scholarly journals Some Instructive Mathematical Errors

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Richard Brent
Keyword(s):  
Incorrect Result ◽  
Mathematical Literature

We describe various errors in the mathematical literature, and consider how some of them might have been avoided, or at least detected at an earlier stage, using tools such as Maple or Sage. Our examples are drawn from three broad categories of errors. First, we consider some significant errors made by highly-regarded mathematicians. In some cases these errors were not detected until many years after their publication. Second, we consider in some detail an error that was recently detected by the author. This error in a refereed journal led to further errors by at least one author who relied on the (incorrect) result. Finally, we mention some instructiveerrors that have been detected in the author's own published papers.

Umbral Calculus

10.37236/24 ◽  
2002 ◽  
Vol 1000 ◽  
Author(s):  
A. Di Bucchianico ◽  
D. Loeb
Keyword(s):  
19Th Century ◽  
Finite Differences ◽  
State Of The Art ◽  
Umbral Calculus ◽  
Current State ◽  
Logical Foundation ◽  
Complete Bibliography ◽  
The 19Th Century ◽  
Mathematical Literature

We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of “magic rules” for lowering and raising indices, through its rebirth in the 1970’s as Rota’s school set it on a firm logical foundation using operator methods, to the current state of the art with numerous generalizations and applications. The survey itself is complemented by a fairly complete bibliography (over 500 references) which we expect to update regularly.

A Symposium on the Publication of Mathematical Literature

SIAM Review ◽  
1964 ◽  
Vol 6 (4) ◽  
pp. 431-454 ◽  
Author(s):  
I. E. Block ◽  
R. F. Drenick
Keyword(s):  
Mathematical Literature

scholarly journals Improved Modular Division Implementation with the Akushsky Core Function

Computation ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 9
Author(s):  
Mikhail Babenko ◽  
Andrei Tchernykh ◽  
Viktor Kuchukov
Keyword(s):  
Approximate Method ◽  
Chinese Remainder Theorem ◽  
Number System ◽  
Residue Number System ◽  
Division Algorithm ◽  
Incorrect Result ◽  
Core Function ◽  
Residue Number ◽  
Division Operation

The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method.

Hypercorrection in English: an intervarietal corpus-based study

2021 ◽  
pp. 1-27
Author(s):  
PETER COLLINS
Keyword(s):  
Qualitative Data ◽  
Sources Of Information ◽  
Web Based ◽  
British English ◽  
Incorrect Result ◽  
Outer Circle ◽  
Long Period ◽  
Inner Circle ◽  
Elicitation Studies

This article aims to provide a fresh approach to the study of hypercorrection, the misguided application of a real or imagined rule – typically in response to prescriptive pressure – in which the speaker's attempt to be ‘correct’ leads to an ‘incorrect’ result. Instead of more familiar sources of information on hypercorrection such as attitude elicitation studies and prescriptive commentary, insights are sought from quantitative and qualitative data extracted from the 2-billion-word Global Web-based English corpus (GloWbE; Davies 2013). Five categories are investigated: case-marked pronouns, -ly and non-ly adverbs, agreement with number-transparent nouns, (extended uses of) irrealis were, and ‘hyperforeign’ noun suffixation. The nature and extent of hypercorrection in these categories, across the twenty English varieties represented in GloWbE, are investigated and discussed. Findings include a tendency for hypercorrection to be more common in American than in British English, and more prevalent in the ‘Inner Circle’ (IC) than in the ‘Outer Circle’ (OC) varieties (particularly with established constructions which have been the target of institutionalised prescriptive commentary over a long period of time).

scholarly journals Quasi cl-supercontinuous functions and their function spaces

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
J. K. Kohli ◽  
Jeetendra Aggarwal
Keyword(s):  
Continuous Functions ◽  
Function Spaces ◽  
Strong Form ◽  
General Topology ◽  
Regular Space ◽  
Basic Properties ◽  
New Class ◽  
Mathematical Literature ◽  
Class Of Functions ◽  
Appl Math

AbstractA new class of functions called ‘quasi cl-supercontinuous functions’ is introduced. Basic properties of quasi cl-supercontinuous functions are studied and their place in the hierarchy of variants of continuity that already exist in the mathematical literature is elaborated. The notion of quasi cl-supercontinuity, in general, is independent of continuity but coincides with cl-supercontinuity (≡ clopen continuity) (Applied General Topology 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772), a significantly strong form of continuity, if range is a regular space. The class of quasi cl-supercontinuous functions properly contains each of the classes of (i) quasi perfectly continuous functions and (ii) almost cl-supercontinuous functions; and is strictly contained in the class of quasi

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