A property P of term rewriting systems (TRSs, for short) is said to be persistent if for any many-sorted TRS R, R has the property P if and only if its underlying unsorted TRS (R) has the property P. This notion was introduced by H. Zantema (1994). In this paper, it is shown that con uence is persistent.

It is shown that δ-connectedness is not a Whitney reversible property. This answers in the negative a question posed by Sam B. Nadler, Jr. in 1978. A topological property P is said to be: (a) a Whitney property provided that if a continuum X has property P, so does μ−1(t) for each Whitney map μ for C(X) and each t ∈ [0, μ(X)) ([6, p. 165]); (b) a Whitney reversible property provided that whenev...

For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and‎ ‎a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$‎, ‎it is shown that the strong Banach-Saks-ness of all evaluation‎ ‎operators on ${mathcal M}$ is a sufficient condition for the weak‎ ‎Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in‎ ‎Y^*$‎, ‎the evaluation op...

Let P be an ordered set. P is said to have the finite cutset property if for every x in P there is a finite set F of elements which are noncomparable to x such that every maximal chain in P meets {x} t.J F. It is well known that this property is equivalent to the space of maximal chains of P being compact. We consider the following question: Which ordered sets P can be embedded in an ordered se...

Let D be a digraph. A subset S of V(D) is stable if every pair vertices in non-adjacent D. collection disjoint paths $$\mathcal {P}$$ path partition V(D), vertex on . We say that set and are orthogonal contains exactly one S. digraph satisfies the $$\alpha $$ -property for maximum D, there to -diperfect induced subdigraph -property. In 1982, Berge proposed characterization digraphs terms forbid...

Pearl’s well-known d-separation criterion for an acylic directed graph (ADG) is a pathwise separation criterion that can be used to efficiently identify all valid conditional independence relations in the Markov model determined by the graph. This paper introduces p-separation, a pathwise separation criterion that efficiently identifies all valid conditional independences under the Andersson-Ma...

We introduce a Cartesian P -property for linear transformations between the space of symmetric matrices and present its applications to the semidefinite linear complementarity problem (SDLCP). With this Cartesian P -property, we show that the SDLCP has GUS-property (i.e., globally unique solvability), and the solution map of the SDLCP is locally Lipschitzian with respect to input data. Our Cart...

A1 Either a property or its negation is positive, but not both: ∀φ[P (¬φ)↔ ¬P (φ)] A2 A property necessarily implied by a positive property is positive: ∀φ∀ψ[(P (φ) ∧ ∀x[φ(x)→ ψ(x)])→ P (ψ)] T1 Positive properties are possibly exemplified: ∀φ[P (φ)→ ♦∃xφ(x)] D1 A God-like being possesses all positive properties: G(x)↔ ∀φ[P (φ)→ φ(x)] A3 The property of being God-like is positive: P (G) C Possib...