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The strength of replacement in weak arithmetic [article]

Stephen Cook, Neil Thapen
2004 arXiv   pre-print
We prove 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 .  ... 
arXiv:cs/0409015v1 fatcat:uaponsgrfzbxjd4bswtwqd6r6i

Helping Pupils Help Themselves Through Self-Evaluation

Monte S. Norton
1960 The Arithmetic Teacher  
Improvement 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.  ... 
doi:10.5951/at.7.4.0203 fatcat:j7hdnipdirfedphhyqbpcoyoa4

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

Kevin Murnane, Richard M. Shiffrin
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).  ... 
doi:10.1037//0278-7393.17.5.855 pmid:1834768 fatcat:6dt53qairrccng6wy3peanjeta

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

Hiroshi Hosobe
2001 Proceedings of the 14th annual ACM symposium on User interface software and technology - UIST '01  
Constraints have been playing an important role 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.  ... 
doi:10.1145/502348.502362 dblp:conf/uist/Hosobe01 fatcat:4s4elek5ffcdtpio5ddjiyv2ru

A modular geometric constraint solver for user interface applications

Hiroshi Hosobe
2001 Proceedings of the 14th annual ACM symposium on User interface software and technology - UIST '01  
Constraints have been playing an important role 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.  ... 
doi:10.1145/502360.502362 fatcat:tdggf64vdvfhlpkwihvmgv4xra

Proof Theory [article]

Jeremy Avigad
2017 arXiv   pre-print
Proof theory began 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.  ... 
arXiv:1711.01994v2 fatcat:3zjao7da6vdljgkb66w2vdjl74

Neo-Logicism and Its Logic

Panu Raatikainen
2019 History and Philosophy of Logic  
It is shown that Hume's Principle is 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.  ... 
doi:10.1080/01445340.2019.1680517 fatcat:oj57elvypvhrbpdk3wipt5jgx4

Reverse Mathematics: The Playground of Logic

Richard A. Shore
2010 Bulletin of Symbolic Logic  
There are then discussions 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  ... 
doi:10.2178/bsl/1286284559 fatcat:llffsna3onbpteovqxs5ki2m54

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]

Thomas Ströder, Cornelius Aschermann, Florian Frohn, Jera Hensel, Jürgen Giesl
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  ... 
doi:10.1007/978-3-662-46681-0_32 fatcat:3754za26a5byhg7s5pbneswm5i

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

Tran Minh-Tien
2008 arXiv   pre-print
Nonvanishing 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.  ... 
arXiv:0801.0852v1 fatcat:ljw4oevtwffczfbzaqobzctgm4

The beginnings of applied mathematics after the Second World War

Peter D. Lax
1998 Quarterly of Applied Mathematics  
On 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.  ... 
doi:10.1090/qam/1668731 fatcat:txdrunrwwja5bch4ceijrigsl4
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