### TABLE IV. Selected concepts of Algebra not necessarily known to those knowing numbers and selected theorems of Graph Theory not necessarily known to those knowing graphs

### Table 4: Comparison of pn with nn References [1] Paul H. Edelman and Robert E. Jamison. The theory of convex geometries. Geometriae Dedicata, 19(3):247{270, Dec. 1985. [2] Martin Farber and Robert E. Jamison. Convexity in graphs and hypergraphs. SIAM J. Algebra and Discrete Methods, 7(3):433{444, July 1986. [3] John L. Pfaltz. Closure lattices. Technical Report CS-94-02, Univ. of Virginia, Jan. 1994.

"... In PAGE 9: ... We can get some sense of the growth of pn by comparing it with other functions. In Table4 , we calculate pn using oating point double arithmetic instead of the long integer arithmetic of Table 3 (which over ows with n gt; 10), and compare it multiplicatively with the function nn. Based on this evidence, we o er without proof, the observation: Theorem 2.... ..."

### Table 1. Axioms for the algebraic theory of the language

"... In PAGE 14: ...1. The axioms for the algebraic theory of the language are given in Table1 . In the de nition we assume ADSeq(d), ADSeq(di), ASeq(w) and ASeq(wi) for i = 1; 2.... In PAGE 14: ... Note that we do not have an axiom x+y = y +x. This equality is derivable using the axioms in Table1 , in particular, Axiom 1. The axioms in the above de nition are not su cient to prove equality of programs like ha; b; ci and ha; hb; cii.... ..."

### Table 1: (Un)decidability of the equational theories of classes of cylindric algebras.

1999

"... In PAGE 6: ... In fact, the expansion Crs+ 3 of Crs3 with a single operation k1 1 has an undecidable equational theory. We summarized these results in Table1 . We note that, similarly to the relation algebra case, the unde- cidable equational theories are in fact r.... ..."

Cited by 4

### Table 4. An examination timetabling by the graph theory

"... In PAGE 7: ...Table4 also shows the final solution obtained by the graph theory. A1 1 4 3 8 7 2 5 6 A2 6 4 3 2 1 7 8 5 A3 1 2 4 3 5 6 7 8 A4 8 7 6 1 4 2 3 5 Fig.... ..."

### Table 1.Experimental investigations for Flowers, Kneser, the Jin graph and the Gr otzch graph. Here G denotes the uniquely-colorable graph displayed in Figure 9.

706

"... In PAGE 27: ... Kneser graphs are described in most graph theory books. In Table1 , we present a sampling of the many graphs we tried during our computational experiments. Note that we often used our probabilistic linear algebra algorithm, selecting p = :4 as a likely... In PAGE 28: ... graph is uniquely 3-colorable, the addition of a single edge between two similarly-colored vertices will result in a new non-3-colorable graph. Table1 also details these experiments. Finally, we investigated all non-3- colorable graphs on six vertices or less: every one has a Nullstellensatz certi cate of degree four.... ..."

### Table 3. Algebraic connectivity of connected graphs on six vertices

"... In PAGE 4: ... Paper n5b55n5d provides pictures of the 509 cubic graphs on fourteen vertices and some non-spectral data. Table3 in n5b24n5d, based on n5b5n5d, contains connected cubic graphs with up to 12 vertices. The pictures, spectrum and coen0ecients of the characteristic polynomials are included.... In PAGE 9: ... Table 2 contains algebraic connectivities for graphs in Table 1. Table3 refers to the table of 112 connected graphs on six vertices from n5b29n5d which is described in Section 1. Using identin0ccation numbers of graphs from n5b29n5d we give algebraic connectivities of the 112 connected graphs.... ..."

### TABLE I 1-D DISCRETE INFINITE AND FINITE TIME AND SPACE SIGNAL PROCESSING AS FOUR INSTANTIATIONS OF THE GENERAL ALGEBRAIC THEORY. THE BOLDED CONCEPTS ARE SUPPLIED BY THE ALGEBRAIC THEORY.

2006

### Table 1: Comparison of algorithmic and algebraic graph replacement approaches

1997

"... In PAGE 40: ... We will use this framework over here for reviewing a number of di erent context sensitive graph replacement approaches (cf. Table1 in Subsection 4.5).... In PAGE 62: ...way for the work presented here. Furthermore, thanks to the two anonymous referees of this chapter for their helpful comments on a previous version, to An- dre Speulmanns for producing a rst version of Table1 (comparison of graph replacement approaches), and to Alexander Bell for his excellent Framemaker to LATEX compiling job. References 1.... ..."

Cited by 31

### Table 3: The axioms for boolean algebras.

1998

"... In PAGE 9: ... n28We have kept our numbering consistent with Groote and Ponse n281994an29; in their setting Sum2 den0cnes n0b-conversion.n29 Let n06 be a pCRL-signature, then the pCRL-theory n05 n06 for n06 consists of the axioms depicted in Table 2 and the axioms for boolean algebras depicted in Table3 . A n06-algebra A is called a pCRL-algebra if A j=n05 n06... ..."