Comparison results between Jacobi and other iterative methods

AbstractSome comparison results between Jacobi iterative method with the modified preconditioned simultaneous displacement (MPSD) iteration and other iterations, for solving nonsingular linear systems, are presented. It is showed that spectral radius of Jacobi iteration matrix B is less than that of several iteration matrices introduced in Liu (J. Numer. Methods Comput. Appl. 1 (1992) 58) under some conditions

(1R,3S,5R,6S)-6-Acet­oxy-3-(4-methyl­phenyl­sulfon­yloxy)tropane

In the title compound [systematic name: (1R,3S,5R,6S)-8-methyl-3-(4-methyl­phenyl­sulfon­yloxy)-8-aza­bicyclo­[3.2.1]octan-6-yl acetate], C17H23NO5S, the fused piperidine ring exists in a chair conformation with the N atom and one C atom displaced by 0.876 (2) and −0.460 (3) Å, respectively, on opposite sides of the mean plane defined by the other four atoms. The fused pyrrolidine ring adopts an envelope conformation with the N atom deviating by 0.644 (3) Å from the mean plane of the other four atoms

Rate and equilibrium constants for the addition of triazolium salt derived N-heterocyclic carbenes to heteroaromatic aldehydes

Heteroaromatic aldehydes are often used preferentially or exclusively in a range of NHC-catalysed processes that proceed through the generation of a reactive diaminoenol or Breslow Intermediate (BI), with the reason for their unique reactivity currently underexplored. This manuscript reports measurement of rate and equilibrium constants for the reaction between N-aryl triazolium NHCs and heteroaromatic aldehydes, providing insight into the effect of the NHC and heteroaromatic aldehyde structure up to formation of the BI. Variation in NHC catalyst and heteroaromatic aldehyde structure markedly affect the observed kinetic parameters of adduct formation, decay to starting materials and onward reaction to BI. In particular, large effects are observed with both 3-halogen (Br, F) and 3-methyl substituted pyridine-2-carboxaldehyde derivatives which substantially favour formation of the tetrahedral intermediate relative to benzaldehyde derivatives. Key observations indicate that increased steric hindrance leads to a reduction in both k2 and k−1 for large (2,6-disubstituted)-N-Ar groups within the triazolium scaffold, and sterically demanding aldehyde substituents in the 3-position, but not in the 6-position of the pyridine-2-carboxaldehyde derivatives. As part of this study, the isolation and characterisation of twenty tetrahedral adducts formed upon addition of N-aryl triazolium derived NHCs into heteroaromatic aldehydes are described. These adducts are key intermediates in NHC-catalysed umpolung addition of heteroaromatic aldehydes and are BI precursors

Vitamin C Prevents Hypogonadal Bone Loss

Epidemiologic studies correlate low vitamin C intake with bone loss. The genetic deletion of enzymes involved in de novo vitamin C synthesis in mice, likewise, causes severe osteoporosis. However, very few studies have evaluated a protective role of this dietary supplement on the skeleton. Here, we show that the ingestion of vitamin C prevents the low-turnover bone loss following ovariectomy in mice. We show that this prevention in areal bone mineral density and micro-CT parameters results from the stimulation of bone formation, demonstrable in vivo by histomorphometry, bone marker measurements, and quantitative PCR. Notably, the reductions in the bone formation rate, plasma osteocalcin levels, and ex vivo osteoblast gene expression 8 weeks post-ovariectomy are all returned to levels of sham-operated controls. The study establishes vitamin C as a skeletal anabolic agent. © 2012 Zhu et al

(1R,3S,5R,6S)-6-Acet­oxy-8-methyl-3-(p-tolyl­sulfon­yloxy)-8-azoniabicyclo­[3.2.1]octane (2R,3R)-2,3-bis­(benzo­yloxy)-3-carboxy­propanoate

The title compound, C17H24NO5S+·C18H13O8 −, is the key inter­mediate during the preparation of lesatropane [systematic name (1R,3S,5R,6S)-6-acetoxy-3-(4-methylphenylsulfonyloxy)tropane], a potential anti­glaucoma agent. The tertiary N atom of the tropane ring is involved in inter­molecular N—H⋯O hydrogen bonding, and the carboxylate groups are involved in inter­molecular O—H⋯O hydrogen bonding

Simultaneous evolutionary expansion and constraint of genomic heterogeneity in multifocal lung cancer.

Recent genomic analyses have revealed substantial tumor heterogeneity across various cancers. However, it remains unclear whether and how genomic heterogeneity is constrained during tumor evolution. Here, we sequence a unique cohort of multiple synchronous lung cancers (MSLCs) to determine the relative diversity and uniformity of genetic drivers upon identical germline and environmental background. We find that each multicentric primary tumor harbors distinct oncogenic alterations, including novel mutations that are experimentally demonstrated to be functional and therapeutically targetable. However, functional studies show a strikingly constrained tumorigenic pathway underlying heterogeneous genetic variants. These results suggest that although the mutation-specific routes that cells take during oncogenesis are stochastic, genetic trajectories may be constrained by selection for functional convergence on key signaling pathways. Our findings highlight the robust evolutionary pressures that simultaneously shape the expansion and constraint of genomic diversity, a principle that holds important implications for understanding tumor evolution and optimizing therapeutic strategies.Across cancer types tumor heterogeneity has been observed, but how this relates to tumor evolution is unclear. Here, the authors sequence multiple synchronous lung cancers, highlighting the evolutionary pressures that simultaneously shape the expansion and constraint of genomic heterogeneity

Outstanding hydrogen evolution reaction catalyzed by porous nickel diselenide electrocatalysts

To relieve our strong reliance on fossil fuels and to reduce greenhouse effects, there is an ever-growing interest in using electrocatalytic water splitting to produce green, renewable, and environment-benign hydrogen fuel via the hydrogen evolution reaction. For commercially feasible water electrolysis, it is imperative to develop electrocatalysts that perform as efficiently as Pt but using only earth-abundant commercial materials. However, the highest performance current catalysts consist of nanostructures made by using complex methods. Here we report a porous nickel diselenide (NiSe_2) catalyst that is superior for water electrolysis, exhibiting much better catalytic performance than most first-row transition metal dichalcogenide-based catalysts, well-studied MoS_2, and WS_2-based catalysts. Indeed NiSe2 performs comparably to the state-of-the-art Pt catalysts. We fabricate NiSe_2 directly from commercial nickel foam by acetic acid-assisted surface roughness engineering. To understand the origin of the high performance, we use first-principles calculations to identify the active sites. This work demonstrates the commercial possibility of hydrogen production via water electrolysis using porous bulk NiSe_2 catalysts

Efficient hydrogen evolution by ternary molybdenum sulfoselenide particles on self-standing porous nickel diselenide foam

With the massive consumption of fossil fuels and its detrimental impact on the environment, methods of generating clean power are urgent. Hydrogen is an ideal carrier for renewable energy; however, hydrogen generation is inefficient because of the lack of robust catalysts that are substantially cheaper than platinum. Therefore, robust and durable earth-abundant and cost-effective catalysts are desirable for hydrogen generation from water splitting via hydrogen evolution reaction. Here we report an active and durable earth-abundant transition metal dichalcogenide-based hybrid catalyst that exhibits high hydrogen evolution activity approaching the state-of-the-art platinum catalysts, and superior to those of most transition metal dichalcogenides (molybdenum sulfide, cobalt diselenide and so on). Our material is fabricated by growing ternary molybdenum sulfoselenide particles on self-standing porous nickel diselenide foam. This advance provides a different pathway to design cheap, efficient and sizable hydrogen-evolving electrode by simultaneously tuning the number of catalytic edge sites, porosity, heteroatom doping and electrical conductivity