We generalise our previous observation on the invariance of the Jarlskog determinant to matter effects in neutrino oscillations. Within the context of standard neutrino oscillation theory with matter effects, we present the complete set of (five) matter invariant observables for neutrino propagation in matter. We give some examples of their application. E-mail:[email protected] E-mail:w.g...

Let be a finite positive Borel measure supported on [−1, 1] and introduce the discrete Sobolev-type inner product 〈f, g〉 = ∫ 1 −1 f (x)g(x) d (x)+ K ∑ k=1 Nk ∑ i=0 Mk,if (ak)g (ak), where the mass points ak belong to [−1, 1], and Mk,i > 0(i = 0, 1, . . . , Nk). In this paper, we obtain generalized trace formula and asymptotics of the averagedTuran determinant for the Sobolev-type orthogonal pol...

In this paper, we examine the characteristics of titles (average length, proportion of titles with subtitles, proportion of interrogatory, and indicative titles) and how they changed over a substantial period of time (half a century). We consistently analyze core literature in five diverse fields, in order to probe the usage of titles as a disciplinary identity building tool. In addition, we st...

Within uncertain technological progress, a firm has to decide when to update its technology and select a new one among a non-decreasing range over time. Under constant return to scale, the best existing technology is implemented. Replacement is triggered not only when the firm operated technology is sufficiently obsolete but also the wedge between the latest and the state of the arts grades is ...

Representations of the wavefunction of the multiparticle Schrödinger equation using an unconstrained sum of Slater determinants have the potential to be very efficient, except that they cannot capture the interelectron cusp. To remedy this shortcoming, we extend these representations to include interelectron geminals and analyze the algorithmic implications of doing so.

Reflection algebras is a class of algebras associated with integrable models with boundaries. The coefficients of Sklyanin determinant generate the center of the reflection algebra. We give a combinatorial description of Sklyanin determinant suitable for explicit computations.

The structures and distributions of light nuclei are investigated within a microscopic correlation model. Two particle correlations are responsible for the scattering of model particles either to low momentum-or to high momentum-states. The low momentum states form the model space while the high momentum states are used to calculate the G-matrix. The three and higher order particle correlations...

We prove three conjectures concerning the evaluation of determinants, which are related to the counting of plane partitions and rhombus tilings. One of them has been posed by George Andrews in 1980, the other two are by Guoce Xin and Christian Krattenthaler. Our proofs employ computer algebra methods, namely the holonomic ansatz proposed by Doron Zeilberger and variations thereof. These variati...

Because QCD in four dimensions is renormalizable, not super-renormalizable, the fluctuations of the fermion determinant are significant at all physical scales. Fortunately the short distance behaviour of QCD is very well understood. In particular, we know that for sufficiently high momentum scales this physics should be accurately described by an improved gauge action. In the truncated determin...