For a rotating inhomogeneous circular disk a way of calculating dynamics of boundary shape perturbation and failure of bearing capacity is proposed in terms of small parameter method. Characteristic equation of plasti...For a rotating inhomogeneous circular disk a way of calculating dynamics of boundary shape perturbation and failure of bearing capacity is proposed in terms of small parameter method. Characteristic equation of plastic zone critical radius is obtained as a first approximation. A formula of critical angular velocity is derived which determines the stability loss of the disc according to the self-balanced form. Efficiency of the proposed method is shown by an illustrative example considered in Section 7. Values of critical angular velocity of rotation are found numerically for different parameters of the disc.展开更多
The article presents the proof of the validity of the generalized Riemann hypothesis on the basis of adjustment and correction of the proof of the Riemanns hypothesis in the work?[1], obtained by a finite exponential ...The article presents the proof of the validity of the generalized Riemann hypothesis on the basis of adjustment and correction of the proof of the Riemanns hypothesis in the work?[1], obtained by a finite exponential functional series and finite exponential functional progression.展开更多
Results of a geochemical and geochronological study of the Paleoproterozoic rock assemblage in the Haisyn block of the Ros-Tikych Domain of the Ukrainian Shield are reported.Within the block,the Haisyn Complex compris...Results of a geochemical and geochronological study of the Paleoproterozoic rock assemblage in the Haisyn block of the Ros-Tikych Domain of the Ukrainian Shield are reported.Within the block,the Haisyn Complex comprises granitoids,including pyroxene-bearing diorites,quartz diorites,granodiorites,amphibole-biotite and biotite granites,and aplite and pegmatite granites.Monazite U-Pb isotope age of charnockitic syenite belonging to the Haisyn Complex was defined at 2027±6 Ma.This age coeval with the time of granulite facies metamorphism and emplacement of numerous granitic intrusions in the area.The Sm–Nd apatite isochron yielded an age of 2100±150 Ma.TheεNd isochron value of-5 indicates a long crustal residence time of the crustal protolith.Geochemical data do not indicate any enrichment of the studied rocks in relation to the Eoarchean and Neoarchean charnockites developed in the same area.So,if the model of partial melting of the older crustal protolith is involved then the degree of melting must be quite high.However,deep negative anomalies of Sr,Eu,Zr,and Ti indicate that plagioclase,zircon,and Fe–Ti oxides probably remained unmelted in the source.The Haisyn block was buried in the lower crust at high temperature and pressure conditions in the Paleoproterozoic time.Such a situation resulted in partial melting of the existing crust and formation of melts,containing undigested zircon and bearing ancient Nd isotope signature.展开更多
文摘For a rotating inhomogeneous circular disk a way of calculating dynamics of boundary shape perturbation and failure of bearing capacity is proposed in terms of small parameter method. Characteristic equation of plastic zone critical radius is obtained as a first approximation. A formula of critical angular velocity is derived which determines the stability loss of the disc according to the self-balanced form. Efficiency of the proposed method is shown by an illustrative example considered in Section 7. Values of critical angular velocity of rotation are found numerically for different parameters of the disc.
文摘The article presents the proof of the validity of the generalized Riemann hypothesis on the basis of adjustment and correction of the proof of the Riemanns hypothesis in the work?[1], obtained by a finite exponential functional series and finite exponential functional progression.
文摘Results of a geochemical and geochronological study of the Paleoproterozoic rock assemblage in the Haisyn block of the Ros-Tikych Domain of the Ukrainian Shield are reported.Within the block,the Haisyn Complex comprises granitoids,including pyroxene-bearing diorites,quartz diorites,granodiorites,amphibole-biotite and biotite granites,and aplite and pegmatite granites.Monazite U-Pb isotope age of charnockitic syenite belonging to the Haisyn Complex was defined at 2027±6 Ma.This age coeval with the time of granulite facies metamorphism and emplacement of numerous granitic intrusions in the area.The Sm–Nd apatite isochron yielded an age of 2100±150 Ma.TheεNd isochron value of-5 indicates a long crustal residence time of the crustal protolith.Geochemical data do not indicate any enrichment of the studied rocks in relation to the Eoarchean and Neoarchean charnockites developed in the same area.So,if the model of partial melting of the older crustal protolith is involved then the degree of melting must be quite high.However,deep negative anomalies of Sr,Eu,Zr,and Ti indicate that plagioclase,zircon,and Fe–Ti oxides probably remained unmelted in the source.The Haisyn block was buried in the lower crust at high temperature and pressure conditions in the Paleoproterozoic time.Such a situation resulted in partial melting of the existing crust and formation of melts,containing undigested zircon and bearing ancient Nd isotope signature.
