Bourgin-Yang version of the Borsuk-Ulam theorem for Z(pk)-equivariant maps

Let G = Z(pk) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V-G = W-G = W-G = {0}. Let S(V) be the sphere of V and suppose f: S(V) -> W is a G-equivariant mapping. We give an estimate for the dimension of the set f(-1){0} in terms of V and W. This extends the Bourgin-Yang version of the Borsuk-Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G-coincidences set of a continuous map from S(V) into a real vector space W'.

Cyclic Voltammetry and Computational Chemistry Studies on the Evaluation of the Redox Behavior of Parabens and other Analogues

Parabens are antimicrobial preservatives widely used in pharmaceutical, cosmetic and food industries. The alkyl chain connected to the ester group defines some important physicochemical characteristics of these compounds, including the partition coefficient and redox properties. The voltammetric and computational analyses were carried out in order to evaluate the redox behavior of these compounds and other phenolic analogues. A strong correlation between chemical substituents inductive effects of parabens with redox potentials was observed. Using cyclic voltammetry and glassy carbon working electrode, only one irreversible anodic peak was observed around 0.8 V for methylparaben (MP), ethylparaben (EP), propylparaben (PP), butylparaben (BP), benzylparaben (BzP) and p-substituted phenolic analogues. The electrodonating inductive effect of alkyl groups was demonstrated by the anodic oxidation potential shift to lower values as the carbon number increases and, therefore the parabens (and other phenolic analogues) oxidation processes to the quinonoidic forms showed great dependence on the substituent pattern.

Cyclic voltammetry and computational chemistry studies on the evaluation of the redox behavior of parabens and other analogues

Parabens are antimicrobial preservatives widely used in pharmaceutical, cosmetic and food industries. The alkyl chain connected to the ester group defines some important physicochemical characteristics of these compounds, including the partition coefficient and redox properties. The voltammetric and computational analyses were carried out in order to evaluate the redox behavior of these compounds and other phenolic analogues. A strong correlation between chemical substituents inductive effects of parabens with redox potentials was observed. Using cyclic voltammetry and glassy carbon working electrode, only one irreversible anodic peak was observed around 0.8 V for methylparaben (MP), ethylparaben (EP), propylparaben (PP), butylparaben (BP), benzylparaben (BzP) and p-substituted phenolic analogues. The electrodonating inductive effect of alkyl groups was demonstrated by the anodic oxidation potential shift to lower values as the carbon number increases and, therefore the parabens (and other phenolic analogues) oxidation processes to the quinonoidic forms showed great dependence on the substituent pattern.

Dynamics of follicular growth and progesterone concentrations in cyclic and anestrous suckling Nelore cows (Bos indicus) treated with progesterone, equine chorionic gonadotropin, or temporary calf removal

The objective of this study was to investigate the effects of eCG and temporary calf removal (TCR) associated with progesterone (P4) treatment on the dynamics of follicular growth, CL size, and P4 concentrations in cyclic (n ¼ 36) and anestrous (n ¼ 30) Nelore cows. Cyclic (C) and anestrous (A) cows were divided into three groups. The control group received 2 mg of estradiol benzoate via intramuscular (IM) injection and an intravaginal device containing 1.9 g of P4 on Day 0. On Day 8, the device was removed, and the animals received 12.5 mg of dinoprost tromethamine IM. After 24 hours, the animals received 1 mg of estradiol benzoate IM. In the eCG group, cows received the same treatment described for the control group but also received 400 UI of eCG at the time of device removal. In the TCR group, calves were separated from the cows for 56 hours after device removal. Ultrasound exams were performed every 24 hours after device removal until the time of ovulation and 12 days after ovulation to measure the size of the CL. On the same day as the CL measurement, blood was collected to determine the plasma P4 level. Statistical analyses were performed with a significance level of P ≤ 0.05. In cyclic cows, the presence of the CL at the beginning of protocol resulted in a smaller follicle diameter at the time of device removal (7.4 ± 0.3 mm in cows with CL vs. 8.9 ± 0.4 mm in cows without CL; P ¼ 0.03). All cows ovulated within 72 hours after device removal. Anestrous cows treated with eCG or TCR showed follicle diameter at fixed-timed artificial insemination (A-eCG 10.2 ± 0.3 and A-TCR 10.3 ± 0.5 mm) and follicular growth rate (A-eCG 1.5 ± 0.2 and A-TCR 1.3 ± 0.1 mm/day) similar to cyclic cows (C-eCG 11.0 ± 0.6 and C-TCR 12.0 ± 0.5 mm) and (C-eCG 1.4 ± 0.2 and C-TCR 1.6 ± 0.2 mm/day, respectively; P ≤ 0.05). Despite the similarities in CL size, the average P4 concentration was higher in the A-TCR (9.6 ± 1.4 ng/mL) than in the A-control (4.0 ± 1.0 ng/mL) and C-TCR (4.4 ± 1.0 ng/mL) groups (P < 0.05). From these results, we conclude that eCG treatment and TCR improved the fertility of anestrous cows by providing follicular growth rates and size of dominant follicles similar to cyclic cows. Additionally, TCR increases the plasma concentrations of P4 in anestrous cows