The Exponential Map for the Conformal Group 0(2,4)

We present a general method to obtain a closed, finite formula for the exponential map from the Lie algebra to the Lie group, for the defining representation of the orthogonal groups. Our method is based on the Hamilton-Cayley theorem and some special properties of the generators of the orthogonal group, and is also independent of the metric. We present an explicit formula for the exponential of generators of the $SO_+(p,q)$ groups, with $p+q = 6$, in particular we are dealing with the conformal group $SO_+(2,4)$, which is homomorphic to the $SU(2,2)$ group. This result is needed in the generalization of U(1) gauge transformations to spin gauge transformations, where the exponential plays an essential role. We also present some new expressions for the coefficients of the secular equation of a matrix.Comment: 16pages,plain-TeX,(corrected TeX

Magma and fluid migration at Yellowstone Caldera in the last three decades inferred from InSAR, leveling and gravity measurements

We studied the Yellowstone caldera geological unrest between 1977 and 2010 by investigating temporal changes in differential Interferometric Synthetic Aperture Radar (InSAR), precise spirit leveling and gravity measurements. The analysis of the 1992–2010 displacement time series, retrieved by applying the SBAS InSAR technique, allowed the identification of three areas of deformation: (i) the Mallard Lake (ML) and Sour Creek (SC) resurgent domes, (ii) a region close to the Northern Caldera Rim (NCR), and (iii) the eastern Snake River Plain (SRP). While the eastern SRP shows a signal related to tectonic deformation, the other two regions are influenced by the caldera unrest. We removed the tectonic signal from the InSAR displacements, and we modeled the InSAR, leveling, and gravity measurements to retrieve the best fitting source parameters. Our findings confirmed the existence of different distinct sources, beneath the brittle-ductile transition zone, which have been intermittently active during the last three decades. Moreover, we interpreted our results in the light of existing seismic tomography studies. Concerning the SC dome, we highlighted the role of hydrothermal fluids as the driving force behind the 1977–1983 uplift; since 1983–1993 the deformation source transformed into a deeper one with a higher magmatic component. Furthermore, our results support the magmatic nature of the deformation source beneath ML dome for the overall investigated period. Finally, the uplift at NCR is interpreted as magma accumulation, while its subsidence could either be the result of fluids migration outside the caldera or the gravitational adjustment of the source from a spherical to a sill-like geometr

The exponential map for the unitary group SU(2,2)

In this article we extend our previous results for the orthogonal group, $SO(2,4)$, to its homomorphic group $SU(2,2)$. Here we present a closed, finite formula for the exponential of a $4\times 4$ traceless matrix, which can be viewed as the generator (Lie algebra elements) of the $SL(4,C)$ group. We apply this result to the $SU(2,2)$ group, which Lie algebra can be represented by the Dirac matrices, and discuss how the exponential map for $SU(2,2)$ can be written by means of the Dirac matrices.Comment: 10 page

Brillouin optical time-domain analysis for geotechnical monitoring

AbstractIn this paper, we show some recent experimental applications of Brillouin optical time-domain analysis (BOTDA) based sensors for geotechnical monitoring. In particular, how these sensors can be applied to detecting early movements of soil slopes by the direct embedding of suitable fiber cables in the ground is presented. Furthermore, the same technology can be used to realize innovative inclinometers, as well as smart foundation anchors

Reshaping-induced spatiotemporal chaos in driven, damped sine-Gordon systems

Spatiotemporal chaos arising from the competition between sine-Gordon-breather and kink-antikink-pair solitons by reshaping an ac force is demonstrated. After introducing soliton collective coordinates, Melnikov's method is applied to the resulting effective equation of motion to estimate the parameter-space regions of the ac force where homoclinic bifurcations are induced. The analysis reveals that the chaos-order threshold exhibits sensitivity to small changes in the force shape. Computer simulations of the sine-Gordon system show good agreement with these theoretical predictions.Comment: 11 pages, 3 figure

Brillouin scattering for refractive index sensing in non-adiabatic tapers

We demonstrate the use of non-adiabatic tapers for refractive index sensing in optical fibers based on Brillouin scattering. By exciting higher order optical modes along the taper, the Brillouin gain spectrum becomes multipeaked, where each peak exhibits a different sensitivity to the refractive index of the surrounding medium. By this method, we demonstrate a sensitivity enhancement of the Brillouin frequency shift to refractive index changes by a factor of ≈ 4, compared to an adiabatic taper with the same waist diameter. Furthermore, the use of the spectral difference between two Brillouin gain peaks provides a temperature-independent measurement of the external refractive index

Analisis Pengaruh Kompetensi Pengurus Bumkam Dan Penyertaan Modal Terhadap Peningkatan Pendapatan Asli Kampung

Badan Usaha Milik Kampung (BUMKam) merupakan lembaga usaha kampung yang dikelola oleh masyarakat dan pemerintahan kampung dalam upaya memperkuat perekonomian kampung dan dibentuk berdasarkan kebutuhan dan potensi kampung. BUMKam merupakan pilar kegiatan ekonomi di desa yang berfungsi sebagai lembaga sosial (social institution) dan komersial (commercial institution). Permasalahan: Belum maksimalnya Pendapatan Asli Kampung yang diperoleh melalui bagi hasil BUMKam pada kampung se-Kecamatan Dente Teladas Kabupaten Tulang Bawang, sejak Tahun 2016-2017 BUMKam dibentuk dan didanai melalui penyertaan modal kampung. Tujuan penelitian dalam tesis ini adalah untuk mengkaji Pengaruh Kompetensi Pengurus BUMKam dan Penyertaan Modal terhadap Peningkatan Pendapatan Asli Kampung (PAK) pada Kecamatan Dente Teladas Kabupaten Tulang Bawang. Metode penelitian yang digunakan adalah deskriptif verifikatif dengan jumlah responden sebanyak 54 orang yang dianalisis secara deskriptif maupun kuantitatif. Hasil analisis regresi variabel kompetensi dan penyertaan modal terhadap peningkatan pendapatan asli kampung didapat persamaan Y=8,780+0,242X1+ 0,472X2. Uji hipotesis secara parsial menunjukkan bahwa terdapat pengaruh kompetensi Pengurus Bumkam terhadap peningkatan pendapatan asli kampung dengan kontribusi pengaruh sebesar 24,2%, penyertaan modal juga berpengaruh positif terhadap peningkatan pendapatan asli kampung dengan kontribusi pengaruh sebesar 47,2%. Uji hipotesis secara bersama-sama menunjukkan terdapat pengaruh positif antara kompetensi Pengurus Bumkam dan penyertaan modal terhadap peningkatan pendapatan asli kampung dengan kontribusi pengaruh sebesar32,9%. Implikasinya adalah Pemerintah Kabupaten melalui Kecamatan melaksanakan pembinaan secara periodik dengan memberikan Bimtek dan pelatihan kepada pengurus Bumkam, Pemerintah Kampung memberikan penyertaan modal pada Bumkam dari Dana Desa yang dianggarkan melalui APBKam

Cost-of-illness in systemic sclerosis: a retrospective study of an italian cohort of 106 patients

Aims: It is increasingly important to determine the economic consequences of diseases considering the policy of limited health–care budgets. In this study we evaluated the annual direct and indirect costs of Systemic Sclerosis (SSc) and we tried also to identify any cost predictors. Methods: We studied 106 patients (103 female, 3 male), 57 affected by Limited Systemic Sclerosis (LSSc) and 49 affected by Diffuse Systemic Sclerosis (DSSc). Mean age was 57 years (SD±13,8) and mean disease duration was 8,9 years (SD±7,2). Direct costs: data were calculated referring to DRG (Disease Related Group) expenses for the in-patients. We referred to national pharmacopoeia to calculate the pharmaceutical cost for the out-patients. Indirect costs: we estimated the expense comparing our cases to literature data. Intangible costs: these are attributable to pain and psychological suffering. It is very difficult to express the intangible costs in monetary terms and they are often conveyed as disability and poorer quality-of-life. We used the Health Assessment Questionnaire "HAQ" and the Short Form-36 "SF-36" to evaluate this issues. Results: Our study confirms, the extremely high costs caused by Systemic Sclerosis (total cost's 2001 year is € 1.173.842,93, and average yearly patient cost is € 11.073,99). Considering an estimated prevalence of 375 cases/106, the total yearly economic impact of SSc in Italy should be € 249.000.000,00. Intangible costs were calculated as modifications of the health status. Average value of the HAQ was significantly higher than the control population (0,94±0,72), average values in the SF-36 were significantly lower than the control population (49,99±19,16 for physical dimension and 58,42±27,71 for mental dimension). The diffuse form of SSc, positivity for anti-Scl 70 antibodies, high skin score and a poor health status (HAQ and SF-36) were found to be cost predictors. Conclusions: As reported in the literature, our study confirms, the extremely high costs for total and single patients caused by Systemic Sclerosis. The DSSc are more expensive than the LSSc approximately 11% (p=0,0067). The direct costs are 30% higher in the DSSc than the LSSc (p<0.001). The indirect and intangible costs are not significantly different. Moreover, our study shows also the possibility of identifying different cost predictors