Search results for "Set theory"
showing 10 items of 751 documents
Regular subclasses in the Sobolev space
2009
Abstract We study some slight modifications of the class α - A C n ( Ω , R m ) introduced in [D. Bongiorno, Absolutely continuous functions in R n , J. Math. Anal. and Appl. 303 (2005) 119–134]. In particular we prove that the classes α - A C λ n ( Ω , R m ) , 0 λ 1 , introduced in [C. Di Bari, C. Vetro, A remark on absolutely continuous functions in R n , Rend. Circ. Matem. Palermo 55 (2006) 296–304] are independent by λ and contain properly the class α - A C n ( Ω , R m ) . Moreover we prove that α - A C n ( Ω , R m ) = ( α - A C λ n ( Ω , R m ) ) ∩ ( α - A C n , λ ( Ω , R m ) ) , where α - A C n , λ ( Ω , R m ) is the symmetric class of α - A C λ n ( Ω , R m ) , 0 λ 1 .
On 𝓕-subnormal subgroups and Frattini-like subgroups of a finite group
1994
Throughout the paper we consider only finite groups.J. C. Beidleman and H. Smith [3] have proposed the following question: “If G is a group and Ha subnormal subgroup of G containing Φ(G), the Frattini subgroup of G, such that H/Φ(G)is supersoluble, is H necessarily supersoluble? “In this paper, we give not only an affirmative answer to this question but also we see that the above result still holds if supersoluble is replaced by any saturated formation containing the class of all nilpotent groups.
Tally languages accepted by alternating multitape finite automata
1997
We consider k-tape 1-way alternating finite automata (k-tape lafa). We say that an alternating automaton accepts a language L\(\subseteq\)(Σ*)k with f(n)-bounded maximal (respectively, minimal) leaf-size if arbitrary (respectively, at least one) accepting tree for any (w1, w2,..., wk) ∈ L has no more than $$f\mathop {(\max }\limits_{1 \leqslant i \leqslant k} \left| {w_i } \right|)$$ leaves. The main results of the paper are the following. If k-tape lafa accepts language L over one-letter alphabet with o(log n)-bounded maximal leaf-size or o(log log n)-bounded minimal leaf-size then the language L is semilinear. Moreover, if a language L is accepted with o(log log(n))-bounded minimal (respe…
Area-minimizing cones in the Heisenberg group H
2021
We present a characterization of minimal cones of class \(C^2\) and \(C^1\) in the first Heisenberg group \(\mathbf{H}\), with an additional set of examples of minimal cones that are not of class \(C^1\).
The exact bounds for the degree of commutativity of a p-group of maximal class, I
2002
Abstract The first major study of p-groups of maximal class was made by Blackburn in 1958. He showed that an important invariant of these groups is the ‘degree of commutativity.’ Recently (1995) Fernandez-Alcober proved a best possible inequality for the degree of commutativity in terms of the order of the group. Recent computations for primes up to 43 show that sharper results can be obtained when an additional invariant is considered. A series of conjectures about this for all primes have been recorded in [A. Vera-Lopez et al., preprint]. In this paper, we prove two of these conjectures.
KLUM@GTAP: Introducing Biophysical Aspects of Land-Use Decisions into a Computable General Equilibrium Model a Coupling Experiment
2008
In this paper, the global agricultural land use model Kleines Land Use Model is coupled to an extended version of the computable general equilibrium model (CGE) Global Trade Analysis Project in order to consistently assess the integrated impacts of climate change on global cropland allocation and its implication for economic development. The methodology is innovative as it introduces dynamic economic land-use decisions based also on the biophysical aspects of land into a state-of-the-art CGE; it further allows the projection of resulting changes in cropland patterns on a spatially more explicit level. A convergence test and illustrative future simulations underpin the robustness and potenti…
On the structure of certain ultradistributions
2009
Let "o" be a nonempty open subset of the k-dimensional euclidean space Rk. In this paper we show that, if S is an ultradistribution in "o", belonging to a class of Roumieu type stable under differential operators, then there is a family f , 2 Nk 0, of elements of L1 loc("o") such that S is represented in the formP 2Nk 0 D"a"f "a". Some other results on the structure of certain ultradistributions of Roumieu type are also given.
Collusion constrained equilibrium
2018
We study collusion within groups in non-cooperative games. The primitives are the preferences of the players, their assignment to non-overlapping groups and the goals of the groups. Our notion of collusion is that a group coordinates the play of its members among different incentive compatible plans to best achieve its goals. Unfortunately, equilibria that meet this requirement need not exist. We instead introduce the weaker notion of collusion constrained equilibrium. This allows groups to put positive probability on alternatives that are suboptimal for the group in certain razor's edge cases where the set of incentive compatible plans changes discontinuously. These collusion constrained e…
Memory limited inductive inference machines
1992
The traditional model of learning in the limit is restricted so as to allow the learning machines only a fixed, finite amount of memory to store input and other data. A class of recursive functions is presented that cannot be learned deterministically by any such machine, but can be learned by a memory limited probabilistic leaning machine with probability 1.
Vagueness and Roughness
2008
The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlak's rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of different perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set, in relation to the rough set, is defined as a family of sets approximated by the so called lower and upper limits. The family is simultaneously considered as a family of all denotations of sharp terms representing a suitable vague term, from the agent's point of view. Some algebraic operations on…