On an almost free damping vibration equation using N-fractional calculus

AbstractIn this paper, an almost free damping vibration equation is discussed by means of N-fractional calculus. Let ϕ∈℘°={ϕ,0≠|ϕν|<∞,ν∈R}. We focus on the following type of equation:ϕm+ε+ϕ1+(ε/m)·a+ϕ·b=0,where m is an integer and ab≠0,a2<4b, a>0,ϕ=ϕ(t),|ε|<1,ε,t∈R. In the case of m=2 and |ε|⪡1, we call this equation as an almost free damping vibration equation. So the solutions are investigated to be given using N-fractional calculus in the case of m=2. Furthermore, we illustrate the shapes of the solution according to the vibration of ε

Masa Miyakoda Graduation Address, 1944

https://scholarlycommons.pacific.edu/cook-nisei/1066/thumbnail.jp

ENSO and its effects on the atmospheric heating processes

El Nino-Southern Oscillation (ENSO) is an important air-sea coupled phenomenon that plays a dominant role in the variability of the tropical regions. Observations, atmospheric and oceanic reanalysis datasets are used to classify ENSO and non-ENSO years to investigate the typical features of its periodicity and atmospheric circulation patterns. Among non-ENSO years, we have analyzed a group, called type-II years, with very small SST anomalies in summer that tend to weaken the correlation between ENSO and precipitation in the equatorial regions. A unique character of ENSO is studied in terms of the quasi-biennial periodicity of SST and heat content (HC) fields over the Pacific-Indian Oceans. While the SST tends to have higher biennial frequency along the Equator, the HC maximizes it into two centers in the western Pacific sector. The north-western center, located east of Mindanao, is strongly correlated with SST in the NINO3 region. The classification of El Nino and La Nina years, based on NINO3 SST and north-western Pacific HC respectively, has been used to identify and describe temperature and wind patterns over an extended-ENSO region that includes the tropical Pacific and Indian Oceans. The description of the spatial patterns within the atmospheric ENSO circulation has been extended to tropospheric moisture fields and low-level moisture divergence during November-December-January, differentiating the role of El Nino, when lame amounts of condensational heat are concentrated in the central Pacific, from La Nina that tends to mainly redistribute heat to Maritime Continents and higher latitudes. The influence of the described mechanisms on equatorial convection in the context of the variability of ENSO on longer timescales for the end of the 20th century is questioned. However, the inaccuracy of the atmospheric reanalysis products in terms of precipitation and the shorter time length of more reliable datasets hamper a final conclusion on this issue

Isointegral Analysis of Body Surface Electrocardiographic Mapping for Assessing Exercise-Induced Changes in Repolarization Properties in Patients with Coronary Artery Disease

To assess the exercise-induced changes in repolarization properties in patients with coronary artery disease, we analyzed body surface ECG mapping. The patients studied had a normal resting 12-lead ECG and were divided into 2 groups: group A (n = 15; coronary artery narrowing [?], exercise thallium defect [?], ST depression 0.1 mV [?]) and group B (n = 17; [+], [+], [+]). All patients in group B showed significant area (< ?10 ?V?s) in the postexercise ST-T isointegral map. Of the patients in group B, 10 (59%) showed significant area in the postexercise QRST isointegral map and 15 (88%) showed “?2SD area (less than mean ?2SD values in group A)” in the difference map between resting and postexercise QRST isointegrals. The correlation coefficient between resting and postexercise QRST isointegrals in 87 lead points was significantly lower in group B (0.28 ± 0.56) than in group A (0.91 ± 0.06, P < 0.001). Our results indicate that patients with ischemic ST depression have a greater decrease in the QRST isointegral values in the precordial region than patients without ischemia and ST depression. There are also low similarities between resting and postexercise QRST isointegral maps. We conclude that ischemic ST depression is related to the dispersion of the exercise-induced changes in repolarization properties