The Geometry of Self-dual 2-forms

We show that self-dual 2-forms in 2n dimensional spaces determine a $n^2-n+1$ dimensional manifold ${\cal S}_{2n}$ and the dimension of the maximal linear subspaces of ${\cal S}_{2n}$ is equal to the (Radon-Hurwitz) number of linearly independent vector fields on the sphere $S^{2n-1}$. We provide a direct proof that for $n$ odd ${\cal S}_{2n}$ has only one-dimensional linear submanifolds. We exhibit $2^c-1$ dimensional subspaces in dimensions which are multiples of $2^c$, for $c=1,2,3$. In particular, we demonstrate that the seven dimensional linear subspaces of ${\cal S}_{8}$ also include among many other interesting classes of self-dual 2-forms, the self-dual 2-forms of Corrigan, Devchand, Fairlie and Nuyts and a representation of ${\cal C}l_7$ given by octonionic multiplication. We discuss the relation of the linear subspaces with the representations of Clifford algebras.Comment: Latex, 15 page

An unexpected long-term complication of genital burn in a child: Secondary cryptorchidism

Genital and perineal burns are rare and challenging injuries with serious long-term complications. Involvement of the testes is a sign of severity. There is limited knowledge in the literature about the management of complications and testes involvement in genital and perineal burns. In this report, we present the case of an 8-year-old boy with secondary cryptorchidism due to burn contracture who was treated by increasing the scrotal volume by Z-plasties, skin graft, and orchidopexy. © 2018 Turkish Association of Trauma and Emergency Surgery

Self-dual Yang-Mills fields in eight dimensions

Strongly self-dual Yang-Mills fields in even dimensional spaces are characterised by a set of constraints on the eigenvalues of the Yang-Mills fields F_{\mu \nu}. We derive a topological bound on {\bf R}^8, \int_{M} ( F,F )^2 \geq k \int_{M} p_1^2 where p_1 is the first Pontrjagin class of the SO(n) Yang-Mills bundle and k is a constant. Strongly self-dual Yang-Mills fields realise the lower bound

Acidólisis enzimática de trioleina con los ácidos palmítico y caprílico: Optimización de los parámetros de la reacción mediante la metodología de superficie de respuesta

An acidolysis reaction of triolein with caprylic and palmitic acids was performed using immobilized sn-1,3 specific lipase from Mucor miehei to produce a reduced calorie spreadable structured lipid (SL). Response surface methodology was applied to model and optimize the reaction conditions using a four-factor five-level central composite rotatable design. The selected factors were time (10-24 h), enzyme load (10-25 wt%), substrate mole ratio (Triolein:Caprylic acid:Palmitic acid), (1:1:1-1:2.5:2.5) and temperature (45-60 °C). The produced SLs were compared to fat extracts of commercial margarine in terms of melting profile and solid fat content (SFC). SL with a melting peak of 42 °C and SFC of 40.69% at 0 °C was very similar to soft margarines. The caloric value of this SL was determined as 37.74 kJ/g, theoretically. The optimum reaction conditions were found as reaction time 14 h; substrate mole ratio 1:2.1:2.1; temperature 58 °C; and enzyme load 15 wt%. Under optimum conditions, the product contained 29.68% COC, 25.47% POC, and 3.80% POP.La reacción de acidolísis de la trioleina con los ácidos caprílico y palmítico se realizó utilizando lipasa inmovilizada Mucor miehei, específica de sn-1, 3, para producir una grasa de untar baja en calorías compuesta de lípidos estructurados (SL). La metodología de superficie de respuesta se aplica para modelar y optimizar las condiciones de reacción utilizando un factor-cuatro y nivel-cinco de diseño central compuesto. Los factores seleccionados fueron el tiempo (10-24 h), la carga de enzima (10-25% en peso), la relación molar de sustratos (Trioleína:Ácido Caprílico:Ácido Palmítico), (1:1:1-1:2.5:2.5) y la temperatura (45-60 °C). Los SLs producidos se compararon con extractos de grasa de margarina comercial en términos de perfil de fusión y contenido de grasa sólida (SFC). El SL con un pico de fusión a 42 °C y SFC de 40,69% a 0 °C era muy similar a las margarinas suaves. El valor calórico de este SL se determinó teóricamente siendo 37,74 kJ/g. Las condiciones óptimas de reacción encontradas fueron 14 h de tiempo de reacción; una relación molar de sustratos 1:2.1:2.1; una temperatura de 58 °C, y una carga enzima de 15% en peso. En condiciones óptimas el producto contenía 29,68% de AOC, 25,47% de POC, y 3,80% de POP

Evaluation of the biocompatibility of experimentally manufactured portland cement: an animal study

Objectives: The purpose of this study was to evaluate the biocompatibility of MTA and the experimentally manufactured portland cement (EMPC). Study design: Twenty one Sprague Dawley (SD) rats were allocated to testing of three groups. Group I and Group II included ProRoot MTA and the EMPC. The materials were mixed with distilled water and placed in polyethylene tubes. The tubes were implanted subcutaneously in the dorsal region of the animals. Group III served as control; the implanted polyethylene tubes remained empty. At 7, 14, and 28 days after the implantation, the animals were sacrificed and the implants were removed with the surrounding tissues. The specimens were prepared for histological examination to evaluate the inflammatory response. Results: No significant difference was found between tissue reactions against the tested materials (p>0.05). Also, control group showed similar results(p>0.05). Conclusions: Results suggest that the EMPC has the potential to be used in clinical conditions in which ProRoot MTA is indicated. MTA and the EMPC show comparable biocompatibility when evaluated in vivo. Although the results are supportive for the EMPC, more studies are required before the safe clinical use of the EMPC

Extracción asistida por microondas de compuestos no polares de cáscaras de pistacho y caracterización de los extractos

Soxhlet and microwave assisted extraction (MAE) methods were used to obtain non-polar compounds from pistachio hull. MAE parameters (liquid to solid ratio, microwave power, and extraction time) were studied to obtain maximum extraction yield. The optimal conditions were found to be liquid to solid ratio of 15:1 (v/w), microwave power of 250 W and extraction time of 12.5 min. The extraction yields were 9.81 and 9.50% for MAE and Soxhlet methods, respectively. The total phenolic content, antioxidant activity and tocopherol content of the extract obtained by MAE was found to be significantly higher than those of the Soxhlet extract (p < 0.05). The results showed that the extract contained α-tocopherols (567.65 mg/kg) and oleic acid (48.46%) as the major tocopherols and fatty acids. These findings propose that hull extracts can be considered as a good source of natural bioactive compounds and MAE can be a good alternative to the traditional Soxhlet method.Se utilizó la extracción mediante Soxhlet y métodos de extracción asistida mediante microondas (MAE) para obtener compuestos no polares de las cascaras de pistacho. Se estudiaron los parámetros para la MAE (relación líquido-sólido, potencia de microondas y tiempo de extracción) para obtener el máximo rendimiento de la extracción. Se encontró que las condiciones óptimas eran una relación líquido a sólido de 15:1 (v/p), potencia de microondas de 250 W y un tiempo de extracción de 12,5 minutos. Los rendimientos de extracción fueron 9.81 y 9.50% para los métodos MAE y Soxhlet, respectivamente. El contenido fenólico total, la actividad antioxidante y el contenido de tocoferoles de los extractos obtenidos por MAE fueron significativamente más altos que los de los extractos de Soxhlet (p < 0,05). Los resultados muestran que el extracto contiene α-tocoferol (567.65 mg/kg) y ácido oleico (48.46%) como los principales tocoferoles y ácidos grasos, respectivamente. Estos hallazgos proponen que los extractos de las cascaras pueden considerarse como una buena fuente de compuestos bioactivos naturales y MAE puede ser una buena alternativa al método Soxhlet tradicional