Recurrent proofs of the irrationality of certain trigonometric values

We use recurrences of integrals to give new and elementary proofs of the irrationality of pi, tan(r) for all nonzero rational r, and cos(r) for all nonzero rational r^2. Immediate consequences to other values of the elementary transcendental functions are also discussed

A Novel Origin of CP Violation

We propose the complex group theoretical Clebsch-Gordon coefficients as a novel origin of CP violation. This is manifest in our model based on SU(5) combined with the double tetrahedral group, T'. Due to the presence of the doublet representations in $T^{\prime}$, there exist complex CG coefficients, leading to explicit CP violation in the model, while the Yukawa couplings and the vacuum expectation of the scalar fields remain real. The tri-bimaximal neutrino mixing matrix arises from the CG coefficients of the T'. In addition to the prediction for theta_{13} ~ theta_{c}/(3 sqrt{2}), the model gives rise to a sum rule, tan^2 theta_{sol} ~ \tan^2 theta_{sol,TBM} + (1/2) theta_{c} cos(delta), which is a consequence of the Georgi-Jarlskog relations in the charged fermion sector. The leptonic Dirac CP violating phase, delta_{ell}, is predicted to be ~227^{o}, which turns out to be the value needed to account for the difference between the experimental best fit value for the solar mixing angle and the TBM prediction. The predicted CP violation measures in the quark sector are also consistent with the current experimental data.Comment: 4 pages; based on talk presented at the 17th International Conference on Supersymmetry and the Unification of Fundamental Interactions (SUSY09), Boston, MA, June 5-10, 200

LFV in semileptonic τ\tau decays and μ−e\mu-e conversion in nuclei in SUSY-seesaw

Here we review the main results of LFV in the semileptonic tau decays $\tau \to \mu PP$ ($PP = \pi^+ \pi^-, \pi^0 \pi^0, K^+ K^-, K^0 \bar{K}^0$), $\tau \to \mu P$ ($P = \pi, \eta, \eta^{\prime}$), and $\tau \to \mu V$ ($V = \rho, \phi$) as well as in $\mu-e$ conversion in nuclei within SUSY-seesaw scenarios, and compare our predictions with the present experimental boundsComment: Talk given by M. J. Herrero in SUSY08 conference, Seou

The Public Library: A Photographic Essay

Over the last eighteen years, photographer Robert Dawson documented hundreds of public libraries throughout the United States. The Public Library presents an inspiring selection of his work—libraries grand and modest, from the reading room at the New York Public Library to Allensworth, California’s one-room Tulare County Free Library, built by former slaves. Essays, letters, and poetry by distinguished writers and librarians complete this impassioned tribute to a vibrant but threatened American institution. With a foreword by Bill Moyers and an afterword by Ann Patchett. Additional contributors include Isaac Asimov, Walker Dawson, Luis Herrera, Barbara Kingsolver, Anne Lamott, Dorothy Lazard, Philip Levine, David Morris, Stuart A. P. Murray, Kevin K. Selders, Dr. Seuss, Charles Simic, Amy Tan, Chip Ward, and E. B. Whit

Effect of missing value methods on Bayesian network classification of hepatitis data

Missing value imputation methods are widely used in solving missing value problems during statistical analysis. For classification tasks, these imputation methods can affect the accuracy of the Bayesian network classifiers. This paper study’s the effect of missing value treatment on the prediction accuracy of four Bayesian network classifiers used to predict death in acute chronic Hepatitis patients. Missing data was imputed using nine methods which include, replacing with most common attribute,support vector machine imputation (SVMI), K-nearest neighbor (KNNI), Fuzzy K-means Clustering (FKMI), K-means Clustering Imputation (KMI), Weighted imputation with K-Nearest Neighbor (WKNNI), regularized expectation maximization (EM), singular value decomposition (SVDI), and local least squares imputation (LLSI). The classification accuracy of the naive Bayes (NB), tree augmented naive Bayes (TAN), boosted augmented naive Bayes (BAN) and general Bayes network classifiers (GBN)were recorded. The SVMI and LLSI methods improved the classification accuracy of the classifiers. The method of ignoring missing values was better than seven of the imputation methods. Among the classifiers, the TAN achieved the best average classification accuracy of 86.3% followed by BAN with 85.1%

Dielectric properties of La0.67sr0.33Mnl-xTix03 with x = 0.4 and 0.6.

The dielectric properties of Ti-substituted La0.67Sr0.33Mn1-xTixO3 with x = 0.4 and 0.6 as a function of frequency and temperature have been investigated. The samples have been prepared using the conventional solid state reaction method at 1300oC. Both samples showed rhombohedral structure with R3C space group. The grain size of x = 0.4 and 0.6 are ~2.5 to 3.3 μm and ~0.4 to 0.9 μm respectively. The dielectric constant, ε' of the samples decreases with frequency but increases with temperature. We have successfully obtained very high dielectric constant material. The highest ε' value for LSMT with x = 0.4 and 0.6 are at frequency of 10 Hz and temperature 300 K, which are ~5.7 x 106 and ~2.4 x 106. The tan δ increases with temperature for x = 0.6 but shows a peak at a certain temperature for x = 0.4. Sample with x = 0.4 has better dielectric properties compared to x = 0.6 sample because it has higher ε' and lower tan δ value. At 175 K and 1 kHz sample with x = 0.4 shows the best dielectric properties with a high ε’ value and low tan δ which are 1.1 x 105 and 0.8 respectively

Supersymmetry of FRW barotropic cosmologies

Barotropic FRW cosmologies are presented from the standpoint of nonrelativistic supersymmetry. First, we reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations. Employing the factorization procedure, the solutions of the latter equations are divided into the two classes of bosonic (nonsingular) and fermionic (singular) cosmological solutions. We next introduce a coupling parameter denoted by K between the two classes of solutions and obtain barotropic cosmologies with dissipative features acting on the scale factors and spatial curvature of the universe. The K-extended FRW equations in comoving time are presented in explicit form in the low coupling regime. The standard barotropic FRW cosmologies correspond to the dissipationless limit K =0Comment: 6 page