Rings having normality in terms of the Jacobson radical

A ring R is defined to be J-normal if for any a, r∈ R and idempotent e∈ R, ae= 0 implies Rera⊆ J(R) , where J(R) is the Jacobson radical of R. The class of J-normal rings lies between the classes of weakly normal rings and left min-abel rings. It is proved that R is J-normal if and only if for any idempotent e∈ R and for any r∈ R, R(1 - e) re⊆ J(R) if and only if for any n≥ 1 , the n× n upper triangular matrix ring Un(R) is a J-normal ring if and only if the Dorroh extension of R by Z is J-normal. We show that R is strongly regular if and only if R is J-normal and von Neumann regular. For a J-normal ring R, it is obtained that R is clean if and only if R is exchange. We also investigate J-normality of certain subrings of the ring of 2 × 2 matrices over R. © 2018, The Author(s)

A space–time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation

We introduce a space–time Trefftz discontinuous Galerkin method for the first-order transient acoustic wave equations in arbitrary space dimensions, extending the one-dimensional scheme of Kretzschmar et al. (IMA J Numer Anal 36:1599–1635, 2016). Test and trial discrete functions are space–time piecewise polynomial solutions of the wave equations. We prove well-posedness and a priori error bounds in both skeleton-based and mesh-independent norms. The space–time formulation corresponds to an implicit time-stepping scheme, if posed on meshes partitioned in time slabs, or to an explicit scheme, if posed on “tent-pitched” meshes. We describe two Trefftz polynomial discrete spaces, introduce bases for them and prove optimal, high-order h-convergence bounds

Factors affecting innovation and imitation of ICT in the agrifood sector

Diffusion of innovations has gained a lot of attention and concerns different scientific fields. Many studies, which examine the determining factors of technological innovations in the agricultural and agrifood sector, have been conducted using the widely used Technology Accepted Model, for a random sample of farmers or firms engaged in agricultural sector. In the present study, a holistic examination of the determining factors that affect the propensity of firms to innovate or imitate, is conducted. The diffusion of ICT tools of firms which are engaged in the NACE 02/03 as well as in the NACE 10/11 classifications for 49 heterogeneous national markets is examined, using the Bass model. The innovation parameter is positively associated with rural income, female employment, export activity and education of farmers, while the imitation parameter is increased in countries whose societies are characterized by uncertainty avoidance

Mass Violence and the Kurds: Introduction to the Special Issue

The Kurds’ experience with modern mass violence is long and complex. Whereas Kurds lived under the Kurdish Emirates for centuries in pre-national conditions in the Ottoman and Persian empires, the advent of nationalism and colonialism in the Middle East radically changed the situation. W

De toekomst van Turkije is niet veilig onder Erdogan

Middle Eastern Studie

Design and synthesis of Kekulè and non-Kekulè diradicaloids via radical peri-annulation strategy: the power of seven Clar’s sextets

This work introduces an approach to uncoupling electrons via maximum utilization of localized aromatic units, i.e., the Clar’s sextets. To illustrate the utility of this concept to the design of Kekulé diradicaloids, we have synthesized a tridecacyclic polyaromatic system where a gain of five Clar’s sextets in the open shell form overcomes electron pairing and leads to the emergence of high degree of diradical character. According to unrestricted symmetry-broken UCAM-B3LYP DFT calculations, the singlet diradical character in this core system is characterized by the y0 value of 0.98 (y0 = 0 for closed shell molecule, y0 = 1 for pure diradical). The efficiency of the new design strategy was evaluated by comparing the Kekulé system with an isomeric non-Kekulé diradical of identical size, i.e., a system where the radical centers cannot couple via resonance and the high-spin ground state is unavoidable. The calculated singlet-triplet gap, i.e., the 〖ΔE〗_ST values, in both of these systems approach zero: -0.3 kcal/mol for the Kekulé and +0.2 kcal/mol for the non-Kekulé diradicaloids. The target isomeric Kekulé and non-Kekulé systems were assembled using a sequence of radical peri-annulations, cross-coupling and C-H activation. The diradicals are kinetically stabilized by six tert-butyl substituents and (triisopropylsilyl)acetylene groups. The Kekulé diradicaloid (K) has a half-life of 42 h under ambient conditions (i.e., exposure to air at the room temperature) while the non-Kekulé diradicaloid (NK) has a half-life of 2h. Both molecules are NMR-inactive but EPR-active at room temperature. The magnetic properties of the Kekulé diradicaloid was studied by superconducting quantum interference device (SQUID) to provide the experimental singlet-triplet energy gap, 〖ΔE〗_ST (K) = -0.8 kcal/mol, which was close to calculated value. Cyclic voltammetry revealed quasi-reversible two-electron oxidation and reduction processes, consistent with the presence of two degenerate partially occupied molecular orbitals