Class Of Fields Research Articles

P-адические L-функции и p-адические кратные дзета значения

Статья посвящена памяти Георгия Вороного. Описываются новые избранные результаты о рядах Эйзенштейна, о (мотивных), (p-адических), (кратных) значениях (круговых) дзета и L-функций, и их приложения, полученные ниже перечисляемыми авторами, а также элементарное введение в эти результаты. Дан краткий обзор новых результатов о (мотивных), (p-адических), (кратных) значениях (круговых) дзета функциях, L-функциях и рядах Эйзенштейна. Статья ориентирована на избранные задачи и не является исчерпывающей. Начало статьи содержит краткое изложение результатов о числах Бернулли, связанных с исследованиями Георгия Вороного. Результаты о кратных значениях дзета функций были представлены Д. Загиром, П. Делинем и А. Гончаровым, А. Гончаровым, Ф. Брауном, К. Глэносом (Glanois) и другими. С. Унвер ("Unver) исследовал кратные p-адические дзета-значения глубины два. Таннакиева интерпретация кратных p-адических дзета-значений дана Х. Фурушо. Краткая история и связи между группами Галуа, фундаментальными группами, мотивами и арифметическими функциями представлены в докладе Ю. Ихара. Результаты о кратных дзета-значениях, группах Галуа и геометрии модулярных многообразий представлены Гончаровым. Интересная унипотентная мотивная фундаментальная группа определена и исследована Делинем и Гончаровым. В данной работе мы кратко упоминаем в рамках (p-адических) L-функций и (p-адических) (кратных) дзета-значений применения подходов Куботы-Леопольдта и Ивасавы, которые основанны на p-адических L-функциях Куботы-Леопольда, и арифметических p-адических L-функциях Ивасавы. Прореферирован ряд недавних работ (и соответствующих результатов): кратные дзета-значения в корнях из единицы, построение семейств мотивных итерированных интегралов с предписанными свойствами по Глэносу (Glanois); явные выражения для круговых p-адических кратных дзета-значений глубины два по Унверу (Unver); связи арифметических степеней циклов Кудлы-Рапопорта на интегральной модели многообразия Шимуры, соответствующей унитарной группе сигнатуры (1,1), с коэффициентами Фурье центральных производных рядов Эйзенштейна рода 2 по Санкарану (Sankaran). Более полно с содержанием статьи можно ознакомиться по приводимому ниже оглавлению: Введение. 1. Сравнения типа Вороного для чисел Бернулли. 2. Римановы дзета-значения. 3. О группах классов колец с теорией дивизоров. Мнимые квадратичные и круговые поля. 4. Ряды Эйзенштейна. 5. Группы классов, поля классов и дзета-функции. 6. Кратные дзета-значения. 7. Элементы неархимедовых локальных полей и неархимедова анализа. 8. Итерированные интегралы и (кратные) дзета-значения. 9. Формальные и p-делимые группы. 10. Мотивы и (p-адические) (кратные) дзета-значения. 11. О рядах Эйзенштейна, ассоциированных с многообразиями Шимуры. Разделы 1-9 и подраздел 11.1 (О некоторых многообразиях Шимуры и модулярных формах Зигеля) можно рассматривать как элементарное введение в результаты раздела 10 и подраздела 11.2 (О несобственном пересечении дивизоров Кудлы-Рапопорта и рядах Эйзенштейна).Я глубоко признателен Н. М. Добровольскому за помощь и поддержку в процессе подготовки статьи к печати.

Paradygmaty nowej dyscypliny

Cel: Celem artykułu jest analiza przesłanek skłaniających do określenia paradygmatów dyscypliny nauki o komunikacji społecznej i mediach w kontekście nowej klasyfikacji dziedzin i dyscyplin nauki. Metody badań: Przy założeniu, że w nowej dyscyplinie dominują przedstawiciele dotychczasowej nauki o mediach oraz bibliologii i informatologii istotne jest podjęcie dyskusji tożsamościowej, wyodrębnienie subdyscyplin oraz udoskonalenie narzędzi badawczych. Wyniki i wnioski: W artykule przedstawiono chronologiczny i problemowy zarys rozwoju badań mediów w Polsce, szczególnie po 2011 roku, z uwzględnieniem aktywności Polskiego Towarzystwa Komunikacji Społecznej. Wartość poznawcza: Zwrócono uwagę na potencjał wynikający z połączenia dyscyplin autonomicznych charakteryzujących się multigenetycznością i otwartością.

Relative Pólya group and Pólya dihedral extensions of [formula omitted

A number field with trivial Pólya group [2] is called a Pólya field. We define “relative Pólya group Po(L/K)” for L/K a finite extension of number fields, generalizing the Pólya group. Using cohomological tools in [1], we compute some relative Pólya groups. As a consequence, we generalize Leriche's results in [17] and prove the triviality of relative Pólya group for the Hilbert class field of K. Then we generalize our previous results [19] on Pólya S3-extensions of Q to dihedral extensions of Q of order 2l, for l an odd prime. We also improve Leriche's upper bound in [16] on the number of ramified primes in Pólya Dl-extensions of Q and prove that for a real (resp. imaginary) Pólya Dl-extension of Q at most 4 (resp. 2) primes ramify.

Blow-ups and class field theory for curves

We propose another proof of the geometric class field theory for curves by considering blow-ups of symmetric products of curves.

On the ramified class field theory of relative curves

We generalize Deligne's approach to tame geometric class field theory to the case of a relative curve, with arbitrary ramification.

Comparison of effects of cervical headgear treatment on skeletal facial changes when the treatment time is altered: a randomized controlled trial.

There is a lack of evidence based on longitudinal information in the field of Class II malocclusion management with cervical headgear (CH), especially in a randomized setting. The main objective of this study was to evaluate skeletal facial changes, particularly in vertical dimensions, after Kloehn-type CH treatment in children when the timing of treatment is altered. Prospective, parallel-group, randomized controlled trial. Screened children with Class II malocclusion were randomized in 1:1 ratio to two groups of equal size by sealed-envelope randomization: the early group (EG), where active CH treatment was started at the age of 7.8 years, and the late group (LG), where CH treatment was started at the age of 9.5 years. The active treatment was continued until normal Class I occlusion on first molars was achieved. Cephalograms were taken at three different time points. Changes in cephalometric measurements were compared between groups and genders. Blinding was applicable for outcome evaluation. Of 67 randomized children, 56 completed the study. Upper face height increased during the CH treatment phase, as the parameter N-ANS increased significantly during the active treatments of EG (P < 0.05) and LG (P < 0.05). Also, the parameter NSL-PL increased significantly during the treatment of EG (P < 0.01) and during the treatment of LG (P < 0.01). The Gonial angle decreased significantly in the early CH treatment group compared to the later treatment group (T0-T2: P < 0.01). CH improved the antero-posterior jaw relationship. No harms were encountered. Although the upper face height increased, the mandible showed anterior rotation after CH treatment. The Gonial angle was significantly decreased in the EG compared to the LG. There were gender-specific differences in both sagittal and vertical dimensions when examining interrelations in dimensional changes. The differences found between the early and later treatment groups were not clinically important when the cephalometric results are considered. ClinicalTrials.gov (NCT02010346).

Koopman-Based Lifting Techniques for Nonlinear Systems Identification

We develop a novel lifting technique for nonlinear system identification based on the framework of the Koopman operator. The key idea is to identify the linear (infinite dimensional) Koopman operator in the lifted space of observables, instead of identifying the nonlinear system in the state space, a process which results in a linear method for nonlinear systems identification. The proposed lifting technique is an indirect method that does not require to compute time derivatives and is therefore well-suited to low-sampling rate data sets. Considering different finite-dimensional subspaces to approximate and identify the Koopman operator, we propose two numerical schemes: a main method and a dual method. The main method is a parametric identification technique that can accurately reconstruct the vector field of a broad class of systems. The dual method provides estimates of the vector field at the data points and is well-suited to identify high-dimensional systems with small datasets. This paper describes the two methods, provides theoretical convergence results, and illustrates the lifting techniques with several examples.

Sample-size dependent temperature dependence of the spontaneous magnetization

It is shown that the precise temperature dependence of the spontaneous magnetization depends on the domain structure and, additionally, on the macroscopic dimensions of the sample. In the multi-domain zero-field ground state of cubic ferromagnets (or antiferromagnets) with half-integer spin, thermal decrease of the spontaneous magnetization is by universal T2 function up to crossover to critical power function. Power functions of temperature that hold over a large temperature range and are independent of spin structure are the typical indication that the spin dynamics is controlled by a boson field. For the magnets with half-integer spin, the T2 function means a three-dimensional boson field. In the mono-domain state prepared by ferromagnetic saturation, all moments are oriented parallel to the field axis. For this one-dimensional spin configuration the boson field can be anticipated to be one-dimensional and the spontaneous magnetization should decrease according to universal T5/2 function (for S = half-integer). However, only for sufficiently large samples the T5/2 function is confirmed. For smaller samples successive crossover events in the sequence T2 → T3/2 → T5/2 can occur for increasing temperature. Occurrence of boson fields with a higher dimensionality (T2, T3/2) in the state of ferromagnetic saturation can be explained by scattering processes of the bosons at the inner surface of the sample. When the diameter of the sample is less than the mean free path of the bosons, all bosons will be reflected (or scattered) at the inner surface of the sample and the resulting boson field can become three-dimensional (T2 universality class). A one-dimensional spin orientation due to the applied demagnetization field but a three-dimensional boson field that controls spin dynamics is possible only for the T2 universality class because there is nearly no interaction between boson field and spins (magnons) in this universality class. With increasing temperature the mean free path of the bosons decreases and only a fraction of the bosons gets scattered at the inner surface of the sample. Crossover to T3/2 function and, eventually, to T5/2 function then can occur. A similar situation as for the polarized ferromagnets is observed in the axial-symmetric zero-field ground state of the hcp ferromagnet cobalt. Only for sufficiently large samples scattering of the bosons at the inner surface of the sample is of no importance and the intrinsic T5/2 function, typical for parallel alignment of all spins, shows up. The mean free path of the bosons can be estimated to be of the order of a few mm for T → 0.

RETRACTION] A Note on Number Knots and the Splitting of the Hilbert Class Field

Several number knots are defined including the five knots introduced by W. Jehne. The question of the splitting of the group extension of the Hilbert class field can be read off in terms of the triviality of these knots.

Magnetic field strengths of hot Jupiters from signals of star–planet interactions

Evidence of star-planet interactions in the form of planet-modulated chromospheric emission has been noted for a number of hot Jupiters. Magnetic star-planet interactions involve the release of energy stored in the stellar and planetary magnetic fields. These signals thus offer indirect detections of exoplanetary magnetic fields. Here we report the derivation of the magnetic field strengths of four hot Jupiter systems using the power observed in Ca II K emission modulated by magnetic star-planet interactions. By approximating the fractional energy released in the Ca II K line we find that the surface magnetic field values for the hot Jupiters in our sample range from 20 G to 120 G, ~10-100 times larger than the values predicted by dynamo scaling laws for planets with rotation periods of ~2 - 4 days. On the other hand, these value are in agreement with scaling laws relating the magnetic field strength to the internal heat flux in giant planets. Large planetary magnetic field strengths may produce observable electron-cyclotron maser radio emission by preventing the maser from being quenched by the planet's ionosphere. Intensive radio monitoring of hot Jupiter systems will help confirm these field values and inform on the generation mechanism of magnetic fields in this important class of exoplanets.

The field of moduli of singular K3 surfaces

We study the field of moduli of singular K3 surfaces. We discuss both the field of moduli over the CM field and over $${{\mathbb {Q}}}$$. As a by-product, we show non-finiteness of isomorphism classes of singular K3 surfaces with field of moduli of bounded degree. Finally, we provide an explicit description of the field of moduli in terms of the 2-torsion of the Galois group of the ring class field over which the K3 surface is defined.

Про спадково незвiднi унiмономiальнi зображення циклiчних p-груп над локальними кiльцями характеристики p

The task of the description up to equivalency of the matrix representations of finite pgroups of order greater then p aver a commutative local ring of characteristics of ps (s &gt; 0) that is not a field contains the classical unsolved problem of pair of matrices over a field. Therefore, consideration of partial cases and the study of special representation matrix representations is importent. Let K be a commutative ring with a identity, G is a finitely generated group with some fixed system of generator elements a1,...,ar. Every matrix representation of the group G over the ring K equivalent to Γ : ai → E+Mi (i = 1,...,r), where E be an identity n×n-matrix, Mi be a monomial n×n-matrix (i = 1,...,r), we call unimonomial. An reducible unimonomial representation over the ring K, in a reducible form of which on diagonal blocks at least one unimonomial representation is formed, we call hereditary reducible over the ring K. A series of unimonomial representations of a finite cyclic p-group H = haiover commutative local principle ideal ring K of characteristic p with nilpotent Jacobson radical of the degree l (1 &lt; l &lt; ∞) of the form a → E + 0 ... 0 1 1 ... 0 0 . . . ... . . . . . . 0 ... 1 0!· diag[ε1ts1,...,εntsn], where si ≥ 0, εi be elements from K∗ (i = 1,...,n), t be an generator element of Jacobson radical ring K. It is making up clear the criterion, when the map of the given form sets the representation of the group H (P|H|−1 j=0 si+j ≥ l (i = 1,...,n), herethe indexes are considered by the module n). It have been found the sufficient condition of hereditary irreducibility of the constructed representations ((Pn i=1 si,n) = 1,tPn i=1 si 6= 0). In addition, we can obtain the hereditary reducibility of the constructed representations in the case when (Pn i=1 si,n) &gt; 1,Qn i=1 εi = 1). Based on the researches of Bondarenko V. M., Bortosh M. Yu. of similarity of the monomial matrices it is making up clear the criterion the equivalence of the constructed representations (the corresponding sequences (s1,...,sn) are cyclically equivalent a relevant productsQn i=1 εi are equal modulo Ann (ts), where s is the largest member of the weight sequence (s1,...,sn)). In the case of the finiteness of the ring K by computation in the GAP system it have been found the number of all, up to equivalence, constructed unimonomial hereditary irreducible matrix representations of a cyclic nontrivial p-group depending on the number of elements of the residue class field of the ring K.

Lorentzian Einstein metrics with prescribed conformal infinity

We prove a local well-posedness theorem for the $(n+1)$-dimensional Einstein equations in Lorentzian signature, with initial data $(\widetilde{g},K)$ whose asymptotic geometry at infinity is similar to that anti-de Sitter (AdS) space, and compatible boundary data $\widehat{g}$ prescribed at the time-like conformal boundary of space-time. More precisely, we consider an $n$-dimensional asymptotically hyperbolic Riemannian manifold $(M, \widetilde{g})$ such that the conformally rescaled metric $x^2 \widetilde{g}$ (with $x$ a boundary defining function) extends to the closure $\overline{M}$ of $M$ as a metric of class $C^{n-1} (\overline{M})$ which is also poly-homogeneous of class $C^p_{\mathrm{polyhom}} (\overline{M})$. Likewise we assume that the conformally rescaled symmetric $(0, 2)$-tensor $x^ 2 K$ extends to $\overline{M}$ as a tensor field of class $C^{n-1} (\overline{M})$ which is polyhomogeneous of class $C^{p-1}_{\mathrm{polyhom}} (\overline{M})$. We assume that the initial data $(\widetilde{g}, K)$ satisfy the Einstein constraint equations and also that the boundary datum is of class $C^p$ on $\partial M \times (-T_0, T_0)$ and satisfies a set of natural compatibility conditions with the initial data. We then prove that there exists an integer $r_n$, depending only on the dimension $n$, such that if $p \geqslant 2q + r_n$, with $q$ a positive integer, then there is $T \gt 0$, depending only on the norms of the initial and boundary data, such that the Einstein equations (1.1) has a unique (up to a diffeomorphism) solution $g$ on $(-T, T) \times M$ with the above initial and boundary data, which is such that $x^2 g \in C^{n-1} ((-T, T) \times \overline{M}) \; \cap \; C^q_{\mathrm{polyhom}} ((-T, T) \times \overline{M})$. Furthermore, if $x^2 \widetilde{g} , x^2 K$ are polyhomogeneous of class $C^{\infty}$ and $\widehat{g}$ is in $C^{\infty} ((-T_0, T_0) \times \partial \overline{M})$, then $x^2 g$ is in $C^{\infty}_{\mathrm{polyhom}} ((-T, T) \times \overline{M})$.

REFINED SWAN CONDUCTORS OF ONE-DIMENSIONAL GALOIS REPRESENTATIONS

For a character of the absolute Galois group of a complete discrete valuation field, we define a lifting of the refined Swan conductor, using higher dimensional class field theory.

Simplified exact SICS

In the standard basis, exact expressions for the components of SIC vectors (belonging to a symmetric informationally complete positive operator valued measure or POVM) are typically very complicated. We show that a simple transformation to a basis adapted to the symmetries of a fiducial SIC vector can result in a massive reduction in complexity. We rely on a conjectural number theoretic connection between SICs in dimension dj and SICs in dimension dj+1 = dj(dj − 2). We focus on the sequence 5, 15, 195, … We rewrite Zauner’s exact solution for the SIC in dimension 5 to make its simplicity manifest and use our adapted basis to convert numerical solutions in dimensions 15 and 195 to exact solutions. Comparing to the known exact solutions in dimension 15, we find that the simplification achieved is dramatic. The proof that the exact vectors are indeed SIC fiducial vectors, also in dimension 195, is guided by the standard ray class hypothesis about the algebraic number fields generated by the SICs. In the course of the calculation, we introduce SIC adapted generators for the ray class field. We conjecture that our result generalizes to every dimension in the particular sequence we consider.

Hubungan Minat Belajar dengan Hasil Belajar dalam Mata Pelajaran SMAW di SMK Negeri 1 Sumatera Barat

The problem in this study is that students are less interested in learning and seen from the daily results obtained from SMAW subject teachers that the learning outcomes of SMAW subjects in the Welding Engineering department are still low. The purpose of this study is to determine whether there is a relationship between interest in learning and learning outcomes in SMAW subjects. This type of research is descriptive correlational research. The sample stated in this study were all students of class XI of the Welding Engineering Department who participated in the 48 Solid Metal Arc Welding subjects. The results of the study revealed a contribution of a positive relationship between interest in learning with student learning outcomes in the field of study SMAW Class XI Welding Engineering students of SMK Negeri 1 West Sumatra 2018/2019 learning year. This gives the meaning of the higher interest in learning, the higher learning outcomes of SMAW learning outcomes.

On the automorphic side of the K-theoretic Artin symbol

Clausen has constructed a homotopical enrichment of the Artin reciprocity symbol in class field theory. On the Galois side, Selmer K-homology replaces the abelianized Galois group, while on the automorphic side the K-theory of locally compact vector spaces replaces classical idelic objects. We supply proofs for some predictions of Clausen regarding the automorphic side.

Hubungan Minat Belajar dengan Hasil Belajar dalam Mata Pelajaran SMAW di SMK Negeri 1 Sumatera Barat

The problem in this study is that students are less interested in learning and seen from the daily results obtained from SMAW subject teachers that the learning outcomes of SMAW subjects in the Welding Engineering department are still low. The purpose of this study is to determine whether there is a relationship between interest in learning and learning outcomes in SMAW subjects. This type of research is descriptive correlational research. The sample stated in this study were all students of class XI of the Welding Engineering Department who participated in the 48 Solid Metal Arc Welding subjects. The results of the study revealed a contribution of a positive relationship between interest in learning with student learning outcomes in the field of study SMAW Class XI Welding Engineering students of SMK Negeri 1 West Sumatra 2018/2019 learning year. This gives the meaning of the higher interest in learning, the higher learning outcomes of SMAW learning outcomes

On Hilbert class field tower for some quartic number fields

We determine the Hilbert 2-class field tower for some quartic number fields k whose 2-class group Ck,2 is isomorphic to Z∕2Z×Z∕2Z.

Tribonacci numbers and primes of the form p = x 2 + 11y 2

Abstract In this paper we show that for any prime number p not equal to 11 or 19, the Tribonacci number T p−1 is divisible by p if and only if p is of the form x 2 + 11y 2. We first use class field theory on the Galois closure of the number field corresponding to the polynomial x 3 − x 2 − x − 1 to give the splitting behavior of primes in this number field. After that, we apply these results to the explicit exponential formula for T p−1. We also give a connection between the Tribonacci numbers and the Fourier coefficients of the unique newform of weight 2 and level 11.