Analytic properties of spherical cusp forms on GL(n)

Let $\phi$ be an $L^2$-normalized spherical vector in an everywhere unramified cuspidal automorphic representation of $\mathrm{PGL}_n$ over $\mathbb{Q}$ with Laplace eigenvalue $\lambda_{\phi}$. We establish explicit estimates for various quantities related to $\phi$ that are uniform in $\lambda_{\phi}$. This includes uniforms bounds for spherical Whittaker functions on $\mathrm{GL}_n(\mathbb{R})$, uniform bounds for the global sup-norm of $\phi$, and uniform bounds for the "essential support" of $\phi$, i.e. the region outside which it decays exponentially. The proofs combine analytic and arithmetic tools.Comment: 18 pages, LaTeX2e, submitted; v2: revised version fixing mainly (45) and its consequences; v3: revised version incorporating suggestions by the referee, e.g. Theorem 2 is now more general than before; v4: final version to appear in Journal d'Analyse Math\'ematique; v5: small corrections added in proo

Generic Birkhoff Spectra

Suppose that $\Omega = \{0, 1\}^ {\mathbb {N}}$ and ${\sigma}$ is the one-sided shift. The Birkhoff spectrum $\displaystyle S_{f}( {\alpha})=\dim_{H}\Big \{ {\omega}\in {\Omega}:\lim_{N \to \infty} \frac{1}{N} \sum_{n=1}^N f(\sigma^n \omega) = \alpha \Big \},$ where $\dim_{H}$ is the Hausdorff dimension. It is well-known that the support of $S_{f}( {\alpha})$ is a bounded and closed interval $L_f = [\alpha_{f, \min}^*, \alpha_{f, \max}^*]$ and $S_{f}( {\alpha})$ on $L_{f}$ is concave and upper semicontinuous. We are interested in possible shapes/properties of the spectrum, especially for generic/typical $f\in C( {\Omega})$ in the sense of Baire category. For a dense set in $C( {\Omega})$ the spectrum is not continuous on ${\mathbb {R}}$, though for the generic $f\in C( {\Omega})$ the spectrum is continuous on ${\mathbb {R}}$, but has infinite one-sided derivatives at the endpoints of $L_{f}$. We give an example of a function which has continuous $S_{f}$ on ${\mathbb {R}}$, but with finite one-sided derivatives at the endpoints of $L_{f}$. The spectrum of this function can be as close as possible to a "minimal spectrum". We use that if two functions $f$ and $g$ are close in $C( {\Omega})$ then $S_{f}$ and $S_{g}$ are close on $L_{f}$ apart from neighborhoods of the endpoints.Comment: Revised version after the referee's repor

Analisis Dampak Aktivitas Pertambangan Nikel PT. X Terhadap Pendapatan Petani Padi Sawah Di Kecamatan Tinanggea Kabupaten Konawe Selatan

Upaya peningkatan pertumbuhan ekonomi nasional maupun daerah akan memanfaatkan potensi sumberdaya alam (SDA). Meskipun demikian, dalam pengelolannya terkadang tidak mengkuti apa yang menjadi langkah-langkah pemanfaatan lingkungan lestari. Tidak jarang dibeberapa negara dapat kita saksikan terjadinya kerusakan lingkungan yang ditimbulkan akibat pengelolaan yang tidak ramah lingkungan. Aktifitas penambangan nikel PT. X di Kecamatan Tinanggea telah menimbulkan degradasi lingkungan. Degradasi lingkungan berdampak pula bagi masyarakat yang berada di sekitar lokasi penambangan nikel PT. X, yakni petani padi sawah. Dampak negatif akibat pebambangan nikel berupa menurunnya kesburan tanah, menurunnya kualitas air irigasi karena mengandung material lumpur yang berasal dari lokasi penambangan nikel, lumpur yang berasal dari lokasi penambangan nikel mengendap dan menimbulkan pendangkalan Bendungan Lapoa, serta menurnnya debit air irigasi akibat konversi lahan dihulu sungai. Degradasi lingkungan akibat penambangan nikel PT. X di Kecamatan Tinanggea menimbulkan dampak negatif berupa menurunnya tingkat pendapatan petani padi sawah. Tingkat pendapatan petani padi sawah menurun sebesar Rp 3.102.476/Ha per musim tanam jika dibandingkan tingkat pendapatan petani padi sawah di Kecamatan Lalembuu.Kata Kunci: Pertambangan nikel, pendapatan, petani, padi sawah Efforts to increase national and regional economic growth will utilize the potential of natural resources (SDA). However, in its management, sometimes it does not follow the steps for sustainable use of the environment. Not infrequently, in some countries we can see the occurrence of environmental damage caused by management that is not environmentally friendly. Nickel mining activities of PT. X in Tinanggea District have caused environmental degradation. Environmental degradation also has an impact on the community around the nickel mining site of PT. X, namely rice farmers. The negative impacts due to nickel mining include decreased soil fertility; decreased quality of irrigation water because it contains mud from nickel mining sites; mud from nickel mining sites settles and causes silting of the Lapoa Dam; and decreased irrigation water discharge due to land conversion upstream of the river. Environmental degradation due to nickel mining PT. X in Tinanggea District has a negative impact in the form of a decrease in the income level of lowland rice farmers. The income level of lowland rice farmers decreased by Rp. 3,102,476/ha per planting season when compared to the income level of lowland rice farmers in Lalembuu District.Keywords: Nickel mining, income, farmers, rice padd

Generic power series on subsets of the unit disk

In this paper, we examine the boundary behaviour of the generic power series $f$ with coefficients chosen from a fixed bounded set $\Lambda$ in the sense of Baire category. Notably, we prove that for any open set $U$ with a non-real boundary point on the unit circle, $f(U)$ is a dense set of $\mathbb{C}$. As it is demonstrated, this conclusion does not necessarily hold for arbitrary open sets accumulating to the unit circle. To complement these results, a characterization of coefficient sets having this property is given.Comment: Wrong grant numbers fixe

Big and little Lipschitz one sets

Given a continuous function $f: {{\mathbb R}}\to {{\mathbb R}}$ we denote the so-called "big Lip" and "little lip" functions by ${{\mathrm {Lip}}} f$ and ${{\mathrm {lip}}} f$ respectively}. In this paper we are interested in the following question. Given a set $E {\subset} {{\mathbb R}}$ is it possible to find a continuous function $f$ such that ${{\mathrm {lip}}} f=\mathbf{1}_E$ or ${{\mathrm {Lip}}} f=\mathbf{1}_E$? For monotone continuous functions we provide the rather straightforward answer. For arbitrary continuous functions the answer is much more difficult to find. We introduce the concept of uniform density type (UDT) and show that if $E$ is $G_\delta$ and UDT then there exists a continuous function $f$ satisfying ${{\mathrm {Lip}}} f =\mathbf{1}_E$, that is, $E$ is a ${{\mathrm {Lip}}} 1$ set. In the other direction we show that every ${{\mathrm {Lip}}} 1$ set is $G_\delta$ and weakly dense. We also show that the converse of this statement is not true, namely that there exist weakly dense $G_{{\delta}}$ sets which are not ${{\mathrm {Lip}}} 1$. We say that a set $E\subset \mathbb{R}$ is ${{\mathrm {lip}}} 1$ if there is a continuous function $f$ such that ${{\mathrm {lip}}} f=\mathbf{1}_E$. We introduce the concept of strongly one-sided density and show that every ${{\mathrm {lip}}} 1$ set is a strongly one-sided dense $F_\sigma$ set.Comment: This is the final preprint version accepted to appear in European Journal of Mathematic

Peningkatan kemandirian dan hasil belajar matematika melalui strategi metakognitif berbasis tutor sebaya bagi siswa kelas V SD YPK persiapan kampung Anny

Tujuan penelitian untuk mengkaji peningkatan kemandirian dan hasil belajar matematika bagi Siswa SD YPK Persiapan Kampung Anny semester genap tahun ajaran 2012/2013 melalui strategi pembelajaran Metakognitif Berbasis Tutor Sebaya. Metode yang digunakan dalam penelitian ini adalah metode penelitian tindakan kelas yang terdiri dua siklus, tiap siklus terdiri dari tiga tahapan yaitu sadar belajar, perencanaan dan monitoring. Data yang diperoleh berupa nilai tes pada akhir siklus I dan pada akhir siklus II. Analisis data dilakukan dengan analisa deskriptif komparatif yaitu membandingkan nilai tes pada kondisi awal, siklus I dan pada siklus II. Hasil penelitian menunjukkan peningkatan kemandirian dan hasil belajar matematika yang dapat dilihat dari meningkatnya indikator-indikatornya meliputi: 1) siswa mampu menyelesaikan tugas dan tanggungjawab sebelum tindakan 62,5%, siklus I 78,125%, dan siklus II 90,32%, 2) siswa mampu mengatasi masalah sebelum tindakan 46,875%, siklus I 62,5%, dan siklus II 80,645%, 3) siswa percaya pada kemampuan diri sendiri sebelum tindakan 18,75%, siklus I 34,375%, dan siklus II 64,516% dan siswa yang nilainya tuntas KKM sebelum tindakan 68,75%, siklus I 71,875%, dan siklus II 83,87%. Berdasarkan uraian diatas disimpulkan bahwa penerapan strategi pembelajaran Metakognitif Berbasis Tutor Sebaya dalam pembelajaran matematika dapat meningkatkan kemandirian dan hasil belajar matematika