Related papers: Attainable numbers and the Lagrange spectrum
Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from…
The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, approximation theory worked as a…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.
The notion of the higher rank numerical range $\Lambda_{k}(L(\lambda))$ for matrix polynomials $L(\lambda)=A_{m}\lambda^{m}+...+A_{1}\lambda+A_{0}$ is introduced here and some fundamental geometrical properties are investigated. Further,…
We review recent progress in the studies of left handed materials.
Several recent papers have focused their attention in proving the correct analogue to the Lieb-Thirring inequalities for non self-adjoint operators and in finding bounds on the distribution of their eigenvalues in the complex plane. This…
A scheme is proposed for realizing simultaneous negative permittivity and negative permeability based on quantum coherence in a four-level dense atomic system here.Under some parametric conditions the system shows that simultaneous negative…
In this paper, we introduce a generalization of Balancing and Balancing-Lucas numbers. We describe some of their properties also we give the related matrix representation and divisibility properties.
Given an irrational number $\alpha$ consider its irrationality measure function $\psi_{\alpha}(t)=\min\limits_{1\le q\le t, q\in\mathbb{Z}}\|q\alpha\|$. The set of all values of $\lambda(\alpha)=(\limsup\limits_{t\to\infty}…
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.
The possibility of the resonance reflection (100 % at maximum) is revealed. The corresponding exactly solvable models with the controllable numbers of resonances, their positions and widths are presented.
In this note we compute values of global linear Harbourne constants over arbitrary fields for up to ten lines. These invariants have appeared recently in the discussions around the Bounded Negativity Conjecture. They seem to be of…
Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them. New inequalities for transcendental numbers are stated in Section 2 and…
The relative distance between eigenvalues of the compression of a not necessarily semibounded self-adjoint operator to a closed subspace and some of the eigenvalues of the original operator in a gap of the essential spectrum is considered.…
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
We give some remarks on limit mixed Hodge structure and spectrum. These are more or less well-known to the specialists, and do not seem to be stated explicitly in the literature. However, they do not seem to be completely trivial to the…
We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as…
In this article, intended for the Handbook of Recursion Theory, we survey recursion theory on the ordinal numbers, with sections devoted to $\alpha$-recursion theory, $\beta$-recursion theory and the study of the admissibility spectrum.
We define the notions of relative $e$-spectra, with respect to $E$-operators, relative closures, and relative generating sets. We study properties connected with relative $e$-spectra and relative generating sets.