on resonance eigenvalues of $H_{\rm c}$ in the open complex sector and that on embedded eigenvalues of $H_{\rm r}$ in the same way as \cite{So1}. To achieve that, we derive Lieb--Thirring type inequalities for isolated eigenvalues of $H$ on several complex subplanes.

math.SP↗
arXiv2020

Some Inclusion Relations for Fuzzy Sets

We give some inclusion relations for arbitrary fuzzy sets with reference to famous inequalities. In particular, we can know that the bounded sum and the algebraic product go well together. We would like to propose the concept of `Fuzzy Set Inequalities' through the present note.

math.GM↗
arXiv2020

Bounds and Gaps of Positive Eigenvalues of Magnetic Schrödinger Operators with No or Robin Boundary Conditions

We consider magnetic Schrödinger operators on a bounded region $Ω$ with the smooth boundary $\partial Ω$ in Euclidean space ${\mathbb R}^d$. In reference to the result from Weyl's asymptotic law and Pólya's conjecture, P. Li and S. -T. Yau(1983) (resp. P. Kröger(1992)) found the lower (resp. upper) bound $\frac{d}{d+2}(2π)^2({\rm Vol}({\mathbb S}^{d-1}){\rm Vol}(Ω))^{-2/d}k^{1+2/d}$ for the $k$-th (resp. ($k+1$)-th) eigenvalue of the Dirichlet (resp. Neumann) Laplacian. We show in this paper that this bound relates to the upper bound for $k$-th excited state energy eigenvalues of magnetic Schrödinger operators with the compact resolvent. Moreover, we also investigate and mention the gap between two energies of particles on the magnetic field. For that purpose, we extend the results by Li, Yau and Kröger to the magnetic cases with no or Robin boundary conditions on the basis of their ideas and proofs.

math.SP↗
arXiv2019

New Proofs of Triangle Inequalities

We give three new proofs of the triangle inequality in Euclidean Geometry. There seems to be only one known proof at the moment. It is due to properties of triangles, but our proofs are due to circles or ellipses. We aim to prove the triangle inequality as simple as possible without using properties of triangles.

math.GM↗