Vacuum stability conditions of the economical 3-3-1 model from copositivity

By applying copositivity criterion to the scalar potential of the economical $3-3-1$ model, we derive necessary and sufficient bounded-from-below conditions at tree level. Although these are a large number of intricate inequalities for the dimensionless parameters of the scalar potential, we present general enlightening relations in this work. Additionally, we use constraints coming from the minimization of the scalar potential by means of the orbit space method, the positivity of the squared masses of the extra scalars, the Higgs boson mass, the $Z'$ gauge boson mass and its mixing angle with the SM $Z$ boson in order to further restrict the parameter space of this model.Comment: 22 pages, 7 figures, added text and references. Matches published versio

Improved bounds for the crossing numbers of K_m,n and K_n

It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing conjecture states that the crossing number cr(K_n) of the complete graph K_n equals Z(n):= floor(n/2) floor((n-1)/2) floor((n-2)/2) floor((n-3)/2)/4. In this paper we show the following improved bounds on the asymptotic ratios of these crossing numbers and their conjectured values: (i) for each fixed m >= 9, lim_{n->infty} cr(K_m,n)/Z(m,n) >= 0.83m/(m-1); (ii) lim_{n->infty} cr(K_n,n)/Z(n,n) >= 0.83; and (iii) lim_{n->infty} cr(K_n)/Z(n) >= 0.83. The previous best known lower bounds were 0.8m/(m-1), 0.8, and 0.8, respectively. These improved bounds are obtained as a consequence of the new bound cr(K_{7,n}) >= 2.1796n^2 - 4.5n. To obtain this improved lower bound for cr(K_{7,n}), we use some elementary topological facts on drawings of K_{2,7} to set up a quadratic program on 6! variables whose minimum p satisfies cr(K_{7,n}) >= (p/2)n^2 - 4.5n, and then use state--of--the--art quadratic optimization techniques combined with a bit of invariant theory of permutation groups to show that p >= 4.3593.Comment: LaTeX, 18 pages, 2 figure

Transcranial focal electrical stimulation via tripolar concentric ring electrodes does not modify the short- and long-term memory formation in rats evaluated in the novel object recognition test

Noninvasive transcranial focal electrical stimulation (TFS) via tripolar concentric ring electrodes (TCREs) has been under development as an alternative/complementary therapy for seizure control. Transcranial focal electrical stimulation has shown efficacy in attenuating penicillin-, pilocarpine-, and pentylenetetrazole-induced acute seizures in rat models. This study evaluated the effects of TFS via TCREs on the memory formation of healthy rats as a safety test of TFS. Short- and long-term memory formation was tested after the application of TFS using the novel object recognition (NOR) test. The following independent groups were used: naïve, control (without TFS), and TFS (treated). The naïve, control, and stimulated groups spent more time investigating the new object than the familiar one during the test phase. Transcranial focal electrical stimulation via TCREs given once does not modify the short- and long-term memory formation in rats in the NOR test. Results provide an important step towards a better understanding for the safe usage of TFS via TCREs

The acute effect of different intensity aerobic and resistance training exercise on the body image in adult women

The purpose of the study was to evaluate the acute effect of different intensity aerobic (AE) and resistance training (RT) exercises on BI in adult women. Participants were 62 adult women (19.47 ± 2.53 yr., range 18 a 33 yr.), who were randomly assigned to three sessions of either: 1) Control group, 2) Low-intensity AE, 3) High-intensity AE, 4) Low-intensity RT, or 5) High-intensity RT. Before and immediately following each experimental intervention, BI, body weight, and arm and leg circumferences were measured. Three familiarization sessions were performed every 7 days before the AE and RT experimental interventions. Also, 5-RM tests were performed one week before the RT experimental interventions. Data were analyzed using mixed 3-way ANOVA, mixed 4-way ANOVA, and post-hoc analysis. An acute effect of RT on BI was observed, regardless of the exercise intensity, women felt more muscular immediately following the RT session. Regardless of the exercise intensity, 30-min of acute RT exercise changed BI perception, contrary to 30 min AE

Practical Based Learning (PBL) for Academic, Technological and Scientific Education in Engineering Courses - Case Study

The increase in the number of students evaded has alerted different segments of society and the public sector to the need to update the guidelines of engineering courses as well as innovation in teaching engineering. In this sense, the objective is to report on the challenges of engineering education in Brazil and the methodological strategies that have been adopted for the modernization of the curricula of engineering courses and consequent reduction of the indicators of avoidance and withdrawal. In addition, involving the use of the 43 academic academics of the University of Cruz Alta (Unicruz) who studied the discipline of Research Methodology in the second semester of 2017 through the Problem Based Learning (PBL) strategy as an innovative strategy education. Finally, in addition to the production of a technical material produced throughout the course, it was observed that there were only 2 students in 1 failed exam, demonstrating that teaching by PBL has high effectiveness for academic achievement in the discipline of research methodology

su(1,1) Algebraic approach of the Dirac equation with Coulomb-type scalar and vector potentials in D + 1 dimensions

We study the Dirac equation with Coulomb-type vector and scalar potentials in D + 1 dimensions from an su(1, 1) algebraic approach. The generators of this algebra are constructed by using the Schr\"odinger factorization. The theory of unitary representations for the su(1, 1) Lie algebra allows us to obtain the energy spectrum and the supersymmetric ground state. For the cases where there exists either scalar or vector potential our results are reduced to those obtained by analytical techniques