The charnockites of Marandahalli, Dharmapuri District, Tamil Nadu India, form a part of the southern granulitic terrain in the Salem Block (SB). The charnockites are medium to coarse grained, inequigranular, with porp...The charnockites of Marandahalli, Dharmapuri District, Tamil Nadu India, form a part of the southern granulitic terrain in the Salem Block (SB). The charnockites are medium to coarse grained, inequigranular, with porphyroblastic and granophyric textures. They are composed of plagioclase feldspars (49 - 66 vol.%), K-feldspar (1 - 5 vol.%) and quartz (21 - 34 vol.%). The mafic minerals include pyroxene (2 - 7 vol.%) and biotite (1 - 12 vol.%). The accessory minerals include magnetite and apatite. Orthopyroxene compositions (MgO 16 - 22 wt.%) fall within the hypersthene series (En55.03Fs43.57Wo1.4) and yield peak metamorphic temperatures of 800˚C - 1000˚C. Biotites show K2O, MgO, FeO, TiO2, and Al2O3 concentrations consistent with magmatic formation, and Ti-in-biotite thermometry suggests temperatures of ~740˚C - 800˚C. Plagioclase compositions (An26-33) plot in the oligoclase field, while K-feldspar (Or93-99) plots in the orthoclase/microcline field. A ternary feldspar geothermometer indicates a retrograde temperature of 2 (65 - 68 wt.%), Na2O > K2O, high CaO (3 - 5 wt.%), MgO (2.5 - 4 wt.%) and Fe2O3 (2 - 6 wt.%). The concentration of V, Rb and Ni, and LREE-rich and HREE-depleted patterns of the rocks indicate low degree of partial melting.展开更多
In this article, the authors study the vector-valued random power series on the unit ball of C^n and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between v...In this article, the authors study the vector-valued random power series on the unit ball of C^n and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between vector-valued random power series and several function spaces are also studied.展开更多
The Bernoulli convolution ν λ measure is shown to be absolutely continuous with L 2 density for almost all 12<λ<1,and singular if λ -1 is a Pisot number. It is an open question whether the Pisot typ...The Bernoulli convolution ν λ measure is shown to be absolutely continuous with L 2 density for almost all 12<λ<1,and singular if λ -1 is a Pisot number. It is an open question whether the Pisot type Bernoulli convolutions are the only singular ones. In this paper,we construct a family of non-Pisot type Bernoulli convolutions ν λ such that their density functions,if they exist,are not L 2. We also construct other Bernolulli convolutions whose density functions,if they exist,behave rather badly.展开更多
文摘The charnockites of Marandahalli, Dharmapuri District, Tamil Nadu India, form a part of the southern granulitic terrain in the Salem Block (SB). The charnockites are medium to coarse grained, inequigranular, with porphyroblastic and granophyric textures. They are composed of plagioclase feldspars (49 - 66 vol.%), K-feldspar (1 - 5 vol.%) and quartz (21 - 34 vol.%). The mafic minerals include pyroxene (2 - 7 vol.%) and biotite (1 - 12 vol.%). The accessory minerals include magnetite and apatite. Orthopyroxene compositions (MgO 16 - 22 wt.%) fall within the hypersthene series (En55.03Fs43.57Wo1.4) and yield peak metamorphic temperatures of 800˚C - 1000˚C. Biotites show K2O, MgO, FeO, TiO2, and Al2O3 concentrations consistent with magmatic formation, and Ti-in-biotite thermometry suggests temperatures of ~740˚C - 800˚C. Plagioclase compositions (An26-33) plot in the oligoclase field, while K-feldspar (Or93-99) plots in the orthoclase/microcline field. A ternary feldspar geothermometer indicates a retrograde temperature of 2 (65 - 68 wt.%), Na2O > K2O, high CaO (3 - 5 wt.%), MgO (2.5 - 4 wt.%) and Fe2O3 (2 - 6 wt.%). The concentration of V, Rb and Ni, and LREE-rich and HREE-depleted patterns of the rocks indicate low degree of partial melting.
文摘In this article, the authors study the vector-valued random power series on the unit ball of C^n and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between vector-valued random power series and several function spaces are also studied.
文摘The Bernoulli convolution ν λ measure is shown to be absolutely continuous with L 2 density for almost all 12<λ<1,and singular if λ -1 is a Pisot number. It is an open question whether the Pisot type Bernoulli convolutions are the only singular ones. In this paper,we construct a family of non-Pisot type Bernoulli convolutions ν λ such that their density functions,if they exist,are not L 2. We also construct other Bernolulli convolutions whose density functions,if they exist,behave rather badly.
