### Table 1: Physical and Geometrical Quantities A = area (m2)

"... In PAGE 1: ... Notation Key This section provides convenient lists of the notational conventions used throughout this chapter. Table1 lists the notation used for various physical and geometrical quantities, Table 2 details the usage of Greek symbols, and Table 3 summarizes the conventions for superscripts and subscripts. 1 Introduction In the following, we shall present the formulation for tracing particles from surfaces to surfaces inside an enclosure.... In PAGE 3: ...3 Table1 : Physical and Geometrical Quantities (cont.) R = random number, from a uniform distribution between 0 and 1 R = speedup ratio of scalar to vector execution times RD = di usely re ected photon RS = specularly re ected photon r = radius (m) S = arc length (m) S1, S2 = square of distance between the rst or second end point of a surface and the intersection point, X(1or2) ? XI 2 (m2) S12 = square of distance between end points of a surface, jX1 ? X2j2 (m2) S = scalar execution rate (MFLOP apos;s) s = path length (m) T = absolute temperature ( K) V = vector execution rate (MFLOP apos;s) X = vector point, fX; Y; Zg (m) XE = point of emission (m) XI = point of intersection (m) X; Y; Z = point in global Cartesian coordinates (m) Table 2: Greek Symbols = absorbance XL; YL = di erence in the X or Y direction between the end points of surface L (m) quot; = emittance = cone angle = re ectance = Stefan Boltzmann constant (W m?2 K?4) = azimuthal angle !... ..."

### Table 1: Physical and Geometrical Quantities A = area (m2)

"... In PAGE 1: ...Monte Carlo Surface to Sur- face Particle Transport Copyright (C) October 1991, Computational Science Education Project Notation Key This section provides convenient lists of the notational conventions used throughout this chapter. Table1 lists the notation used for various physical and geometrical quantities, Table 2 details the usage of Greek symbols, and Table 3 summarizes the conventions for superscripts and subscripts. 1 Introduction In the following, we shall present the formulation for tracing particles from surfaces to surfaces inside an enclosure.... In PAGE 3: ...3 Table1 : Physical and Geometrical Quantities (cont.) R = random number, from a uniform distribution between 0 and 1 R = speedup ratio of scalar to vector execution times RD = di usely re ected photon RS = specularly re ected photon r = radius (m) S = arc length (m) S1, S2 = square of distance between the rst or second end point of a surface and the intersection point, X(1 or 2) ? XI 2 (m2) S12 = square of distance between end points of a surface, jX1 ? X2j2 (m2) S = scalar execution rate (MFLOP apos;s) s = path length (m) T = absolute temperature ( K) V = vector execution rate (MFLOP apos;s) X = vector point, fX; Y; Zg (m) XE = point of emission (m) XI = point of intersection (m) X; Y; Z = point in global Cartesian coordinates (m) Table 2: Greek Symbols = absorbance XL; YL = di erence in the X or Y direction between the end points of surface L (m) quot; = emittance = cone angle = re ectance = Stefan Boltzmann constant (W m?2 K?4) = azimuthal angle !... ..."

### Table 4 Global Quantities

"... In PAGE 8: ...Tidal Tail in Arp 299 the individual B-band luminosities are estimated by sum- ming the light over irregular polygons drawn around each system, and are therefore also very approximate. The re- sults of this division are given in Table4 , and we use these values in concert with the following statistical properties of normal Hubble types: MH2=MHI increases towards earlier Hubble types (Young amp; Knezek 1989, Young amp; Scoville 1991). The high values in Table 4 suggests progenitor types later than Sab and earlier than Sc.... In PAGE 8: ... The re- sults of this division are given in Table 4, and we use these values in concert with the following statistical properties of normal Hubble types: MH2=MHI increases towards earlier Hubble types (Young amp; Knezek 1989, Young amp; Scoville 1991). The high values in Table4 suggests progenitor types later than Sab and earlier than Sc. They also argue against low surface brightness progenitors (de Blok amp; van der Hulst 1998) MHI=LB increases towards later Hubble types (Roberts amp; Haynes 1994; Giovanelli amp; Haynes 1990).... In PAGE 8: ... They also argue against low surface brightness progenitors (de Blok amp; van der Hulst 1998) MHI=LB increases towards later Hubble types (Roberts amp; Haynes 1994; Giovanelli amp; Haynes 1990). The high values in Table4 suggest types later than Sa (Wardle amp; Knapp 1986, Bregman et al. 1992), and later than Sb (Roberts amp; Haynes 1994).... ..."

### Table 4 Global Quantities

"... In PAGE 8: ...Tidal Tail in Arp 299 the individual B-band luminosities are estimated by sum- ming the light over irregular polygons drawn around each system, and are therefore also very approximate. The re- sults of this division are given in Table4 , and we use these values in concert with the following statistical properties of normal Hubble types: MH2=MHI increases towards earlier Hubble types (Young amp; Knezek 1989, Young amp; Scoville 1991). The high values in Table 4 suggests progenitor types later than Sab and earlier than Sc.... In PAGE 8: ... The re- sults of this division are given in Table 4, and we use these values in concert with the following statistical properties of normal Hubble types: MH2=MHI increases towards earlier Hubble types (Young amp; Knezek 1989, Young amp; Scoville 1991). The high values in Table4 suggests progenitor types later than Sab and earlier than Sc. They also argue against low surface brightness progenitors (de Blok amp; van der Hulst 1998) MHI=LB increases towards later Hubble types (Roberts amp; Haynes 1994; Giovanelli amp; Haynes 1990).... In PAGE 8: ... They also argue against low surface brightness progenitors (de Blok amp; van der Hulst 1998) MHI=LB increases towards later Hubble types (Roberts amp; Haynes 1994; Giovanelli amp; Haynes 1990). The high values in Table4 suggest types later than Sa (Wardle amp; Knapp 1986, Bregman et al. 1992), and later than Sb (Roberts amp; Haynes 1994).... ..."

### Table 1: Minkowski functionals expressed in terms of the corresponding geometric quantities.

1999

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### Table 1. Non-geometric strategy (ies) used in solving version A and version B

"... In PAGE 18: ...Arithmetic / Algebraic strategies All students showed remarkable ability to describe informally and orally the relationships between the different components of the problem, including BI and the perimeter of triangle ABC, rather than representing them symbolically. A summary of the different global strategies and solution paths used by students in trying to solve the given problem is presented in Table1 . The geometric approaches are not included in the table.... In PAGE 19: ... - Using algebraic procedures to solve an equation, such as transposing terms, adding or subtracting the same quantities in both sides, manipulating symbols as if they were numbers, inversing operations, etc. Table1 shows the main global strategies used by each participant, as well as whether they have reached no solution (NS), a correct (CR) or incorrect (IC) result. It is important to note that, in addition to the strategies presented in the table as being used by each participant, all participants have actually used arithmetic forward operations (AO), but we included the code only for the cases when it was the only strategy used by the participant.... ..."

### Table 1. Global and local stretch of some large geometric models

2003

Cited by 6

### Table 1. The coordinate transformation and geometrical representation of global motion models.

2004

"... In PAGE 3: ... The optimal transformation depends on types of relations between two overlapping frames. Table1 lists and illustrates the spatial relationship of four commonly used motion models: translation, rigid, affine and projective models. Among the motion models listed in Table 1, the projective model is a good approximation for two cases.... In PAGE 3: ... Table 1 lists and illustrates the spatial relationship of four commonly used motion models: translation, rigid, affine and projective models. Among the motion models listed in Table1 , the projective model is a good approximation for two cases. One is when the movement of the camera is small compared to its depth; the motion model can be approximated as if the camera is at a fixed tripod.... ..."

Cited by 2