Hyperbolic triangles without embedded eigenvalues

We consider the Neumann Laplacian acting on square-integrable functions on a triangle in the hyperbolic plane that has one cusp. We show that the generic such triangle has no eigenvalues embedded in its continuous spectrum. To prove this result we study the behavior of the real-analytic eigenvalue branches of a degenerating family of triangles. In particular, we use a careful analysis of spectral projections near the crossings of these eigenvalue branches with the eigenvalue branches of a model operator.Comment: 65 pages, 4 figures, to appear in Annals of Mathematics http://annals.math.princeton.edu/articles/1159

Reliable a-posteriori error estimators for hphp-adaptive finite element approximations of eigenvalue/eigenvector problems

We present reliable a-posteriori error estimates for $hp$-adaptive finite element approximations of eigenvalue/eigenvector problems. Starting from our earlier work on $h$ adaptive finite element approximations we show a way to obtain reliable and efficient a-posteriori estimates in the $hp$-setting. At the core of our analysis is the reduction of the problem on the analysis of the associated boundary value problem. We start from the analysis of Wohlmuth and Melenk and combine this with our a-posteriori estimation framework to obtain eigenvalue/eigenvector approximation bounds.Comment: submitte

ANALISIS FAKTOR TINGKATAN PRODUK DALAM KEPUTUSAN MEMILIH JASA PENDIDIKAN DI BUSINESS TRAINING CENTER (BTC) MALANG

Keywords: Depth of product\ud This research is a type of survey research with the title "Analysis Depth Factors In Decision Choosing Products Education Services at Business Training Center (BTC) Malang".\ud The purpose of this study is the first, to determine the factors that influence the product level in the decision to choose education services at Business Training Center (BTC) Malang. Second, to determine the factors that most influence the product level in the decision to choose education services at Business Training Center (BTC) Malang.\ud The hypothesis in this study is the first, alleged that the factors influencing the product level in the decision to choose education services at Business Training Center (BTC) Malang. Second, alleged that the levels of potential products (potential product) the most influence in the decision to choose education services at Business Training Center (BTC) Malang.\ud The analytical tool used is that factor analysis is an analysis tool that serves to summarize many variables into several factors.\ud From the results of the study with 19 variables included in the study reduced to 6 factors: first with a total value of 26.696% variance and eigenvalue of 5.072, the second factor variants with a total value amounting to 8.917% and an eigenvalue of 1.694, the third factor with a total value variance of 8.455% and an eigenvalue of 1.606. The fourth factor variants with a total value amounting to 8.211% and an eigenvalue of 1.560. Factors fifth with a total value of the variant of 6.845% and an eigenvalue of 1.301 and sixth factor variants with a total value amounting to 6.583% and an eigenvalue of 1.251. From the value of this factor, the first hypothesis is accepted.\ud Of some value above the highest value on the factor eigenvalue is the main benefit (core benefits) that concluded that the main benefit factor (core benefit) is a major factor in the decision of selecting students viewed educational services at the Business Training Center (BTC), Malang, the second hypothesis rejected

On the Eigenvalue Density of Real and Complex Wishart Correlation Matrices

Wishart correlation matrices are the standard model for the statistical analysis of time series. The ensemble averaged eigenvalue density is of considerable practical and theoretical interest. For complex time series and correlation matrices, the eigenvalue density is known exactly. In the real case, however, a fundamental mathematical obstacle made it forbidingly complicated to obtain exact results. We use the supersymmetry method to fully circumvent this problem. We present an exact formula for the eigenvalue density in the real case in terms of twofold integrals and finite sums.Comment: 4 pages, 2 figure