A strong edge coloring of a graph is a proper edge coloring in which every color class is an induced matching. The strong chromatic index χspGq of a graph G is the minimum number of colors in a strong edge coloring of G. Let ∆ ě 4 be an integer. In this note, we study the properties of the odd graphs, and show that every planar graph with maximum degree at most ∆ and girth at least 10∆ ́ 4 has a...

Approximate analytical formulas for the self-consistent renormalization of P,T-odd and P-odd weak nuclear potentials by the residual nucleon-nucleon strong interaction are derived. The contact spin-flip nucleon-nucleon interaction reduces the constant of the P,T-odd potential 1.5 times for the proton and 1.8 times for the neutron. Renormalization of the P-odd potential is caused by the velocity...

let g(v,e) be a graph with p vertices and q edges. a graph g is said to have an odd mean labeling if there exists a function f : v (g) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : e(g) → {1, 3, 5,...,2q - 1} defined by f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd is a bijection. a graph that admits an odd mean lab...

Music is one of the strongest triggers of emotions. Recent studies have shown strong emotional predispositions for musical instrument timbres. They have also shown significant correlations between spectral centroid and many emotions. Our recent study on spectral centroid-equalized tones further suggested that the even/odd harmonic ratio is a salient timbral feature after attack time and brightn...

It is now well established that at a superconductor/ferromagnet (S/F) interface an unconventional superconducting state arises in which the pairing is odd-frequency. The hallmark signature of this superconducting state is generally understood to be an enhancement of the electronic density of states (DoS) at subgap energies close to the S/F interface. However, here we show that an odd frequency ...

A detailed discussion of the point in polygon problem for arbitrary polygons is given. Two concepts for solving this problem are known in literature: the even–odd rule and the winding number, the former leading to ray-crossing, the latter to angle summation algorithms. First we show by mathematical means that both concepts are very closely related, thereby developing a first version of an algor...

Manifestations of P-,T-odd weak interaction between nucleons in nucleus are considered. Renormalization of this interaction due to residual strong interaction is studied. Mean squared matrix elements of P-,T-odd weak interaction between compound states are calculated. Correlators between P-,T-odd and P-odd, T-even weak interaction matrix elements between compound states are considered and estim...