Fully ab initio atomization energy of benzene via W2 theory

The total atomization energy at absolute zero, (TAE$_0$) of benzene, C$_6$H$_6$, was computed fully {\em ab initio} by means of W2h theory as 1306.6 kcal/mol, to be compared with the experimentally derived value 1305.7+/-0.7 kcal/mol. The computed result includes contributions from inner-shell correlation (7.1 kcal/mol), scalar relativistic effects (-1.0 kcal/mol), atomic spin-orbit splitting (-0.5 kcal/mol), and the anharmonic zero-point vibrational energy (62.1 kcal/mol). The largest-scale calculations involved are CCSD/cc-pV5Z and CCSD(T)/cc-pVQZ; basis set extrapolations account for 6.3 kcal/mol of the final result. Performance of more approximate methods has been analyzed. Our results suggest that, even for systems the size of benzene, chemically accurate molecular atomization energies can be obtained from fully first-principles calculations, without resorting to corrections or parameters derived from experiment.Comment: J. Chem. Phys., accepted. RevTeX, 12 page

Assessment of W1 and W2 theories for the computation of electron affinities, ionization potentials, heats of formation, and proton affinities

The performance of two recent {\em ab initio} computational thermochemistry schemes, W1 and W2 theory [J.M.L. Martin and G. de Oliveira, J. Chem. Phys. 111, 1843 (1999}], is assessed for an enlarged sample of thermochemical data consisting of the ionization potentials and electron affinities in the G2-1 and G2-2 sets, as well as the heats of formation in the G2-1 and a subset of the G2-2 set. We find W1 theory to be several times more accurate for ionization potentials and electron affinities than commonly used (and less expensive) computational thermochemistry schemes such as G2, G3, and CBS-QB3: W2 theory represents a slight improvement for electron affinities but no significant one for ionization potentials. The use of a two-point $A+B/L^5$ rather than a three-point $A+B/C^L$ extrapolation for the SCF component greatly enhances the numerical stability of the W1 method for systems with slow basis set convergence. Inclusion of first-order spin-orbit coupling is essential for accurate ionization potentials and electron affinities involving degenerate electronic states: inner-shell correlation is somewhat more important for ionization potentials than for electron affinities, while scalar relativistic effects are required for the highest accuracy. The mean deviation from experiment for the G2-1 heats of formation is within the average experimental uncertainty. W1 theory appears to be a valuable tool for obtaining benchmark quality proton affinities.Comment: Journal of Chemical Physics, in press (303115JCP). 2 RevTeX files, first is text and tables, second is E-PAPS tables S-1 through S-5. Additional supplementary material (total energies, basis function exponents) available at http://theochem.weizmann.ac.il/web/papers/w1w2.htm

2,4-Bis(4-bromo­phen­yl)-3-aza­bicyclo­[3.3.1]nonan-9-one

The title compound, C20H19Br2NO, shows a chair–chair conformation for the aza­bicycle with an equatorial disposition of the 4-bromo­phenyl groups [dihedral angle between the aromatic rings = 16.48 (3)°]. In the crystal, a short Br⋯Br contact [3.520 (4) Å] occurs and the structure is further stabilized by N—H⋯O hydrogen bonds and C—H⋯O inter­actions

2,4-Bis(4-chloro­phen­yl)-3-aza­bicyclo­[3.3.1]nonan-9-one

In the mol­ecular structure of the title compound, C20H19Cl2NO, the mol­ecule exists in a twin-chair conformation with equatorial dispositions of the 4-chloro­phenyl groups on both sides of the secondary amino group; the dihedral angle between the aromatic ring planes is 31.33 (3)°. The crystal structure is stabilized by N—H⋯O inter­actions, leading to chains of molecules

A Comparative Study of Chi-Square Goodness-of-Fit Under Fuzzy Environments

Testing goodness-of-fit plays a vital role in data analysis.  This problem seems to be much more complicated in the presence of vague data.  In this paper, the chi-square goodness-of-fit under trapezoidal fuzzy numbers (tfns.) is proposed using alpha cut interval method.  And the ranking grades of tfns. are also used to compute the chi-square test statistic.  The proposed technique is illustrated with two different numerical examples along with different methods of ranking grades for a concrete comparative study. Keywords: Chi-square Test, Fuzzy Sets, Trapezoidal Fuzzy Numbers, Alpha Cut, Ranking Function, Graded Mean Integration Representation

A Comparative Study of Latin Square Design Under Fuzzy Environments Using Trapezoidal Fuzzy Numbers

This paper deals with the problem of Latin Square Design (LSD) test using Trapezoidal Fuzzy Numbers (Tfns.).  The proposed test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function, Total Integral Value and Graded Mean Integration Representation.  Finally a comparative view of the conclusions obtained from various test is given.  Moreover, two numerical examples having different conclusions have been given for a concrete comparative study.   Keywords: LSD, Trapezoidal Fuzzy Numbers, Alpha Cut, Membership Function, Ranking Function, Total Integral Value, Graded Mean Integration Representation.   AMS Mathematics Subject Classification (2010): 62A86, 62F03, 97K8

One-Factor ANOVA Model Using Trapezoidal Fuzzy Numbers Through Alpha Cut Interval Method

Most of our traditional tools in descriptive and inferential statistics is based on crispness (preciseness) of data, measurements, random variable, hypotheses, and so on.  By crisp we mean dichotomous that is, yes-or-no type rather than more-or-less type.  But there are many situations in which the above assumptions are rather non-realistic such that we need some new tools to characterize and analyze the problem.  By introducing fuzzy set theory, different branches of mathematics are recently studied.  But probability and statistics attracted more attention in this regard because of their random nature.  Mathematical statistics does not have methods to analyze the problems in which random variables are vague (fuzzy). In this regard, a simple and new technique for testing the hypotheses under the fuzzy environments is proposed.  Here, the employed data are in terms of trapezoidal fuzzy numbers (TFN) which have been transformed into interval data using  interval method and on the grounds of the transformed fuzzy data, the one-factor ANOVA test is executed and decisions are concluded.  This concept has been illustrated by giving two numerical examples. Keywords: Fuzzy set, , Trapezoidal fuzzy number (TFN), Test of hypotheses, One-factor ANOVA model, Upper level data, Lower level data

Comparable Effects ofIsolated and CombinedAssisted and Resisted Sprint Training Programmes on Cardio Vascular Fitness among College Women Athletes

The present study was designed to find out the effects of isolated and combinedassisted and resisted sprint training programmeson cardio vascular fitness among collegewomen athletes. For this purpose,sixty(N=60) college female athletes who were studying various colleges affiliated to Bharathidasan University, Tiruchirappalli,Tamilnadu India were selected randomly as subjects. The age of the subjects was ranged between 18-21 years. The subjects were assigned at random into four groups of fifteen each (n=15) namely, Assisted Sprint Training Group (ASTG), Resisted Sprint Training Group (RSTG), Combined Assisted and Resisted Sprint Training Group (ARSTG), and Control Group (CG).Group-I underwent Assisted Sprint Training, Group-II underwent Resisted Sprint Training, Group-III underwent Combined Assisted and Resisted Sprint Trainingand Group-IV acted as Control. For all three experimental groups, the training period was limited to twelve weeks, and there could be no more than three sessions each week. The training schedule for mixed assisted and resisted sprint training was limited to alternate weeks for a total of twelve weeks. Cooper\u27s 12-minute run/walk test were used to measure the dependent variable of cardiovascular fitness. Every subject was tested for every one of the chosen factors both before and right after training. The pre and post assessment developments in the groups were analyze with t-test and analysis of covariance. The Scheffe’s post hoc test was also calculated for pair wise comparisons. For all cases 0.05 level of confidence was fixed. The study\u27s findings demonstrated that there was a significant difference in cardiovascular fitness between all three experimental group such as Assisted Sprint Training Group (ASTG), Resisted Sprint Training Group (RSTG), and Combined Assisted and Resisted Sprint Training Group (ARSTG). Additionally, the study\u27s findings supported that the Combined Assisted and Resisted Sprint Training Group (ARSTG) outperformed the Assisted Sprint Training Group (ASTG) and Resisted Sprint Training Group (RSTG) in terms of cardiovascular fitness

PHARMACOGNOSTICAL AND PRELIMINARY PHYTOCHEMICAL SCREENING OF AAVAARAI VIDHAI CHOORANAM

  Objective: To study the organoleptic characters, physio chemical properties and preliminary phytochemicals screening of Siddha formulations Aavaarai Vidhai Chooranam (AVC).Methods: The study drug, AVC was prepared as per procedure given in the text Neerizhivu maruthuvam. Organoleptic characteristics were assessed by appearance, colour, taste and odour. The physiochemical property of trial drug was screened for moisture content, total ash value, acid insoluble ash, water soluble extractive value, alcohol soluble extractive value, pH, reducing sugar, total sugar, total solid content and fat content. Preliminary Phytochemical evaluation of AVC was carried out by the standard procedure. The drug was screened for alkaloids, amino acids & proteins, anthraxquinone, carbohydrate, flavonoids, glycosides, phenols quinones, resins, saponins, steroids tanins, terpenoids and sugar. For which the aqueous extraction of the trial drug was taken by dissolving the 5 g of sample with 50 ml of distilled water and heated over water bath at 60°C. Then extract was filtered and used the filtrates for testing.Results: The trial drug, AVC shown organoleptic characters as per literature evidence, physiochemical properties as moisture content, total ash value, acid insoluble ash, water soluble extractive value, alcohol soluble extractive value, pH, reducing sugar, total sugar, total solid content and fat content were found within normal limits, preliminary phytochemical test showed the presence of flavonoids, tannins, steroids, terpenoids, alkaloids, carbohydrate, proteins, phenols and sugar.Conclusion: Organoleptic characters, physio chemical properties and preliminary photochemica shows that the drug has the quality and potency to treat against diabetes mellitus. To confirm this activity, further research should be done to assess the safety and efficacy of the drug AVC