Spectral stability of the Coulomb-Dirac Hamiltonian with anomalous magnetic moment

We show that the point spectrum of the standard Coulomb-Dirac operator H_0 is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment H_a as the anomaly parameter tends to 0. For negative angular momentum quantum number kappa, this holds for all Coulomb coupling constants c for which H_0 has a distinguished self-adjoint realisation. For positive kappa, however, there are some exceptional values for c, and in general an index shift between the eigenvalues of H_0 and the limits of eigenvalues of H_a appears, accompanied with additional oscillations of the eigenfunctions of H_a very close to the origin

On the characterization of the Friedrichs extension of ordinary or elliptic differential operators with a strongly singular potential

AbstractThe second-order singular elliptic differential operator T0u ≔ 1k{∑ Ds(astDtu) + qu} with Ds ≔ i∂s + bs is considered on C0∞(G) ⊂ L2(G; k) where G ≔ {x ¦ x ϵ Rn, 0 ⩽ 1 < ¦ x ¦ < m ⩽ ∞, n ⩾ 2}. (The general one-dimensional Sturm-Liouville operator is dealt with on an arbitrary interval (l, m) of the real line.) Conditions in addition to the usual ones are imposed on the coefficients which make T0 bounded from below (but still allow strong negative singularities of q at ∂G) so that it possesses a Friedrichs extension TF with domain D(TF) = {u ¦ u ϵ D(T0∗), there exists a sequence {uj} ⊂ C0∞(G) such that ∥uj − u ∥ → 0 and (T0(uj − uj′), uj − uj′) → 0 as j, j′ → ∞}. (1)Unifying and at the same time simplifying and generalizing ideas to be found in the work of Friedrichs [2, 3] and Kato [19] for the special case ast = δst, bs = 0, k = 1 it is shown that (1) can be characterized by D(TF) = {u ¦ u ϵ Hloc2(G) ∩ L2(G; k), ∫G ∑ ast(Dsu)(̄Dtu) dx < ∞, T0u ϵ L2(G; k)}. (2) If ∫ dttn − 1a(t) (a(t) smallest eigenvalue of (ast)) converges at l or m the boundary condition liminfr→l+m−∫|ξ|=1|u(rξ)|2dwn=0 (to be imposed on the “distinguished” representatives of the equivalence classes u ϵ Hloc2(G)) has to be added to (2).Equation (2) is derived without recourse to the theory of sesquilinear forms in Hilbert space so that the condition q+12u ϵ L2(G) (q+ positive part of q), which has to be assumed from the start when forms are considered (as Friedrichs and Kato do), can entirely be dispensed with. It is shown that it is a consequence of the other conditions to be imposed on u

Examining the Impact of Covid-19 Pandemic on Jordan's Tourism Industry: Income, Expenditures, and Revenues

Purpose: The worldwide COVID-19 pandemic will undoubtedly harm the world economy, according to the majority of economists, even though it is impossible to estimate the economic harm it will cause. This paper examines the Corona pandemic's economic effects on Jordan's tourism industry.   Theoretical Framework: In light of the changes that the world went through as a result of the Corona pandemic and its economic and social repercussions on most countries of the world, The industry of tourism and travel has been devastated by the Corona pandemic to a much greater extent than previous studies have suggested, and the recovery process is taking longer than the anticipated 10-month average recovery time. In order to ensure the expansion of the tourism sector's operational sustainability and capacity, both private and government procedures support needs to be coordinated.   Design/methodology/approach: By studying the monthly tourism income and the variables affecting it, such as the number of travelers coming to Jordanian airports, the number of booked hotel rooms, the number of overnight tourists and one-day visitors, and tourism spending, which is mainly affected by the number of Jordanians leaving the country for tourism purposes, using monthly data for the period from 2017 to the end of 2020.   Findings: The study showed the enormous effects of the Corona crisis on the tourism sector, as tourism income decreased by more than From 3 billion JOD, and the rate of decline in tourism income and spending for the year 2020 was more than 70% which resulted from a decrease in all variables affecting them at high rates that reached 100% in some months that witnessed complete closures.   Research, Practical &amp; Social implications: This paper Focus on the tourism industry sectors. The Chow Breakpoint test was applied to look at the crisis's starting point and determine whether there was a structural change. In this test, the data was split into two sub-samples (pre-crisis from 1/2017 to 2/2020 and the second period from 3/2020 to 12/2020) in order to see if there were any significant differences between the two periods, which determine whether there is a structural change or not. The test contrasts the squared remainders of each subsample equation and the entire sample equation.   Originality/value: A disease known as Corona (COVID-19) has recently taken over the world. As a result of industrial closure projects, this disease has forced changes in the industry's performance and operations, adding to the study's originality and raising important questions about its recovery implications. About Jordan's tourism industry. The knowledge gap between economic science and the general public is characterized and critically analyzed in this paper after COVID-19

[rac-2-(1-Amino­eth­yl)phenyl-κ2 C 1,N](ethyl­endiamine-κ2 N,N′)palladium(II) 3-methyl­benzoate monohydrate

In the title compound, [Pd(C8H10N)(C2H8N2)](C8H7O2)·H2O, the palladium ion is coordinated in a distorted square-planar fashion by the two N atoms from the chelating ethyl­enediamine group and by the N and a C atom of the deprotonated chiral amine. The resulting cationic complex, the 3-methyl­benzoate anion and the hydrate water mol­ecule are inter­connected by N—H⋯O and O—H⋯O hydrogen bonds

Debilitating consequences of drooling

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The political role of intellectuals

The article points out that the role of intellectuals in society and its relationship with the government amid the unfolding global financial crisis affected all spheres of social life. The authors proceed from the assumption that a change in the very nature of society, the increasing complexity and accelerating social dynamics, involves changing social community and "intelligentsia" in terms of structural and functional features. It is the rate of flow of social processes in the modern and continuously establishing society has led the authors to the treatment allocation of functional features, which constitute the social community of intellectuals. We believe that intelligentsia carries two major functions in society: stabilization of its social system and the function of its critical analysis. These features obviously have a different direction of its vector, hence, we base our reasoning on the ideas of Gramsci and distinguish its two types: conventional and organic

Introduction

This is my introduction to the special issue on Evolution and Moral Epistemology that I edited for Ratio. Political Philosophy and Ethic