In describing musical performances, the use of the term vibrato can imply any periodic (or quasiperiodic) fluctuation in pitch, amplitude, or timbre of a sustained musical tone. The current study focused only upon analysis and evaluation of ‘pitch vibrato’ observed in recorded performances on a number of string instruments (three violins, a viola, a cello, and a bass violin). In order to gain a...

Denote by Tn,q the set of trees with n vertices and matching number q. Guo [On the Laplacian spectral radius of a tree, Linear Algebra Appl. 368 (2003) 379–385] gave the tree in Tn,q with the greatest value of the largest Laplacian eigenvalue. In this paper, we give another proof of this result. Using our method, we can go further beyond Guo by giving the tree in Tn,q with the second largest va...

The Q-state Potts model can be extended to noninteger and even complex Q by expressing the partition function in the Fortuin-Kasteleyn (F-K) representation. In the F-K representation the partition function Z(Q,a) is a polynomial in Q and v=a-1 (a=e(betaJ)) and the coefficients of this polynomial, Phi(b,c), are the number of graphs on the lattice consisting of b bonds and c connected clusters. W...

We show that by using a perturbed photonic Dirac-cone, one can realize ultra-narrow and finite Q-factor peak in the wavevector space, with both value width separately tunable. also discuss lower bound minimal viable given Q-value while maintaining sufficient Q differentiation among modes. The strong angular frequency Q-selection finds applications optical devices where angle- frequency-selectio...

It is demonstrated that any realistic model of quintessence should be based on Supergravity since, when the scalar field is on tracks today, Q ≈ m Pl. This improves the agreement between theoretical predictions and the current observations. In particular, a generic property is that ratio ωQ ≡ pQ/ρQ is pushed towards −1. A string-inspired model is proposed where the potential is given by V (Q) =...