Zeros of Dedekind zeta functions under GRH

Assuming GRH, we prove an explicit upper bound for the number of zeros of a Dedekind zeta function having imaginary part in $[T-a,T+a]$. We also prove a bound for the multiplicity of the zeros.Comment: Some misprints corrected, simplified proof for a lemma. This version will appear in Mathematics of Computatio

Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH

Let \psi_\K be the Chebyshev function of a number field \K. Under GRH we prove an explicit upper bound for |\psi_\K(x)-x| in terms of the degree and the discriminant of \K. The new bound improves significantly on previous known results.Comment: Some misprints corrected. This is the final version which will appear in Mathematics of Computatio

Smoothed Particle Hydrodynamic Simulations of Viscous Accretion Discs Around Black Holes

Viscous Keplerian discs become sub-Keplerian close to a black hole since they pass through sonic points before entering into it. We study the time evolution of polytropic viscous accretion discs (both in one and two dimensional flows) using Smoothed Particle Hydrodynamics. We discover that for a large region of the parameter space, when the flow viscosity parameter is less than a critical value, standing shock waves are formed. If the viscosity is very high then the shock disappears. In the intermediate viscosity the disc oscillates very significantly in viscous time-scale. Our simulations indicate that these centrifugally supported high density region close to a black hole plays an active role in the flow dynamics, and consequently, the radiation dynamics.Comment: MNRAS style 6 pages of output, macros included. MNRAS (submitted

Generalized Pohst inequality and small regulators

Current methods for the classification of number fields with small regulator depend mainly on an upper bound for the discriminant, which can be improved by looking for the best possible upper bound of a specific polynomial function over an hypercube. In this paper, we provide new and effective upper bounds for the case of fields with one complex embedding and degree between five and nine: this is done by adapting the strategy we have adopted to study the totally real case, but for this new setting several new computational issues had to be overcome. As a consequence, we detect the four number fields of signature (6,1) with smallest regulator; we also expand current lists of number fields with small regulator in signatures (3,1), (4,1) and (5,1).Comment: 23 pages. Accepted for publication on Mathematics of Computation. The title has been changed under referee's suggestion. Several misprints have been correcte

The Legal Questing Beast: Vocational Students’ Research Strategies, Motivations and Emotions

In the context of the Bar Vocational Course, this project enquired how students perceive their research strategies when they interact with repositories of legal information. The research captured and analysed the students' descriptions of these engagements and their motivations for as well as their emotional responses to undertaking research tasks. Some tentative comparisons are made between the students' strategies and those reported by a small number of junior barristers

The New Transverse-Facial Artery Musculomucosal Flap for Intraoral Reconstructions

With the bilateral progression of the 2 pedicled flaps, we were able to successfully restore both form and function of the soft palate, with a single-stage straightforward procedure, preserving at the same time the natural course of the facial arteries. Both flaps healed uneventfully. Six days after operation, the patient was placed on a liquid diet with no velopharyngeal insufficiency. This is to our knowledge the first extensive palatal reconstruction carried out with intraoral flaps onl

PENERAPAN MODEL P[EMBELAJARAN KOOPERATIF TIPE THINK PAIR SHARE UNTUK MENINGKATKAN HASIL BELAJAR MATA PELAJARAN SOSIOLOGI KELAS X IIS 1 SMA N 3 BOYOLALI TAHUN PELAJARAN 2016/2017

ABSTRAK Agatha Anggraeni Kirana Putri. K8413002. PENERAPAN MODEL PEMBELAJARAN KOOPERATIF TIPE THINK PAIR SHARE UNTUK MENINGKATKAN HASIL BELAJAR MATA PELAJARAN SOSIOLOGI KELAS X IIS 1 SMA NEGERI 3 BOYOLALI TAHUN PELAJARAN 2016/2017. Skripsi, Surakarta: Fakultas Keguruan dan Ilmu Pendidikan. Universitas Sebelas Maret. April 2017. Penelitian ini dilakukan dengan tujuan untuk meningkatkan hasil belajar Sosiologi peserta didik kelas X IIS 1 SMA Negeri 3 Boyolali tahun pelajaran 2016/2017 melalui penerapan model pembelajaran kooperatif tipe Think Pair Share. Penelitian ini merupakan Penelitian Tindakan Kelas yang dilaksanakan dalam dua siklus. Dalam setiap siklus terdiri dari tahap Perencanaan, Pelaksanaan Tindakan, Observasi dan Refleksi. Subjek penelitian adalah peserta didik kelas X IIS 1 SMA Negeri 3 Boyolali yang terdiri dari 36 peserta didik. Sumber data diperoleh dari guru dan peserta didik. Teknik utama dalam penelitian ini melalui observasi dan test, sedangkan teknik pendukung pengumpulan data menggunakan wawancara dan dokumentasi. Analisis data dengan menggunakan teknik analisis deskriptif kualitatif dan kuantitatif. Hasil penelitian menunjukkan bahwa penerapan model pembelajaran Kooperatif tipe Think Pair Share dapat meningkatkan hasil belajar peserta didik pada mata pelajaran Sosiologi Kelas X IIS 1 SMA Negeri 3 Boyolali tahun pelajaran 2016/2017, yang dimulai dari tahap pratindakan, siklus I dan siklus II. Hasil belajar ranah kognitif pada tahap Pra Tindakan menunjukkan 75,41 dengan prosentase ketuntasan peserta didik sebesar 64%. Hasil belajar mengalami peningkatan pada Siklus I menjadi 81,02 dengan prosentase ketuntasan sebesar 75%. Kemudian hasil belajar pada Siklus II kembali meningkat menjadi 85,11 dan prosentase ketuntasan sebesar 92%. Sedangkan pada ranah afektif diperoleh prosentase pada Siklus I sebesar 76% menjadi 83% pada Siklus II. Kemudian prosentase ranah Psikomotor mengalami peningkatan dari 72% pada Siklus I menjadi 89% pada Siklus II. Simpulan Penelitian Tindakan Kelas ini adalah penerapan model pembelajaran Kooperatif tipe Think Pair Share dapat meningkatkan hasil belajar peserta didik kelas X IIS 1 SMA N 3 Boyolali. Kata Kunci: Penelitian Tindakan Kelas, Think Pair Share, Hasil Belajar ABSTRACT Agatha Anggraeni Kirana Putri. K8413002. THE IMPLEMENTATION OF COOPERATIVE LEARNING MODEL OF THINK PAIR SHARE TYPE TO INCREASE THE LEARNING OUTCOMES IN SOCIOLOGY SUBJECT STUDENTS OF X IIS 1 AT SENIOR HIGH SCHOOL 3 BOYOLALI IN THE ACADEMIC YEAR OF 2016/2017. Thesis. Surakarta: Teacher Training and Education Faculty of Sebelas Maret University. April 2017. The research purpose is to increase the learning outcomes in Sociology subject through the implementation of cooperative learning model of Think Pair Share type to the students of X IIS 1 Senior High School 3 Boyolali year of 2016/2017. This research is as a classroom action research ( CAR ) which acted for two cycles. Each cycle consists of the steps of Planning, Actuating, Observing, and Reflecting. The subject of this research is students X IIS 1 Senior High School 3 Boyolali as many as 36 students. The sources of data are collected from the teacher and the students. The main data collection technique used are observation and test, while the proponent technique used interview and documentation technique. Data analysis used are qualitative and quantitative data analysis. The result of this research showed that the implementation of Cooperative learning model in Think Pair Share type can improve the learning outcomes on Sociology subjects students of X IIS 1 Senior High School 3 Boyolali, which is started from pre-action stage, cycle I, and cycle II. In the step of Pre Action the learning outcome on the cognitive domain shows 75,41 with the completeness percentage retrieved 64%. The learning outcome increase 81,02 on the first cycle with the completeness percentage retrieved 75%. Then, on second cycle the learning outcome increase 85,11 with the completeness percentage retrived 92%. While, the learning outcomes of the affective learning completeness percentage obtained on cycle I was 76% to 83% in cycle II. Then the sphere Psychomotor precentage from 72% in the cycle I to 89% in cycle II. The conclusion of this Class Action Research is that the Implemantation of Cooperative Learning Model of Think Pair Share type can increase the learning outcomes in Sociology subject students of X IIS 1 at Senior High School 3 Boyolali in The Academic Year of 2016/2017. Keyword: Classroom Action Research, Think Pair Share, Students Learning Outcome