P-集合的代数模型

利用线性方程组解的理论,给出P-集合的一个代数模型,并研究了该代数模型的一些基本性质.

关于Clifford代数中多项式解的一个结果

利用代数基本定理,证明以Clifford代数所基于的结合代数的一子空间作系数空间,一类特殊的多项式方程在该子空间中至少存在一个根.

一元n次多项式根的圆环覆盖定理

本文的主要结果是利用相容矩阵范数的性质给出了一元ｎ次多项式根的圆环覆盖定理，即一元ｎ次多项式的所有非零复根必全都落在复平面上同一个圆环区域内．特别，ｎ次二项式的所有非零复根必都落在同一个圆周上．这一结果，可以改进盖尔斯果林（Ｇｅｒｓｓｇｏｒｉｎ）的圆盘覆盖定理的结果．

一元n次多项式根的园环复盖定理

本文的主要结果是利用三种不同的相容矩阵范数,分别给出了任意一个一元n次多项式的所有复根必全都落在复平面的一个园环区域内。

Optimal estimation of zonal velocity and transport through Luzon Strait using variational data assimilation technique

A P-vector method was optimized using variational data assimilation technique, with which the vertical structures and seasonal variations of zonal velocities and transports were investigated. The results showed that westward and eastward flowes occur in the Luzon Strait in the same period in a year. However the net volume transport is westward. In the upper level (0m -500m),the westward flow exits in the middle and south of the Luzon Strait, and the eastward flow exits in the north. There are two centers of westward flow and one center of eastward flow. In the middle of the Luzon Strait, westward and eastward flowes appear alternately in vertical direction. The westward flow strengthens in winter and weakens in summer. The net volume transport is strong in winter (5.53 Sv) but weak in summer (0.29 Sv). Except in summer, the volume transport in the upper level accounts for more than half of the total volume transport (0m bottom). In summer, the net volume transport in the upper level is eastward (1.01 Sv), but westward underneath.

Absolute geostrophic currents in global tropical oceans

A set of absolute geostrophic current(AGC) data for the period January 2004 to December 2012 are calculated using the P-vector method based on monthly gridded Argo profi les in the world tropical oceans. The AGCs agree well with altimeter geostrophic currents, Ocean Surface Current Analysis-Real time currents, and moored current-meter measurements at 10-m depth, based on which the classical Sverdrup circulation theory is evaluated. Calculations have shown that errors of wind stress calculation, AGC transport, and depth ranges of vertical integration cannot explain non-Sverdrup transport, which is mainly in the subtropical western ocean basins and equatorial currents near the Equator in each ocean basin(except the North Indian Ocean, where the circulation is dominated by monsoons). The identifi ed nonSverdrup transport is thereby robust and attributed to the joint effect of baroclinicity and relief of the bottom(JEBAR) and mesoscale eddy nonlinearity.

Heat and salt transport throughout the North Pacific Ocean

Absolute geostrophic currents in the North Pacific Ocean are calculated using the P-vector method and gridded Argo profiling data from January 2004 to December 2012. Three-dimensional structures and seasonal variability of meridional heat transport(MHT) and meridional salt transport(MST) are analyzed. The results show that geostrophic and Ekman components are generally opposite in sign, with the southward geostrophic component dominating in the subtropics and the northward Ekman component dominating in the tropics. In combination with the net surface heat flux and the MST through the Bering Strait, the MHT and MST of the western boundary currents(WBCs) are estimated for the fi rst time. The results suggest that the WBCs are of great importance in maintaining the heat and salt balance of the North Pacifi c. The total interior MHT and MST in the tropics show nearly the same seasonal variability as that of the Ekman components, consistent with the variability of zonal wind stress. The geostrophic MHT in the tropics is mainly concentrated in the upper layers, while MST with large amplitude and annual variation can extend much deeper. This suggests that shallow processes dominate MHT in the North Pacific, while MST can be affected by deep ocean circulation. In the extratropical ocean, both MHT and MST are weak. However, there is relatively large and irregular seasonal variability of geostrophic MST, suggesting the importance of the geostrophic circulation in the MST of that area.

CONTINUOUS MAPPINGS IN P_a(E;F)

Let E and F be Banach spaces over the same field K which is either the field R or the field C.The character of continuous mappings in P a(E;F) which is a vector space of all polynomials from E into F is discussed.In particular,some equivalent conditions for a mapping P in P a(E;F) to be continuous are established.This is very important and useful to determine a mapping P in P a(E;F) to be either continuous or not in theory or practice.