For every inference rule +d there is a closely related inference rule −d allowing to infer that some literals q cannot be consequences of D via +d. The relationship between +d and −d is described as the Principle of Strong Negation (Antoniou et al. 2000). These inference rules are placed adjacently to emphasize this relationship. Some notation in the inference rules requires explanation. Given ...

We prove that any family of compact convex sets in R which satisfy the (p, q)-property (p ≥ q ≥ d+1) can be pierced with Õ((pq) q−1 q−d ) points for d ≥ 3 and O((pq) q−1 q−2 ) for d = 2. This improves (already for d = 2 and q = 3) the previously best known bound (of Õ(p 2+d)) provided in Alon and Kleitman’s celebrated proof of the Hadwiger Debrunner conjecture (for the case q = d+ 1). We also p...

A family of sequences with large size and good correlation property arising from M-ary Sidelnikov sequences of period q d − 1 Abstract—Let q be any prime power and let d be a positive integer greater than 1. In this paper, we construct a family of M-ary sequences of period q − 1 from a given M-ary, with M |q − 1, Sidelikov sequence of period q d −1. Under mild restrictions on d, we show that th...

Abstract In this paper we transfer a small data global existence and scattering result by Wang Hudzik to the more general case of modulation spaces $M_{p, q}^s(\mathbb{R}^d)$ where q = 1 $s \geq 0$ or $q \in (1, \infty]$ \gt \frac{d}{q^{\prime}}$ non-linear Schrödinger equation with higher-order anisotropic dispersion.

Let G be a elementary abelian p-group of order q = p. Let V be a faithful indecomposable modular representation of G with dimension 2. We consider representations of the form S(S(V )). In particular we prove that S(S(V )) is projective whenever d+m ≥ q, and either d < p and m < q or m < p and d < q. More generally we show that if d+m ≥ q and d < q, m < q, then each summand of S(S(V )) is induce...

‎‎For a finite group $G$ and a subgroup $H$ of $G$‎, ‎the relative commutativity degree of $H$ in $G$‎, ‎denoted by $d(H,G)$‎, ‎is the probability that an element of $H$ commutes with an element of $G$‎. ‎Let $mathcal{D}(G)={d(H,G):Hleq G}$ be the set of all relative commutativity degrees of subgroups of $G$‎. ‎It is shown that a finite group $G$ admits three relative commutativity degrees if a...

In most stochastic inventory models, such as continuous review models and periodic review models, it has been assumed that the stockout period during a cycle is small enough to be neglected so that the average number of cycles per year can be approximated as D/Q, where D is the average annual demand and Q is the order quantity. This assumption makes the problem more tactable, but it should not ...

In most stochastic inventory models, such as continuous review models and periodic review models, it has been assumed that the stockout period during a cycle is small enough to be neglected so that the average number of cycles per year can be approximated as D/Q, where D is the average annual demand and Q is the order quantity. This assumption makes the problem more tactable, but it should not ...

In this Appendix, we summarize some basic properties of the three classes of functional diversity measures: (1) functional Hill number ) (Q D q which quantifies the effective number of equally abundant and equally distinct species in an assemblage with a constant species pairwise distance Q, where Q denotes Rao’s quadratic entropy; (2) mean functional diversity MD(Q) = Q Q D q × )] ( [ which qu...

An abelian threefold $$A_{/{\mathbb {Q}}}$$ of prime conductor N is favorable if its 2-division field F an $${\mathcal {S}}_7$$ -extension over $${\mathbb {Q}}$$ with ramification index 7 {Q}}_2$$ . Let A be and let B a semistable variety $$N^d$$ B[2] filtered by d copies A[2]. We obtain class theoretic criterion on to guarantee that isogenous $$A^d$$ fortiori, unique up isogeny.