Class Of Fields Research Articles

이중언어 중국인 석박사 학생의 유학생활 만족도와 개선방안 연구

This study aims to study Chinese master's and doctoral students in bilingual courses to find out their satisfaction with their study abroad life and suggest improvements. Using phenomenological methods, the researcher selected eight Chinese students with master's and doctoral courses in bilingualism at N University as participants in the study. Data obtained through one-on-one in-depth interviews in Chinese were analyzed using the method suggested by Colaizzi. As a result, Chinese master's and doctoral students were generally satisfied with Korean life, especially studying abroad for master's and doctoral courses, but they reported inconveniences in the fields of major classes, non-major classes, school human relations, school administration and facilities, and through these, the researcher suggested five improvement measures. This study is meaningful as basic data that supplements the gap between previous studies on bilingual master's and doctoral courses. In the future, qualitative and quantitative studies are needed on research participants from a large scale of various backgrounds.

Density of Selmer ranks in families of even Galois representations, Wiles' formula, and global reciprocity

This paper concerns the distribution of Selmer ranks in a family of even Galois representations in residual characteristic p=2 obtained by allowing ramification at auxiliary primes. The main result is a Galois cohomological analogue of a theorem of Friedlander, Iwaniec, Mazur and Rubin on the distribution of Selmer ranks in a family of twists of elliptic curves. The Selmer groups are constructed as prescribed by the Galois cohomological method for GL(2): At each ramified place, the local Selmer condition is the tangent space of a smooth quotient of the local deformation ring. By methods of global class field theory, the Selmer group at the minimal level is computed explicitly. The infinitude of primes for which the Selmer rank increases by one is proved, and the density of such primes is shown to be 1/192. The proof combines Wiles' formula and the global reciprocity law. The result has implications for the algebraic structure of even deformation rings and the distribution of their presentations in families.

Development studies meet Pierre Bourdieu: the case of Chinese Private FDI in Zambia

ABSTRACTInspired by Bourdieu's field theory and utilising the case of Zambia, this article aims to enhance the understanding of the intricate relationship between Chinese private investors and sub-Saharan state institutions. The study proposes an epistemological framework that integrates sociological, anthropological and neo-institutional approaches to development studies. Through extensive fieldwork and over 75 interviews with both Chinese and Zambian stakeholders, we explore various contexts in which group-actors related to foreign capital in Zambia operate. We argue that three separate habiti – inhabited by the Zambian political class, Chinese investors and ‘ordinary’ Zambians – are crucial for comprehending private foreign capital operations in this sub-Saharan state. The ordinary Zambians and Zambian political class fields converge primarily during elections, while interactions between ordinary Zambians and Chinese investors have remained very limited (predominantly employee–employer relations), creating an ideational structure of hostility. In contrast, the Zambian political class and Chinese private investor fields crosscut and are mutually constitutive.

On the $\lambda$-invariant of Selmer Groups Arising from Certain Quadratic Twists of Gross Curves

Let $q$ be a prime with $q \equiv 7 \mod 8$, and let $K=\mathbb{Q}(\sqrt{-q})$. Then $2$ splits in $K$, and we write $\mathfrak{p}$ for either of the primes $K$ above $2$. Let $K_\infty$ be the unique $\mathbb{Z}_2$-extension of $K$ unramified outside $\mathfrak{p}$. For certain quadratic and biquadratic extensions $\mathfrak{F}/K$, we prove a simple exact formula for the $\lambda$-invariant of the Galois group of the maximal abelian 2-extension unramified outside $\mathfrak{p}$ of the field $\mathfrak{F}_\infty = \mathfrak{F} K_\infty$. Equivalently, our result determines the exact $\mathbb{Z}_2$-corank of certain Selmer groups over $\mathfrak{F}_\infty$ of a large family of quadratic twists of the higher dimensional abelian variety with complex multiplication, which is the restriction of scalars to $K$ of the Gross curve with complex multiplication defined over the Hilbert class field of $K$. We also exhibit computations of the associated Selmer groups over $K_n$ in the case when the $\lambda$-invariant is equal to $1$; here $K_n$ denotes the $n$-th layer of $K_\infty/K$.

The interconnection between local and global m-th powers and Grunwald-Wang theorem

The relation between local and global solution of an equation can be discussed with the method of class field theory and algebraic number theory. In this piece of writing, the author will introduce the behavior of both local and global m-th power in some specific number field. Of course, the result in this paper can be extended into the function field, but it will not be involved in this paper. This paper will prove that if k(_(2^t ))/k is cyclic then the Local m-th powers everywhere is equivalent to the global m-th power. In the Non-cyclic case this decomposition becomes P(m,S)=k^mk^m. This paper will also prove some useful propositions in topological group theory, which will be used in the proof of Grunwald-Wang theorem. Grunwald-Wang theorem states that we can find a cyclic extension with given local behaviors. To describe the extension, this paper combines character theory with a topological group, one can depict the cyclic extension. This theorem can be used in the further exploration of central simple algebra.

Upaya Guru Kelas dalam Menanamkan Pendidikan Karakter Jujur Melalui Metode Bercerita di TK Kemala Bhayangkari Muara Bungo

This research is motivated by several problems that the author found at the Bhayangkari Muara Bungo Kindergarten, students often lie, every time they say a word, many children don't want to be honest, and also lie, if asked, many also answer by lying, children don't want to admit their mistakes, because children are afraid of being scolded. and are afraid of being punished by the teacher, therefore children are afraid to be more open or honest. The purpose of this research is to find out how class teachers try to instill honest character education through the method of telling stories to children at the Kemala Bhayangkari Muara Bungo Kindergarten. This research is descriptive qualitative field research (filed research). The research was located at Kemala Bhayangkari Muara Bungo Kindergarten. The key informants were the class teachers and the supporting informants were the study teachers and the school principal. This research technique is snowball sampling, and the data collection techniques for this research are observation, interviews and documentation. The results of this research show that class teachers and field teachers tell stories through the Sikancil & Simonyet fairy tale and the Honesty Cup because fairy tales, one of the intrinsic elements in fairy tales, is that they have a message or moral message. Fairy tales can really be used as social media that can shape a character. children because fairy tales have moral values that children can learn. Telling stories using puppets can improve children's pronunciation because it can attract students' attention so that students are happy and can easily understand what is being told and taught. Telling stories using picture media, students will be able to read the contents of the story by looking at the pictures shown by the teacher, telling stories using picture media, students will be more enthusiastic about listening to stories presented by the teacher, telling stories using picture media will help to clarify messages or events so that children pay more attention to the story being told.

On the abc$abc$ conjecture in algebraic number fields

AbstractIn this paper, we prove a weak form of the conjecture generalised to algebraic number fields. Given integers satisfying , Stewart and Yu were able to give an exponential bound in terms of the radical over the integers (Stewart and Yu [Math. Ann. 291 (1991), 225–230], Stewart and Yu [Duke Math. J. 108 (2001), no. 1, 169–181]), whereas Győry was able to give an exponential bound in the algebraic number field case for the projective height in terms of the radical for algebraic numbers (Győry [Acta Arith. 133 (2008), 281–295]). We generalise Stewart and Yu's method to give an improvement on Győry's bound for algebraic integers over the Hilbert Class Field of the initial number field K. Given algebraic integers in a number field K satisfying , we give an upper bound for the logarithm of the projective height in terms of norms of prime ideals dividing , where L is the Hilbert Class Field of K. In many cases, this allows us to give a bound in terms of the modified radical as given by Masser (Proc. Amer. Math. Soc. 130 (2002), no. 11, 3141–3150). Furthermore, by employing a recent bound of Győry (Publ. Math. Debrecen 94 (2019), 507–526) on the solutions of S‐unit equations, our estimates imply the upper bound where is an effectively computable constant. Further, given conditions on the largest prime ideal dividing , we obtain a sub‐exponential bound for in terms of the radical. Independently, as a direct application of his bounds on the solutions of S‐unit equations(Győry ([Publ. Math. Debrecen 94 (2019), 507–526]), Győry (Publ. Math. Debrecen 100 (2022), 499–511) also attains results mentioned above, including the above inequality, but over the base field K, as discussed in Section 6. As a consequence of our results, we will give an application to the effective Skolem–Mahler–Lech problem and give an improvement to a result by Lagarias and Soundararajan (J. Théor. Nombres Bordeaux 23 (2011), no. 1, 209–234) on the XYZ conjecture.

DEVELOPMENT OF A MATRIX MODULE TO IMPROVE YOUR UNDERSTANDING CAPABILITY OF MATHEMATICAL CONCEPTS

Mathematics subjects, which ideally are logical and useful subjects, have so far been less favored by students. The reality in schools is that there are still many who have difficulty understanding the concept of material, oneYof theYcausesYof thisYproblem is becauseY learningYis stillYteacher-centered and hasYnot been developed by the teacher's own teaching materials in learning. TheYpurpose ofYthis study was to develop aYmatrix module inYimproving theYabilityYtoYunderstand mathematical concepts.YThe type of researchYis research andYdevelopment (R&D), with the ADDIEYmodel (analyze, design, development, implementation, evaluation). Data collectionYtechniques are questionnaires, andYtests. Data analysisYtechniques are qualitative dataYanalysis and quantitative data analysis. Based on research and discussion that the results of the validation test from the validator show that it is very valid. The resultsYof the validationYof the material section obtained an average of 79.54% with a valid category. The results of the validation of media experts obtained an average of 92.59% with a very valid category and the results of the validation of linguists obtained an average of 90% with a very valid category. From the three validators, theYresults of the module validity obtained an average of 87.37% with a very valid category. practicality results were obtained based on limited class trials and field trials. The results of practicality in the limitedYclass trialYobtained results of 2.86 with a percentage of 71.5% in the very practical category. The results of practicality in field trials obtained results of 3.61 with aYpercentage of 90.25 and were categorized as very practical. The results of the effectiveness of the limited class trialYmodule with an average score of 0.80 in the high category, and the results of the effectiveness of the field class trial with theyacquisition of anyaverage scoreyof 0.66 inythe mediumYcategory. The developedYmodule is expected to beYused in improvingYthe ability to understand mathematical concepts in matrixYmaterial.

Explicit upper bounds on the average of Euler–Kronecker constants of narrow ray class fields

Explicit upper bounds on the average of Euler–Kronecker constants of narrow ray class fields

“When We Come to Your Class … We Feel Not Like We're in Prison”: Resisting Prison-School’s Dehumanizing and (De)Socializing Mechanisms Through Abolitionist Praxis

Education research increasingly conceptualizes how social interactions and contexts of public schools replicate practices found in prisons. Yet prison-schooling is often left out of education research. Concurrently, prison-schooling is where we educate a disproportionate amount of multiply marginalized youth, specifically disabled Girls of Color. The lack of attention to prison-schools has limited how teaching in youth carceral facilities can be examined for its challenges and supports of disabled Girls of Color. Centering the girls’ words from class observations, field notes, and interviews, this study describes and intervenes in dehumanizing and (de)socializing mechanisms in prison-school education. We explore attempts and impacts of countering prison-school education through a sociocritical literacy course infused with an abolitionist praxis. We end with discussion on the limits of countering prison-school through courses alone, suggesting abolition across multiple scales instead.

On special values of generators of modular function fields

Let N be a positive integer and ζN be a primitive Nth root of unity. Let X(N) be the modular curve of level N and FX(N),Q(ζN) be its field of meromorphic functions with Fourier coefficients in Q(ζN). Let u and v be nonconstant functions in FX(N),Q(ζN) which generate a sufficiently large subfield of FX(N),Q(ζN) over Q(ζN). In this paper, we give sufficient conditions for generating the ray class field of an imaginary quadratic field K modulo N over K(ζN) by the special values of u and v.

Implementation of Discovery Learning Models to Improve Student Mastery of Zakat Management Materials In Fiqih Study

Quality education will emerge from schools that have good quality, therefore improving the quality and good learning outcomes. This study discusses the implementation of the Discovery Learning Learning Model to improve Student Mastery in Zakat Management Materials in the Fiqih Study Field in Class VIII Mtsn 6 Pasuruan. The formulation of the problem is how to plan discovery learning models, how to implement discovery learning to improve students' mastery of zakat management materials in the field of Fiqih studies, what are the supporting and inhibiting factors for implementing discovery learning to improve student mastery of zakat management materials in the field of Fiqih studies, in research This includes descriptive research using a qualitative approach. While the data collection techniques in this study used the techniques of observation, interviews, and documentation. While the data analysis technique used is descriptive qualitative. Research result. Discovery learning-based Fiqih learning planning at MTSN 6 Pasuruan was realized in the form of a syllabus along with the development of lesson plans. The lesson plan is designed as a teacher's guide for teaching, what is unique is that in addition to containing competency indicators to be achieved, the lesson plan developed by the teacher is also loaded in full and in detail according to the scenario of the stages of the discovery model. Implementation of Fiqih learning based on discovery learning at MTSN 6 Pasuruan was carried out in accordance with the stages of implementation of the discovery learning model (Stimulation, problem statement, data collection, data processing, generalization). What is different from the discovery model, in general, is the way and innovation teachers in delivering, always updated according to technological developments and collaborating with existing media. This makes students able to complete their discoveries very well. Supporting and Inhibiting Factors Fiqih learning is based on discovery learning using repeating the core material into the subject matter, Providing several questions that are relevant to the material presented.

EFFORTS TO INCREASE TEACHER COMPETENCY IN TEACHING THROUGH THE USE OF THE MERDEKA TEACHING PLATFORM AT SDN PAKIS V SURABAYA ACADEMIC YEAR 2022/2023

The implementation of the Independent Learning Curriculum is a major change in the education system in Indonesia. These changes not only affect classroom teaching methods, but also affect school structure and management systems. In this context, the role of the school principal becomes very important, especially in supervising the curriculum implementation process.
 Principal supervision is very important in implementing the Independent Learning Curriculum for several reasons. Supervising the implementation of the Independent Learning Curriculum is not an easy task. A good understanding of this curriculum is required, as well as skills in supervision and school management. Therefore, it is important for school principals to continue to improve their competence in this matter.
 This research was conducted using the school action research method which lasted for 2 cycles. Each cycle consists of planning, implementation, observation and reflection stages. The research method used by researchers is to carry out academic supervision which includes traditional supervision and clinical supervision with subj. 10 Class teachers and fields of study
 The results of this research show that the implementation of the use of good practices in PMM through academic supervision in cycle 2 in the learning category is very good with a score of 4.2. With the results above, the implementation of the use of good practices in PMM through academic supervision is considered successful because the results are good and in accordance with the predetermined indicators of success in increasing teacher professionalism.

Characterizing absolutely irreducible integer-valued polynomials over discrete valuation domains

Rings of integer-valued polynomials are known to be atomic, non-factorial rings furnishing examples for both irreducible elements for which all powers factor uniquely (absolutely irreducibles) and irreducible elements where some power has a factorization different from the trivial one.In this paper, we study irreducible polynomials F∈Int(R) where R is a discrete valuation domain with finite residue field and show that it is possible to explicitly determine a number S∈N that reduces the absolute irreducibility of F to the unique factorization of FS.To this end, we establish a connection between the factors of powers of F and the kernel of a certain linear map that we associate to F. This connection yields a characterization of absolute irreducibility in terms of this so-called fixed divisor kernel. Given a non-trivial element v of this kernel, we explicitly construct non-trivial factorizations of Fk, provided that k≥L, where L depends on F as well as the choice of v. We further show that this bound cannot be improved in general. Additionally, we provide other (larger) lower bounds for k, one of which only depends on the valuation of the denominator of F and the size of the residue class field of R.

An infinite dimensional version of the intermediate value theorem

Let mathfrak {f}= I-k be a compact vector field of class C^1 on a real Hilbert space mathbb {H}. In the spirit of Bolzano’s Theorem on the existence of zeros in a bounded real interval, as well as the extensions due to Cauchy (in mathbb {R}^2) and Kronecker (in mathbb {R}^k), we prove an existence result for the zeros of mathfrak {f} in the open unit ball mathbb {B} of mathbb {H}. Similarly to the classical finite dimensional results, the existence of zeros is deduced exclusively from the restriction mathfrak {f}|_mathbb {S} of mathfrak {f} to the boundary mathbb {S} of mathbb {B}. As an extension of this, but not as a consequence, we obtain as well an Intermediate Value Theorem whose statement needs the topological degree. Such a result implies the following easily comprehensible, nontrivial, generalization of the classical Intermediate Value Theorem: If a half-line with extremeq notin mathfrak {f}(mathbb {S})intersects transversally the functionmathfrak {f}|_mathbb {S}for only one point of mathbb {S}, then any value of the connected component ofmathbb {H}{setminus }mathfrak {f}(mathbb {S})containingqis assumed bymathfrak {f}inmathbb {B}. In particular, such a component is bounded.

Ramification theory of reciprocity sheaves, II Higher local symbols

We construct a theory of higher local symbols along Paršin chains for reciprocity sheaves. Applying this formalism to differential forms, gives a new construction of the Paršin–Lomadze residue maps, and applying it to the torsion characters of the fundamental group gives back the reciprocity map from Kato’s higher local class field theory in the geometric case. The higher local symbols satisfy various reciprocity laws. The main result of the paper is a characterization of the modulus attached to a section of a reciprocity sheaf in terms of the higher local symbols.

New symmetry reduction method for (1+1)-dimensional differential-difference equations

We propose a new symmetry reduction method for (1+1)-dimensional differential-difference equations (DDEs), namely, the λ-symmetry reduction method of solving ordinary differential equations is generalized to DDEs. Order-reduction processes are a consequence of the invariance of the given DDE under vector fields of the new class. These vector fields satisfy a new prolongation formula. A simple example of order-reduction is provided to illustrate the application.

Heuristics for Anti-cyclotomic ℤ p -extensions

This paper studies Iwasawa invariants in anti-cyclotomic towers. We do this by proposing two heuristics supported by computations. First we propose the Intersection Heuristics: these model “how often” the p-Hilbert class field of an imaginary quadratic field intersects the anti-cyclotomic tower and to what extent. Second we propose the Invariants Heuristics: these predict that the Iwasawa invariants and usually vanish for imaginary quadratic fields where p is non-split.

Infinite Hilbert class field tower

Infinite Hilbert class field tower

Class fields, Dirichlet characters, and extended genus fields of global function fields

AbstractWe study the extended genus field of an abelian extension of a rational function field. We follow the definition of Anglès and Jaulent, which uses the class field theory. First, we show that the natural definition of extended genus field of a cyclotomic function field obtained by means of Dirichlet characters is the same as the one given by Anglès and Jaulent. Next, we study the extended genus field of a finite abelian extension of a rational function field along the lines of the study of genus fields of abelian extensions of rational function fields. In the absolute abelian case, we compare this approach with the one given by Anglès and Jaulent.