The analysis of cross-correlations is extensively applied for understanding of interconnections in stock markets. Variety of methods are used in order to search stock cross-correlations including the Random Matrix Theory (RMT), the Principal Component Analysis (PCA) and the Hierachical ‎Structures.‎ In ‎this work‎, we analyze cross-crrelations between price fluctuations of 20 ‎company ‎stocks‎...

in this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

we investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. a self-adjoint linear operator a is defined in a suitable hilbert space h such that the eigenvalues of such a problem coincide with those of a . we discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. finally, we obtain th...

the purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of sturm-liouville problem with equation of the form w??=(?2f(x)?r(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in c2(a,b which has a single zero (so called turning point) at point 0x=x and r(x) is a continuously differentiable function. ...

A self a ne tile in R is a set T of positive Lebesgue measure satisfying A T d D T d where A is an expanding n n real matrix with j det A j m an integer and D fd dmg R n a set of m digits Self a ne tiles arise in many contexts including radix expansions fractal geometry and the construction of compactly sup ported orthonormal wavelet bases of L R They are also studied as interesting tiles In th...

In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...

An algebraic realization of the quantum rotor for non-zero spin values (integer as well as half-integer) is established by constructing a model Hamiltonian out of rotationally invariant functions of the generators of SU(3). The eigenvalues of this Hamiltonian in the leading normal-SU(3) symmetry for 25Mg and the so-called leading pseudo-SU(3) symmetries for 159Dy and 165Er are compared with the...

In this paper we consider the B-spline IgA approximation of the second-order eigenvalue problem −∆u = λu on Ω = (0, 1), with zero Dirichlet boundary conditions and with ∆ = ∑d j=1 ∂ ∂xj , d ≥ 1. We use B-splines of degree p = (p1, . . . , pd) and maximal smoothness and we consider the natural Galerkin approach. By using elementary tensor arguments, we show that the eigenvalue-eigenvector struct...

The stability analysis of islanded inverter-based microgrids (IBMGs) is increasingly an important and challenging topic due to the nonlinearity of IBMGs. In this paper, a new linear model for such microgrids as well as an iterative method to correct the linear model is proposed. Using the linear model makes it easy to analyze the eigenvalues and stability of IBMGs due to the fact that it derive...

In this note, we study some of the simplest algebraic self-maps of projective spaces. These maps, which we call monomial maps, are in one-to-one correspondence with nonsingular integer matrices, and are closely related to toral endomorphisms. In Theorem 1 we give a lower bound for the topological entropy of monomial maps and in Theorem 2 we give a formula for algebraic entropy (as defined by Be...