We consider symmetric 2 degree of freedom Hamiltonian systems which are resonant because of the symmetry, such as the spherical pendulum. Perturbing such a system by breaking the symmetry (e.g. adding a magnetic term) creates bifur-cations in the geometry of the families of periodic orbits, and the aim of this paper is to study this geometry. For brevity, we consider only the cases of symmetry ...

Using main lemma: Let L = G/ √ k, and recall we defined yi = Lxi. For every i < j, apply the lemma to xi − xj , then with probability at least 1− 2/n3, ∥yi − yj∥ = ∥L(xi − xj)∥ = ∥G(xi − xj)∥/ √ k ∈ (1± ε)∥xi − xj∥. ∗These notes summarize the material covered in class, usually skipping proofs, details, examples and so forth, and possibly adding some remarks, or pointers. The exercises are for s...

^vnte a book which shall form a complete clinical handbook and Work of reference at the bedside and in the ward during the taking of a case. Nowadays, to accomplish this purpose in anything like a reasonable space, brevity must be everywhere studied and care taken to exclude all extraneous or impertinent matter. This book well fulfils the purpose for which it was written, and we cordially recom...

By introducing a ubiquity property for rectangles, we prove the mass transference principle from rectangles to i.e., if sequence of forms system (a full measure property), then limsup set defined by shrinking these smaller has Hausdorff or say transfer brevity. The sets generated balls appear at most fundamental level in Diophantine approximation: one follows Dirichlet's theorem, other Minkowsk...

the literature on the life and works of Wagner is already extensive and we are told that he ranks third in bibliographical status to Jesus and Napoleon. But much of this is rather diffuse and turgid so that it is a great pleasure to find that Bryan Magee has now produced a Wagnerian analysis refreshing in its clarity, directness and brevity. This little monograph consists of five essays dealing...

East Asian languages are thought to handle reference differently from English, particularly in terms of the marking of definiteness and number. We present the first Data-Text corpus for Referring Expressions in Mandarin, and we use this corpus to test some initial hypotheses inspired by the theoretical linguistics literature. Our findings suggest that function words deserve more attention in Re...

This paper develops the team-building models under uncertainty of agents abilities described by Pareto distribution, and is organized as follows. At first, some properties of Pareto distribution required for further presentation are briefly discussed in Section 2. Then the solution of the team incentive problem is given in Section 3. Section 4 presents the team-building problem statement. Secti...

Rule extraction is a technique aimed at transforming highly accurate opaque models like neural networks into comprehensible models without losing accuracy. G-REX is a rule extraction technique based on Genetic Programming that previously has performed well in several studies. This study has two objectives, to evaluate two new fitness functions for G-REX and to show how G-REX can be used as a ru...

Flash fiction, stories of extreme brevity, is a subgenre short story writing in which special attention paid to the choice words, grammar and punctuation actively involve reader act unravelling multiple layers meaning evoked. Upon reading flash, “Readers move time such way that it catapults them from beginning end back again” (Rohrberger 2004: 7). The brevity flash abrupt ending bring full circ...