2,2-Dimethyl-5-[(pyridin-2-yl­amino)­methyl­idene]-1,3-dioxane-4,6-dione

In the title compound, C12H12N2O4, the dihedral angle between the pyridine and enamine planes is 3.5 (3)°, while the angle between the dioxanedione (seven atoms) and enamine planes is 4.6 (3)°. The dioxane ring approximates an envelope conformation

The visualization of the space probability distribution for a particle moving in a double ring-shaped Coulomb potential

The analytical solutions to a double ring-shaped Coulomb potential (RSCP) are presented. The visualizations of the space probability distribution (SPD) are illustrated for the two-(contour) and three-dimensional (isosurface) cases. The quantum numbers (n, l, m) are mainly relevant for those quasi quantum numbers (n' ,l' ,m' ) via the double RSCP parameter c. The SPDs are of circular ring shape in spherical coordinates. The properties for the relative probability values (RPVs) P are also discussed. For example, when we consider the special case (n, l, m)=(6, 5, 0), the SPD moves towards two poles of axis z when the P increases. Finally, we discuss the different cases for the potential parameter b which is taken as negative and positive values for c>0 . Compared with the particular case b=0 , the SPDs are shrunk for b=-0.5 while spread out for b=0.5.Comment: 26 pages, 5 tables and 3 figures, Advances in High Energy Physics, in pres

The visualization of the space probability distribution for a moving particle I: in a single ring-shaped Coulomb potential

We first present the exact solutions of the single ring-shaped Coulomb potential and then realize the visualizations of the space probability distribution for a moving particle within the framework of this potential. We illustrate the two-(contour) and three-dimensional (isosurface) visualizations for those specifically given quantum numbers (n, l, m) essentially related to those so-called quasi quantum numbers (n',l',m') through changing the single ring-shaped Coulomb potential parameter b. We find that the space probability distributions (isosurface) of a moving particle for the special case and the usual case are spherical and circular ring-shaped, respectively by considering all variables in spherical coordinates. We also study the features of the relative probability values P of the space probability distributions. As an illustration, by studying the special case of the quantum numbers (n, l, m)=(6, 5, 1) we notice that the space probability distribution for a moving particle will move towards two poles of axis z as the relative probability value P increases. Moreover, we discuss the series expansion of the deformed spherical harmonics through the orthogonal and complete spherical harmonics and find that the principal component decreases gradually and other components will increase as the potential parameter b increases.Comment: 28 pages, 6 tables, 1 figure

Guaranteed Cost Control Design of 4D Lorenz-Stenflo Chaotic System via T-S Fuzzy Approach

This paper investigates the guaranteed cost control of chaos problem in 4D Lorenz-Stenflo (LS) system via Takagi-Sugeno (T-S) fuzzy method approach. Based on Lyapunov stability theory and linear matrix inequality (LMI) technique, a state feedback controller is proposed to stabilize the 4D Lorenz-Stenflo chaotic system. An illustrative example is provided to verify the validity of the results developed in this paper

Correlation of the Cerebral Microvascular Blood Flow with Brain Temperature and Electro-Acupuncture Stimulation

ObjectiveTo investigate the relationship between the temperature and the microvascular blood flow of the cerebral cortex, and the influence of electro-acupuncture (EA) on the cortical microcirculation.MethodsHigh temperature spots on the anterior ectosylvian and low temperature spots on the posterior suprasylvian on the cortical surface of 20 cats were identified using cortical infrared thermography (CIT); the blood flow in the microcirculation on these spots was measured with laser-Doppler flowmetry. EA was given at Zusanli (ST 36) and changes in the blood flow in the cerebral cortex microcirculation were detected.Results1) The mean temperatures on the high (34.83±0.24°C) and low (32.28±0.27°C) temperature spots were significantly different (P<0.001); this was indicative of a temperature difference on the cortical surface; 2) The average blood flow in the microcirculation of the high (266.8±19.2 PU) and low (140.8±9.9 PU) temperature spots was significantly different (P<0.001). 3) On the cortical high temperature spots, the mean blood flow in the microcirculation significantly increased from 266.8±86.8 PU before EA, to 422.5±47.4 PU following 5 minutes of EA (58.35%; P<0.01), and 431.8±52.8 PU 5 minutes after ceasing EA (61.84%; P<0.01). 4) On the low temperature spots, there were no significant differences in blood flow following 5 minutes of EA (146.3±11.5 PU), and 5 minutes after ceasing EA (140.5±11.6 PU), when compared with that before acupuncture (140.8±9.9 PU; P>0.9).ConclusionThe high temperature spots of the cortex are active functional regions of neurons with higher blood flow and a stronger response to EA. EA induces a significant increase in blood flow in the high temperature spots of the cortex