Under the guidauce of Prof. Chin Yuanshun, the author has studied a conjecture in the 16th problem of Hilbert’s 'there is no limit cycle around a critical focus of order 3'. Denoting this conjecture by integr...Under the guidauce of Prof. Chin Yuanshun, the author has studied a conjecture in the 16th problem of Hilbert’s 'there is no limit cycle around a critical focus of order 3'. Denoting this conjecture by integrals, we divide it into three cases: (ⅰ) exponential function; (ⅱ) logarithmic function; and (ⅲ) power function. In this letter, it has been proved that the conjecture holds true under case (ⅱ). With regard to (ⅰ) and (ⅲ) we have also obtained some results, which will be given else-展开更多
In this letter we shall describe the automorphisms of SL1（R） and GL1（R）, R local rings with 2 not being a unit of R and the residue field of R not being F2. In this way we obtain that the automorphisms are the sta...In this letter we shall describe the automorphisms of SL1（R） and GL1（R）, R local rings with 2 not being a unit of R and the residue field of R not being F2. In this way we obtain that the automorphisms are the standard.展开更多
We denote by π（x） the characteristi function of the interval （0, 1）, πk=h-1πx/h and π（?）（x）= h-1π（x/h-j）（0≤j≤n-1,h=n/1）. For w∈EA, construct Rhu = （Rhw）f, where （Rkw）f.
文摘Under the guidauce of Prof. Chin Yuanshun, the author has studied a conjecture in the 16th problem of Hilbert’s 'there is no limit cycle around a critical focus of order 3'. Denoting this conjecture by integrals, we divide it into three cases: (ⅰ) exponential function; (ⅱ) logarithmic function; and (ⅲ) power function. In this letter, it has been proved that the conjecture holds true under case (ⅱ). With regard to (ⅰ) and (ⅲ) we have also obtained some results, which will be given else-
文摘In this letter we shall describe the automorphisms of SL1（R） and GL1（R）, R local rings with 2 not being a unit of R and the residue field of R not being F2. In this way we obtain that the automorphisms are the standard.
文摘We denote by π（x） the characteristi function of the interval （0, 1）, πk=h-1πx/h and π（?）（x）= h-1π（x/h-j）（0≤j≤n-1,h=n/1）. For w∈EA, construct Rhu = （Rhw）f, where （Rkw）f.
