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We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
We introduce a new method for computing spectra of molecules for which a spin-spin term in the Hamiltonian has an important effect. In previous calculations, matrix elements of the spin-spin term and of the potential were obtained by…
We construct a family of integrable vertex model based on the typical four-dimensional representations of the quantum group deformation of the Lie superalgebra $sl(2|1)$. Upon alternation of such a representation with its dual this model…
We study resonant x-ray scattering (RXS) at Np M_{4,5} edges in the triple-\textbf{k} multipole ordering phase in NpO_{2}, on the basis of a localized electron model. We derive an expression for RXS amplitudes to characterize the spectra…
An S matrix approach is developed to describe elastic scattering resonances of systems where the scattered particle is asymptotically confined and the scattering potential lacks continuous symmetry. Examples are conductance resonances in…
The standard model of leptons is extended to accommodate a discrete Z_3 X Z_2 family symmetry. After rotating the charged-lepton mass matrix to its diagonal form, the neutrino mass matrix reveals itself as very suitable for explaining…
We develop a matrix bordering technique that can be applied to an irreducible spectrally arbitrary sign pattern to construct a higher order spectrally arbitrary sign pattern. This technique generalizes a recently developed triangle…
As neutrino experiments are starting to probe the detailed structure of the neutrino mass matrix, we present sumrules relating its matrix elements for a class of models with approximate $L_e-L_{\mu}-L_{\tau}$ symmetry and the observables in…
In this article we show the existence of limiting spectral distribution of a symmetric random matrix whose entries come from a stationary Gaussian process with covariances satisfying a summability condition. We provide an explicit…
A new method is proposed for fitting non-relativistic binary-scattering data and for extracting the parameters of possible quantum resonances in the compound system that is formed during the collision. The method combines the well-known…
We study the scattering theory for the Gross-Neveu model on the half-line. We find the reflection matrices for the elementary fermions, and by fusion we compute the ones for the two-particle bound-states, showing that they satisfy…
The sum-product conjecture of Erd\H os and Szemer\'edi states that, given a finite set $A$ of positive numbers, one can find asymptotic lower bounds for $\max\{|A+A|,|A\cdot A|\}$ of the order of $|A|^{1+\delta}$ for every $\delta <1$. In…
We give an efficient algorithm which can obtain a relative error approximation to the spectral norm of a matrix, combining the power iteration method with some techniques from matrix reconstruction which use random sampling.
Consider an $n \times p$ data matrix $X$ whose rows are independently sampled from a population with covariance $\Sigma$. When $n,p$ are both large, the eigenvalues of the sample covariance matrix are substantially different from those of…
We study the constraints imposed by neutrino oscillation experiments on the minimal extension of the Standard Model that can explain neutrino masses, which requires the addition of just two singlet Weyl fermions. The most general…
The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact…
The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of identifying symmetric signings of matrices with natural spectral…
Curious spectral properties of an ensemble of random unitary matrices appearing in the quantization of a map p -> p+alpha, q -> q+f(p+alpha) in [Giraud et al. nlin.CD/0403033] are investigated. When alpha=m/n with integer co-prime m,n and…
In this thesis, the possibility of interpreting the solar and atmospheric neutrino data within the context of theoretical models is being explored. In particular, the implications of the Minimal Supersymmetric Standard Model augmented by a…
We use super-spectral curve to investigate irregular conformal states of integer and half-odd integer rank. The spectral curve is the loop equation of supersymmetrized irregular matrix model. The case of integer rank corresponds to the…