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1.
Victor Pambuccian 《Journal of Geometry》1996,56(1-2):126-130
On the basis of the theory
– of Pasch-free 2-dimensional geometry, Pasch's axiom is shown to be equivalent to the conjunction of the following two axioms: In any right triangle the hypotenuse is greater than the leg and If AOB is right, B lies between O and C, and D is the footpoint of the perpendicular from B to AC, then the segment OA is greater than the segment BD. This represents an attempt to split the Pasch axiom with respect to
–. Only the question whether the second of the above two axioms is really weaker than Pasch's axiom, remains open. 相似文献
2.
Let áA, B | Am=1, Bn=At, BAB-1=Ar?\langle A, B\,\vert\, A^\mu=1,\, B^\nu=A^t,\, BAB^{-1}=A^\rho\rangle
where and are relative prime numbers, t = /s and s = gcd( – 1,), and is the order of modulo . We prove that if (1) = 2, and (2) is embeddable into the multiplicative group of some skew field, then is circular. This means that there is some additive group N on which acts fixed point freely, and |((a)+b)((c)+d)| 2 whenever a,b,c,d N, a0c, are such that (a)+b(c)+d. 相似文献
3.
Donna M. Carr Jean -Pierre Levinski Donald H. Pelletier 《Archive for Mathematical Logic》1990,30(1):59-72
For every uncountable regular cardinal and any cardinal,P
denotes the set
. Furthermore, < denotes=" the=" binary=" operation=" defined=">P
byx<> iffxy¦x<>.By anideal over
P
we mean a proper, non-principal,-complete ideal overP
extending the ideal dual to the filter generated by
. For any idealI overP
,I
+ denotes the setP
–I, andI
* the filter dual toI. 相似文献
4.
С. Г. Мерзляков 《Analysis Mathematica》1989,15(1):3-16
A=(a
ij)
i
j=1
— k-o ,a
ij
. :
相似文献
5.
Let be a domain in C, 0, and let
n
0
() be the set of polynomials of degreen such thatP(0)=0 andP(D), whereD denotes the unit disk. The maximal range
n
is then defined to be the union of all setsP(D),P
n
0
(). We derive necessary and, in the case of ft convex, sufficient conditions for extremal polynomials, namely those boundaries whose ranges meet
n
. As an application we solve explicitly the cases where is a half-plane or a strip-domain. This also implies a number of new inequalities, for instance, for polynomials with positive real part inD. All essential extremal polynomials found so far in the convex cases are univalent inD. This leads to the formulation of a problem. It should be mentioned that the general theory developed in this paper also works for other than polynomial spaces.Communicated by J. Milne Anderson. 相似文献
6.
Charles M. Newman 《Constructive Approximation》1991,7(1):389-399
LetV(t) be the even function on (–, ) which is related to the Riemann xi-function by (x/2)=4
–
exp(ixt–V(t))dt. In a proof of certain moment inequalities which are necessary for the validity of the Riemann Hypothesis, it was previously shown thatV'(t)/t is increasing on (0, ). We prove a stronger property which is related to the GHS inequality of statistical mechanics, namely thatV' is convex on [0, ). The possible relevance of the convexity ofV' to the Riemann Hypothesis is discussed.Communicated by Richard Varga. 相似文献
7.
B. Le Gac 《Analysis Mathematica》1992,18(2):103-109
(X
k
),k=1,2,... —
k
2
>1; (X
k
) , E(X
k
X
t
)=0 p
k<>(p+1)
(p,k,l=1, 2, ...) , , ,
|