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71.
We deal with iterative algebras of functions of
-valued logic lacking projections, which we call algebras without projections. It is shown that a partially ordered set of algebras of functions of
-valued logic, for
, without projections contains an interval isomorphic to the lattice of all iterative algebras of functions of
-valued logic. It is found out that every algebra without projections is contained in some maximal algebra without projections, which is the stabilizer of a semigroup of non-surjective transformations of the basic set. It is proved that the stabilizer of a semigroup of all monotone non-surjective transformations of a linearly ordered 3-element set is not a maximal algebra without projections, but the stabilizer of a semigroup of all transformations preserving an arbitrary non one-element subset of the basic set is. 相似文献
72.
We study a semigroup of linear operators on a Banach space X which satisfies the condition codim X
0<, where
We show that X
0 is closed and establish some properties of the asymptotic behavior of the subspaces complementing X
0 to X. 相似文献
73.
Let be a space of homogeneous type, and be the generator of a semigroup with Gaussian kernel bounds on . We define the Hardy spaces of for a range of , by means of area integral function associated with the Poisson semigroup of , which is proved to coincide with the usual atomic Hardy spaces on spaces of homogeneous type.
74.
We study the class of bounded C
0-semigroups T=(T
t
)
t0 on a Banach space X satisfying the asymptotic finite dimensionality condition: codim X
0(T)<, where X
0(T):={x X:limt T
t
x=0}. We prove a theorem which provides some necessary and sufficient conditions for asymptotic finite dimensionality. 相似文献
75.
We investigate the minimal number of generators and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the semigroup. The main result is that for every bound C there exist, up to isomorphism, only finitely many divisorial ideals I such that (I)C. It follows that there exist only finitely many Cohen–Macaulay divisor classes. Moreover, we determine the minimal depth of all divisorial ideals and the behaviour of and depth in arithmetic progressions in the divisor class group.The results are generalized to more general systems of linear inequalities whose homogeneous versions define the semigroup in a not necessarily irredundant way. The ideals arising this way can also be considered as defined by the nonnegative solutions of an inhomogeneous system of linear diophantine equations.We also give a more ring-theoretic approach to the theorem on minimal number of generators of divisorial ideals: it turns out to be a special instance of a theorem on the growth of multigraded Hilbert functions. 相似文献
76.
Let P=(P
t
)
t>0 be a submarkovian semigroup of kernels on a measurable space (X,). An additive kernel of P is a kernel K from X into ]0,[ such that P
t
K(x,A)=K(x,A+t) for every t>0,xX and every Borel subset A of ]0,[. It is proved in this paper that for every potential f of P, there exits an additive kernel K of P, unique (up to equivalence) such that f=K1=0
K(,dt). This result is already well known for regular potentials of right processes. If U=(U
p
)
p>0 is a sub-Markovian resolvent of kernels on (X,), we give a notion of additive kernel of U and we prove a similar integral representation of potentials of U. 相似文献
77.
Let G be a complex semisimple group with real form G
. For the action of G
× G
on G by left and right translation, we define and study an orbit-type stratification of G. In particular, we compute the dimension of an arbitrary stratum; we identify certain strata of low codimension in G, the union of whose closures contains every nonprincipal stratum; and we describe the boundaries and adjacency relations of the maximal connected domains in G that contain only principal orbits. 相似文献
78.
Nathan L. Harshman 《International Journal of Theoretical Physics》2007,46(8):1929-1946
The notion that elementary systems correspond to irreducible representations of the Poincaré group is the starting point for
this paper, which then goes on to discuss how a semigroup for the time evolution of unstable states and resonances could emerge
from the underlying Poincaré symmetry. Important tools in this analysis are the Clebsch-Gordan coefficients for the Poincaré
group. 相似文献
79.
Jitender Kumar 《代数通讯》2013,41(12):5152-5169
In order to study the structure of A +(B n )—the affine near-semiring over a Brandt semigroup—this work completely characterizes the Green's classes of its semigroup reducts. In this connection, this work classifies the elements of A +(B n ) and reports the size of A +(B n ). Further, idempotents and regular elements of the semigroup reducts of A +(B n ) have also been characterized and studied some relevant semigroups in A +(B n ). 相似文献
80.
Nándor Sieben 《Czechoslovak Mathematical Journal》2008,58(3):683-692
The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms
of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid.
The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to
the original groupoid. 相似文献