Mathematical analysis of the dynamics of COVID-19 in Africa under the influence of asymptomatic cases and re-infection

Coronavirus pandemic (COVID-19) hit the world in December 2019, and only less than 5% of the 15 million cases were recorded in Africa. A major call for concern was the significant rise from 2% in May 2020 to 4.67% by the end of July 15, 2020. This drastic increase calls for quick intervention in the transmission and control strategy of COVID-19 in Africa. A mathematical model to theoretically investigate the consequence of ignoring asymptomatic cases on COVID-19 spread in Africa is proposed in this study. A qualitative analysis of the model is carried out with and without re-infection, and the reproduction number is obtained under re-infection. The results indicate that increasing case detection to detect asymptomatically infected individuals will be very effective in containing and reducing the burden of COVID-19 in Africa. In addition, the fact that it has not been confirmed whether a recovered individual can be re-infected or not, then enforcing a living condition where recovered individuals are not allowed to mix with the susceptible or exposed individuals will help in containing the spread of COVID-19.     

Multiple silicon-hydrogen bond activations at adjacent rhodium and iridium centers

The reaction of 1 equiv of primary silanes, SiH(3)R (R = Ph, Mes), with [RhIr(CO)(3)(dppm)(2)] yields mono(silylene)-bridged complexes of the type [RhIr(H)(2)(CO)(2)(μ-SiHR)(dppm)(2)] (R = Ph or Mes), while for R = Ph the addition of 2 equiv yields the bis(silylene)-bridged complexes, [RhIr(CO)(2)(μ-SiHPh)(2)(dppm)(2)]. The kinetic isomer of this bis(silylene)-bridged product has the phenyl substituent axial on one silylene unit and equatorial on the other, and in the presence of excess silane this rearranges to the thermodynamically preferred "axial-axial" isomer, in which the phenyl substituents on each bridging silylene unit are axial and parallel to one another. The reaction of 1 equiv of diphenylsilane with [RhIr(CO)(3)(dppm)(2)] produces the mono(silylene)-bridged product, [RhIr(H)(2)(CO)(2)(μ-SiPh(2))(dppm)(2)], and the subsequent addition of silane in the presence of CO yields the silyl/silylene product [RhIr(H)(SiPh(2)H)(CO)(3)(κ(1)-dppm)(μ-SiPh(2))(dppm)]. The reaction of [RhIr(CO)(3)(dppm)(2)] with 2 equiv of SiH(2)Me(2) yields the analogous product [RhIr(H)(SiMe(2)H)(CO)(3)(κ(1)-dppm)(μ-SiMe(2))(dppm)]. Low-temperature NMR spectroscopic observation of some key intermediates, such as [RhIr(H)(SiH(2)Ph)(CO)(2)(μ-CO)(dppm)(2)], formed during the formation of the mono(silylene)-bridged species provides evidence for a mechanism involving initial Si-H bond activation at Rh, followed by the subsequent Si-H bond activation at Ir. The Si-H bond activation of a second equivalent of silane seems to be initiated by dissociation of the Rh-bound end of one diphosphine. The reaction of diphenylsilane with the cationic complex [RhIr(CH(3))(CO)(2)(dppm)(2)][CF(3)SO(3)] gives rise to a different reactivity pattern in which Si-H bond activation is initiated at Ir. In this case, the cationic silyl-bridged species, [RhIr(CH(3))(CO)(2)(κ(1):η(2)-SiHPh(2))(dppm)(2)][CF(3)SO(3)], contains an agostic Si-H interaction with Rh. In solution, at ambient temperature, this complex converts to two species, [RhIr(H)(COCH(3))(CO)(μ-H)(μ-SiPh(2))(dppm)(2)][CF(3)SO(3)] and [RhIr(CO)(2)(μ-H)(μ-SiPh(2))(dppm)(2)] [CF(3)SO(3)], formed by the competing methyl migration to CO and reductive elimination of methane, respectively. In the diphenylsilylene dihydride product, a weak interaction between the bridging silicon and the terminal Ir-bound hydride is proposed on the basis of NMR evidence.     

类星体Q1232+134及其多重红移系统

Q1234+134是1982年在室女座星系团区域内发现的一颗类星体。本文介绍了用UK Schmidt的物端棱镜巡天和美国Palomar山天文台5m望远镜的分光观测结果;列出了全部的发射线和它们的红移值Z_e=2.364±0.002;对吸收光谱进行了分析,给出了29根吸收线和两个较可靠的吸收线红移系统(Z_aⅠ=2.279,Z_aⅡ=2.249)及一个可能系统(Z_aⅢ=1.734)。最后,对本文的结果进行了讨论。     

Chimeric platinum-polyamines and DNA binding. Kinetics of DNA interstrand cross-link formation by dinuclear platinum complexes with polyamine linkers

The first observation of a polyamine-DNA interaction using 2D [(1)H, (15)N] HSQC NMR spectroscopy allows study of the role of the linker in polynuclear platinum-DNA interactions and a novel "anchoring" of the polyamine by Pt-DNA bond formation allows examination of the details of conformational B → Z transitions induced by the polyamine. The kinetics and mechanism of the stepwise formation of 5'-5' 1,4-GG interstrand cross-links (IXLs) by fully (15)N-labeled [{trans-PtCl((15)NH(3))(2)}(2){μ-((15)NH(2)(CH(2))(6)(15)NH(2)(CH(2))(6)(15)NH(2))}](3+) (1,1/t,t-6,6, 1) and [{trans-PtCl((15)NH(3))(2)}(2){μ-((15)NH(2)(CH(2))(6)(15)NH(2)(CH(2))(2)(15)NH(2)(CH(2))(6)(15)NH(2))}](4+) (1,1/t,t-6,2,6, 1') with the self-complementary oligonucleotide 5'-{d(ATATGTACATAT)(2)} (duplex I) are compared to the analogous reaction with 1,0,1/t,t,t (BBR3464) under identical conditions (pH 5.4, 298 K). Initial electrostatic interactions with the DNA are delocalized and followed by aquation to form the monoaqua monochloro species. The rate constant for monofunctional adduct formation, k(MF), for 1 (0.87 M(-1) s(-1)) is 3.5 fold higher than for 1,0,1/t,t,t (0.25 M(-1) s(-1); the value could not be calculated for 1' due to peak overlap). The evidence suggests that several conformers of the bifunctional adduct form, whereas for 1,0,1/t,t,t only two discrete conformers were observed. The combined effect of the conformers observed for 1 and 1' may play a crucial role in the increased potency of these novel complexes compared to 1,0,1/t,t,t. Treated as a single final product, the rate of formation of the 5'-5' 1,4-GG IXL, k(CH), for 1 (k(CH) = 4.37 × 10(-5) s(-1)) is similar to that of 1,0,1/t,t,t, whereas the value for 1' is marginally higher (k(CH) = 5.4 × 10(-5) s(-1)).     

Hyperfinite construction of G-expectation

The hyperfinite G-expectation is a nonstandard discrete analogue of G-expectation (in the sense of Robinsonian nonstandard analysis). A lifting of a continuous-time G-expectation operator is defined as a hyperfinite G-expectation which is infinitely close, in the sense of nonstandard topology, to the continuous-time G-expectation. We develop the basic theory for hyperfinite G-expectations and prove an existence theorem for liftings of (continuous-time) G-expectation. For the proof of the lifting theorem, we use a new discretization theorem for the G-expectation (also established in this paper, based on the work of Dolinsky et al. [Weak approximation of G-expectations, Stoch. Process. Appl. 122(2) (2012), pp. 664–675]).