Elementary proofs of Embedding Theorems for Potential Spaces of Radial Functions

We present elementary proofs of weighted embedding theorems for radial potential spaces and some generalizations of Ni's and Strauss' inequalities in this setting.Comment: 19 page

Lyapunov-type Inequalities for Partial Differential Equations

In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in $N-$dimensional domains $\Omega$. We also consider singular and degenerate elliptic problems with $A_p$ coefficients involving the $p-$Laplace operator with zero Dirichlet boundary condition. As an application of the inequalities obtained, we derive lower bounds for the first eigenvalue of the $p-$Laplacian, and compare them with the usual ones in the literature

Growth-induced blisters in a circular tube

The growth of an elastic film adhered to a confining substrate might lead to the formation of delimitation blisters. Many results have been derived when the substrate is flat. The equilibrium shapes, beyond small deformations, are determined by the interplay between the sheet elastic energy and the adhesive potential due to capillarity. Here, we study a non-trivial generalization to this problem and consider the adhesion of a growing elastic loop to a confining \emph{circular} substrate. The fundamental equations, i.e., the Euler Elastica equation, the boundary conditions and the transversality condition, are derived from a variational procedure. In contrast to the planar case, the curvature of the delimiting wall appears in the transversality condition, thus acting as a further source of adhesion. We provide the analytic solution to the problem under study in terms of elliptic integrals and perform the numerical and the asymptotic analysis of the characteristic lengths of the blister. Finally, and in contrast to previous studies, we also discuss the mechanics and the internal stresses in the case of vanishing adhesion. Specifically, we give a theoretical explanation to the observed divergence of the mean pressure exerted by the strip on the container in the limit of small excess-length

Radial Solutions for Hamiltonian Elliptic Systems with Weights

We prove the existence of infinitely many radial solutions for elliptic systems in Rn with power weights. A key tool for the proof will be a weighted imbedding theorem for fractional-order Sobolev spaces, that could be of independent interest.Comment: 13 page

Students’ Perception On Quizizz As Online Quiz Learning Tool

Digital technology can be used as media in the learning process. One of the innovations that can be used by a teacher in the digital learning process is the assignment or quiz to students. The quiz can be used by the teachers to figure out how far students master the material and for students, it is very useful to find out how far they master the material. Online quizzes are expected to be able to make students active towards active learning. This study looked at Quizizz as a digital game-based learning tool for doing English quizzes while learning from a distance. Its goal was to find out how students saw Quizizz as a tool for digital quiz-based learning and how it was used for formative assessment. This research uses descriptive qualitative research. The subject of the research was third semester students of STKIP AL Maksum. The data were collected using questionnaire. The questioner will be given by google form. The results of this study showed that students liked Quizizz as a digital quiz-based learning tool because it helped them learn and got them involved, had clear rules and goals, clear results and immediate feedback, and let them talk to each other. They also did well on the formative assessment quiz Quizizz in English class. Also, the activities on Quizizz let students show what they knew, got feedback, and took charge of their own learning. Key words:  students’ perception, Quizizz, online quiz

THE SPEECH ACTS OF BANTENESE FAMILY IN MEDAN JOHOR

This research focuses on the types of speech acts and the meaning of the utterances used by Bantenese family. The study aims to find out the types of speech acts, the dominant type of speech acts used by Bantenese family in Medan Johor and the interpretation of the reason of Bantenese use these types of speech acts in their dialogues. This thesis conducts on the descriptive qualitative method. Descriptive design simply describes what data shows. This research elaborates on the utterances assumed to contain illocutionary acts. The findings of the research show the speech acts that occurred on Bantenese family in Medan Johor are assertive, directive, expressive, commissive and declarative. The presentations are: assertives acts 27.5%, directives acts 58.75%, commissives acts 5%, expressives acts 7.5%, and declaratives acts 1.25%. If elaborated, there are several dialogues in Bantenese family. There are between parents to children, children to parents, between sisters and brothers, husband and wife, grandmother to grandchildren and the last between aunt to nephew. The writer also finds that Bantenese usually or often used the statement in command, request, advice, offering, suggesting, confirmation, boasting, resigning and expressing something. It is shown from pragmatic meaning that is utterenced by Bantenese. In daily communication or dialogue in Bantenese family, they often say 'A' but the meaning is 'B' . They say with the statement that has meaning something. &nbsp