A search on Dirac equation

The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schrodinger like one. Earlier results are discussed in a unified framework and certain solutions of a large class of potentials are given.Comment: 9 page

Finitely presented quadratic algebras of intermediate growth

In this article, we give two examples of finitely presented quadratic algebras (algebras presented by quadratic relations) of intermediate growth

Finitely presented quadratic algebras of intermediate growth

In this article, we give two examples of finitely presented quadratic algebras (algebras presented by quadratic relations) of intermediate growth

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

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

Application of stem cells and adipose-derived stem cell exosomes on dermal wound healing

The skin is the largest organ in the human body and plays a significant role in protecting the body from external threats, containing tissues that sustain the body's homeostasis. Wound healing in the skin is a complex process involving the interaction of various cell types in the target tissue, including but not limited to cytokines and growth factors. In extreme cases, disorders of the cardiorespiratory system, such as chronic diseases, may prevent the process of wound healing entirely. Numerous studies have been conducted to discover methods to restore the ability of chronic wounds to cure themselves, but this remains one of the most significant medical problems. Exosomes derived from stem cells have been extensively proposed as a treatment for dermal wound recovery. Different types of stem cells have varying therapeutic potential. Exosomes, a component of paracrine, have the function of enhancing the effectiveness of stem cells. This article discusses the wound healing process as well as the mechanism of stem cell and adipose-derived exosome therapy on cutaneous wound healing and its clinical applications

Supersymmetry and the relationship between a class of singular potentials in arbitrary dimensions

Abstract The eigenvalues of the potentials r 6 and of the special cases of these potentials such as Kratzer and GoldmanKrivchenkov potentials, are obtained in N -dimensional space. The explicit dependence of these potentials in higher-dimensional space is discussed, which has not been previously covered

Acidolisis de aceite de pistacho con los ácidos palmítico y caprílico en un reactor de recirculación de lecho compacto: optimización mediante metodología de superficie de respuesta

The acidolysis reaction of terebinth fruit oil with caprylic and palmitic acid has been investigated. The reaction was catalyzed by lipase (Lipozyme IM from Rhizomucormiehei) and carried out in recirculating packed bed reactor. The effects of reaction parameters have been analyzed using response surface methodology. Reaction time (3.5–6.5 h), enzyme load (10–20%), substrate flow rate (4–8 mL·min-1) and substrate mole ratios (Terebinth oil : Palmitic acid : Caprylic acid, 1:1.83:1.22–1:3.07:2.05) were evaluated. The optimum reaction conditions were 5.9 h reaction time, 10% enzyme load, 4 mL·min-1 substrate flow rate and 1:3.10:2.07 substrate mole ratio. The structured lipid obtained at these optimum conditions had 52.23% desired triacylglycerols and a lower caloric value than that of terebinth fruit oil. The melting characteristics and microstructure of the structured lipid were similar to those of commercial margarine fat extracts. The results showed that the structured lipid had the highest oxidative stability among the studied fats.Se ha investigado la reacción de acidolisis del aceite de pistacho con los ácidoscaprílico y palmítico. La reacción fue catalizada por la lipasa Lipozyme IM de Rhizomucormiehei y realizada mediante recirculación del reactor de lecho compacto. Los efectos de los parámetros de la reacción han sido analizados mediante el uso de la metodología de superficie de respuesta. El tiempo de reacción (3.5 hasta 6.5 h), la carga de enzima (10–20%), el caudal de sustrato (4–8 mL·min-1) relaciones molares de los sustrato (aceite de pistacho: ácido palmítico: ácido caprílico, 1: 1,83: 1,22–1: 3,07: 2,05) fueron evaluados. Las condiciones óptimas de reacción fueron 5,9 h de tiempo de reacción, el 10% de carga de la enzima, 4 mL·min-1 de caudal de sustrato y 1: 3,10: 2,07 de relación molar de sustratos. Los lípidos estructurados obtenidos en las condiciones óptimas tenías 52,23% de triacilgliceroles deseados y un valor calórico menor que la de encina aceite de la fruta. Características de fusión y microestructura de lípido estructurado fueron similares a las de los extractos de grasa margarina comerciales. Los resultados mostraron que el lípido estructurado tenía una estabilidad oxidativa más alta entre las grasas estudiadas

Supersymmetry and the relationship between a class of singular potentials in arbitrary dimensions

The eigenvalues of the potentials $V_{1}(r)=\frac{A_{1}}{r}+\frac{A_{2}}{r^{2}}+\frac{A_{3}}{r^{3}}+\frac{A_{4 }}{r^{4}}$ and $V_{2}(r)=B_{1}r^{2}+\frac{B_{2}}{r^{2}}+\frac{B_{3}}{r^{4}}+\frac{B_{4}}{r^ {6}}$, and of the special cases of these potentials such as the Kratzer and Goldman-Krivchenkov potentials, are obtained in N-dimensional space. The explicit dependence of these potentials in higher-dimensional space is discussed, which have not been previously covered.Comment: 13 pages article in LaTEX (uses standard article.sty). Please check "http://www1.gantep.edu.tr/~ozer" for other studies of Nuclear Physics Group at University of Gaziante