Analytic descriptions of parabolic X-ray mirrors

On X-ray beamlines and telescopes, glancing-incidence mirrors with parabolic profiles are used to collimate, focus, and collect light. Here, analytic descriptions for paraboloidal, plane-parabolic, and parabolic cylindrical mirrors in several congruent geometries that are commonly used in fabrication, metrology, and modeling are provided. The exact expressions are derived directly from Fermat's principle, without coordinate transformations, in several mirror-centered coordinate systems, including one with the surface tangent to the central point of intersection. Coefficients for a sixth-order polynomial series approximation are calculated for that coordinate system.

Hydrophobic and Anti-Fouling Performance of Surface on Parabolic Morphology

The hydrophobicity and anti-fouling properties of materials have important application value in industrial and agricultural production and people’s daily life. To study the relationship between the unit width L₀ of the parabolic hydrophobic material and the hydrophobicity and anti-fouling properties, the rough surface structure of the parabolic with different widths was prepared by grinding with different SiC sandpapers, and further, to obtain hydrophobic materials through chemical oxidation and chemical etching, and modification with stearic acid (SA). The morphology, surface wetting and anti-fouling properties of the modified materials were characterized by SEM and contact angle measurement. The oil–water separation performance and self-cleaning performance of the materials were explored. The surface of the modified copper sheet forms a rough structure similar to a paraboloid. When ground with 1500 grit SiC sandpaper, it is more conducive to increase the hydrophobicity of the copper sheet surface and increase the contact angle of water droplets on the copper surface. Additionally, the self-cleaning and anti-fouling experiments showed that as L₀ decreases, copper sheets were less able to stick to foreign things such as soil, and the better the self-cleaning and anti-fouling performance was. Based on the oil–water separation experiment of copper mesh, the lower L₀ has a higher oil–water separation efficiency. The results showed that material with parabolic morphology has great self-cleaning, anti-fouling, and oil–water separation performance. The smaller the L₀ was, the larger the contact angle and the better hydrophobic performance and self-cleaning performance were.

Post-treatment serological changes in some patients with early syphilis exhibit a parabolic trend

Early syphilis accounts for a large proportion of patients with syphilis. Non- Treponema pallidum tests are commonly used to assess treatment effectiveness by analyzing the serological titer before treatment and six months after treatment. However, serological changes during the first three months after completion of treatment have not been completely understood. This prompted us to investigate whether serum titers of patients exhibit a continuous decrease post-treatment and to assess the trend of change in serological titer during this period. One hundred and seventy-three eligible patients with early syphilis were included in the analysis. Pre-treatment serological titers and those at three and six months post-treatment were compared and analyzed. Serological recovery was defined as a 4-fold or greater decrease in titer from pre-treatment level. Forty patients (23.1%) were found to have an increased serum titer at three months after treatment. Among the 40 patients, 13 patients had primary syphilis, 5 patients had secondary syphilis, and 22 patients had early latent syphilis. The proportion of patients with primary syphilis was higher, and their initial titers were significantly lower. No significant differences were observed with respect to age, gender, or initial treatment. The assessment results of 17 patients (9.8% of the total patients) change. Serological changes in some patients exhibit a parabolic pattern that may affect the clinician’s assessment of patient recovery. Therefore, more frequent assessment of serological titer might be required within the first six months post-treatment.

Effective potential for magnetic resonance measurements of restricted diffusion

The signature of diffusive motion on the NMR signal has been exploited to characterize the mesoscopic structure of specimens in numerous applications. For compartmentalized specimens comprising isolated subdomains, a representation of individual pores is necessary for describing restricted diffusion within them. When gradient waveforms with long pulse durations are employed, a quadratic potential profile is identified as an effective energy landscape for restricted diffusion. The dependence of the stochastic effective force on the center-of-mass position is indeed found to be approximately linear (Hookean) for restricted diffusion even when the walls are sticky. We outline the theoretical basis and practical advantages of our picture involving effective potentials.

Mechatronic Prototype of Parabolic Solar Tracker

In the last 30 years numerous attempts have been made to improve the efficiency of the parabolic collectors in the electric power production, although most of the studies have focused on the industrial production of thermoelectric power. This research focuses on the application of this concentrating solar thermal power in the unexplored field of building construction. To that end, a mechatronic prototype of a hybrid paraboloidal and cylindrical-parabolic tracker based on the Arduido technology has been designed. The prototype is able to measure meteorological data autonomously in order to quantify the energy potential of any location. In this way, it is possible to reliably model real commercial equipment behavior before its deployment in buildings and single family houses.

One hundred years of complex dynamics

Holomorphic dynamics has been a key area of study for 100 years. In this survey, we focus on the dynamics of rational functions.

Two types of burst firing in gonadotrophin-releasing hormone neurones

Gonadotrophin-releasing hormone (GnRH) neurones fire spontaneous bursts of action potentials, although little is understood about the underlying mechanisms. In the present study, we report evidence for two types of bursting/oscillation driven by different mechanisms. Properties of these different types are clarified using mathematical modelling and a recently developed active-phase/silent-phase correlation technique. The first type of GnRH neurone (1-2%) exhibits slow (∼0.05 Hz) spontaneous oscillations in membrane potential. Action potential bursts are often observed during oscillation depolarisation, although some oscillations were entirely subthreshold. Oscillations persist after blockade of fast sodium channels with tetrodotoxin (TTX) and blocking receptors for ionotropic fast synaptic transmission, indicating that they are intrinsically generated. In the second type of GnRH neurone, bursts were irregular and TTX caused a stable membrane potential. The two types of bursting cells exhibited distinct active-phase/silent-phase correlation patterns, which is suggestive of distinct mechanisms underlying the rhythms. Further studies of type 1 oscillating cells revealed that the oscillation period was not affected by current or voltage steps, although amplitude was sometimes damped. Oestradiol, an important feedback regulator of GnRH neuronal activity, acutely and markedly altered oscillations, specifically depolarising the oscillation nadir and initiating or increasing firing. Blocking calcium-activated potassium channels, which are rapidly reduced by oestradiol, had a similar effect on oscillations. Kisspeptin, a potent activator of GnRH neurones, translated the oscillation to more depolarised potentials, without altering period or amplitude. These data show that there are at least two distinct types of GnRH neurone bursting patterns with different underlying mechanisms.