一四八九年德国数学家韦德曼（Widman）在一本算术书中正式采用和号,一六三零年被公认为运算符号。如1+2+3+…+98+99+100=?记为sum from k=1 to 100 k=?（和号∑读作西格马） n个数a<sub>1</sub>,a<sub>2</sub>...一四八九年德国数学家韦德曼（Widman）在一本算术书中正式采用和号,一六三零年被公认为运算符号。如1+2+3+…+98+99+100=?记为sum from k=1 to 100 k=?（和号∑读作西格马） n个数a<sub>1</sub>,a<sub>2</sub>…a<sub>n</sub>连加,简记作sum from k=1 to n a<sub>k</sub>,即a<sub>1</sub>+a<sub>2</sub>+…+a<sub>n</sub>=sum from k=1 to n a<sub>k</sub>。a<sub>k</sub>称为和式的通项,k称为通项a<sub>k</sub>的下标,∑下面的k=1及顶上的n表示k从1依次取自然数到n。所以k也称为流动下标。和号的简单性质:展开更多
In the present investigation we have discussed the flow of a Jeffrey-six constant incompressible fluid between two infinite coaxial cylinders in the presence of heat transfer analysis. The governing equations of Jeffr...In the present investigation we have discussed the flow of a Jeffrey-six constant incompressible fluid between two infinite coaxial cylinders in the presence of heat transfer analysis. The governing equations of Jeffrey-six constant fluid along with energy equation have been derived in cylindrical coordinates. The highly nonlinear equations are simplified with the help of non-dimensional parameters and then solved analytically with the help of homotopy analysis method （HAM） for two fundamental flows namely Couette and Generalized Couette flow. The effects of emerging parameters are discussed through graphs. The convergence of the HAM solution has been discussed by plotting h-curves.展开更多
The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, the peristaltic motion of non-Newtonian Jeffrey six constant fluid is observed in an annulus with ...The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, the peristaltic motion of non-Newtonian Jeffrey six constant fluid is observed in an annulus with ciliated tips in the presence of heat and mass transfer. The effects of viscous dissipation are also considered. The flow equations of non-Newtonian fluid for the two-dimensional tube in cylindrical coordinates are simplified using the low Reynolds number and long wave-length approximations. The main equations for Jeffrey six constant fluid are considered in cylindrical coordinates system. The resulting nonlinear problem is solved using the regular perturbation technique in terms of a variant of small dimensionless parameter α. The results of the solutions for velocity, temperature and concentration field are presented graphically. B_k is Brinkman number, ST is soret number, and SH is the Schmidth number. Outcome for the longitudinal velocity, pressure rise, pressure gradient and stream lines are represented through graphs. In the history, the viscous-dissipation effect is usually represented by the Brinkman number.展开更多
T-tym phocyte migration under flow is critical for immune responses, but the mechanisms by which flow modulates the migratory beha- viors of T-lymphocytes remain unclear. Human peripheral blood T-lymphocytes （PBTLs）...T-tym phocyte migration under flow is critical for immune responses, but the mechanisms by which flow modulates the migratory beha- viors of T-lymphocytes remain unclear. Human peripheral blood T-lymphocytes （PBTLs）, when stimulated with phorboL 12-myristate 13-acetate （PMA）, stretched their ceU bodies dramatically and moved alongthe flow direction. In contrast, stromal ceil-derived factor- lα-stimulated PBTI.s deformed and migrated in a random manner. Here we elucidated the molecular mechanisms underlying flow- induced directionality and deformation of PMA-stimulated PBTLs. PMA primed PBTLs for polarization under flow, with protein kinase C （PKC）-δ enriched in the leading edge, PKC-β1 in the microtubuie organizing center, and PKC-1311 in the uropod and peripheral region. PKC-δ regulated cell protrusions in the leading edge through Tiaml/Racl/caLmoduUn, whereas PKC-β regulated RhoA/Rho- associated kinase activity and microtubule stability to modulate uropod contractility and detachment. Our findings indicate that PKC-δ and -β coordinate in the cell Leading edge and uropod, respectively, to modu｜ate the directionality and deformability of migratory T-Lymphocytes under flow.展开更多
文摘一四八九年德国数学家韦德曼（Widman）在一本算术书中正式采用和号,一六三零年被公认为运算符号。如1+2+3+…+98+99+100=?记为sum from k=1 to 100 k=?（和号∑读作西格马） n个数a<sub>1</sub>,a<sub>2</sub>…a<sub>n</sub>连加,简记作sum from k=1 to n a<sub>k</sub>,即a<sub>1</sub>+a<sub>2</sub>+…+a<sub>n</sub>=sum from k=1 to n a<sub>k</sub>。a<sub>k</sub>称为和式的通项,k称为通项a<sub>k</sub>的下标,∑下面的k=1及顶上的n表示k从1依次取自然数到n。所以k也称为流动下标。和号的简单性质:
文摘In the present investigation we have discussed the flow of a Jeffrey-six constant incompressible fluid between two infinite coaxial cylinders in the presence of heat transfer analysis. The governing equations of Jeffrey-six constant fluid along with energy equation have been derived in cylindrical coordinates. The highly nonlinear equations are simplified with the help of non-dimensional parameters and then solved analytically with the help of homotopy analysis method （HAM） for two fundamental flows namely Couette and Generalized Couette flow. The effects of emerging parameters are discussed through graphs. The convergence of the HAM solution has been discussed by plotting h-curves.
文摘The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, the peristaltic motion of non-Newtonian Jeffrey six constant fluid is observed in an annulus with ciliated tips in the presence of heat and mass transfer. The effects of viscous dissipation are also considered. The flow equations of non-Newtonian fluid for the two-dimensional tube in cylindrical coordinates are simplified using the low Reynolds number and long wave-length approximations. The main equations for Jeffrey six constant fluid are considered in cylindrical coordinates system. The resulting nonlinear problem is solved using the regular perturbation technique in terms of a variant of small dimensionless parameter α. The results of the solutions for velocity, temperature and concentration field are presented graphically. B_k is Brinkman number, ST is soret number, and SH is the Schmidth number. Outcome for the longitudinal velocity, pressure rise, pressure gradient and stream lines are represented through graphs. In the history, the viscous-dissipation effect is usually represented by the Brinkman number.
文摘T-tym phocyte migration under flow is critical for immune responses, but the mechanisms by which flow modulates the migratory beha- viors of T-lymphocytes remain unclear. Human peripheral blood T-lymphocytes （PBTLs）, when stimulated with phorboL 12-myristate 13-acetate （PMA）, stretched their ceU bodies dramatically and moved alongthe flow direction. In contrast, stromal ceil-derived factor- lα-stimulated PBTI.s deformed and migrated in a random manner. Here we elucidated the molecular mechanisms underlying flow- induced directionality and deformation of PMA-stimulated PBTLs. PMA primed PBTLs for polarization under flow, with protein kinase C （PKC）-δ enriched in the leading edge, PKC-β1 in the microtubuie organizing center, and PKC-1311 in the uropod and peripheral region. PKC-δ regulated cell protrusions in the leading edge through Tiaml/Racl/caLmoduUn, whereas PKC-β regulated RhoA/Rho- associated kinase activity and microtubule stability to modulate uropod contractility and detachment. Our findings indicate that PKC-δ and -β coordinate in the cell Leading edge and uropod, respectively, to modu｜ate the directionality and deformability of migratory T-Lymphocytes under flow.
