‎‎we exhibit an explicit construction for the second cohomology group‎ ‎$h^2(l‎, ‎a)$ for a lie ring $l$ and a trivial $l$-module $a$‎. ‎we show how the elements of $h^2(l‎, ‎a)$ correspond one-to-one to the‎ ‎equivalence classes of central extensions of $l$ by $a$‎, ‎where $a$‎ ‎now is considered as an abelian lie ring‎. ‎for a finite lie‎ ‎ring $l$ we also show that $h^2(l‎, ‎c^*) cong m(l)$‎...

LetG be a finite p-group,K a field of characteristic p, and J the radical of the group algebra K[G]. We study modular representations using some new results of the theory of extensions of modules. More precisely, we describe the K[G]-modules M such that J2M = 0 and give some properties and isomorphism invariants which allow us to compute the number of isomorphism classes of K[G]-modulesM such t...

It is well-known that a ring R is semiperfect if and only if RR (or RR) is a supplemented module. Considering weak supplements instead of supplements we show that weakly supplemented modules M are semilocal (i.e., M/Rad(M) is semisimple) and that R is a semilocal ring if and only if RR (or RR) is weakly supplemented. In this context the notion of finite hollow dimension (or finite dual Goldie d...

Evidence suggests that compression and shear wave elastography are sensitive to the mechanical property changes occuring in dying cells following chemotherapy, and can hence be used to monitor cancer treatment response. A qualitative and quantitative understanding of the mechanical changes at the cellular level would allow to better infer how these changes affect macroscopic tissue mechanical p...

We introduce the cylindrical module A♮H, where H is a Hopf algebra with S2 = idH and A is a Hopf module algebra over H. We show that there exists a cyclic map between the cyclic module of the crossed product algebra A⋊H and ∆(A♮H), the cyclic module related to the diagonal of A♮H. In the cocommutative case, ∆(A♮H) ∼= C•(A ⋊H). Finally we approximate ∆(A♮H) by a spectral sequence and we give an ...

This paper focuses on the geometric theory of scroll compressor, which includes the determination of the discharge angle, the calculation of the volume in different compression stages, the axial gas force under the condition that the number of scroll turns equals an arbitrary real number. NOMENCLATURE . (J :expanding angle of the involute (rad) a :initial angle of the involute (rad) 6 : orbitin...

ObjectivesTo our knowledge no previous study has assessed the performance of a rapid antigen diagnostic immunoassay (RAD) conducted at point care (POC). We evaluated Panbio™ COVID-19 Ag Rapid Test Device for diagnosis coronavirus 2019 disease (COVID-19) in symptomatic patients (n = 412) attending primary healthcare centres.MethodsRAD was performed immediately after sampling following manufactur...

Six double mutants and a quadruple mutant were derived from four UV radiation-hypersensitive single mutants (rad-1, rad-2, rad-3 and rad-7). Sensitivities of the 11 strains to UV, gamma-radiation and methyl methanesulfonate (MMS) were compared. Of the six double mutants, only the rad-1;rad-2 and rad-3;rad-7 doubles were no more hypersensitive than the most sensitive single mutant to UV-radiatio...

The use of the bone marrow culture technique was studied as a means to prepare donor marrow for bone marrow transplantation to avoid lethal graft-versus-host disease (GVHD). Preliminary experiments demonstrated the rapid loss of theta-positive cells in such cultures, so that theta-positive cells were not detected after 6 days. Initial experiments in C3H/HeJ (H-2k, Hbbd) recipients prepared with...