Bounding Selmer groups for the Rankin--Selberg convolution of Coleman families

Let $f$ and $g$ be two cuspidal modular forms and let $\mathcal{F}$ be a Coleman family passing through $f$, defined over an open affinoid subdomain $V$ of weight space $\mathcal{W}$. Using ideas of Pottharst, under certain hypotheses on $f$ and $g$ we construct a coherent sheaf over $V \times \mathcal{W}$ which interpolates the Bloch-Kato Selmer group of the Rankin-Selberg convolution of two modular forms in the critical range (i.e. the range where the $p$-adic $L$-function $L_p$ interpolates critical values of the global $L$-function). We show that the support of this sheaf is contained in the vanishing locus of $L_p$.Comment: Final version. To appear in Canadian Jour. Mat

Hyperelliptic Curves with Maximal Galois Action on the Torsion Points of their Jacobians

In this article, we show that in each of four standard families of hyperelliptic curves, there is a density-$1$ subset of members with the property that their Jacobians have adelic Galois representation with image as large as possible. This result constitutes an explicit application of a general theorem on arbitrary rational families of abelian varieties to the case of families of Jacobians of hyperelliptic curves. Furthermore, we provide explicit examples of hyperelliptic curves of genus $2$ and $3$ over $\mathbb Q$ whose Jacobians have such maximal adelic Galois representations.Comment: 24 page

The explicit Local Langlands Correspondence for G2G_2 II: character formulas and stability

We write down character formulas for non-supercuspidal representations of $G_2$ considered by Aubert-Xu, and show that stability for $L$-packets uniquely pins down the Local Langlands Correspondence constructed by Aubert-Xu, thus proving unique characterization of the LLC \textit{loc.cit.}Comment: 19 page

The explicit Local Langlands Correspondence for GSp4\mathrm{GSp}_4, Sp4\mathrm{Sp}_4 and stability (with an application to Modularity Lifting)

We give a purely local proof of the explicit Local Langlands Correspondence for $\mathrm{GSp}_4$ and $\mathrm{Sp}_4$. Moreover, we give a unique characterization in terms of stability of $L$-packets and other properties. Finally, in the appendix, we give an application of our explicit local Langlands correspondence to modularity lifting.Comment: 38 page

Bioinspired Coordinated Path Following for Vessels with Speed Saturation Based on Virtual Leader

This paper investigates the coordinated path following of multiple marine vessels with speed saturation. Based on virtual leader strategy, the authors show how the neural dynamic model and passivity-based techniques are brought together to yield a distributed control strategy. The desired path following is achieved by means of a virtual dynamic leader, whose controller is designed based on the biological neural shunting model. Utilizing the characteristic of bounded and smooth output of neural dynamic model, the tracking error jump is avoided and speed saturation problem is solved in straight path. Meanwhile, the coordinated path following of multiple vessels with a desired spatial formation is achieved through defining the formation reference point. The consensus of formation reference point is realized by using the synchronization controller based on passivity. Finally, simulation results validate the effectiveness of the proposed coordinated algorithm

English Teaching Reform in Local Undergraduate Colleges Based on Interlanguage Fossilization

The interlanguage fossilization is a distinguishing characteristic of second language acquisition and plays an important role in promoting the foreign language teaching in China. According to survey four main problems of English teaching in local undergraduate colleges have been found, involving language environment, teaching methods, teacher-student relationship and test mode. Therefore, this paper expounds the characteristics, classification and basic causes of interlanguage petrochemical phenomena, and proposes the main measures of English teaching reform in local undergraduate colleges from the perspective of theory of interlanguage fossilization. The reform measures are as follows (a)foster a good language learning environment, (b) emphasize learning strategy in the teaching process, (c) innovate teaching concepts and teaching models,(d) select high-quality teaching materials and strengthen teacher promotion

Observer-based Control Barrier Functions for Safety Critical Systems

This paper considers the safety-critical control design problem with output measurements. An observer-based safety control framework that integrates the estimation error quantified observer and the control barrier function (CBF) approach is proposed. The function approximation technique is employed to approximate the uncertainties introduced by the state estimation error, and an adaptive CBF approach is proposed to design the safe controller which is obtained by solving a convex quadratic program (QP). Theoretical results for CBFs with a relative degree 1 and a higher relative degree are given individually. The effectiveness of the proposed control approach is demonstrated by two numerical examples.Comment: 7 pages, 2 Figure

An Approach for Chinese-Japanese Named Entity Equivalents Extraction Using Inductive Learning and Hanzi-Kanji Mapping Table

Named Entity Translation Equivalents extraction plays a critical role in machine translation (MT) and cross language information retrieval (CLIR). Traditional methods are often based on large-scale parallel or comparable corpora. However, the applicability of these studies is constrained, mainly because of the scarcity of parallel corpora of the required scale, especially for language pairs of Chinese and Japanese. In this paper, we propose a method considering the characteristics of Chinese and Japanese to automatically extract the Chinese-Japanese Named Entity (NE) translation equivalents based on inductive learning (IL) from monolingual corpora. The method adopts the Chinese Hanzi and Japanese Kanji Mapping Table (HKMT) to calculate the similarity of the NE instances between Japanese and Chinese. Then, we use IL to obtain partial translation rules for NEs by extracting the different parts from high similarity NE instances in Chinese and Japanese. In the end, the feedback processing updates the Chinese and Japanese NE entity similarity and rule sets. Experimental results show that our simple, efficient method, which overcomes the insufficiency of the traditional methods, which are severely dependent on bilingual resource. Compared with other methods, our method combines the language features of Chinese and Japanese with IL for automatically extracting NE pairs. Our use of a weak correlation bilingual text sets and minimal additional knowledge to extract NE pairs effectively reduces the cost of building the corpus and the need for additional knowledge. Our method may help to build a large-scale Chinese-Japanese NE translation dictionary using mono-lingual corpora