H\"older Continuity of the Integrated Density of States for the Fibonacci Hamiltonian

We prove H\"older continuity of the integrated density of states for the Fibonacci Hamiltonian for any positive coupling, and obtain the asymptotics of the H\"older exponents for large and small couplings.Comment: 18 page

Spectral transitions for the square Fibonacci Hamiltonian

We study the spectrum and the density of states measure of the square Fibonacci Hamiltonian. We describe where the transitions from positive-measure to zero-measure spectrum and from absolutely continuous to singular density of states measure occur. This shows in particular that for almost every parameter from some open set, a positive-measure spectrum and a singular density of states measure coexist. This provides the first physically relevant example exhibiting this phenomenon

Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians

We consider the spectrum of discrete Schr\"odinger operators with Sturmian potentials and show that for sufficiently large coupling, its Hausdorff dimension and its upper box counting dimension are the same for Lebesgue almost every value of the frequency.Comment: 12 pages, to appear in Commun. Math. Phy

Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set

We construct multidimensional Schrödinger operators with a spectrum that has no gaps at high energies and that is nowhere dense at low energies. This gives the first example for which this widely expected topological structure of the spectrum in the class of uniformly recurrent Schrödinger operators, namely the coexistence of a half-line and a Cantor-type structure, can be confirmed. Our construction uses Schrödinger operators with separable potentials that decompose into one-dimensional potentials generated by the Fibonacci sequence and relies on the study of such operators via the trace map and the Fricke-Vogt invariant. To show that the spectrum contains a half-line, we prove an abstract Bethe–Sommerfeld criterion for sums of Cantor sets which may be of independent interest

The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian

We study the spectrum of the Fibonacci Hamiltonian and prove upper and lower bounds for its fractal dimension in the large coupling regime. These bounds show that as $\lambda \to \infty$, $\dim (\sigma(H_\lambda)) \cdot \log \lambda$ converges to an explicit constant ($\approx 0.88137$). We also discuss consequences of these results for the rate of propagation of a wavepacket that evolves according to Schr\"odinger dynamics generated by the Fibonacci Hamiltonian.Comment: 23 page

Analyze Critical Thinking Skills and Scientific Attitude in Physics Learning Used Inquiry Training and Direct Instruction Learning Model

This study was aimed to determine the differences: (1) the difference of critical thinking skills of students' that using Inquiry Training and Direct Instruction. (2) The difference of critical thinking skills among students who at high scientific attitude and students who at low scientific attitude. (3) To see if there is interaction between inquiry learning model of the scientific attitude students' to increase the ability to critical thinking. This is a quasi experimental research. Which students of private junior high school Two Raya Kahean District Simalungun. Population choose random sample of each class. Instrument used consisted of: (1) test the scientific attitude of students through a questionnaire with 25 statements questionnaire number (2) test the critical thinking skills in the form of descriptions by 9 questions. The data were analyzed according to ANAVA. It showed that: (1) There are differences in students' critical thinking of skills achievement Inquiry Training model and Direct Instruction model, (2) there was a difference of students' critical thinking in scientific attitude at high is better than who thought there is a difference of students' critical thinking in scientific attitude at low. (3) There was no interaction between Inquiry Training model and Direct Instruction with the scientific attitude students' to increase student's critical thinking of skills

Kebijakan India Menahan Duta Besar Italia Untuk India Pada Insiden Enrica Lexie Tahun 2013

Integration Course emerged as an integration course program which is the renewal of the license under the Migration Act related to the National Migration Integration as steps to improve the conditions of immigrants in Germany. But there are several obstacles in the Integration Course that immigrants who come from different corners of the world and immigrated in Germany will be the acculturation effect on social life in Germany, the lack of protection of all immigrants of all religions, and there is a shift in the demographic features native German speakers ,Qualitative research method is descriptive that will describe, record, analyze and interpret the condition or event associated with the problems posed and to develop the data obtained from various sources. The qualitative research to understand an issue or social phenomena are presented descriptively or with an explanation.The purpose of this paper is, in order to determine the condition of immigrants, knowing the background of the formation Integration Course, determine the effect or against immigrants in Germany. Because immigrants are people who want to get a life assured, adequate, safe, then Germany as a country that receives immigrants with a high amount, must pay attention to guarantee the lives of the immigrants

Repetitions in beta-integers

Classical crystals are solid materials containing arbitrarily long periodic repetitions of a single motif. In this paper, we study the maximal possible repetition of the same motif occurring in beta-integers -- one dimensional models of quasicrystals. We are interested in beta-integers realizing only a finite number of distinct distances between neighboring elements. In such a case, the problem may be reformulated in terms of combinatorics on words as a study of the index of infinite words coding beta-integers. We will solve a particular case for beta being a quadratic non-simple Parry number.Comment: 11 page