Search Results (5)

We give some of our results over the past few years about rogue waves concerning some partial differential equations, such as the focusing nonlinear Schrödinger equation (NLS), the Kadomtsev–Petviashvili equation (KPI), the Lakshmanan–Porsezian–Daniel equation (LPD) and the Hirota equation (H). For the NLS and KP equations, we give different types of representations of the solutions, in terms of Fredholm determinants, Wronskians and degenerate determinants of order $2N$. These solutions are called solutions of order N. In the case of the NLS equation, the solutions, explicitly constructed, appear as deformations of the Peregrine breathers $P_N$ as the last one can be obtained when all parameters are equal to zero. At order N, these solutions are the product of a ratio of two polynomials of degree $N(N+1)$ in x and t by an exponential depending on time t and depending on $2N-2$ real parameters: they are called quasi-rational solutions. For the KPI equation, we explicitly obtain solutions at order N depending on $2N-2$ real parameters. We present different examples of rogue waves for the LPD and Hirota equations. Full article

Background and Objectives: The aim was to compare the activity of the masseter muscles in children with different types of breathing. Materials and Methods: A cross-sectional study was conducted including patients aged 6–12 years with mixed dentition, who came for oral care at the Master’s Degree in Pediatric Dentistry program at the Complutense University of Madrid (UCM), according to inclusion and exclusion criteria. The sample was divided into three groups: nasal breathers without dental alterations (control group), oral breathers with dental malocclusion, and oral breathers with previous orthodontic treatment. An electromyography was performed, and statistic methods were conducted with a 95% confidence to contrast hypothesis. Results: A total of 122 children were analyzed and distributed into three groups. The electrical muscle activity of masseters was significantly different between the study groups (p < 0.001 for all comparisons). Pairwise comparisons revealed a significantly higher electrical muscle activity in the control group (nasal breathers) during chewing compared to both groups of oral breathers (p < 0.001 for both comparisons). Orthodontic treatment decreased electrical muscle activity during isometric contraction in oral breathers compared to nasal breathers (p < 0.001), but did not significantly affect electrical muscle activity during chewing. Higher decompensation values were obtained in oral breathers without previous orthodontic treatment compared the other study groups (p < 0.001 for both comparisons), although electrical muscle activity values were similar in both groups of oral breathers (p > 0.05 for both comparisons). Conclusions: Differences in electrical muscle activity between nasal and oral breathers can be confirmed. Oral breathers with and without orthodontic treatment showed lower electrical muscle activity of masseters during chewing than nasal breathers, while at isometric contraction, only oral breathers with previous orthodontic treatment showed lower electrical activity. Higher decompensation values were found in oral breathers without previous orthodontic treatment, in comparison to the control group and oral breathers with previous orthodontic treatment. Full article

Background: Many patients with obstructive sleep apnea (OSA) are mouth-breathers. Mouth-breathing not only narrows the upper airway, consequently worsening the severity of OSA, but also it affects compliance with nasal continuous positive airway pressure (CPAP) treatment. This study aimed to investigate changes in OSA by the use of mouth tape in mouth-breathers with mild OSA. Method: Mouth-breathers with mild OSA who met inclusion criteria and tolerated the sealing of the mouth were enrolled in the study. We used 3M silicone hypoallergenic tape was used to seal the mouths of the participants during sleep. The home sleep test (HST) used in this study was ApneaLink^®. Subjects received both a baseline HST and an outcome HST to be used 1 week later while their mouths were taped. The changes between the baseline and the outcome HSTs were compared, and the factors that influenced the differences in the sleep-test parameters after the shift of the breathing route were analyzed. A “responder” was defined as a patient who experienced a reduction from the baseline snoring index of at least 50% under mouth-taping in the HST; otherwise, patients were considered as having a poor response. Results: A total of 20 patients with mild OSA were included. Following the taping of the mouth, a good response was found in 13 patients (65%). The median apnea/hypopnea index (AHI) decreased significantly, from 8.3 to 4.7 event/h (by 47%, p = 0.0002), especially in supine AHI (9.4 vs. 5.5 event/h, p = 0.0001). The median snoring index (SI) was also improved (by 47%, 303.8 vs. 121.1 event/h, p = 0.0002). Despite no significant difference in the mean saturation, improvements in the oxygen desaturation index (8.7 vs. 5.8, p = 0.0003) and the lowest saturation (82.5% vs. 87%, p = 0.049) were noted. The change in AHI was associated with baseline AHI (r = −0.52, p = 0.02), oxygen desaturation index (ODI) (r = −0.54, p = 0.01), and SI (r = −0.47, p = 0.04). The change in SI was strongly associated with baseline SI (r = −0.77, p = 0.001). Conclusions: Mouth-taping during sleep improved snoring and the severity of sleep apnea in mouth-breathers with mild OSA, with AHI and SI being reduced by about half. The higher the level of baseline AHI and SI, the greater the improvement was shown after mouth-taping. Mouth-taping could be an alternative treatment in patients with mild OSA before turning to CPAP therapy or surgical intervention. Full article

In this article we present a new method for construction of exact solutions of the Landau-Lifshitz-Gilbert equation (LLG) for ferromagnetic nanowires. The method is based on the established relationship between the LLG and the nonlinear Schrödinger equation (NLS), and is aimed at resolving an old problem: how to produce multiple-rogue wave solutions of NLS using just the Darboux-type transformations. The solutions of this type—known as P-breathers—have been proven to exist by Dubard and Matveev, but their technique heavily relied on using the solutions of yet another nonlinear equation, the Kadomtsev-Petviashvili I equation (KP-I), and its relationship with NLS. We have shown that in fact one doesn’t have to use KP-I but can instead reach the same results just with NLS solutions, but only if they are dressed via the binary Darboux transformation. In particular, our approach allows us to construct all the Dubard-Matveev P-breathers. Furthermore, the new method can lead to some completely new, previously unknown solutions. One particular solution that we have constructed describes two “positon”-like waves, colliding with each other and in the process producing a new, short-lived rogue wave. We called this unusual solution (in which a rogue wave is begotten after the impact of two solitons) the “impacton”. Full article

The purpose of this research was to determine the effect of respiratory obstruction due tonsils hypertrophy on bolus organization, lip posture, bolus propulsion, and on associated head and mandible movements during the preparatory oral and oral phases of swallowing in children. This is a transversal study in children with tonsils hypertrophy (Group 1 − n = 21, 8 girls and 13 boys; mean age 4.5 years) and nasal breathers children without tonsils hypertrophy (Group 2 − n = 10, 4 girls and 6 boys; mean age 4.6 years). The groups were evaluated for respiratory patterns (oroscopy, anterior rhinoscopy and nasopharyngoendoscopy), dental evaluation and videofluoroscopy of swallowing, for liquids and paste food. No significant differences were detected (p > 0.05) between groups regarding liquid volume ingested, bolus organization, lip posture, bolus propulsion, or the presence of associated head and mandible movements. The results indicate that respiratory obstruction caused by tonsil hypertrophy in children with normal occlusion did not influence the variables studied regarding the preparatory oral and oral phases of swallowing for both consistencies. Full article