### Table 2. Constant c in the strengthened Cauchy-Schwarz inequality for the Poisson bilinear form

in Digital Object Identifier (DOI) 10.1007/s00607-002-1464-y Problem Dependent Generalized Prewavelets

2002

"... In PAGE 11: ... Then, a short calculation shows that the problem dependent generalized prewavelet wa p, p 2 Xedge can be described by the following stencil: C0 C0 0:3; 0:7; C00:3C1 for a point p not near the boundary; C0 C0 0:3C22 3; 0:83C22 3; 0C1 for a point p near the boundary: This shows that an approximate subspace correction, constructed by an Gauss-Seidel relaxation in the direction of the functions wa p, is similar to the classical red-black Gauss-Seidel relaxation and the computational cost is nearly the same. Table2 depicts the constant c in the strengthened Cauchy-Schwarz inequality between the spaces VnC01 and Wn obtained by a numerical calculation. The constant c seems to be smaller than 0:25 independent of the number of unknowns.... ..."

### Table 2. Complexity of the structures after constant multiplication expansion at 5V

1996

"... In PAGE 12: ... Moreover, the programmable hardware has additional control overhead. Table2 also reveals a considerable increases in some of the critical paths. This is a considerable penalty since, as we have noted in section 2, a high speed design is always desirable due to its potential for allowing voltage reduction.... ..."

Cited by 6

### Table 2. Complexity of the structures after constant multiplication expansion at 5V

in Reprint from: Design and Test of Computers, 1995 An Integrated CAD Environment for Low-Power Design

"... In PAGE 12: ... Moreover, the programmable hardware has additional control overhead. Table2 also reveals a considerable increases in some of the critical paths. This is a considerable penalty since, as we have noted in section 2, a high speed design is always desirable due to its potential for allowing voltage reduction.... ..."

### Table 1. Complexity classification of a taxonomy of constant propagation: the known results

2001

"... In PAGE 3: ... 2 The Taxonomy and Complexity Results 2.1 Known Results Table1 summarizes the already known complexity results. Problems with a polynomial time algorithm are emphasized in a light shade of grey, those be-... In PAGE 5: ... The multiple value problem has been shown NP-complete in the acyclic case and PSPACE-complete in the presence of unrestricted control flow [8]. In the remainder of this section we aim at successively filling the white parts in Table1 . To this end, we start with providing new undecidability results, then give some new intractability results and finally indicate that constant propagation can be achieved efficiently for the class of Presburger constants.... In PAGE 10: ... 3 Summary and Conclusions The decidability and complexity considerations of this paper are summarized in Table 2. In fact, we almost completely succeeded in filling the white fields of Table1 . As apparent, only two upper bounds are left open in the supplemented table.... ..."

Cited by 9

### Table 1: Whose ratings are used where?

"... In PAGE 17: ... TAPESTRY gave two approaches for filtering: automatic, where the system evaluates what is interesting to the user, and social, where users help each other. Table1 summarizes a few paradigmatic systems developed until now or under development, emphasizing the users profile and matching techniques. Sift and Newsweeder represent two examples of automatic filtering systems.... In PAGE 18: ... Anonymous access is possible for search, browse or even retrieval, but users are always suggested to identify themselves for profile management. Explicit Implicit Tecniques Arguments Grouplens (1992) Usenet Numeric Vector Numeric Vector (reading time) Cosine measure (user profile) versus (users profiles) Collaborative filter system Sift (1994) Usenet Keywords list - Boolean (IS) versus (user profile) Filter system Newsweeder (1994) Usenet Numeric Vector Numeric Vector (user history) Cosine measure (IS) versus (user profile) Content based-filter system Fab (1994) Web Numeric Vector Numeric Vector (user history) Cosine measure (IS) and (users profiles) versus (user profile) Collaborative and content-based filter system ReferralWeb (1994) Web (user profile) versus (community profile) Collaborative and social filtering Remarks mention of a person or a document System Information Source (IS) Profile Matching Table1... In PAGE 29: ... (Morita and Shinoda, 1994) use reading duration in place of the read/ignore attribute. Table1 shows the result of combining these forms with the types of usage data described in (Nichols, Twidale and Paice, 1997). Action Notes Purchase (Price) buys item Assess evaluates or recommends Repeated Use (Number) e.... In PAGE 29: ...g. multiple check out stamps Save / Print saves document to personal storage Delete deletes an item Refer cites or otherwise refers to item Reply (Time) replies to item Mark add to a apos;marked apos; or apos;interesting apos; list Examine / Read (Time) looks at whole item Consider (Time) looks at abstract Glimpse sees title / surrogate in list Associate returns in search but never glimpses Query association of terms from queries Table1 Potential types of implicit rating information Some of the data sources have additional information (e.g.... In PAGE 30: ... Hence this category would not contain any reference to the actual value of a rating only the fact that a rating had, or had not, occurred. The Repeated Use category in Table1 could really refer to any of the other categories of data. However, it has an appealing analogue with conventional library practice, that of date stamps in the back of a borrowed book.... In PAGE 30: ... Systems usually allow users to read a shortened or summary version of a document; bibliographic databases often have an abstract rather than the full-text of an article. At the bottom of the list in Table1 the action Associate refers to items which are closely connected to those that are examined, e.... In PAGE 30: ...hat are examined, e.g. items in the second page of hits which is never reached by the user. The action Query refers to query terms which have been used by searchers and can then be reused by subsequent searchers who use related terms (Koenig, 1990). The collection of these types of implicit data does not pose difficult technological problems: many information access tools could easily be modified to record most of the categories of data in Table1 . In addition, there is a considerable body of research in LIS on the closely related field of transaction log analysis, e.... In PAGE 31: ... The test subjects in the Morita amp; Shinoda experiment were asked to read items continuously, a very different scenario from their usual news-reading habits. A separate source of implicit data for Web users are the files of bookmarks, or hotlists, of Web pages; the Mark category from Table1 . The Siteseer system (Rucker and Polanco, 1997) uses the overlap between bookmark files to create virtual communities of interest and then recommends URLs pages from a users apos; virtual neighbours.... ..."

### Table 2.1: Examples of structured matrices associated with some bilinear forms

### Table 3.4: Constant in the strength- ened Cauchy-Schwarz inequality for semi- coarsening and generalized prewavelets. Let b(y) 0 be a non-negative function. The constants in the strengthened Cauchy-Schwarz inequality are printed in Table 3.3 and Table 3.4 for some bilinear forms. Let us prove the estimate

### Table 1. Comparison of computational complexity of the 4 trans- forms for an N x N image.

"... In PAGE 3: ... Therefore, the number of multiplications and additions is much higher (in the sense that the constant that is involved is higher) than in the case of directionlets [3]. Table1 summarizes the comparison of computational complexity of these methods. 4.... ..."

### Table 1: Non-supersingular elliptic curves for co-GDH Signatures. E is a curve over the prime field Fq and p is the largest prime dividing its order. The MOV reduction maps the curve onto the field Fq6. D is the discriminant of the complex multiplication field of E/Fq.

"... In PAGE 14: ... D is the discriminant of the complex multiplication field of E/Fq. Table1 gives some values of D that lead to suitable curves for our signature scheme. For example, we get a curve E/Fq where q is a 168-bit prime.... ..."

### Table 1: Non-supersingular elliptic curves for co-GDH Signatures. E is a curve over the prime field Fq and p is the largest prime dividing its order. The MOV reduction maps the curve onto the field Fq6. D is the discriminant of the complex multiplication field of E/Fq.

in Abstract

"... In PAGE 14: ... D is the discriminant of the complex multiplication field of E/Fq. Table1 gives some values of D that lead to suitable curves for our signature scheme. For example, we get a curve E/Fq where q is a 168-bit prime.... ..."