Rota-Baxter簇系统与Gr\"obner-Shirshov基

从Yang-Baxter簇方程和Volterra积分方程得到的Rota-Baxter簇代数的概念出发,我们引入Rota-Baxter簇系统的概念,推广了Brzezinski提出的Rota-Baxter系统.我们证明这个概念也与结合Yang-Baxter簇对和pre-Lie簇代数有关.此外,作为Rota-Baxter簇系统的一个类比,我们引入平均簇系统的概念,并证明平均簇系统会得到dialgebra簇结构.我们还研究dendriform代数上的Rota-Baxter簇系统,并展示它们如何诱导quadri簇代数结构.最后,我们用Gr\"obner-Shirshov基的方法给出Rota-Baxter簇系统的一个线性基.     

Family sequencing and cooperation

This paper analyzes a single-machine scheduling problem with family setup times both from an optimization and a cost allocation perspective. In a family sequencing situation jobs are processed on a single machine, there is an initial processing order on the jobs, and every job within a family has an identical cost function that depends linearly on its completion time. Moreover, a job does not require a setup when preceded by another job from the same family while a family specific setup time is required when a job follows a member of some other family.     

Separately normal maps

It is shown that a separately normal map is holomorphic and a separately normal family which is separately uniformly normal is a normal family extending a result by Barth that a separately holomorphic map into hyperbolic spaces is holomorphic and a separately normal family of maps into hyperbolic spaces is a normal family.     

On the Helly Number for Line Transversals to Parallel Triangles

We prove two results about the problem of finding the Helly number for line transversals to a family of parallel triangles in the plane: (1) If each three triangles of a family of parallel right triangles are intersected by an ascending (or a descending) line, then there is an ascending (or a descending) line that intersects all     

A simple permutoassociahedron

In the early 1990s, a family of combinatorial CW-complexes named permutoassociahedra was introduced by Kapranov, and it was realised by Reiner and Ziegler as a family of convex polytopes. The polytopes in this family are “hybrids” of permutohedra and associahedra. Since permutohedra and associahedra are simple, it is natural to search for a family of simple permutoassociahedra, which is still adequate for a topological proof of Mac Lane’s coherence. This paper presents such a family.     

Admissibility of prediction intervals

Admissibility of prediction intervals is considered in a specified family. It is shown that the best invariant prediction interval is strongly admissible in a location family and in a scale family. Though the similar result has not been obtained for a location and scale family, the best invariant prediction interval for a normal distribution is shown to be weakly admissible.     

Quantum families of quantum group homomorphisms

The notion of a quantum family of maps has been introduced in the framework of C*-algebras. As in the classical case, one may consider a quantum family of maps preserving additional structures (e.g. quantum family of maps preserving a state). In this paper, we define a quantum family of homomorphisms of locally compact quantum groups. Roughly speaking, we show that such a family is classical. The purely algebraic counterpart of the discussed notion, i.e. a quantum family of homomorphisms of Hopf algebras, is introduced and the algebraic counterpart of the aforementioned result is proved. Moreover, we show that a quantum family of homomorphisms of Hopf algebras is consistent with the counits and coinverses of the given Hopf algebras. We compare our concept with weak coactions introduced by Andruskiewitsch and we apply it to the analysis of adjoint coaction.     

Vanishing of Chern Classes of the De Rham Bundles for Some Families of Moduli Spaces

Given a family of nonsingular complex projective surfaces, there is a corresponding family of Hilbert schemes of zero dimensional subschemes. We prove that the Chern classes, with values in the rational Chow groups, of the de Rham bundles for such a family of Hilbert schemes vanish. A similar result is proved for any relative moduli space of rank one sheaves with trivial integral first Chern class over any family of complex projective surfaces.     

Cones for the Moulton planes

We present a two-parameter family of affinely connected surfaces which admit the cylinder group as a collineation group of their geodesics. The Moulton Planes in the radial model of Betten, the circular cone, as well as the real affine plane, are part of this family. The Moulton Planes occur in this family in the same way as the real affine plane is contained in a family of cones with decreasing steepness.      

On the complexity of recognizing directed path families

A Directed Path Family is a family of subsets of some finite ground set whose members can be realized as arc sets of simple directed paths in some directed graph. In this paper we show that recognizing whether a given family is a Directed Path family is an NP-Complete problem, even when all members in the family have at most two elements. If instead of a family of subsets, we are given a collection of words from some finite alphabet, then deciding whether there exists a directed graph G such that each word in the language is the set of arcs of some path in G, is a polynomial-time solvable problem.     

Maximal Monotone Operators, Convex Functions and a Special Family of Enlargements

This work establishes new connections between maximal monotone operators and convex functions. Associated to each maximal monotone operator, there is a family of convex functions, each of which characterizes the operator. The basic tool in our analysis is a family of enlargements, recently introduced by Svaiter. This family of convex functions is in a one-to-one relation with a subfamily of these enlargements. We study the family of convex functions, and determine its extremal elements. An operator closely related to the Legendre–Fenchel conjugacy is introduced and we prove that this family of convex functions is invariant under this operator. The particular case in which the operator is a subdifferential of a convex function is discussed.     

Normality and sharing functions

In this paper, we proved some normality criteria for a family of meromorphic functions, where a holomorphic function is shared by every function from the family and a linear differential polynomial generated by the members of the family.     

Fuzzy φψ-continuous Functions between L-topological Spaces (Ⅱ)

In the present paper, sum operation on sum spaces of a family of L-topological spaces is defined. Fuzzy φψ-continuity from sum spaces of a family of L-topological spaces into L-product spaces and from sum spaces of a family of L-topological spaces into L-topological spaces are investigated.     

A one parameter family of locally quartically convergent zero-finding methods

A one parameter family of iteration functions for finding simple and multiple zeros of analytic functions is derived. The family includes, as a special case, Traub's quartic square root method and, as limiting cases, the Kiss method of order 4, the Halley and the Newton methods. All the methods of the family are locally quartically convergent for a simple or multiple zero with known multiplicity. The asymptotic error constants for the methods of the family are given. The decreasing ratio at infinity of iteration functions is discussed. The optimum parameter of the family for polynomials is given.     

Friedberg Numberings of Families of n-Computably Enumerable Sets

We establish a number of results on numberings, in particular, on Friedberg numberings, of families of d.c.e. sets. First, it is proved that there exists a Friedberg numbering of the family of all d.c.e. sets. We also show that this result, patterned on Friedberg's famous theorem for the family of all c.e. sets, holds for the family of all n-c.e. sets for any n>2. Second, it is stated that there exists an infinite family of d.c.e. sets without a Friedberg numbering. Third, it is shown that there exists an infinite family of c.e. sets (treated as a family of d.c.e. sets) with a numbering which is unique up to equivalence. Fourth, it is proved that there exists a family of d.c.e. sets with a least numbering (under reducibility) which is Friedberg but is not the only numbering (modulo reducibility).     

A new family of Geodesic transitive graphs

We present a new family of locally geodesic transitive graphs with arbitrarily large diameter and valencies, containing a particular case to be geodesic transitive. We also prove that it is a unique family in some generalised family of graphs.     

On a family of distributions attaining the Bhattacharyya bound

A family of distributions for which an unbiased estimator of a functiong(θ) of a real parameter θ can attain the second order Bhattacharyya lower bound is derived. Indeed, we obtain a necessary and sufficient condition for the attainment of the second order Bhattacharyya bound for a family of mixtures of distributions which belong to the exponential family. Furthermore, we give an example which does not satisfy this condition, but where the Bhattacharyya bound is attainable for a non-exponential family of distributions.     

A generalization of obligation rules for minimum cost spanning tree problems

Tijs et al. [23] introduce the family of obligation rules for minimum cost spanning tree problems. We give a generalization of such family. We prove that our family coincides with the set of rules satisfying an additivity property and a cost monotonicity property. We also provide two new characterizations for the family of obligation rules using the previous properties. In the first one, we add a property of separability; and in the second one, we add core selection.     

On dual quermassintegrals of mixed intersection bodies

In this paper, it is shown that a family of inequalities involving mixed intersection bodies holds. The Busemann intersection inequality is the first of this family. All of the members of this family are strengthened versions of classical inequalities between pairs of dual quermassintegrals of a star body.     

Numeric vs. symbolic homotopy algorithms in polynomial system solving: a case study

We consider a family of polynomial systems which arises in the analysis of the stationary solutions of a standard discretization of certain semi-linear second-order parabolic partial differential equations. We prove that this family is well-conditioned from the numeric point of view, and ill-conditioned from the symbolic point of view. We exhibit a polynomial-time numeric algorithm solving any member of this family, which significantly contrasts the exponential behavior of all known symbolic algorithms solving a generic instance of this family of systems.