Marves constructions

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Marves construction and plant hire - Facebook

Marves construction and plant hire - Facebook

The Trace Inverted checkbox in the Impedance Profile mode of the Properties panel. Pullback Distance – the distance from the plane edge to the board edge. Frequency – this is the frequency at which the material is tested and the value that Dk / Df correspond to a certain frequency. Frequency is also taken from material references. Description – enter a meaningful description. Constructions – for dielectric layers, this displays the constructions of the layer. The numerical reference relates to the structure of the woven glass fabric used in the dielectric layer material; these are standard references used by PCB fabricators. Resin – displays the resin percentage of the layer.Notes on Constructions and Resin:The choice of laminate construction can significantly impact both cost and performance. As should be expected, a single-ply construction will typically represent a cost savings compared to a multiple-ply construction. The magnitude of this savings will depend on the specific glass styles involved and a host of other parameters. Performance can also be affected and should be considered when specifying the constructions to be used. First, single-ply constructions are often lower in resin content. The other main benefit of single-ply constructions is dielectric thickness control, beyond resin content considerations. Tighter thickness tolerances can be achieved using a single-ply construction.Constructions with relatively lower resin contents are often preferred since they result in less z-axis expansion and can therefore improve reliability in many applications. In addition, lower resin contents can also improve dimensional stability, resistance to warpage, and dielectric Ramanujan graphs of degree q. In our terminology, it is a “one-parameter” family. So far as we are able to determine, this family is new and is not contained in any other explicitly known family. However, as pointed out in the remark above, it is an explicit q-covering of the complete graph \(K_q\).4 Some constructions of Ramanujan graphsAt present there are not too many methods for explicitly constructing Ramanujan graphs. In this section, we reprise most of the known methods. Note that the authors have written Matlab codes for all of the constructions in this section, except the Winnie Li construction in Sect. 4.3; these codes are available upon request.The available construction methods can be divided into two categories, which for want of a better terminology we call “one-parameter” and “two-parameter” constructions. One-parameter constructions are those for which, once the degree d of the graph is specified, the number n of vertices is also fixed by the procedure. In contrast, two-parameter constructions are those in which it is possible to specify d and n independently. The methods of Lubotzky–Phillips–Sarnak (LPS) and of Gunnells are two-parameter, while those of Winnie Li and Bibak et al. are one-parameter. Of course, not all combinations of d and n are permissible.Some of the methods discussed here lead to bipartite Ramanujan graphs. It is presumably of interest to show that these constructions in fact lead to nonbipartite Ramanujan graphs. This is done below.All but one of the constructions described below are Cayley graphs. So we begin by describing that concept. Suppose G is a group, and that \(S \subseteq G\) is “symmetric” in that \(a \in S\) implies that \(a^{-1} \in S\). Then the Cayley graph \(\mathcal {C}(G,S)\) has the elements of G as the vertex set, and the edge set is of the form \((x,xa), x \in G, a \in S\). Due to the symmetry of S, the graph is undirected even if G is noncommutative.4.1 Lubotzky–Phillips–Sarnak constructionThe Lubotzky–Phillips–Sarnak (referred to as LPS hereafter) construction [22] makes use of two unequal primes p, q, each of which is \(\equiv 1 ~\mathrm{mod}~4\). As is customary,

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1 IntroductionA fundamental theme in graph theory is the study of the spectral gap of a regular (undirected) graph, that is, the difference between the two largest eigenvalues of the adjacency matrix of such a graph. Analogously, the spectral gap of a bipartite, biregular graph is the difference between the two largest singular values of its biadjacency matrix (please see Sect. 2 for detailed definitions). Ramanujan graphs (respectively Ramanujan bigraphs) are graphs with an optimal spectral gap. Explicit constructions of such graphs have multifaceted applications in areas such as computer science, coding theory, and compressed sensing. In particular, in [8] the first and third authors show that Ramanujan graphs can provide the first deterministic solution to the so-called matrix completion problem. Prior to the publication of [8], the matrix completion problem had only a probabilistic solution. The explicit construction of Ramanujan graphs has been classically well studied. Some explicit methods are known, for example, by the work of Lubotzky, Phillips, and Sarnak [22], Margulis [26], Li [21], Morgenstern [27], Gunnells [19], Bibak et al. [6]. These methods are drawn from concepts in linear algebra, number theory, representation theory and the theory of automorphic forms. In contrast, however, no explicit methods for constructing unbalanced Ramanujan bigraphs are known. There are a couple of abstract constructions in [5, 14], but these are not explicit.Footnote 1This article has three goals. 1. [Explicit construction of unbalanced Ramanujan bigraphs]: First and foremost, we present for the first time explicit constructions of an infinite family of unbalanced Ramanujan bigraphs. Our construction, presented in Sect. 3, is based on “array code” matrices from LDPC (low-density parity check) coding theory. Apart from being the first explicit constructions, they also have an important computational feature: the biadjacency matrices are obtained immediately upon specifying two parameters, a prime number q and an integer \(l \ge 2\). 2. [Comparison of computational aspects of known constructions]: The second goal of this article is to revisit some of the earlier-known constructions of Ramanujan graphs and (balanced) bigraphs and compare the amount of work involved in constructing the various classes of graphs and obtaining. Marves construction and plant hire - Facebook

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Of Ramanujan graphs and balanced bigraphs, and no explicit constructions of an unbalanced Ramanujan bigraph. In this paper, we presented for the first time an infinite family of unbalanced Ramanujan bigraphs with explicitly constructed biadjacency matrices. In addition, we have also shown how to construct the adjacency matrices for the currently available families of Ramanujan graphs. These explicit constructions, as well as forthcoming ones based on [5, 14], are available for only a few combinations of degree and size. In contrast, it is known from [24, 25] that Ramanujan graphs are known to exist for all degrees and all sizes. The main limiting factor is that these are only existence proofs and do not lead to explicit constructions. A supposedly polynomial-time algorithm for constructing Ramanujan graphs of all degrees and sizes is proposed in [11]. But it is still a conceptual algorithm and no code has been made available. Therefore it is imperative to develop efficient implementations of the ideas proposed in [25], and/or to develop other methods to construct Ramanujan graphs of most degrees and sizes. We should also note that the work of [24, 25] shows the existence of balanced, bipartite graphs of all degrees and sizes. Therefore, in Sect. 5 of this article, we have also looked at how the constructions of [22] and Gunnells [19] can be further analyzed to derive nonbipartite Ramanujan graphs.It is worth pointing out that efficient solutions of the matrix completion problem do not really require the existence of Ramanujan graphs of all sizes and degrees. It is enough if the “gaps” in the permissible values for the degrees and the sizes are very small. If this extra freedom leads to substantial simplification in the construction procedures, then it would be a worthwhile tradeoff. However, research on this problem is still at a nascent stage.Finally, in Sect. 7, we address another issue in the matrix completion problem, namely the “missing measurements” problem. This leads to the problem of the construction of a Ramanujan bigraph (not necessarily balanced) in which a certain set of edges is prohibited. In a typical real-life application, the

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Qualitative noun often has in view one individualrather than the class as a whole.1John 4:8 o qeoV agaph estin God is love22. DefiniteA definite noun lays the stress on individual identity. It has in viewmembership in a class, but this particular member is already marked outby the author. [Wallace lists many examples.]Luke 5:8 Simwn PetroV prosepesen toiV gonasinIhsou Simon Peter fell at the feet of Jesus.Special Uses and Non-Uses of the ArticleA. Anarthrous Pre-Verbal Predicate Nominatives (Involving Colwell'sRule)1. Statement of the Rule: a definite nominative that precedes theverb is usually anarthrous.2. Clarification of the Rule: the converse is not true; anarthrous preverbalPNs are usually qualitative. theos in John 1:1c is probably qualitative(thus, not identifying the logos with the person of o theos, but stressingthat their natures are the same: "What God was, the Word was"[NEB]).B. The Article with Multiple Substantives Connected by Kai (GranvilleSharp Rule and Related Constructions)1. Statement of the Granville Sharp Rule: both substantives(nouns, particples, adjectives) refer to the same person in the article-substantive-kai-substantive(TSKS) construction when:both are personalboth are singularboth are non-proper (i.e., common terms, not proper names)Example: Eph 1:3 o qeoV kai pathr2. Validity of the Rule Within the New Testament: always valid; Titus2:13 & 2Pet 1:1 impacted. Exceptions outside the NT are capableof linguistic explanation and do not affect the christologically significanttexts.3. TSKS Constructions Involving Impersonal, Plural, and Proper Nounsa. Proper Names: always distinct individuals (e.g., "the Peterand James")b. Plural Personal Constructions: three different sematic groupspossible: (1) distinct, (2) identical, (3) overlap (three subgroups). Thisbreaks down:participle + participle = identicalnoun + noun = distinct or overlap (affects Eph 2:20; 4:11)adjective + adjective = identical or overlapmixed constructions: mixed semantic valuesc. Impersonal Constructions: three different semantic groups possible:(1) distinct, (2) identical, (3) overlap (three subgroups). All are represented,though #2 (identical) is rare. Affects Acts 2:23; 20:21; 2Thess 2:1; etc.Adjectives"Non-Adjectival" Uses of the AdjectiveThe Adverbial Use of the AdjectiveUsually reserved for special termsThe Independent or Substantival Use of the Adjective Usually articularThe Use of the Positive, Comparative, and Superlative Forms of the AdjectiveA. The Use of the Positive Adjective1. Normal Usage: only one object in view2. Positive for Comparative: implicit comparison between two substantives3. Positive for Superlative: implicit comparison between three or moresubstantivesB. The Use of the Comparative Adjective1. Normal Usage: explicit comparison between two; adjective usuallyfollowed by genitive or h2. Comparative for Superlative: comparison of three or more3. Comparison for Elative: very + positive form of adjective;no comparison is made (thus, isxupoteros would be very strong rather thanstronger)C. The Use of the Superative Adjective1. "Normal" Usage: the extreme in a comparisonof three or more2. Superlative for Elaitve: very + positive form of the adjective3. Superlative for Comparative: only two are compared; frequentwith prwtos, rare with other termsThe Relation of Adjective to NounA. When the Article is Present1. The Attributive Positions: adjective modifies the nouna. First Attributive: article-adjective-noun b. Second Attributive: article-noun-article-adjectivec. Third Attributive: noun article adjective2. The Predicate Positions: adjective makes assertion about the nouna. First Predicate: adjective-article-nounb. Second Predicate: article-noun-adjectiveB. When the Article Is Absent1. The