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111.
Shivam Kumar 《Resonance》2007,12(9):25-39
Are there perfect squares which on division by 7 leave remainder 3? Are there perfect squares which on division by 3 leave
remainder 7? (A “remainder of 7” on division by 3 is the same as a remainder of 1.) The answers: ‘NO’ and ‘YES’, respectively.
These facts are stated by number theorists as follows: 3 is a quadratic non-residue modulo 7; 7 is a quadratic residue modulo 3. The notion of quadratic residue is far reaching, and the key theorem here is the Law of Quadratic Reciprocity, first stated
by Euler in 1783, but without proof, and first proved by Gauss, in 1796. The theorem is easy to state but is mysterious, as
it reveals a connection between two questions that appear unconnected. Let p, q be distinct odd primes; then the questions are: “Is p a quadratic residue modulo q?” and “Is q a quadratic residue modulo p?” Gauss had a high regard for this result and called it Theorema Aureum, the Golden Theorem. Though it has been proved in many different ways, it retains its mystery. In this two part article we
give three proofs of the theorem. The first one, described in this part, is based on group theory. 相似文献
112.
Santosh Kumar Singh Achyut Narayan Kesari Prashant Kumar Rai Geeta Watal 《Indian journal of clinical biochemistry : IJCB》2007,22(2):48-52
The present study reveals the effect of Musa paradisiaca stem juice on blood glucose level (BGL) of normal & diabetic rats.
The dose of 500 mg/kg bodyweight produces a significant rise of 28.3% in blood glucose level after 6h of oral administration
in normal rats. Whereas, in sub diabetic rats the same dose produces a rise of 16.4% in blood glucose levels within 1h during
glucose tolerance test (GTT) and a rise of 16% after 4 h in fasting blood glucose levels of severe diabetic cases. These results
were unexpected and important to report as other species of Musa like Musa sapientum has been reported for its hypoglycemic
effect. 相似文献
113.
Zaiqiao Meng Hong Shen Huimin Huang Wei Liu Jing Wang Arun Kumar Sangaiah 《Information processing & management》2018,54(6):1277-1291
Search result diversification is an effective way to tackle query ambiguity and enhance result novelty. In the context of large information networks, diversifying search result is also critical for further design of applications such as link prediction and citation recommendation. In previous work, this problem has mainly been tackled in a way of implicit query intent. To further enhance the performance on attributed networks, we propose a novel search result diversification approach via nonnegative matrix factorization. Our approach encodes latent query intents as well as nodes as representation vectors by a novel nonnegative matrix factorization model, and the diversity of the results accounts for the query relevance and the novelty w.r.t. these vectors. To learn the representation vectors of nodes, we derive the multiplicative updating rules to train the nonnegative matrix factorization model. We perform a comprehensive evaluation on our approach with various baselines. The results show the effectiveness of our proposed solution, and verify that attributes do help improve diversification performance. 相似文献
114.
Sujeet Kumar Sharma Mohamed Sarrab Hafedh Al-Shihi 《Interactive Learning Environments》2017,25(7):847-858
The growth of Smartphone usage, increased acceptance of electronic learning (E-learning), the availability of high reliability mobile networks and need for flexibility in learning have resulted in the growth of mobile learning (M-learning). This has led to a tremendous interest in the acceptance behaviors related to M-learning users among the information systems researchers. Despite a large amount of significant research in the field of M-learning, the measurement of user acceptance of M-learning has not received attention. This research study intends to develop and validate a survey that measures users’ acceptance of M-learning. A total sample of 806 university and higher college students from different institutes in Oman participated in this study. This research study was conducted in two stages. The first stage using a sample size of 388 students initiated a generic questionnaire, and examined factorial validity and reliability. The second stage that was conducted using different sample of 418 students employed confirmatory factor analysis to establish factorial validity and measurement invariance. A correlated six-factor model (Flexibility, Suitability, Enjoyment, Efficiency, Economic and Social) was fit using maximum likelihood estimation. The internal consistency and item reliability of Mobile Learning Acceptance Measure was found to be at acceptable level for both samples. 相似文献
115.
Ajay Kumar 《Resonance》2011,16(1):61-64
According to similarity property principle, structurally similar molecules tend to have similar properties. Similar molecules
exhibit similar biological activities. However, there is no hard and fast rule that the compounds with similar chemical structure
will have similar functions. There are several compounds of similar chemical structure with significantly different biological
actions and activities. Structure similarity of natural products can be investigated using Tanimoto coefficient and Euclidean
distance measurements. To do this, the molecules are decomposed into smaller fragments, and a dictionary, of the fragments
are prepared. Using the dictionary, 2D fingerprints are formed. With the fingerprints Tanimoto coefficient and Euclidean distance
are quantitated. 相似文献
116.
117.
The living system on earth is largely using oxygen for burning metabolic fuel for energy. The toxicity of oxygen is largely due to the formation of free radicals in living systems. Stress is also responsible for the generation of free radicals. The evidence for the involvement of free radicals and oxidative injury in producing metabolic disturbance, maladjustment and many diseases has been accumulating since long. It is largely believed that the root cause of many chronic diseases is stress induced free radicals and resultant oxidative injury. 相似文献
118.
119.
Ishrat Husain Ramesh Chander Jitendra Kumar Saxena Abbas Ali Mahdi Farzana Mahdi 《Indian journal of clinical biochemistry : IJCB》2015,30(1):72-77
The antidyslipidemic activity of Ocimum sanctum leaf extract was studied in streptozotocin induced diabetic rats. In this model, there was significant increase in plasma markers of diabetic-dyslipidemia following diminution of lipid metabolizing enzymes. Oral administration of leaf extract (500 mg/kg b.w.p.o.) for 15 days resulted in significant decrease in diabetogenic and dyslipidemia parameters; namely blood glucose, glycosylated hemoglobin, lipid peroxide, free fatty acids, small dense low density lipoprotein, lipid and protein components of plasma lipoproteins, adipose and liver. The regulation of lipids was accompanied by stimulation of postheparin lipolytic activity, reactivation of lecithin cholesterol acyl transferase and hepatic lipoprotein lipase enzymes. The results of the present study demonstrated antidyslipidemic and antioxidant activities in leaf extract of O. sanctum which could be used in prevention of diabetic-dyslipidemia and related complications. 相似文献
120.
HS Batra Ashwini Kumar TK Saha Pratibha Misra Vivek Ambade 《Indian journal of clinical biochemistry : IJCB》2015,30(2):230-233
To establish utility of single enzymatic marker for the diagnosis of acute pancreatitis. This is a cohort study. Tertiary care centre proven cases of acute pancreatitis (n = 50) admitted in surgery ward between December 2011 and May 2013 were included in the study. Serum amylase and lipase were performed along with many analytes. All relevant data including serum lab values and imaging were collected. All 50 patients included in the study had raised serum lipase, 42 patients had both amylase and lipase raised, 8 patients had amylase normal but lipase raised. In smaller hospitals where limited lab and radiological facilities are available, estimation of serum lipase will be a better choice over serum amylase in diagnosis of acute pancreatitis. 相似文献