These are the notes for a short course on Borcherds Products held in Aachen on 1st2nd August 2012. The lectures are intended for someone who does not know what a Borcherds product is, but does know what a modular form is. In preparing these notes I’ve used the following sources: [1, 2, 3, 4, 5]. All the correct statements in these notes are taken from those sources, and all the mistakes are my ...

This paper presents the approaches IRIT developed for the VLNetChallenge regarding recommender systems in the context of video lectures. The first task aims at recommending newly acquired lectures after viewing an “old” lecture. We use random walk algorithms based on a graph composed of author, category, event, and lecture nodes and associated relationships. The second task aims at recommending...

With emerge of the COVID-19 pandemic, video-based lectures (VBLs) was widely used as an effective online faculty development tool. VBLs varies from short videos (5-minute) to long one (1-2 hours). So, current study aims evaluate effectiveness versus VBLs. A total 21 (9) and (12) were produced, in 2020, by authors. The metadata for all downloaded YouTube [VBLs overview data, audiences’ engagemen...

These notes are a short introduction to the pinch technique. We present the oneloop calculations for basic QCD Green’s functions. The equivalence between the pinch technique and the background field method is explicitly shown at the one-loop level. We review the absorptive pinch technique in the last sections. These lectures are a compilation of relevant papers on this subject and are prepared ...

In these lectures I will present an introduction to the modern way of studying the properties of glassy systems. I will start from soluble models of increasing complications, the Random Energy Model, the p-spins interacting model and I will show how these models can be solved due their mean field properties. Finally, in the last section, I will discuss the difficulties in the generalization of ...

More than 70 international conference participants attended the workshop on Monday 12th Sept 2005. During that afternoon session, the short lectures of several research groups were presented as listed below. As there was no time left for the discussion on Monday, this was postponed to Tuesday afternoon, 13th Sept 2005. During 70 minutes the points listed below were discussed by more than 30 con...

In these lectures I will study some properties that are shared by many glassy systems. I will shown how some of these properties can be understood in the framework of the mean field approach based on the replica method and I will discuss which are the difficulties which we have to face when we apply the replica method to realistic short range models. We finally present a partially successfully ...

In this note we give a short and elementary proof of more general version Whitney’s theorem that 3-connected planar graphs have unique embedding in the plane. A consequence is also cubic plane cannot be embedded higher genus with simple dual. The aim paper to promote proof, which especially well suited for lectures presenting theorem.

In these lectures I will study some properties that are shared by many glassy systems. I will shown how some of these properties can be understood in the framework of the mean eld approach based on the replica method and I will discuss which are the diiculties which we have to face when we apply the replica method to realistic short range models. We nally present a partially successfully applic...

An important aspect of education is to promote higher-order thinking skills to learners. However, in the lecture environment, learners are passively engaged and it is unlikely for higher-order thinking to occur. Although interventions such as “clickers” can be used to increase engagement in lectures, this does not necessarily promote higher-order thinking. Approaches such as collaborative learn...