Distinct parts partitions without sequences

Partitions without sequences of consecutive integers as parts have been studied recently by many authors, including Andrews, Holroyd, Liggett, and Romik, among others. Their results include a description of combinatorial properties, hypergeometric representations for the generating functions, and asymptotic formulas for the enumeration functions. We complete a similar investigation of partitions into distinct parts without sequences, which are of particular interest due to their relationship with the Rogers-Ramanujan identities. Our main results include a double series representation for the generating function, an asymptotic formula for the enumeration function, and several combinatorial inequalities.Comment: 15 page

Generalized Matching Preclusion in Bipartite Graphs

The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal such sets are precisely sets of edges incident to a single vertex. The conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond these, and it is defined as the minimum number of edges whose deletion results in a graph with neither isolated vertices nor perfect matchings. In this paper we generalize this concept to get a hierarchy of stronger matching preclusion properties in bipartite graphs, and completely characterize such properties of complete bipartite graphs and hypercubes

Serum leptin and resistin in type 1 and type 2 diabetes mellitus

Background: Leptin is a hormone, secreted by adipocytes that control the food intake. It is an anorexigenic hormone, which leads to the suppression of appetite. Obesity is characterized by hyperleptinemia due to the development of leptin resistance 1.  Resistin is a adipokine, resisting insulin secreted from scortal cell and macrophages of adipose cell.  Diabetes is a chronic disorder presenting with high blood sugar values, either due to less production of insulin or insulin insensitivity. These adipokines have a direct correlation with diabetes. So their levels tend to vary in diabetes. Aim: To estimate the levels of Serum Leptin, Resistin, Insulin, FBS and lipid profile   in Type 1 and Type 2 diabetes mellitus patient. Material and methods: A cross sectional analytical studies was conducted in DR B R AMC. Study group included 80 known case of diabetes mellitus. 40 patients type 1 DM in group 1 and 40 patients with Type 2 DM was included as group 2. Results: BMI, FBS, Lipid profile had no significant difference among both the groups. Insulin was high in type 1 diabetes mellitus, but with no statistical significance. Leptin levels are significantly high in Type 1 DM compared to type 2 DM.&nbsp

Comparative study of copper, zinc levels in uncontrolled type 2 diabetes mellitus with normal subjects

accounts for majority of the cases, can lead to multiorgan complications. Direct association of minerals  , Trace elements and vitamins in the pathogenesis and natural cause of  type 2 diabetes mellitus has been observed in many research studies. Aim: To estimate the levels of Copper , Zinc and HBA1c in uncontrolled Type 2 Diabetes mellitus patient. Material and methods: A cross sectional analytical studies was conducted in DR B R AMC. Study group included 40 known case of uncontrolled Diabetes mellitus. Results: In the present Study serum copper levels in uncontrolled Type 2 Diabetes Mellitus patients was 204.3 ± 49.0 and in controls it was132.4 ± 20.2. There was a statistically significant increase in the mean copper values in uncontrolled Type 2 Diabetes Mellitus patients  (P< 0.0001). Serum Zinc levels in uncontrolled Type 2 Diabetes Mellitus patients was 174.7 ± 31.0  µg/dl and in the controls it was 207.4 ± 36.6 µg/dl. There was a statistically significant decrease in the mean Zinc values  (P<0.0001).  Conclusion: Trace elements play a vital role in maintaining the normal metabolism and homeostasis.&nbsp

Generalized Matching Preclusion in Bipartite Graphs

The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal such sets are precisely sets of edges incident to a single vertex. The conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond these, and it is defined as the minimum number of edges whose deletion results in a graph with neither isolated vertices nor perfect matchings. In this paper we generalize this concept to get a hierarchy of stronger matching preclusion properties in bipartite graphs, and completely characterize such properties of complete bipartite graphs and hypercubes

Management of coronary disease in patients with advanced kidney disease

BACKGROUND Clinical trials that have assessed the effect of revascularization in patients with stable coronary disease have routinely excluded those with advanced chronic kidney disease. METHODS We randomly assigned 777 patients with advanced kidney disease and moderate or severe ischemia on stress testing to be treated with an initial invasive strategy consisting of coronary angiography and revascularization (if appropriate) added to medical therapy or an initial conservative strategy consisting of medical therapy alone and angiography reserved for those in whom medical therapy had failed. The primary outcome was a composite of death or nonfatal myocardial infarction. A key secondary outcome was a composite of death, nonfatal myocardial infarction, or hospitalization for unstable angina, heart failure, or resuscitated cardiac arrest. RESULTS At a median follow-up of 2.2 years, a primary outcome event had occurred in 123 patients in the invasive-strategy group and in 129 patients in the conservative-strategy group (estimated 3-year event rate, 36.4% vs. 36.7%; adjusted hazard ratio, 1.01; 95% confidence interval [CI], 0.79 to 1.29; P=0.95). Results for the key secondary outcome were similar (38.5% vs. 39.7%; hazard ratio, 1.01; 95% CI, 0.79 to 1.29). The invasive strategy was associated with a higher incidence of stroke than the conservative strategy (hazard ratio, 3.76; 95% CI, 1.52 to 9.32; P=0.004) and with a higher incidence of death or initiation of dialysis (hazard ratio, 1.48; 95% CI, 1.04 to 2.11; P=0.03). CONCLUSIONS Among patients with stable coronary disease, advanced chronic kidney disease, and moderate or severe ischemia, we did not find evidence that an initial invasive strategy, as compared with an initial conservative strategy, reduced the risk of death or nonfatal myocardial infarction

Health status after invasive or conservative care in coronary and advanced kidney disease

BACKGROUND In the ISCHEMIA-CKD trial, the primary analysis showed no significant difference in the risk of death or myocardial infarction with initial angiography and revascularization plus guideline-based medical therapy (invasive strategy) as compared with guideline-based medical therapy alone (conservative strategy) in participants with stable ischemic heart disease, moderate or severe ischemia, and advanced chronic kidney disease (an estimated glomerular filtration rate of <30 ml per minute per 1.73 m2 or receipt of dialysis). A secondary objective of the trial was to assess angina-related health status. METHODS We assessed health status with the Seattle Angina Questionnaire (SAQ) before randomization and at 1.5, 3, and 6 months and every 6 months thereafter. The primary outcome of this analysis was the SAQ Summary score (ranging from 0 to 100, with higher scores indicating less frequent angina and better function and quality of life). Mixed-effects cumulative probability models within a Bayesian framework were used to estimate the treatment effect with the invasive strategy. RESULTS Health status was assessed in 705 of 777 participants. Nearly half the participants (49%) had had no angina during the month before randomization. At 3 months, the estimated mean difference between the invasive-strategy group and the conservative-strategy group in the SAQ Summary score was 2.1 points (95% credible interval, 120.4 to 4.6), a result that favored the invasive strategy. The mean difference in score at 3 months was largest among participants with daily or weekly angina at baseline (10.1 points; 95% credible interval, 0.0 to 19.9), smaller among those with monthly angina at baseline (2.2 points; 95% credible interval, 122.0 to 6.2), and nearly absent among those without angina at baseline (0.6 points; 95% credible interval, 121.9 to 3.3). By 6 months, the between-group difference in the overall trial population was attenuated (0.5 points; 95% credible interval, 122.2 to 3.4). CONCLUSIONS Participants with stable ischemic heart disease, moderate or severe ischemia, and advanced chronic kidney disease did not have substantial or sustained benefits with regard to angina-related health status with an initially invasive strategy as compared with a conservative strategy