Boolean Dimension, Components and Blocks

We investigate the behavior of Boolean dimension with respect to components and blocks. To put our results in context, we note that for Dushnik-Miller dimension, we have that if $\dim(C)\le d$ for every component $C$ of a poset $P$, then $\dim(P)\le \max\{2,d\}$; also if $\dim(B)\le d$ for every block $B$ of a poset $P$, then $\dim(P)\le d+2$. By way of constrast, local dimension is well behaved with respect to components, but not for blocks: if $\text{ldim}(C)\le d$ for every component $C$ of a poset $P$, then $\text{ldim}(P)\le d+2$; however, for every $d\ge 4$, there exists a poset $P$ with $\text{ldim}(P)=d$ and $\dim(B)\le 3$ for every block $B$ of $P$. In this paper we show that Boolean dimension behaves like Dushnik-Miller dimension with respect to both components and blocks: if $\text{bdim}(C)\le d$ for every component $C$ of $P$, then $\text{bdim}(P)\le 2+d+4\cdot2^d$; also if $\text{bdim}(B)\le d$ for every block of $P$, then $\text{bdim}(P)\le 19+d+18\cdot 2^d$.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1712.0609

Dimension and cut vertices: an application of Ramsey theory

Motivated by quite recent research involving the relationship between the dimension of a poset and graph-theoretic properties of its cover graph, we show that for every $d\geq 1$, if $P$ is a poset and the dimension of a subposet $B$ of $P$ is at most $d$ whenever the cover graph of $B$ is a block of the cover graph of $P$, then the dimension of $P$ is at most $d+2$. We also construct examples which show that this inequality is best possible. We consider the proof of the upper bound to be fairly elegant and relatively compact. However, we know of no simple proof for the lower bound, and our argument requires a powerful tool known as the Product Ramsey Theorem. As a consequence, our constructions involve posets of enormous size.Comment: Final published version with updated reference

Translation Salience: A Model of Equivalence in Translation (Arabic/English)

The term equivalence describes the relationship between a translation and the text from which it is translated. Translation is generally viewed as indeterminate insofar as there is no single acceptable translation - but many. Despite this, the rationalist metaphor of translation equivalence prevails. Rationalist approaches view translation as a process in which an original text is analysed to a level of abstraction, then transferred into a second representation from which a translation is generated. At the deepest level of abstraction, representations for analysis and generation are identical and transfer becomes redundant, while at the surface level it is said that surface textual features are transferred directly. Such approaches do not provide a principled explanation of how or why abstraction takes place in translation. They also fail to resolve the dilemma of specifying the depth of transfer appropriate for a given translation task. By focusing on the translator�s role as mediator of communication, equivalence can be understood as the coordination of information about situations and states of mind. A fundamental opposition is posited between the transfer of rule-like or codifiable aspects of equivalence and those non-codifiable aspects in which salient information is coordinated. The Translation Salience model proposes that Transfer and Salience constitute bipolar extremes of a continuum. The model offers a principled account of the translator�s interlingual attunement to multi-placed coordination, proposing that salient information can be accounted for with three primary notions: markedness, implicitness and localness. Chapter Two develops the Translation Salience model. The model is supported with empirical evidence from published translations of Arabic and English texts. Salience is illustrated in Chapter Three through contextualized interpretations associated with various Arabic communication resources (repetition, code switching, agreement, address in relative clauses, and the disambiguation of presentative structures). Measurability of the model is addressed in Chapter Four with reference to emerging computational techniques. Further research is suggested in connection with theme and focus, text type, cohesion and collocation relations

A characterization of robert's inequality for boxicity

AbstractF.S. Roberts defined the boxicity of a graph G as the smallest positive integer n for which there exists a function F assigning to each vertex x ϵG a sequence F(x)(1),F(x)(2),…, F(x)(n) of closed intervals of R so that distinct vertices x and y are adjacent in G if and only if F(x)(i)∩F(y)(i)≠∅ for i = 1, 2, 3, …, n. Roberts then proved that if G is a graph having 2n + 1 vertices, then the boxicity of G is at most n. In this paper, we provide an explicit characterization of this inequality by determining for each n ⩾ 1 the minimum collection Cn of graphs so that a graph G having 2n + 1 vertices has boxicity n if and only if it contains a graph from Cn as an induced subgraph. We also discuss combinatorial connections with analogous characterization problems for rectangle graphs, circular arc graphs, and partially ordered sets

Embedding finite posets in cubes

AbstractIn this paper we define the n-cube Qn as the poset obtained by taking the cartesian product of n chains each consisting of two points. For a finite poset X, we then define dim2 X as the smallest positive integer n such that X can be embedded as a subposet of Qn. For any poset X we then have log2 |X| ⩽ dim2 X ⩽ |X|. For the distributive lattice L = 2 X, dim2 L = |X| and for the crown Skn, dim2 (Skn) = n + k. For each k ⩾ 2, there exist positive constants c1 and c2 so that for the poset X consisting of all one element and k-element subsets of an n-element set, the inequality c1 log2 n < dim2(X) < c2 log2 n holds for all n with k < n. A poset is called Q-critical if dim2 (X − x) < dim2(X) for every x ϵ X. We define a join operation ⊕ on posets under which the collection Q of all Q-critical posets which are not chains forms a semigroup in which unique factorization holds. We then completely determine the subcollection M ⊆ Q consisting of all posets X for which dim2 (X) = |X|

The Significance of Dolomitized Hunton Strata in the Kinta and Bonanza Fields of the Arkoma Basin

The Hunton Group has been a prolific hydrocarbon-producing reservoir across much of Oklahoma and western Arkansas. The group is a Silurian-Devonian aged interval that is comprised of sequences of limestone, dolomite, and calcareous shale. The group is divided into several formations. The subdivisions include the Chimneyhill Subgroup, Henryhouse, Haragan and Bois d\u27Arc Formations. Reservoir quality in the Hunton Group is significantly dependent upon the diagenetic events and depositional environments of the sediments. Most hydrocarbon production, from within the Hunton Group, comes from members that have undergone dolomite replacement of the parent limestone. The higher amounts of porosity and permeability are associated with secondary dissolution in packstones and grainstones. The changes in facies and diagenesis are major factors in reservoir productivity. Understanding the relationships between reservoir facies and diagenesis is crucial for the successful development of these fields. A better understanding of the origin and diagenesis of these dolomite horizons will be very beneficial in the further development of the Kinta and Bonaza Fields

The Future of Carrier Aviation

In early 1992 it had been predicted that the axe would fall on the Navy budget, as on those of the other services, when President Bush unveiled his proposal for the fiscal 1993 (FY 1993) federal budget in his January 1992 State of the Union Address. An announcement that the Navy would be forced to pare down to nine or ten deployable carriers would have surprised no one and would have been consistent with reductions in the Army and Air Force. Although naval leadership held firm to a party-line commitment of twelve carriers, very few staff officers working on the new budget believed that a dozen carriers were realistically affordable