Ideal Graph of a Graph

In this paper, we introduce ideal graph of a graph and study some of its properties. We characterize connectedness, isomorphism of graphs and coloring property of a graph using ideal graph. Also, we give an upper bound for chromatic number of a graph

Clinical Profile of Hospitalised Patients with Episode of Hypoglycemia

BACKGROUND: Hypoglycaemia is a common finding in both emergency department and medical wards. Clinical practice has shown that hypoglycaemia is common in both diabetics and nondiabetics. Few studies have shown hypoglycaemia as one of the predictors of mortality in hospitalized patients. Apart from diabetes, several risk factors contribute to hypoglycaemia. AIM & OBJECTIVES: The main aim of the study is to identify the clinical pattern of hospitalized patients with at least one episode of documented hypoglycaemia and to find out and analyse the risk factors associated with hypoglycaemia. Also it was aimed to determine the incidence of hypoglycaemia in patients admitted to medical wards and to identify if hypoglycaemia with associated risk factors predict increased mortality in hospitalized patient. MATERIALS AND METHODS: 119 patients who were admitted in the Institute of Internal Medicine, Madras Medical College & RGGGH during six months period of April 2015 to September 2015 and had at least one episode of hypoglycaemia were enrolled in the study after obtaining consent. pregnant women and patients under 18 years of age were excluded from the study. Thorough history was taken and complete clinical examination and relevant investigations were carried out. Data thus obtained was statistically analysed by means of chi square ‘t’ test. RESULTS: About 3/4th of the study sample were found to be males with patients in the age group of 41-60 years (54.6%) of age being most common followed by 61-80 years of age (34.5%). Hypoglycaemia occurred in both diabetics and non diabetics. Renal failure (57.98%), Diabetes (56.3%) and Alcoholism (49.57%) were found to be common risk factors. Incidence of hypoglycaemia is found to be 1.05%. Presence of sepsis, heart failure, multiple risk factors and elderly age were found to increase the mortality in patients. CONCLUSION: Hypoglycaemia in hospitalised patient occurs in both diabetics and non diabetics. Renal dysfunction, sepsis, Alcoholism are common precipitating factors of Hypoglycaemia. Presence of sepsis, heart failure, multiple risk factors and elderly age were found to increase mortality in hospitalised hypoglycaemic patients

On two theta function identities of Ramanujan

On page 310 of his second notebook, Ramanujan recorded two theta function identities. B. C. Berndt proved them by the method of parameterization. The purpose of this article is to give an elementary proof for those two identities and also we have obtained two theta function identities which are analogues to the identities of Ramanujan. Further, we establish two distinct formula for 3-core partitions in terms of divisor function

Ethyl 6-amino-5-cyano-2,4-bis­(4-methyl­phen­yl)-4H-pyran-3-carboxyl­ate

In the title compound, C23H22N2O3, the pyran ring adopts a twisted boat conformation. The tolyl rings and carboxyl­ate group are attached to the pyran ring with torsion angles of −77.1 (2), 59.5 (3) and 17.8 (3)°, respectively. The ethyl group is disordered over two orientations with a site-occupancy ratio of 0.508 (5):0.492 (5). In the crystal, mol­ecules are linked by N—H⋯N and N—H⋯O hydrogen bonds, generating a chain running the a axis. Weak C—H⋯O, C—H⋯N and C—H⋯π inter­actions are also observed

Bio-chemical studies on the Hepatoprotective Effect of Eclipta Alba and Piper Longum

Hepatoprotective efficacy of BHE on CCl4 intoxicated rats was performed to propose a new insight to the pharmacological action of BHE, which is a combined biherbal ethanolic extract made up of equal quantities of leaves of Eclipta alba and the seeds of Piper longum. Since polyherbal formulations are generally considered to be more effective due to the synergistic activity than a single herbal drug,the study has been undertaken to evaluate the protective effect of biherbal extract in comparison with its individual plants Eclipta alba and Piper longum. The present investigation has been divided into two parts. In one part of the investigation the plants have been processed, screened for the phytochemicals and tested for free radical scavenging activities by using standard models in vitro. THE PHYTOCHEMICAL INVESTIGATION OF THE PLANTS REVEALED THE FOLLOWING RESULTS: In the present investigation, preliminary phytochemical screening of EAE, PLE and BHE showed the presence of constituents like alkaloid, carbohydrates, phytosterol, tannins, phenol, flavonoids, glycosides, terpene, saponins and lignin. In all these extracts proteins, gums and mucilage were found to be absent. The presence of phytochemicals was confirmed by HPTLC finger printing of individual preparations of different extracts of Eclipta alba and piper longum. The estimation of the macronutrients like carbohydrates, proteins, lipids and micronutrients present in the leaves of Eclipta alba and seeds of the piper longum showed the nutritive value of the plants. The BHE showed a concentration dependent scavenging activities of the free radicals such as DPPH, super oxide, hydroxyl, nitric oxide, hydrogen peroxide and acted as an efficient chelator of ferric and ferrous ions. It was also found to be effective in reducing the formation of protein carbonyl groups.BHE contained considerable amount of the flavonoid and phenolic compounds which could be accounted for the free radical scavenging activities. The inhibitory action of the BHE on DNA fragmentation induced by fenton reactants in the hepatic tissue was studied. In the CCl4 intoxicated animals the extent of DNA damage was detected by the increased mobility of the DNA molecule due to the decrease in the molecular weight. On the other hand the BHE at the concentration of 20μg/ml and 40μg/ml protected the DNA from damage was evidenced by the decreased mobility of the DNA molecule suggested that these extracts have compounds which may combat against free radical-mediated degradation to the deoxyribose sugar moiety of DNA. The second part of the investigation comprises of the evaluation of non-toxic dosage by acute and chronic toxicity on mice and albino Wistar strain rat models according to the guidelines of OECD. After assessing the dosage by acute and chronic toxicity studies efficacy of the single and the biherbal drugs have been ascertained by using CCl4 induced hepatotoxicity model in rats. The hepatoprotective nature of the drugs has been assessed by various biochemical estimations and histological observations. Rats treated with standard drug silymarin have also been utilised in this study to compare the hepatoprotective efficacy of the test drugs. In the acute toxicity studies death was recorded during the treatment period in the experimental rats which received 500mg/kg body weight of Biherbal extract orally. So from this the ED50 dose of 50 mg/kg was selected for the hepatoprotective efficacy studies. The three month daily oral application of BHE to rats yielded no signs of toxicity. The dosage range and study duration applied in this study are relevant for long-term human use. Male albino rats were pre-treated with 50 mg/kg of BHE intubation for 14 days and intoxicated with CCl4 on days 7 to 14. Normal rats were maintained with the BHE to assess the drug toxicity. Standard drug silymarin was used as positive control for comparison. BIOCHEMICAL ANALYSIS OF THE BLOOD AND SERUM REVEALED SOME IMPORTANT RESULTS AS FOLLOWS: In the present investigation a significant reduction in the liver weight, serum urea and bilirubin levels were seen in the BHE pre-treated animals when compared to that of rats intoxicated with CCl4. Decreased level of blood glucose in CCl4 induced rats were found to be normalized on BHE supplementation. The total protein and albumin levels in serum were increased in BHE pretreated, CCl4 insulted animals showing the regeneration of hepatic cells. This increase in the protein level are more pronounced in BHE treated animals, when compared with the group IV and V, which received its individual preparations EAE and PLE. The serum levels of the liver marker enzymes like AST ALT, ALP, ACP, γGT 5'-NT, ICD and LDH were significantly increased in CCl4 intoxicated animals. BHE treatment reverted the increased levels of these enzymes to near normalcy, which was comparable to that of silymarin a standard drug in the present study. The parallel decrease in the concentration of serum lipids and lipoproteins along with the increase of these parameters in liver tissues of CCl4 insulted rats were normalized on BHE treatment .The increased serum phospholipids were also brought back to normal levels. The decrease in liver total protein and glycogen in the rats treated with CCl4 were normalized on BHE supplementation. The BHE was effective in reducing the levels of in vivo lipid peroxidation products like MDA, CD, iron, nitric oxides and LOOH in the tissues of CCl4 rats. The in vitro nonenzymatic lipid peroxidation induced by the presence ascorbate, Fe2+/Fe3+ and H2O2 were also significantly reduced by BHE treatment. Pretreatment with BHE to CCl4 treated rats increased the activities of SOD, CAT, GPX, GST and GR indicates the enhanced antilipid peroxidative nature of the BHE. Elevated levels of non-enzymic antioxidants such as vitamin C, vitamin E, Vitamin A, thiols, uric acid, and cereloplasmin in BHE treated animals offer protection against the oxidative injury caused by the free radicals produced by CCl4 in the present study. The decreased level of membrane bound enzymes such Na+/K+- ATPase, Mg2+- ATP ase and Ca2+- ATP ase in the liver tissues of CCl4 intoxicated rats may be because of the alteration of membrane lipid composition due to the release of free radicals. The rats which received BHE, EAE, and PLE restored the enzyme levels to near normal levels, which could be due to the ability of plant extracts to protect the membranes from oxidative damage through inhibition of lipid peroxidation. The activity of gluconeogenic enzymes and glycolytic enzymes in liver were found to be significantly decreased in CCl4 intoxicated rats. These decreased enzymes levels were restored to normal levels in BHE pretreated rats indicating that the BHE has got protective action on the mitochondria from damage enabling them to secreate the enzymes and keeping the blood glucose in normal levels. A significant decrease in the levels of Glycoprotein was observed in CCl4 treated animals due to the increased load of the toxic metabolites. The increase in glycoprotein content of BHE treated animals suggested the cytoprotective nature of the formulation. The histopathological observations which showed a faster regeneration of the hepatic cells in rats pretreated with BHE seems to suggest the possibility of BHE being able to condition the hepatic cells towards accelerated regeneration

Ethyl 2-(6-amino-5-cyano-3,4-dimethyl-2H,4H-pyrano[2,3-c]pyrazol-4-yl)acetate

In he title compound, C13H16N4O3, the pyrazole ring is planar (r.m.s. deviation = 0.054 Å). The pyran ring is not planar; the mean plane makes a dihedral angle of 1.9 (1)° with the pyrazole ring. In the crystal structure, inter­molecular N—H⋯N and N—H⋯O inter­actions lead to a linear chain motif

On Gosper's Pi(q) and Lambert series identities

In an interesting article entitled `Experiments and discoveries in q-trigonometry'', R. W. Gosper conjectured few beautiful Pi(q) and Lambert series identities. Many people have attempted confirming some of those identities in the Gosper's list, mainly by using Gosper's q-trigonometric identities. In this paper we either prove or disprove all the Pi(q) and Lambert series identities in the Gosper's list by mainly using S. Ramanujan's theta function identities and W. N. Bailey's summation formula. In the process, we obtain three new Gosper kind of identities

4-Bromo-N-(4-hy­droxy­benzyl­idene)­aniline

In the title compound, C13H10BrNO, the benzene ring planes are inclined at an angle of 48.85 (17)°, resulting in a nonplanar mol­ecule. A characteristic of aromatic Schiff bases with N-aryl substituents is that the terminal phenyl rings are twisted relative to the HC=N plane. In this case, the HC=N unit makes dihedral angles of 11.1 (4) and 38.5 (3)° with the hy­droxy­benzene and bromo­benzene rings, respectively. In the crystal, the molecules are linked by O—H⋯N hydrogen bonds to form infinite (C8) chains along the b axis

4-[(E)-(4-Methyl­phen­yl)imino­meth­yl]phenol

In the title compound, C14H13NO, the two rings show significant deviation from coplanarity, with a dihedral angle between the two planes of 49.40 (5)°. The hy­droxy group is involved in an inter­molecular O—H⋯N hydrogen bond, forming an extended one-dimensional zigzag chain along (001)

(Z)-4-{1-[(2-Hy­droxy­ethyl)­amino]­ethyl­idene}-3-methyl-1-phenyl-1H-pyrazol-5(4H)-one

In the title compound C14H17N3O2, the dihedral angle between the rings is 16.68 (13)°. Although the compound crystallizes in the keto form, the possibility of keto-enamine–enol-imine tautomerism is explained by a strong intra­molecular N—H⋯O hydrogen bond