u-symmetric matrices u 中文意思是什麼
u-symmetric matrices u
解釋
對稱陣-
The paper is concerned with periodic solutions to nonautonomous second order hamilton systems where, m : [ 0, t ] - s ( rn, rn ) is a continuous mapping in the space s ( rn, rn ) of symmetric real ( n x n ) - matrices, such that for some u > 0 and all ( t, z ) [ 0, t ] x rn, ( m ( t ) x, x ) > u | x | 2. a s ( rn, rn ), f : [ 0, t ] x rn r is continuous and f : [ 0, t ] xr r exists, is continuous and we study the existence of periodic solutions of the systems by using ekeland variational principle and the saddle points theorem. we suppose that the nonlinearity vf and potential f belongs to a class of unbounded functional. our work improves the existed results. we obtained the results of multiplicity of periodic solutions of the systems by using lusternik - schnirelman category theory and the generalized saddle points theorem, and the functional does not need the condition of constant definite. at last, we obtained the existence of infinity many distinct periodic solutions of the corresponding non - perturbation systems by using the symmetric mountain pass theorem
（ ? ， ? ）為r ~ n中內積， | ? |為對應范數。 f [ 0 ， t ] r ~ n r連續， ? f （ t ， x ）存在且連續， h l ~ 1 （ 0 ， t ； r ~ n ） 。利用ekeland變分原理和鞍點定理討論了該系統周期解的存在性，把非線性項和位勢函數放寬到一類無界函數，推廣了這方面工作的一些已有結果；利用廣義鞍點定理和lusternik - schnirelman疇數理論得到了該系統的多重周期解，取掉了泛函的常定要求；最後利用對稱山路定理得到沒有擾動時系統的無窮多周期解。 -
The explicit method is widely used for its simpleness and little memory consumed with local time step and variable coefficients implicit residual smooth to accelerate the convergence procedure. according to yoon and jameson ' s ideas, an efficient implicit lu - sgs algorithm is carefully constructed by combing the advantages of lu factorization and symmetric - gauss - seidel technique in such a way to make use the l and u operators scalar diagonal matrices, thus the numeric algorithm requires only scalar inversion. the computational efficiency is greatly improved with this scheme
顯式方法具有簡單，消耗內存小等優點，並採用當地時間步長、變系數隱式殘值光順等加速收斂措施，在定常流動的模擬中得到了廣泛的應用;根據yoon和jameson提出的簡化正、負矩陣分裂，構造的l 、 u運算元只需進行標量對角陣求逆，極大提高了流場數值求解過程的計算效率;採用newton類型的偽時間子迭代技術使時間推進精度提高至二階。
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