arXiv subjects

J. Rodrigo

Publications and source records attributed to J. Rodrigo.

5 recordsLinked to original sources

arXiv2025

On the minimum number of non-monochromatic simplices for Sperner labelings of a regular triangulation

Attending to an open problem in the literature stated by Mirzakhani and Vondr\'ak, we give a lower bound of the number of non-monochromatic simplices for Sperner labelings of the vertices of a triangulation of a given $ k$-simplex with vertices of integer coordinates. This triangulation maximizes the number of simplices over all the triangulations of the $ k$-simplex with vertices of integer coordinates.

math.CO↗

arXiv2024

Markoff $m$-triples with $k$-Fibonacci components

We classify all solution triples with $k$-Fibonacci components to the equation $x^2+y^2+z^2=3xyz+m,$ where $m$ is a positive integer and $k\geq 2$. As a result, for $m=8$, we have the Markoff triples with Pell components $(F_2(2), F_2(2n), F_2(2n+2))$, for $n\geq 1$. For all other $m$ there exists at most one such ordered triple, except when $k=3,$ $a$ is odd, $b$ is even and $b\geq a+3$, where $(F_3(a),F_3(b),F_3(a+b))$ and $(F_3(a+1),F_3(b-1),F_3(a+b))$ share the same $m$.

math.GM↗

arXiv2024

A classification of Markoff-Fibonacci m-triples

We classify all solution triples with Fibonacci components to the equation $a^2+b^2+c^2=3abc+m,$ for positive $m$. We show that for $m=2$ they are precisely $(1,F(b),F(b+2))$, with even $b$; for $m=21$, there exist exactly two Fibonacci solutions $(1,2,8)$ and $(2,2,13)$ and for any other $m$ there exists at most one Fibonacci solution, which, in case it exists, is always minimal (i.e. it is a root of a Markoff tree). Moreover, we show that there is an infinite number of values of $m$ admitting exactly one such solution.

math.NT↗

arXiv2014

Disorder driven inhomogeneous phase in the 2D-superconducting film of titanium nitride

Typically the superconducting phase weakens at several points with the increase in disorder before it is distroyed in the 2d-thin films. This may lead to an inhomogeneous superconducting state without a continuous phase. Here we present scanning tunneling spectroscopy measurements at 0.1 K in the disordered polycrystalline film of TiN describing the nanoscale size features of the superconducting state. The imaging shows imcommensurate charge density modulations, originating at the crystalline bounadries, and intercepted on large scale by the beat patterns in the regions of overlap. Electronic coherence is maintained over length scale minimum of crystalline sizes, and suffers scattering across low angle crystalline boundaries. The superconducting state fluctuates at the positions of the charge density modulations and zones of the weak phase appear in the vicinity of the beats. Our data shows that the BCS-like behavior evolves into the V-shaped density of states in such inhomogeneous regions as a result of the competition between the superconducting correlations with that of the strong electron-electron repulsive interactions assisted by the inelastic scattering at the crystalline boundaries.

cond-mat.supr-con↗

arXiv2014

Conductance behavior with temperature and magnetic field in the disordered films of titanium nitride

We report in this paper the temperature and mangetic field dependence of the conductance in the polycrystalline film of titanium nitride, before and after heating at ambient conditions. The difference between the two films is the room temperature sheet resistance which remains within 15 percent and both the films show superconducting transition at lower temperatures. The zero field and the high field data, respectively, corresponds to the superconducting and the normal states. Both the films display Atshuler-Aronov zero bias anamoly in their normal states, and the superconducting gap openeing up at low fields. However the heated film has a smaller gap owing to more pronounced zero bias suppression of the density of states. The normal states in both the films are similar to the quasi-2d-disordered metal and its behavior is studied with temperature. Our data suggests that the zero bias anamoly suppresses the superconducting gap with increase in the disorder.

cond-mat.supr-con↗