Faulhaber's Theorem on Power Sums

We observe that the classical Faulhaber's theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression $a+b, a+2b, ..., a+nb$ is a polynomial in $na+n(n+1)b/2$. While this assertion can be deduced from the original Fauhalber's theorem, we give an alternative formula in terms of the Bernoulli polynomials. Moreover, by utilizing the central factorial numbers as in the approach of Knuth, we derive formulas for $r$-fold sums of powers without resorting to the notion of $r$-reflexive functions. We also provide formulas for the $r$-fold alternating sums of powers in terms of Euler polynomials.Comment: 12 pages, revised version, to appear in Discrete Mathematic

The Hypolipidemic Activity of Heterocyclic Thiosemicarbazones, Thioureas and Their Metal Complexes in Sprague Dawley Male Rats

Heterocyclic thiosemicarbazones, thioureas and their copper, nickel, and cobalt complexes were shown to be potent hypolipidemic agents in male Sprague Dawley rats at 8 mg/kg/day, orally. These agents lowered the activity of rat hepatic rate limiting enzymes for the synthesis of cholesterol and triglycerides. The effects of these agnets on cytoplasmic ATP-dependent citrate lyase, acetyl CoA synthetase and HMG-CoA reductase activities were reduced by a magnitude to explain the reduction of serum cholesterol levels afforded by the compounds. The reduction of acetyl CoA carboxylase, sn-glycerol-3-phosphate synthetase and phosphotidylate phosphohydrolase activities caused by the derivatives is of sufficient magnitude to explain the observed reduction in serum triglycerides after administration of the agents

The Anti-Inflammatory Activity of Boron Derivatives in Rodents

Acyclic amine-carboxyboranes were effective anti-inflammatory agents in mice at 8 mg/kg x 2. These amine-carboxyboranes were more effective than the standard indomethacin at 8 mg/kg x 2, pentoxifylline at 50 mg/kg x 2, and phenylbutazone at 50 mg/kg x 2. The heterocyclic amine derivatives as well as amine-carbamoylboranes, carboalkoxyboranes, and cyanoboranes were generally less active. However, selected aminomethyl-phosphonate-N-cyanoboranes demonstrated greater than 60% reduction of induced inflammation. The boron compounds were also active in the rat induced edema, chronic arthritis, and pleurisy screens, demonstrating activity similar to the standard indomethacin. The compounds were effecive in reducing local pain and decreased the tail flick reflex to pain. The derivatives which demonstrated good anti-inflammatory activity were effective inhibitors of hydrolytic lysosomal, and proteolytic enzyme activities with IC50 50 values equal to -6M in mouse macrophages, human leukocytes, and Be Sal osteofibrolytic cells. In these same cell lines, the agents blocked prostaglandin cyclooxygenase activity with IC50 values of -6M. In mouse macrophage and human leukocytes, 5′ lipoxygenase activity was also inhibited by the boron derivatives with IC50 values of 10-6M. These IC50 values for inhibition of these enzyme activities are consistent with published values of known anti-inflammatory agents which target these enzymes

The Hypolipidemic Activity of Boronated Nucleosides in Male Mice and Rats

The boronated nucleosides with varying bases and sugar moieties were shown to be potent hypolipidemic agents in rodents. The 3′– aminocynaoborane dideoxythymidine derivative caused reductions in serum cholesterol and triglyceride levels, tissue lipids, VLDL and LDL cholesterol levels while elevating HDL cholesterol levels in rodents. The agents suppressed rat hepatic acetyl CoA synthetase, HMG-CoA reductase, acyl-CoA cholesterol acyl transferase, phosphatidylate phosphohydrolase and lipoprotein lipase activities while elevating cholesterol-7α-hydroxylase activity from 25 to 100 μM

Bioluminescence Imaging of Heme Oxygenase-1 Upregulation in the Gua Sha Procedure

Gua Sha is a traditional Chinese folk therapy that employs skin scraping to cause subcutaneous microvascular blood extravasation and bruises. The protocol for bioluminescent optical imaging of HO-1-luciferase transgenic mice reported in this manuscript provides a rapid in vivo assay of the upregulation of the heme oxygenase-1 (HO-1) gene expression in response to the Gua Sha procedure. HO-1 has long been known to provide cytoprotection against oxidative stress. The upregulation of HO-1, assessed by the bioluminescence output, is thought to represent an antioxidative response to circulating hemoglobin products released by Gua Sha. Gua Sha was administered by repeated strokes of a smooth spoon edge over lubricated skin on the back or other targeted body part of the transgenic mouse until petechiae (splinter hemorrhages) or ecchymosis (bruises) indicative of extravasation of blood from subcutaneous capillaries was observed. After Gua Sha, bioluminescence imaging sessions were carried out daily for several days to follow the dynamics of HO-1 expression in multiple internal organs

The \u3cem\u3eChlamydomonas\u3c/em\u3e Genome Reveals the Evolution of Key Animal and Plant Functions

Chlamydomonas reinhardtii is a unicellular green alga whose lineage diverged from land plants over 1 billion years ago. It is a model system for studying chloroplast-based photosynthesis, as well as the structure, assembly, and function of eukaryotic flagella (cilia), which were inherited from the common ancestor of plants and animals, but lost in land plants. We sequenced the ∼120-megabase nuclear genome of Chlamydomonas and performed comparative phylogenomic analyses, identifying genes encoding uncharacterized proteins that are likely associated with the function and biogenesis of chloroplasts or eukaryotic flagella. Analyses of the Chlamydomonas genome advance our understanding of the ancestral eukaryotic cell, reveal previously unknown genes associated with photosynthetic and flagellar functions, and establish links between ciliopathy and the composition and function of flagella

Regional variations in and correlates of disability-free life expectancy among older adults in China

<p>Abstract</p> <p>Background</p> <p>Considerable socioeconomic and health inequalities have been reported in China. However, because of a lack of appropriate data, limited research has been conducted on variations in disability-free life expectancy (DFLE) among older adults. This study aimed to use the most up-to-date disability survey data to explore geographical variations in DFLE at age 60 in China and to identify the socioeconomic and health care factors that partially account for these variations.</p> <p>Methods</p> <p>This study used 2006 mortality data extrapolated from the 1990 and 2000 Census and disability data from a national disability survey conducted in 2006. Disability was performance based and was diagnosed by trained physicians. DFLE was calculated by region using the Sullivan method. Multiple linear regression models by gender were conducted to explore correlates of DFLE.</p> <p>Results</p> <p>DFLE at age 60 varied widely by region, from 11.2 to 20.8 years in 2006. Per capita gross domestic product, proportion of urban residents, and access to health care were the primary factors associated with geographical variations in DFLE.</p> <p>Conclusion</p> <p>The pattern of differences in DFLE by region mirrors the pattern of regional economic development in China. Countermeasures to decrease regional differences in DFLE include accelerating regional economic development and improving health care distribution.</p