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Tomohiro Yamada

Publications and source records attributed to Tomohiro Yamada.

At least 37 records · Page 2Linked to original sources
arXiv2020

High Performance Heat Conductor with Small Spring Constant for Cryogenic Applications

We developed a soft and high thermal conductive heat link for cryogenic applications. The measured maximum thermal conductivity was approximately 18500 W/m/K at 10 K. This spring constant was 1/43 of that of a single thick wire with the same cross-sectional area at room temperature. We realized these performances by utilizing high purity aluminum (99.9999 %, 6N) and by stranding many thin wires that are 0.15 mm in diameter. The electrical Residual Resistivity Ratio (RRR) was also measured and used to estimate the thermal conductivity by Wiedemann-Franz law. We observed the size effect on the electrical conductivity, and evaluated the effect of mechanical deformation to the RRR. These evaluations allow us to design a pragmatic heat link for cryogenic application.

physics.ins-det↗
arXiv2020

Necessary conditions for binomial collisions

We shall give some necessary conditions for the equation $\binom{x}{a}=\binom{y}{b}$ to hold: if $\binom{2n+δ}{n-m}=\binom{2n+l}{n-k}$ with $δ=0$ or $1$, $0 (cn/\log n)^{40/21}$ for some constant $c$.

math.NT↗
arXiv2017

A generalization of the Ramanujan-Nagell equation

We shall show that, for any positive integer $D>0$ and any primes $p_1, p_2$ not dividing $D$, the diophantine equation $x^2+D=2^s p_1^k p_2^l$ has at most $63$ integer solutions $(x, k, l, s)$ with $x, k, l\geq 0$ and $s\in \{0, 2\}$.

math.NT↗
arXiv2017

Quasiperfect numbers with the same exponent

We study some divisibility properties of quasiperfect numbers. We show that if $N=(p_1 p_2 \cdots p_t)^{2a}=m^2$ is quasiperfect, then $2a+1$ is divisible by $3$ and $N$ has at least one prime factor smaller than $\exp 716.7944$. Moreover, we find some lower bounds concerning quasiperfect numbers of the form $N=m^2$ with $m$ squarefree.

math.NT↗
arXiv2015

Explicit Chen's theorem

We show that every even number $>\exp\exp 36$ can be represented as the sum of a prime and a product of at most two primes.

math.NT↗
arXiv2015

Explicit formulae for primes in arithmetic progressions, I

We shall give an explicit formula for $ψ(x, q, a)$ with an error term of the form $C/\log^αx$ under the condition that $q<\log^{α_1} x$ is nonexceptional, for various values of $α$ and $α_1$. We shall also give an explicit formula for $ψ(x, q, a)$ with error terms $C/\log^A x$ working whether $q$ is exceptional or nonexceptional, but under the condition that $\frac{0.4923A}πq^{1/2}\log^2 q<\log x/\log\log x$. Moreover, we shall give an explicit form of Bombieri-Vinogradov theorem over non-exceptional moduli.

math.NT↗
arXiv2007

On the divisibility of odd perfect numbers by a high power of a prime

We study some divisibility properties of multiperfect numbers. Our main result is: if $N=p_1^{α_1}... p_s^{α_s} q_1^{2β_1}... q_t^{2β_t}$ with $β_1, ..., β_t$ in some finite set S satisfies $σ(N)=\frac{n}{d}N$, then N has a prime factor smaller than C, where C is an effective computable constant depending only on s, n, S.

math.NT↗
arXiv2007

On some properties of $σ(N)$

We show asymptotic upper and lower bounds for the greatest common divisor of N and $σ(N)$. We also show that there are infinitely many integers N with fairly large g.c.d. of N and $σ(N)$.

math.NT↗