Hypercomplex geometric derivative from a Cauchy-like integral formula

The derivation and integration of hipercomplex functions have been investigated along the years, see [7], [11], [14]. The main purpose of this brief article is to give a geometrical interpretation for quaternionic derivatives, based on a recent determination of a Cauchy-like formula for quaternions, see [3]. © 2011 Academic Publications.

Intermolecular Contacts Influencing the Conformational and Geometric Features of the Pharmaceutically Preferred Mebendazole Polymorph C

Mebendazole (MBZ) is a common benzimidazole anthelmintic that exists in three different polymorphic forms, A, B, and C. Polymorph C is the pharmaceutically preferred form due to its adequated aqueous solubility. No single crystal structure determinations depicting the nature of the crystal packing and molecular conformation and geometry have been performed on this compound. The crystal structure of mebendazole form C is resolved for the first time. Mebendazole form C crystallizes in the triclinic centrosymmetric space group and this drug is practically planar, since the least-squares methyl benzimidazolylcarbamate plane is much fitted on the forming atoms. However, the benzoyl group is twisted by 31(1)degrees from the benzimidazole ring, likewise the torsional angle between the benzene and carbonyl moieties is 27(1)degrees. The formerly described bends and other interesting intramolecular geometry features were viewed as consequence of the intermolecular contacts occurring within mebendazole C structure. Among these features, a conjugation decreasing through the imine nitrogen atom of the benzimidazole core and a further resonance path crossing the carbamate one were described. At last, the X-ray powder diffractogram of a form C rich mebendazole mixture was overlaid to the calculated one with the mebendazole crystal structure. (C) 2008 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 98:2336-2344, 2009

A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

The Applicability Of Ordered Mesoporous Sba-15 And Its Hydrophobic Glutaraldehyde-bridge Derivative To Improve Ibuprofen-loading In Releasing System.

The mesoporous SBA-15 silica with uniform hexagonal pore, narrow pore size distribution and tuneable pore diameter was organofunctionalized with glutaraldehyde-bridged silylating agent. The precursor and its derivative silicas were ibuprofen-loaded for controlled delivery in simulated biological fluids. The synthesized silicas were characterized by elemental analysis, infrared spectroscopy, (13)C and (29)Si solid state NMR spectroscopy, nitrogen adsorption, X-ray diffractometry, thermogravimetry and scanning electron microscopy. Surface functionalization with amine containing bridged hydrophobic structure resulted in significantly decreased surface area from 802.4 to 63.0 m(2) g(-1) and pore diameter 8.0-6.0 nm, which ultimately increased the drug-loading capacity from 18.0% up to 28.3% and a very slow release rate of ibuprofen over the period of 72.5h. The in vitro drug release demonstrated that SBA-15 presented the fastest release from 25% to 27% and SBA-15GA gave near 10% of drug release in all fluids during 72.5 h. The Korsmeyer-Peppas model better fits the release data with the Fickian diffusion mechanism and zero order kinetics for synthesized mesoporous silicas. Both pore sizes and hydrophobicity influenced the rate of the release process, indicating that the chemically modified silica can be suggested to design formulation of slow and constant release over a defined period, to avoid repeated administration.

A New Goniothalamin N-acylated Aza-derivative Strongly Downregulates Mediators Of Signaling Transduction Associated With Pancreatic Cancer Aggressiveness.

In this study, a novel concise series of molecules based on the structure of goniothalamin (1) was synthesized and evaluated against a highly metastatic human pancreatic cancer cell line (Panc-1). Among them, derivative 8 displayed a low IC50 value (2.7 μM) and its concentration for decreasing colony formation was 20-fold lower than goniothalamin (1). Both compounds reduced the levels of the receptor tyrosine kinase (AXL) and cyclin D1 which are known to be overexpressed in pancreatic cancer cells. Importantly, despite the fact that goniothalamin (1) and derivative 8 caused pancreatic cancer cell cycle arrest and cell death, only derivative 8 was able to downregulate pro-survival and proliferation pathways mediated by mitogen activated protein kinase ERK1/2. Another interesting finding was that Panc-1 cells treated with derivative 8 displayed a strong decrease in the transcription factor (c-Myc), hypoxia-inducible factor-1α (HIF-1α) and vascular endothelial growth factor (VEGF) protein levels. Notably, the molecular effects caused by derivative 8 might not be related to ROS generation, since no significant production of ROS was observed in low concentrations of this compound (from 1.5 up to 3 μM). Therefore, the downregulation of important mediators of pancreatic cancer aggressiveness by derivative 8 reveals its great potential for the development of new chemotherapeutic agents for pancreatic cancer treatment.

The Geometric Curvature Of The Spine Of Runners During Maximal Incremental Effort Test.

This study sought to analyse the behaviour of the average spinal posture using a novel investigative procedure in a maximal incremental effort test performed on a treadmill. Spine motion was collected via stereo-photogrammetric analysis in thirteen amateur athletes. At each time percentage of the gait cycle, the reconstructed spine points were projected onto the sagittal and frontal planes of the trunk. On each plane, a polynomial was fitted to the data, and the two-dimensional geometric curvature along the longitudinal axis of the trunk was calculated to quantify the geometric shape of the spine. The average posture presented at the gait cycle defined the spine Neutral Curve. This method enabled the lateral deviations, lordosis, and kyphosis of the spine to be quantified noninvasively and in detail. The similarity between each two volunteers was a maximum of 19% on the sagittal plane and 13% on the frontal (p<0.01). The data collected in this study can be considered preliminary evidence that there are subject-specific characteristics in spinal curvatures during running. Changes induced by increases in speed were not sufficient for the Neutral Curve to lose its individual characteristics, instead behaving like a postural signature. The data showed the descriptive capability of a new method to analyse spinal postures during locomotion; however, additional studies, and with larger sample sizes, are necessary for extracting more general information from this novel methodology.

Geometric morphometrics of the wing as a tool for assigning genetic lineages and geographic origin to Melipona beecheii (Hymenoptera: Meliponini)

The stingless bee Melipona beecheii presents great variability and is considered a complex of species. In order to better understand this species complex, we need to evaluate its diversity and develop methods that allow geographic traceability of the populations. Here we present a fast, efficient, and inexpensive means to accomplish this using geometric morphometrics of wings. We collected samples from Mexico, Guatemala, El Salvador, Nicaragua, and Costa Rica and we were able to correctly assign 87.1% of the colonies to their sampling sites and 92.4% to their haplotype. We propose that geometric morphometrics of the wing could be used as a first step analysis leaving the more expensive molecular analysis only to doubtful cases.

Higher-derivative supersymmetric gauge theory

We study the one-loop low-energy effective action for the higher-derivative superfield gauge theory coupled to chiral matter.

Potent Cardioprotective Effect of the 4-Anilinoquinazoline Derivative PD153035: Involvement of Mitochondrial K(ATP) Channel Activation

Background: The aim of the present study was to evaluate the protective effects of the 4-anilinoquinazoline derivative PD153035 on cardiac ischemia/reperfusion and mitochondrial function. Methodology/Principal Findings: Perfused rat hearts and cardiac HL-1 cells were used to determine cardioprotective effects of PD153035. Isolated rat heart mitochondria were studied to uncover mechanisms of cardioprotection. Nanomolar doses of PD153035 strongly protect against heart and cardiomyocyte damage induced by ischemia/reperfusion and cyanide/aglycemia. PD153035 did not alter oxidative phosphorylation, nor directly prevent Ca(2+) induced mitochondrial membrane permeability transition. The protective effect of PD153035 on HL-1 cells was also independent of AKT phosphorylation state. Interestingly, PD153035 activated K(+) transport in isolated mitochondria, in a manner prevented by ATP and 5-hydroxydecanoate, inhibitors of mitochondrial ATP-sensitive K(+) channels (mitoK(ATP)). 5-Hydroxydecanoate also inhibited the cardioprotective effect of PD153035 in cardiac HL-1 cells, demonstrating that this protection is dependent on mitoK(ATP) activation. Conclusions/Significance: We conclude that PD153035 is a potent cardioprotective compound and acts in a mechanism involving mitoK(ATP) activation.

Modelling grain boundary migration during geometric dynamic recrystallization

High-angle grain boundary migration is predicted during geometric dynamic recrystallization (GDRX) by two types of mathematical models. Both models consider the driving pressure due to curvature and a sinusoidal driving pressure owing to subgrain walls connected to the grain boundary. One model is based on the finite difference solution of a kinetic equation, and the other, on a numerical technique in which the boundary is subdivided into linear segments. The models show that an initially flat boundary becomes serrated, with the peak and valley migrating into both adjacent grains, as observed during GDRX. When the sinusoidal driving pressure amplitude is smaller than 2 pi, the boundary stops migrating, reaching an equilibrium shape. Otherwise, when the amplitude is larger than 2 pi, equilibrium is never reached and the boundary migrates indefinitely, which would cause the protrusions of two serrated parallel boundaries to impinge on each other, creating smaller equiaxed grains.

A Geometric Approach for Turbo Decoding of Reed-Solomon Codes in QAM Modulation Schemes

This work studies the turbo decoding of Reed-Solomon codes in QAM modulation schemes for additive white Gaussian noise channels (AWGN) by using a geometric approach. Considering the relations between the Galois field elements of the Reed-Solomon code and the symbols combined with their geometric dispositions in the QAM constellation, a turbo decoding algorithm, based on the work of Chase and Pyndiah, is developed. Simulation results show that the performance achieved is similar to the one obtained with the pragmatic approach with binary decomposition and analysis.

In Vitro Sun Protection Factor Evaluation of Sunscreens Containing Rutin and its Derivative

This research aimed at determining spectrophotometrically (290 to 320nm) the in vitro Sun Protection Factor (SPF) of sunscreens developed with rutin (R) or succinate rutin (SR), in association or not with UVB filter. Formulations were developed based on phosphate-base O/W emulsions, with (B) or not (A) the presence of polyacrylamide/C13-14 isoparaffin/laureth-7 (PIL), in accordance with the following associations: (a) control; (b) 1.0 % SR; (c) 0.1 % R; (d) 7.5 % ethylhexyl methoxycinnamate (EHMC); (e) 7.5 % EHMC + 0.1 % RS; (0 7.5 % EHMC + 0.1 % R. It was verified a statistical significative elevation of the SPF from 13.93 +/- 0.02 (Af) to 16.63 +/- 0.27 (Bf) and also in relation to 15.53 +/- 0.14 (Bd). According to the results, the EHMC had distinct behavior depending on the presence of bioactive substance and viscosity agent, thus, rutin obtained better profile as a SPF booster in these experimental conditions with the presence of PIL.

New Rapid Derivative Spectrophotometric and Chromatographic Methods for Assay of Loratadine in Tablets and Syrups

New rapid first-derivative spectrophotometric (UVDS) and a stability-indicating high performance liquid chromatographic (HPLC) methods were developed, validated and successfully applied in the analysis of loratadine (LT) in tablets and syrups. In the UVDS method, 0.1 M HCl was used as solvent. The measurements were made at 312.4 nm in the first order derivative spectra. The HPLC method was carried out on a RP-18 column with a mobile phase composed of methanol-water-tetrahydrofuran (50:30:20, v/v/v). UV detection was made at 247 nm. For HPLC methods the total analysis time was <3min, adequate for routine quality control of tablets and syrups containing loratadine.

UV-Derivative Spectrophotometric and Stability-Indicating High-Performance Liquid Chromatographic Methods for Determination of Simvastatin in Tablets

A stability-indicating high-performance liquid chromatographic (HPLC) and a second-order derivative spectrophotometric (UVDS) analytical methods were validated and compared for determination of simvastatin in tablets. The HPLC method was performed with isocratic elution using a C18 column and a mobile phase composed of methanol:acetonitrile:water (60:20:20, v/v/v) at a flow rate of 1.0 ml/min. The detection was made at 239 nm. In UVDS method, methanol and water were used in first dilution and distilled water was used in consecutive dilutions and as background. The second-order derivative signal measurement was taken at 255 nm. Analytical curves showed correlation coefficients > 0.999 for both methods. The quantitation limits (QL) were 2.41 mu g/ml for HPLC and 0.45 mu g/ml for UVDS, respectively. Intra and inter-day relative standard deviations were < 2.0 %. Statistical analysis with t- and F-tests are not exceeding their critical values demonstrating that there is no significant difference between the two methods at 95 % confidence level.