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The strength of replacement in weak arithmetic
[article]

2004
*
arXiv
*
pre-print

We prove

arXiv:cs/0409015v1
fatcat:uaponsgrfzbxjd4bswtwqd6r6i
*the*independence*of*this scheme from various*weak*theories*of**arithmetic*, sometimes under a complexity assumption. ...*The**replacement*(or collection or choice) axiom scheme asserts bounded quantifier exchange. ... Introduction We are concerned with*the**strength**of*various theories*of*bounded*arithmetic*associated with*the*complexity classes P, TC 0 , and AC 0 . ...##
###
Helping Pupils Help Themselves Through Self-Evaluation

1960
*
The Arithmetic Teacher
*

Improvement

doi:10.5951/at.7.4.0203
fatcat:j7hdnipdirfedphhyqbpcoyoa4
*in**Arithmetic*is dependent—dependent upon*the*individual's awareness*of*various*weaknesses*, a desire to improve*in*this area, and a knowledge*of**the*procedures that possibly may bring about ... This idea*of*self-improvement is carried on*in**arithmetic*classes*in*our school through*the*use*of*our self-evaluation plan. ...*The*student is asked to think seriously about his work quality, effort, progress,*strengths*,*weaknesses*, and other areas*of*importance*in*regard to his arith- metic class. ...##
###
Page 323 of Infertility and Reproductive Medicine Clinics of North America Vol. 5, Issue 2
[page]

1994
*
Infertility and Reproductive Medicine Clinics of North America
*

*STRENGTHS*AND

*WEAKNESSES*This brief review

*of*

*the*theory

*of*case-control studies may permit a better understanding

*of*some

*of*

*the*

*strengths*and

*weaknesses*

*of*this type

*of*study summarized

*in*Table 1. ... It isa simple exercise

*of*

*arithmetic*to show that when A, B, C, Dare

*replaced*by a, b, c, d divided by their appropriate sampling fractions, f; and f2, then

*the*sampling fractions drop out

*of*

*the*relative ...

##
###
Interference and the representation of events in memory

1991
*
Journal of Experimental Psychology. Learning, Memory and Cognition
*

*the*

*weak*-other items on

*the*pure-

*weak*list. ... Similarly,

*weak*items on

*the*mixed list are compared with items on a list composed

*of*all

*weak*items (pure-

*weak*),

*the*total number

*of*different items again being equal. ... Both would be

*replaced*by effects

*of*session length and session

*strength*(if such existed). ...

##
###
Page 10 of Review of Educational Research Vol. 4, Issue 1
[page]

1934
*
Review of Educational Research
*

Bagley’s study (2)

*of*education, crime, and social progress involved (a) an identification*of**the*elements*of**weakness**in*American education and (b) an effort to*replace*these with elements*of**strength*... ; Bowden’s study (8)*of**arithmetic*, based on an analysis*of*newspapers and a study*of*details*of**the*various occupations; and Finley and Caldwell’s study (18)*of*biology*in**the*public press to determine ...##
###
Page 10 of Review of Educational Research Vol. 4, Issue 1
[page]

1934
*
Review of Educational Research
*

Bagley’s study (2)

*of*education, crime, and social progress involved (a) an identification*of**the*elements*of**weakness**in*American education and (b) an effort to*replace*these with elements*of**strength*... ; Bowden’s study (8)*of**arithmetic*, based on an analysis*of*newspapers and a study*of*details*of**the*various occupations; and Finley and Caldwell’s study (18)*of*biology*in**the*public press to determine ...##
###
A modular geometric constraint solver for user interface applications

2001
*
Proceedings of the 14th annual ACM symposium on User interface software and technology - UIST '01
*

Constraints have been playing an important role

doi:10.1145/502348.502362
dblp:conf/uist/Hosobe01
fatcat:4s4elek5ffcdtpio5ddjiyv2ru
*in**the*user interface field since its infancy. ... A prime use*of*constraints*in*this field is to automatically maintain geometric layouts*of*graphical objects. ... It restricts*the*medium and*weak**strengths*to basically linear constraints. ...##
###
A modular geometric constraint solver for user interface applications

2001
*
Proceedings of the 14th annual ACM symposium on User interface software and technology - UIST '01
*

Constraints have been playing an important role

doi:10.1145/502360.502362
fatcat:tdggf64vdvfhlpkwihvmgv4xra
*in**the*user interface field since its infancy. ... A prime use*of*constraints*in*this field is to automatically maintain geometric layouts*of*graphical objects. ... It restricts*the*medium and*weak**strengths*to basically linear constraints. ...##
###
Proof Theory
[article]

2017
*
arXiv
*
pre-print

Proof theory began

arXiv:1711.01994v2
fatcat:3zjao7da6vdljgkb66w2vdjl74
*in**the*1920's as a part*of*Hilbert's program, which aimed to secure*the*foundations*of*mathematics by modeling infinitary mathematics with formal axiomatic systems and proving those ... Today such a viewpoint has applications*in*mathematics, computer science, and*the*philosophy*of*mathematics. ... Theories*of*nonstandard*arithmetic*and analysis can be calibrated*in*terms*of**the**strength**of*standard theories [19] . 7. ...##
###
Neo-Logicism and Its Logic

2019
*
History and Philosophy of Logic
*

It is shown that Hume's Principle is

doi:10.1080/01445340.2019.1680517
fatcat:oj57elvypvhrbpdk3wipt5jgx4
*in*reality not stronger than*the*very*weak*Robinson*Arithmetic*Q. ...*The*rather unrestrained use*of*second-order logic*in**the*neo-logicist program is critically examined. ... My understanding*of**the*development*of**the*axiomatic systems*of*second-order logic has greatly benefited from certain postings by Martin Davis for*the*FOM list back*in*1999-2000. ...##
###
Reverse Mathematics: The Playground of Logic

2010
*
Bulletin of Symbolic Logic
*

There are then discussions

doi:10.2178/bsl/1286284559
fatcat:llffsna3onbpteovqxs5ki2m54
*of*some interactions between reverse mathematics and*the*major branches*of*mathematical logic*in*terms*of**the*techniques they supply as well as theorems for analysis. ... While retaining*the*usual base theory and working still within second order*arithmetic*, theorems are described that range from those far below*the*usual systems to ones far above. ... Introduction*The*general enterprise*of*calibrating*the**strength**of*classical mathematical theorems*in*terms*of**the*axioms (typically*of*set existence) needed to prove them was begun by Harvey Friedman ...##
###
Page 17 of Mathematical Reviews Vol. , Issue 91H
[page]

1991
*
Mathematical Reviews
*

*The*same algebra is used to show that there is a neat 3-reduct

*of*a CA, which is not neatly embeddable

*in*a CA;,-7.

*The*problem

*of*whether 3a —7 can be

*replaced*by a+ 1

*in*

*the*above results is open. ...

*The*author shows that

*the*system ACAp

*of*

*arithmetic*comprehension is equivalent, over

*the*

*weak*base theory RCA»

*of*recursive comprehension, to

*the*Radon-Nikodym theorem. ...

##
###
AProVE: Termination and Memory Safety of C Programs
[chapter]

2015
*
Lecture Notes in Computer Science
*

*The*particular

*strength*

*of*AProVE when analyzing C is its capability to reason about pointer

*arithmetic*combined with direct memory accesses (as, e.g.,

*in*standard implementations

*of*string algorithms) ... As a prerequisite for termination, AProVE also proves memory safety

*of*C programs. ...

*Strengths*and

*Weaknesses*

*The*

*strength*

*of*our approach for C is that it handles algorithms where

*the*control flow depends on explicit pointer

*arithmetic*and on detailed information about

*the*contents

*of*...

##
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Statistics of local density of states in the Falicov-Kimball model with local disorder
[article]

2008
*
arXiv
*
pre-print

Nonvanishing

arXiv:0801.0852v1
fatcat:ljw4oevtwffczfbzaqobzctgm4
*of**the*most probable value*of**the*local density*of*states at*the*Fermi energy indicates*the*existence*of*extended states*in**the*two-dimensional disordered interacting system. ... Statistics*of**the*local density*of*states*in**the*two-dimensional Falicov-Kimball model with local disorder is studied by employing*the*statistical dynamical mean-field theory. ...*The*author is grateful to thank*the*Max Planck Institute for*the*Physics*of*Complex Systems at Dresden for sharing computer facilities where*the*numerical calculations were performed. ...##
###
The beginnings of applied mathematics after the Second World War

1998
*
Quarterly of Applied Mathematics
*

On

doi:10.1090/qam/1668731
fatcat:txdrunrwwja5bch4ceijrigsl4
*the*other hand, Fejer has shown that*the**arithmetic*means*of**the*partial sums display no such overshoot; this is a consequence*of*positivity*of**the*kernel expressing*the**arithmetic*means*in*terms*of*... Cesaro has defined,*in*a natural way,*arithmetic*means*of*any order*of*a sequence, even*of*fractional order. ... about*weak*convergence stated*in*Sec. 2. ...
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