It is known that a ring R is left Noetherian if and only if every left R-module has an injective (pre)cover. We show that (1) if R is a right n-coherent ring, then every right R-module has an (n, d)-injective (pre)cover; (2) if R is a ring such that every (n, 0)-injective right R-module is n-pure extending, and if every right R-module has an (n, 0)-injective cover, then R is right n-coherent. As applications of these results, we give some characterizations of (n, d)-rings, von Neumann regular rings and semisimple rings.
This paper provides an introduction to the economic analysis of R&D cooperation among firms. Basing on some stylized facts, we survey the relevant theoretical literature in order to discuss the benefits and the costs that firms face when they cooperate in R&D. We then analyze the pros and the cons of R&D cooperation from a policy-making perspective. We find that R&D cooperation is usually considered welfare improving and can be promoted by several policies. Finally, we discuss paths of research not yet taken in the theoretical literature.
We examine the problem of determining the solutions to the Diophantine equation n(n + d) . . . (n + (k - 1)d) = by(2), where d is fixed and the largest prime divisor of b is no more than Ck. Here, C is fixed but arbitrary. Under some rather minor conditions, it is shown that there are finitely many solutions that can be effectively computed. Some new, largely combinatorial, ideas are introduced into the general theory to handle the case of arbitrary C as considered here.
Stanoiu, M.
Canton, L.
Kozier, K. S.
Nankov, N.
Plompen, A.
Rao, R.
Roubtsov, D.
Rouki, C.
Svenne, J. P.
Interest has risen recently concerning the angular distribution of neutron elastic scattering on deuterium at low incident energies. The main subject is the amount of backscatter at energies below 3.2 MeV observed in differential cross-section measurements and represented in various evaluations. These various angles of approach encompass fundamental nuclear-data measurements, three-body nuclear-theory calculations, evaluated nuclear-data libraries and associated data processing, and the simulation of critical experiments involving heavy water. A new theoretical approach on the basis of three-nucleon theory was made that resulted in new angular distributions. At the GELINA neutron time-of-flight facility a new experimental setup was developed to measure elastic scattering of neutrons on deuterium in the energy range of interest. The technique proposed is complementary to the earlier works by detecting the scattered neutron instead of the recoiling deuterium. The setup is an array of two HPGe detectors, each with a B-10 neutron-gamma converter. Preliminary GELINA findings using a C6D6 target indicate less backscatter than predicted by ENDF/B-VII.0, in contrast to the nuclear-theory results. It is expected that completion of the planned work will reduce the uncertainty of the energy-angle distributions for deuterium elastic scattering and contribute to an improved deuterium evaluation in a future release of ENDF/B-VII.
Let n be a non-zero integer. A set of m positive integers {a 1, a 2, ... , a(m)} such that a(i)a(j) + n is a perfect square for all 1 <=3D i < j <=3D m is called a Diophantine m-tuple with the property D(n). In a series of papers, Dujella studied the quantity M-n =3D sup {vertical bar S vertical bar : S has the property D(n)} and showed for vertical bar n vertical bar >=3D 400 that M-n <=3D 15.476 log vertical bar n vertical bar and if vertical bar n vertical bar > 10(100), then M-n < 9.078 log vertical bar n vertical bar. We refine his argument to show that C-n <=3D 2 log vertical bar n vertical bar + O (log vertical bar n vertical bar/(log log vertical bar n vertical bar)(2)), where the implied constant is effectively computable and C-n =3D sup {|S boolean AND [1, n(2)]vertical bar : S has the property D(n)}. Together with earlier work of Dujella, this implies M-n <=3D 2.6071 log vertical bar n vertical bar + O (log vertical bar n vertical bar/(log log vertical bar n vertical bar(2)), where the implied constant is effectively computable.
Dzielak, Monika
Trzybinski, Damian
Czerwinska, Jolanta
Majchrzak, Bartosz
Tudek, Barbara
Wozniak, Krzysztof
Mieczkowski, Adam
N-(4-Bromobenzyl)-2-(5,6-dimethyl-1H-benzo[d]imidazol-2-yl)benzeneamine was obtained by condensation of N-(4-bromobenzyl)-3,1-benzoxazine-2,4-dione (N-(4-bromobenzyl)isatoic anhydride) with 4,5-dimethyl-1,2-phenylenediamine in refluxing acetic acid. This is a rare example of condensation of N-substituted 3,1-benzoxazine-2,4-dione with 1,2-phenylenediamine, which resulted in the formation of a benzimidazole derivative with a moderate yield. Crystallographic studies and initial biological screening were performed for the obtained product.
Mark Twain said he never had to remember anything because he always told the truth. Similarly, directors historically have not worried about what they did, because, if they acted in diligently and in good faith, they were shielded by the business judgment rule. However, recent developments, including both the results of notorious corporate scandals and the adoption of the Sarbanes-Oxley Act, with increased duties to monitor accounting and the relationship between the corporation and its auditors, appear to have increased the showing necessary to establish directors? compliance with the duties of care and loyalty. Elements of this showing may include the adoption of an internal audit function and increased scrutiny by the audit committee.