The connection between entropy and the absorption spectra of Schwarzschild black holes for light and massless scalar fields

We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein interpretation of the area of a black hole as a measure of its entropy. Thus, entropy considerations make the well known fact that large wavelengths are only marginally absorbed by black holes, a natural consequence of thermodynamics. We also study numerically the ingoing radial propagation of a scalar field wave in a Schwarzschild metric, relaxing the standard assumption which leads to the eikonal equation, that the wave has zero spatial extent. We find that if these waves have wavelengths larger that the Schwarzschild radius, they are very substantially reflected, fully to numerical accuracy. Interestingly, this critical wavelength approximately coincides with the one derived from entropy considerations of the EM field, and is consistent with well known limit results of scattering in the Schwarzschild metric. The propagation speed is also calculated and seen to differ from the value $c$, for wavelengths larger than $R_{s}$, in the vicinity of $R_{s}$. As in all classical wave phenomena, whenever the wavelength is larger or comparable to the physical size of elements in the system, in this case changes in the metric, the zero extent 'particle' description fails, and the wave nature becomes apparent.Comment: 14 Pages, 4 figures. Accepted for publication in the Journal Entrop

Painful Hemorrhage of Vestibular Papillae: A Probably Underreported Complication of Vestibular Papillomatosis

Dermatoscòpia; Hemorràgia de papil·les vestibulars; Genitals femeninsDermoscopy; Vestibular papillae hemorrhage; Female genitaliaDermatoscopia; Hemorragia de papilas vestibulares; Genitales femeninosVestibular papillomatosis (VP) is a common, harmless, and permanent variation of the vulvar skin for those assigned female at birth. VP manifests as small and flesh-colored bumps on the labia minora (small skin folds surrounding the vagina) and vulvar vestibule (skin under the labia minora). Unlike infections or harmful growths, VP does not pose any health risks and is not associated with sexually transmitted infections (STIs) like human papillomavirus (HPV) or genital warts. In this article, we explore who typically experiences VP, its appearance, texture, color, and how it differs from other vulvar bumps. A 29-year-old woman had a painful red lesion on her labia minora. She had no significant medical history. The lesion was consistent with vestibular papillomatosis and possibly caused by tight clothing. She declined a biopsy and was advised to avoid irritants. After two weeks, the lesion had decreased in size and pain, leading to a diagnosis of self-resolving hemorrhage of a vestibular papilla. Understanding the appearance and behavior of Vestibular Papillomatosis (VP) is crucial for distinguishing it from other genital lesions. Clinicians should be sensitive to patients’ emotional distress and provide appropriate education. Dermoscopy was a valuable tool in diagnosing a case of VP hemorrhage, suggesting a traumatic origin. This case expands our knowledge of VP and emphasizes its consideration in diagnosing genital lesions. More research is needed to understand the impact of VP complications on patients’ quality of life

A Model for the Strings of Eta Carinae

We propose a model based on ionization shadows to explain the formation of the long and narrow strings of Eta Carinae. Five strings are known, all located along the symmetry axis outside the Homunculus. The model assumes that each string is formed in a shadow behind a dense clump near the symmetry axis. The surrounding gas is ionized first, becomes much hotter, and compresses the gas in the shadow. This leads to the formation of a radial, dense, long, and narrow region, i.e., a string. Later the neutral material in the strings is ionized, and becomes brighter. Still later it re-expands, and we predict that in about 200 years the strings will fade. The condition for the model to work is that the ionization front, due to the diffuse ionizing recombination radiation of the surrounding gas, proceeds into the shadow at a velocity slower than the compression speed. From that we get a condition on the mass loss rate of the mass loss episode that formed the strings, which should be less than 10^{-4} Mo/year. The model can also explain the strings in the planetary nebula NGC 6543.Comment: 8 pages; Submitted to A&

Ligand synthesis catalyst and complex metal ion: multicomponent synthesis of 1,3-bis(4-phenyl-[1,2,3]triazol-1-yl)-propan-2-ol copper(i) complex and application in copper-catalyzed alkyne-azide cycloaddition

A new bistriazole copper complex was synthesized by direct treatment of an alkyne, an azide, and CuI as copper salt through in situ ligand formation under a multicomponent reaction process. This complex was analyzed by XPS, TGA, DSC, and SEM techniques and revealed a triangular-shapedmorphology, high thermal stability, and catalytic power in CuAAC reactions, requiring only 2.5% mol catalyst to afford 1,2,3-triazoles in good yields which can be reused at least for 4 cyclesCONACYT, proyecto 13505

1.3 mm Polarized emission in the circumstellar disk of a massive protostar

We present the first resolved observations of the 1.3 mm polarized emission from the disk-like structure surrounding the high-mass protostar Cepheus A HW2. These CARMA data partially resolve the dust polarization, suggesting a uniform morphology of polarization vectors with an average position angle of 57° ± 6° and an average polarization fraction of 2.0% ± 0.4%. The distribution of the polarization vectors can be attributed to (1) the direct emission of magnetically aligned grains of dust by a uniform magnetic field, or (2) the pattern produced by the scattering of an inclined disk. We show that both models can explain the observations, and perhaps a combination of the two mechanisms produces the polarized emission. A third model including a toroidal magnetic field does not match the observations. Assuming scattering is the polarization mechanism, these observations suggest that during the first few 104 years of high-mass star formation, grain sizes can grow from1 mm to several 10s μm.Fil: Fernandez Lopez, Manuel. Provincia de Buenos Aires. Gobernación. Comision de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomia; ArgentinaFil: Stephens, I. W.. Harvard-Smithsonian Center for Astrophysics; Estados Unidos. Boston University; Estados Unidos. University of Illinois; Estados UnidosFil: Girart, J. M.. Harvard-Smithsonian Center for Astrophysics; Estados Unidos. Institut de Ciències de l’Espai; EspañaFil: Looney, L.. University of Illinois; Estados UnidosFil: Curiel, S.. Universidad Nacional Autónoma de México; MéxicoFil: Segura Cox, D.. University of Illinois; Estados UnidosFil: Eswaraiah, C.. National Tsing Hua University; República de ChinaFil: Lai, S. P.. National Tsing Hua University; República de Chin

El trademarketing y su relación con las ventas en productos de consumo masivo en el canal tradicional de la empresa Molitalia en la ciudad de Trujillo en el año 2021

La presente tesis tuvo como objetivo poder determinar la relación entre el trademarketing y su influencia en las ventas de la empresa “MOLITALIA” en la ciudad de Trujillo, en el año 2021. Se trata de un estudio de tipo correlacional-descriptiva de corte trasversal. Se aplicó una encuesta para la medición de las variables, trademarketing y ventas, está encuesta está relaborada por 20 preguntas, que contienen ocho dimensiones: merchandising, visual merchandising, material POP, activaciones BTL, abastecimiento y distribución, valor de venta, incremento de ventas, valor percibido. Existe 5 opciones de respuesta para cada un a de las preguntas planteadas que fueron aplicadas a través de la escala de Liket. Se trabajó con una muestra de 208 personas, todos clientes de la empresa “MOLITALIA”, estos clientes en su totalidad estuvieron enfocados en el canal tradicional mayorista. El procesamiento estadístico de los datos se realizó con el paquete de Sofware estadístico SPSS en su versión 2.0. El instrumento fue validado por docentes de la Universidad Privada del Norte, quienes son especialistas en el tema. Los resultados se presentan a través de figuras y cuadros, con la finalidad de hacer una representación gráfica de los resultados obtenidos. Finalmente se determinó que existe una relación entre trademarketing y ventas, además el coeficiente de correlación Spearman, confirma lo anteriormente mencionado, considerando así, la relación de ambas variables