A discrete approach to Wirtinger's inequality

Considering Wirtinger's inequality for piece-wise equipartite functions we find a discrete version of this classical inequality. The main tool we use is the theorem of classification of isometries. Our approach provides a new elementary proof of Wirtinger's inequality that also allows to study the case of equality. Moreover it leads in a natural way to the Fourier series development of $2\pi$-periodic functions.Comment: 9 page

Nota sobre la presencia de minerales arcillosos de transformación en facies evaporíticas del Bundsandstein superior de Sierra Calderona (Ibérica suroriental, Valencia)

En lutitas de la facies Rot, en la Cordillera Ibérica, zona sudoriental, se ha determinado la presencia de interestratificados (14c,-14m,), que denotan el carácter evaporítico de estas facies

Minerals i roques industrials del País Valencià

Quins són els minerals i roques d'interès industrial presents en el subsòl del País Valencià

Equilibrios al estado sólido entre frases de solución sólida en sistemas minerales binarios: Sistema RbBr-RbI

X-ray diffraction has been used to study the de equilimixtion in solid state of Rb(BrXIi..) solid solutions The compositions of the phases in equilibrium at room temnerature are 0.18 RbBr-0.82 RbI and 0.96 RbBr-0.04 ÉZb1, respectively. The maximum critical  temperature of the demixtion is 422ºC, corresponding to the composition X~t.1= 0.35. AS a result of this experimental work the existente of a  single-phase region at high-temperature and a two-phases region at interdifracmediate and  low-temperature has been established

Nota sobre la composición química y mineralógica de los piroxenos monoclínicos existentes en lso basaltos de Fruniz (Vizcaya)

Clinopyroxenes from the Fruniz (Vizcaya) basalts have been studied by chemical analysis and X-ray diffraction. The chemical analysis carried out by atomic absorption spectrography has led to the following structural composition Wo44,4 En 47,2 Fs  8,4 which is in agreement with the composition Wo 42  En 48 Fs 10 obtained irom the interpretation of the crystal powder patterns. According to these data the mineralogical composition of these pyroxenes is situated between endiopside and augite

Equilibrios al estado sólido entre frases de solución sólida en sistemas minerales binarios: Sistema RbBr-RbI

X-ray diffraction has been used to study the de equilimixtion in solid state of Rb(BrXIi..) solid solutions The compositions of the phases in equilibrium at room temnerature are 0.18 RbBr-0.82 RbI and 0.96 RbBr-0.04 ÉZb1, respectively. The maximum critical  temperature of the demixtion is 422ºC, corresponding to the composition X~t.1= 0.35. AS a result of this experimental work the existente of a  single-phase region at high-temperature and a two-phases region at interdifracmediate and  low-temperature has been established