共查询到20条相似文献，搜索用时 31 毫秒
1.
The following properties of the geodesic straightest lines of a system of two Monge equations in E
4 are established: | 1. |
The vector tangent to a geodesic straightest line remains tangent under parallel translation along the line, and this property characterizes a geodesic straightest line.
| | 2. |
The geodesic curvature vanishes along geodesic straightest lines and only along such lines.
|
Translated from Ukrainskií Geometricheskií Sbornik, No. 30, 1987, pp. 112–116. 相似文献
2.
Given a point x in a convex figure M, let (x) denote the number of all affine diameters of M passing through x. It is shown that, for a convex figure M, the following conditions are equivalent. | (i) |
(x)2 for every pointx intM.
| | (ii) |
either(x)3 or(x) on intM. Furthermore, the setB={x intM:(x) is either odd or infinite } is dense inM.
|
相似文献
3.
Let ( X, ) be a continuous dynamical system on a locally compact space X with countable base. In this note we prove the equivalence of the following statements: | 1. |
(X, ) is unstable;
| | 2. |
The kernelf Vf=
0
f((t, ·)) dt, is a proper kernel.
|
As application, every unstable dynamical system possesses a section S in the form S={ p= q}, such that p and q are lower semicontinuous and >0 on X. 相似文献
4.
The main result in this paper is the following:
Theorem. Assume that W is a k-connected compact PL n-manifold with boundary, BdW is (k–1)-connected, k1( BdW is 1-connected for k=1), 0 h2k, 2 n–h>5 and there exists a normal block (n-h-1)- bundle v over W, then
| (1) |
There is a neat PL embedding W D{su2n–h}which normal block bundle is isomorphic to v.
| | (2) |
There is a PL embedding WS
2n–h–1
which normal block bundle is isomorphic to v.
|
相似文献
5.
Two partial orders P and Q on a set X are complementary (written as PQ) if they share no ordered pairs (except for loops) but the transitive closure of the union is all possible ordered pairs. For each positive integer n we form a graph Pos
n
consisting of all nonempty partial orders on {1, , n} with edges denoting complementation. We investigate here properties of the graphs Pos
n
. In particular, we show: | – |
The diameter of Pos
n
is 5 for alln>2 (and hence Pos
n
is connected for alln);
| | – |
With probability 1, the distance between two members of Pos
n
is 2;
| | – |
The graphs Pos
n
are universal (i.e. every graph occurs as an induced subgraph of some Pos
n
);
| | – |
The maximal size (n) of an independent set of Pos
n
satisfies the asymptotic formula|
相似文献
6.
We give the general solution of the nonsymmetric partial difference functional equation f(x + t,y) + f(x – t,y) – 2f(x,y)/t
2 = f(x,y + s) + f(x,y – s) – 2f(x,y)/s
2 (N) analogous to the well-known wave equation (
2/ x
2
–
2/ y
2) f(x,y) = 0 with the aid of generalized polynomials when no regularity assumptions are imposed on f. The result is as follows.
Theorem. Let R be the set of all real numbers. A function f: R × R R satisfies the functional equation (N) for all x, y R, s, t R\{0}, and s t if and only if there exist
| (i) |
additive functions A, B: R R
| | (ii) |
a function C: R × R R which is additive in each variable, and
| | (iii) |
polynomials
|
相似文献
7.
The major sequences of length n are defined as the words with n letters taken from the integers 1, 2, , n and containing at least
| 1. |
letter equal ton
| | 2. |
letters equal or more thann – 1,n – 1 letters equal or more than 2.
|
相似文献
8.
A pointwise version of the Howard-Bezem notion of hereditary majorization is introduced which has various advantages, and its relation to the usual notion of majorization is discussed. This pointwise majorization of primitive recursive functionals (in the sense of Gödel's T as well as Kleene/Feferman's) is applied to systems of intuitionistic and classical arithmetic ( H and H
c) in all finite types with full induction as well as to the corresponding systems with restricted induction and c. | 1) |
H and are closed under a generalized fan-rule. For a restricted class of formulae this also holds forH
c andc.
| | 2) |
We give a new and very perspicuous proof that for each one can construct a functional such that
is a modulus of uniform continuity for on {1n(nn)}. Such a modulus can also be obtained by majorizing any modulus of pointwise continuity for .
| | 3) |
The type structure of all pointwise majorizable set-theoretical functionals of finite type is used to give a short proof that quantifier-free choice with uniqueness (AC!)1,0-qf. is not provable within classical arithmetic in all finite types plus comprehension [given by the schema (C):y
0x
(yx=0A(x)) for arbitraryA], dependent -choice and bounded choice. Furthermore separates several -operators.
|
相似文献
9.
Continuing earlier work on construction of harmonic spaces from translation invariant Dirichlet spaces defined on locally compact abelian groups, it is shown that the potential kernel for a non-symmetric translation invariant Dirichlet form on a locally compact abelian group under the extra assumptions that | (i) |
the potential kernel is absolutely continuous and the canonical l.s.c. density is continuous in the complement of the neutral element.
| | (ii) |
the theory is of local type.
| | (iii) |
the underlying group is not discrete, can be interpreted as the potential kernel for a translation invariant axiomatic theory of harmonic functions, in which (among other properties) the domination axiom is fulfilled.
|
相似文献
10.
A - hyperfactorization of K
2n
is a collection of 1-factors of K
2n
for which each pair of disjoint edges appears in precisely of the 1-factors. We call a -hyperfactorization trivial if it contains each 1-factor of K
2n
with the same multiplicity (then =(2 n–5)!!). A -hyperfactorization is called simple if each 1-factor of K
2n
appears at most once. Prior to this paper, the only known non-trivial -hyperfactorizations had one of the following parameters (or were multipliers of such an example) | (i) |
2n=2
a
+2, =1 (for alla3); cf. Cameron [3];
| | (ii) |
2n=12, =15 or 2n=24, =495; cf. Jungnickel and Vanstone [8].
|
In the present paper we show the existence of non-trivial simple -hyperfactorizations of K
2n
for all n5. 相似文献
11.
The positive half A
+ of an ordered abelian group A is the set { x Ax 0} and M
A
+ is a module if for all x, y M also x + y, |x – y| M. If A
+
\M then M() is the module generated by M and . S
M is unbounded in M if (x M)( y S)(x y) and is dense in M if (x 1, x 2 M)(y S) (x 1 <> 2 x 1 y x 2). If M is a module, or a subgroup of any abelian group, a real-valued g: M R is subadditive if g(x + y) g(x) + g(y) for all x, y M. The following hold: | (1) |
IfM andM
* are modules inA andM
M
*
A
+ then a subadditiveg:M R can always be extended to a subadditive functionF:M
*
R when card(M) = 0 and card(M
*
) 1, or wheneverM
* possesses a countable dense subset.
| | (2) |
IfZ
A is a subgroup (whereZ denotes the integers) andg:Z
+
R is subadditive with
g(n)/n = – theng cannot be subadditively extended toA
+ whenA does not contain an unbounded subset of cardinality
.
| | (3) |
Assuming the Continuum Hypothesis, there is an ordered abelian groupA of cardinality 1 with a moduleM and elementA
+
/M for whichA
+
= M(), and a subadditiveg:M R which does not extend toA
+. This even happens withg 0.
| | (4) |
Letg:A
+
R be subadditive on the positive halfA
+ ofA. Then the necessary and sufficient condition forg to admit a subadditive extension to the whole groupA is: sup{g(x + y) – g(x)x –y} < +="> for eachy <> inA.
| | (5) |
IfM is a subgroup of any abelian groupA andg:M K is subadditive, whereK is an ordered abelian group, theng admits a subadditive extensionF:A K.
| | (6) |
IfA is any abelian group andg:A R is subadditive, theng = + where:A R is additive and 0 is a non-negative subadditive function:A R. IfA is aQ-vector space may be takenQ-linear.
| | (7) |
Ifg:V R is a continuous subadditive function on the real topological linear spaceV then there exists a continuous linear functional:V R and a continuous subadditive:V R such thatg = + and 0. ifV = R
n
this holds for measurable subadditiveg with a continuous and measurable.
|
相似文献
12.
Let P=PG(2 t + 1, q) denote the projective space of order q and of dimension 2 t+13. A set of lines of P is called a blockade if it fulfills the following two conditions. | 1. |
Every (t+1)-dimensional subspace of P contains at least one line of .
| | 2. |
If x is the intersecting point of two lines of , then every (t+1)-dimensional subspace of P through x contains at least one line of through x.
|
The most interesting examples of these blockades are the geometric spreads and the line sets of Baer subspaces of P. In our main result we shall classify the blockades under the additional property that there exists a t-dimensional subspace T of P such that each point of T is incident with at most one line of . As a corollary we determine the blockades of minimal cardinality. 相似文献
13.
Renormalization arguments are developed and applied to independent nearest-neighbor percolation on various subsets of
d
, d2, yielding: | – |
Equality of the critical densities,p
c
(), for a half-space, quarter-space, etc., and (ford>2) equality with the limit of slab critical densities.
| | – |
Continuity of the phase transition for the half-space, quarter-space, etc.; i.e., vanishing of the percolation probability,
(p), atp=p
c
().
|
Corollaries of these results include uniqueness of the infinite cluster for such 's and sufficiency of the following for proving continuity of the full-space phase transition: showing that percolation in the full-space at density p implies percolation in the half-space at the same density. 相似文献
14.
Let A
H be the Herbrand normal form of A and A
H,D a Herbrand realization of A
H. We show | (i) |
There is an example of an (open) theory + with function parameters such that for someA not containing function parameters
| | (ii) |
Similar for first order theories + if the index functions used in definingA
H are permitted to occur in instances of non-logical axiom schemata of , i.e. for suitable ,A
| | (iii) |
In fact, in (1) we can take for + the fragment (
1
0
-IA)+ of second order arithmetic with induction restricted to
1
0
-formulas, and in (2) we can take for the fragment (
1
0,b
-IA) of first order arithmetic with induction restricted to formulas VxA(x) whereA contains only bounded quantifiers.
| | (iv) |
On the other hand,|
相似文献
15.
For Jordan elements J in a topological algebra B with unit e, an open group B
–1 of invertible elements and continuous inversion we consider the similarity orbits S
G
(J)={ gJg
–1: gG} ( G the group B
–1{ e+ c: cI}, IB a bilateral continuous embedded topological ideal). We construct rational local cross sections to the conjugation mapping
and give to the orbit S
G
( J) the local structure of a rational manifold. Of particular interest is the case B=L(H) (bounded linear operators on a separable Hilbert space H), I=B, for which we obtain the following: | 1. |
If for a Hilbert space operator there exist norm continuous local similarity cross sections, then these can be chosen to be rational, especially holomorphic or real analytic.
| | 2. |
The similarity orbit of a nice Jordan operator is a rational (especially holomorphic or real analytic) submanifold ofL(H).
|
相似文献
16.
Let SG(1,3)p 5 be a smooth, irreducible, non degenerate surface in the complex grassmannian G(1,3). Assume deg(S)=9, we show that S is one of the following surfaces: | (a) |
A K3 surface blown up in one point.
| | (b) |
The image of P2 by the linear system
| | (c) |
The image of P2 by the linear system
.
|
相似文献
17.
We develop the theory of “branch algebras”, which are infinite-dimensional associative algebras that are isomorphic, up to
taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees.
In particular, for every field
% MathType!End!2!1! we contruct a
% MathType!End!2!1! which
| – |
• is finitely generated and infinite-dimensional, but has only finitedimensional quotients;
|
| – |
• has a subalgebra of finite codimension, isomorphic toM
2(k);
|
| – |
• is prime;
|
| – |
• has quadratic growth, and therefore Gelfand-Kirillov dimension 2;
|
| – |
• is recursively presented;
|
| – |
• satisfies no identity;
|
| – |
• contains a transcendental, invertible element;
|
| – |
• is semiprimitive if
% MathType!End!2!1! has characteristic ≠2;
|
| – |
• is graded if
% MathType!End!2!1! has characteristic 2;
|
| – |
• is primitive if
% MathType!End!2!1! is a non-algebraic extension of
% MathType!End!2!1!;
|
| – |
• is graded nil and Jacobson radical if
% MathType!End!2!1! is an algebraic extension of
% MathType!End!2!1!.
|
The author acknowledges support from TU Graz and UC Berkeley, where part of this research was conducted. 相似文献
18.
We show that the percolation transition for the two-dimensional Ising model is sharp. Namely, we show that for every reciprocal temperature >0, there exists a critical value h
c
() of external magnetic field h such that the following two statements hold. | (i) |
Ifh>h
c
(), then the percolation probability (i.e., the probability that the origin is in the infinite cluster of + spins) with respect to the Gibbs state ,h
for the parameter (,h) is positive.
| | (ii) |
Ifhh
c
(), then the connectivity function
,h
+
(0,x) (the probability that the origin is connected by + spins tox with respect to ,h
) decays exponentially as |x|.
|
We also shows that the percolation probability is continuous in (, h) except on the half line {(, 0);
c
}. 相似文献
19.
A=( a
ij)
i
j=1
— k-o , a
ij
. : |
相似文献
20.
It is shown that some well-known properties of the Sobolev space L
p
l
() do not admit extension to the space L
p
l
() of the functions with l-th order derivatives in L
p
(), l>1, without requirements to the domain . Namely, we give examples of such that | (i) |
L
p
l
()L
() is not dense inL
p
l
(),
| | (ii) |
L
p
l
()L
() is not a Banach algebra.
| | (iii) |
the strong capacitary inequality for the norm inL
p
l
() fails.
|
In the Appendix necessary and sufficient conditions are given for the imbeddings L
p
l
() L
q
(, ) and H
p
l
( R
n
) L
q
( R
n
, ), where p1, p> q>0, is a measure and H
p
l
() is the Bessel potential space, 1 p, l>0. 相似文献
|
|
|
|
|
|
