### Table 2. Crisp and fuzzy information in systems. system input data resulting mathematical framework

"... In PAGE 8: ... A fuzzy system can simultaneously have several of the above attributes. Table2 gives an overview of the relationships between fuzzy and crisp system descriptions and variables. In this text we will focus on the last type of systems, i.... ..."

### Table 2. Domains and Competencies for Secondary Mathematics EXCET. Source: Preparation Manual for the EXCET (Mathematics 17), State Board for Educator Certification. [S2]

"... In PAGE 3: ... Course Content In choosing two course areas for development of the initial components of the computer- based program, the developers considered the emphasis placed upon algebra and precalculus concepts in the test framework of the EXCET and decided to develop a College Algebra course and a Precalculus (with Analytic Geometry and Trigonometry) course. Table2 below outlines the test framework for the EXCET in Secondary Mathematics. The number of competencies within each domain is directly correlated to the emphasis placed on each domain in the examination.... ..."

### Table 1: Summary of Notation

2006

"... In PAGE 3: ... 2 Framework In this section we present our mathematical framework. All notation is summarized in Table1 . We consider an infectious disease that is endemic in a population of size N consisting of S susceptible people and I infected people (N = S + I).... ..."

Cited by 1

### Tableaux calculi for modal predicate logics with and without the Barcan formula can be found in [32]. Just like the identity of individuals gives rise to many philosophical ques- tions in modal predicate logic, it also gives rise to many deep mathematical questions. As a result, various alternative semantic frameworks have been developed for modal predicate logic during the 1990s, including the Kripke bundles of Shehtman and Skvortsov [37] and the category-theoretic seman- tics proposed by Ghilardi [16] The notion of (axiomatic) completeness is another source of interesting mathematical questions in modal predicate logic. It turns out that the mini- mal predicate logical extension of many well-behaved and complete proposi- tional modal logics need not be complete. The main (negative) result in this area is that among the extensions of S4, propositional modal logics L whose minimal predicate logical extension is complete must have either L S5 or

### Table 1: The five layers and their main functions.

2000

"... In PAGE 3: ...oordination layers of the architecture. This paper emphasizes progress since 1994. We also present new results on the safety and performance analysis of the hybrid system formed by the combined action of the coordination and regulation layer control systems and some results on the control of the combined system formed by the link, coordination, and regulation layers of the AHS architecture. Table1 summarizes the functions of the five-layer PATH AHS architecture, and the mathematical framework used in the design of each layer. Section2 presents an overview of the architecture and describes each layer.... ..."

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### Table 2 Mathematical Software Packages Utilized Mathematical

1999

"... In PAGE 4: ... Problem originally suggested by H. S. Fogler of the University of Michigan ** Problem preparation assistance by N. Brauner of Tel-Aviv University MATHEMATICAL PACKAGES USED IN THE COMPARISON Table2 lists the various mathematical software packages that were used in the solutions to the problem set and the individuals who kindly provided the solution set. These individuals had considerable experience with the software package that they utilized.... ..."

Cited by 1

### Table 12 displays the performance of the OSLSE framework of Section 2. In all but one case, the desired optimality tolerance was achieved at the pre-processing stage. Since the OSLSE framework makes the underlying tree structure transparent to the MIP pre-processor, significant tightening of the formulation is possible.

2001

"... In PAGE 18: ... Table12 : DCAP: Improved Computations using OSLSE 7. Concluding Remarks Stochastic integer programs remain among the most formidable problems in mathematical pro- gramming.... ..."

### Table 1. Mathematical notations.

"... In PAGE 3: ...o interaction between peers. Note that we only have one ISP in our model. The issues of multiple ISPs and multihoming are much more complicated and will appear in our future work. Lastly, Table1 contains all notations used in our mathematical model. Let a39a40a27a30a29 denote the traffic demand (or transmission rate in unit of Mbps) from peer a2 to peer a31 .... ..."

### Table I. Mathematical Notations

2005

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### Table 1: Mathematical notation.

1999

Cited by 1