Inequalities, Absolute Value, and Logical Connectives

1992 ◽  
Vol 85 (9) ◽  
pp. 756-757
Author(s):  
Charles R. Parish
Keyword(s):  
Problem Solving ◽  
Function Concept ◽  
Real Numbers ◽  
Appropriate Use ◽  
Standard Definition ◽  
Absolute Value ◽  
Algebra Students ◽  
Logical Connectives ◽  
Definition Of ◽  
Ordered Pairs

Algebra students often have difficulty in sorting out and correctly using the concepts involved in the solution of linear inequalities. The introduction of the concept of absolute value causes additional complications for many students. Two of the major problem areas are (1) the concept of absolute value as normally defined and (2) the recognition and appropriate use of the logical connectives and and or in the solution of problems that combine inequalities with absolute value. One way to alleviate students' confusion and promote their problem-solving ability in such a setting is to adopt an approach different from that found in current textbooks. This approach involves consideration of the function concept as the graph generated by associated ordered pairs of real numbers rather than functional values as obtained from the standard definition of absolute value.

Thinking the Unthinkable: The Story of Complex Numbers (with a Moral)

1988 ◽  
Vol 81 (7) ◽  
pp. 583-592 ◽  
Author(s):  
Israel Kleiner
Keyword(s):  
History Of Mathematics ◽  
Complex Numbers ◽  
Real Numbers ◽  
Usual Definition ◽  
History Of ◽  
Definition Of ◽  
The Impact ◽  
Ordered Pairs

The usual definition of complex numbers, either as ordered pairs (a, b) of real numbers or as “numbers” of the form a + bi, does not give any indication of their long and tortuous evolution, which lasted about three hundred years. I want to describe this evolution very briefly because I think some lessons can be learned from this story, just as from many other such stories concerning the evolution of a concept, result, or theory. These lessons have to do with the impact of the history of mathematics on our understanding of mathematics and on our effectiveness in teaching it. But more about the moral of this story later.

Teaching Cost Management: A Strategic Emphasis

2009 ◽  
Vol 24 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Edward J. Blocher
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Cost Management ◽  
Management Accounting ◽  
Cost Accounting ◽  
Appropriate Use ◽  
The Past ◽  
Management Accountants ◽  
Strategic Emphasis ◽  
Definition Of

ABSTRACT: Cost management has been tied in the past to the concepts of score-keeping, attention directing, and problem solving, but the expectations of accountants in today's world have changed dramatically, extending well beyond these concepts. This paper presents a different way to view cost management. It is not a planning or decision-making focus, but instead a focus on helping the organization be successful, through the implementation of an effective competitive strategy. Strategy is implemented by the appropriate use of cost management methods. The “why strategy?” question is answered by a review of survey findings, a discussion of the potential errors in nonstrategic decision making, and a review of changes at the Institute of Management Accountants that reflect a greater emphasis on strategy, including a new definition of management accounting which focuses on strategy. The paper shows the strategy-based content flowcharts for each of the three courses: management accounting, cost accounting, and advanced management accounting.

Hermite-Hadamard and simpson-like type inequalities for differentiable p-quasi-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5945-5953 ◽  
Author(s):  
İmdat İsçan ◽  
Sercan Turhan ◽  
Selahattin Maden
Keyword(s):  
Convex Functions ◽  
Real Numbers ◽  
Absolute Value ◽  
Special Means ◽  
Quasi Convexity

In this paper, we give a new concept which is a generalization of the concepts quasi-convexity and harmonically quasi-convexity and establish a new identity. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are p-quasi-convex. Some applications to special means of real numbers are also given.

A practical metric for melanopic metrology

2019 ◽  
Vol 51 (8) ◽  
pp. 1178-1191 ◽  
Author(s):  
SM Berman ◽  
RD Clear
Keyword(s):  
Ganglion Cell ◽  
Retinal Ganglion Cell ◽  
Vision Research ◽  
Spectral Response ◽  
Retinal Ganglion ◽  
Standard Definition ◽  
Standard Unit ◽  
Vision Science ◽  
The Past ◽  
Definition Of

Over the past decade, there has been a growing interest in lighting research on the effects of the recently discovered melanopsin receptor (also referred to as the intrinsically photosensitive retinal ganglion cell) and its impacts on health and vision. Presently, there is not a generally accepted metrology for dealing with the spectral response of the melanopsin receptor as applied to both lighting and vision research. A proposition to handle this issue from a vision science perspective has been presented in 2014 in the journal Trends in Neurosciences and from a more lighting perspective in 2017 in Lighting Research and Technology. These propositions are complex, and do not retain the CIE standard definition of a lumen. In this paper, we propose an approach based on effective watts and melanopic/photopic ratios that is both simpler and more closely aligned with CIE standard unit definitions. In addition, we include some practical examples of how such ratios are accessible now, and can be used for both lighting and vision research as well as applications.

The Humdrum Use of Ultimate Authority: Defining and Analysing Chapter VII Resolutions

2009 ◽  
Vol 78 (3) ◽  
pp. 309-342 ◽  
Author(s):  
Patrik Johansson
Keyword(s):  
Cold War ◽  
United Nations ◽  
Security Council ◽  
Security Council Resolution ◽  
Post Cold War ◽  
Standard Definition ◽  
The Status ◽  
Definition Of ◽  
The Cold War ◽  
Business As Usual

AbstractUnder Chapter VII of the Charter of the United Nations, the Security Council has the unique authority to make decisions that are binding on member states. However, the lack of a standard definition of what makes a Security Council resolution "a Chapter VII resolution" has caused disagreement regarding the status of several resolutions. This is unfortunate as the international community should never have to doubt whether a Security Council resolution is in fact adopted under Chapter VII or not. It is also unnecessary. This article addresses this problem by proposing a definition of Chapter VII resolutions, based on two criteria referred to as "Article 39 determinations" and "Chapter VII decisions". On the basis of the proposed definition, the article describes and analyses a dramatic increase in the use of Chapter VII during the post-Cold War era. It concludes that as Chapter VII has come to constitute the majority of Security Council resolutions in recent years, the resort to Chapter VII no longer signifies exceptional determination and resolve, which it did during the Cold War; instead Chapter VII today implies business as usual. An appendix lists all Chapter VII resolutions from 1946–2008.

Analogue of a theorem of Khintchine in fields of formal power series

1966 ◽  
Vol 62 (4) ◽  
pp. 637-642 ◽  
Author(s):  
T. W. Cusick
Keyword(s):  
Power Series ◽  
Positive Constant ◽  
Classical Result ◽  
Real Numbers ◽  
Linear Forms ◽  
Absolute Value ◽  
The Difference ◽  
Image Position ◽  
Formal Power ◽  
Positive Integers

For a real number λ, ‖λ‖ is the absolute value of the difference between λ and the nearest integer. Let X represent the m-tuple (x1, x2, … xm) and letbe any n linear forms in m variables, where the Θij are real numbers. The following is a classical result of Khintchine (1):For all pairs of positive integers m, n there is a positive constant Г(m, n) with the property that for any forms Lj(X) there exist real numbers α1, α2, …, αn such thatfor all integers x1, x2, …, xm not all zero.

The Standard Definition of Magic Matrix

2021 ◽  
Vol 10 (08) ◽  
pp. 2714-2724
Author(s):  
兴祥 刘
Keyword(s):  
Standard Definition ◽  
Definition Of

Comment on a Standard Definition of Response Rates

1984 ◽  
Vol 21 (3) ◽  
pp. 336 ◽  
Author(s):  
Frederick Wiseman ◽  
Maryann Billington
Keyword(s):  
Response Rates ◽  
Standard Definition ◽  
Definition Of

Tongue Thrust: A Point of View

1976 ◽  
Vol 41 (2) ◽  
pp. 172-184 ◽  
Author(s):  
Marvin L. Hanson
Keyword(s):  
Orthodontic Treatment ◽  
Point Of View ◽  
Patient Age ◽  
Present Evidence ◽  
Standard Definition ◽  
Myofunctional Therapy ◽  
Developmental Factors ◽  
Patient Âgé ◽  
Definition Of ◽  
Tongue Thrust

The purpose of the present paper is to present evidence to support the following hypotheses: (1) there is a relationship between tongue thrust and malocclusion, and it is probably a reciprocal one; (2) tongue thrust may yield spontaneously to nonthrusting patterns; (3) if tongue thrust does not yield spontaneously to nonthrusting patterns, some form of treatment should be considered; (4) if myofunctional therapy is the treatment of choice, its timing with respect to patient age, developmental factors, and orthodontic treatment should be an individual matter. The need for more definitive research is described. In order for such research to be meaningful, a standard definition of tongue thrust is required. Such a definition is proposed.

scholarly journals Final coalgebras as greatest fixed points in ZF set theory

1999 ◽  
Vol 9 (5) ◽  
pp. 545-567 ◽  
Author(s):  
LAWRENCE C. PAULSON
Keyword(s):  
Fixed Points ◽  
Set Theory ◽  
Theorem Prover ◽  
Infinite Length ◽  
Special Cases ◽  
Definition Of ◽  
Recursive Definitions ◽  
Ordered Pairs

A special final coalgebra theorem, in the style of Aczel (1988), is proved within standard Zermelo–Fraenkel set theory. Aczel's Anti-Foundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions. Variant ordered pairs and tuples, of possibly infinite length, are special cases of variant functions. Analogues of Aczel's solution and substitution lemmas are proved in the style of Rutten and Turi (1993). The approach is less general than Aczel's, but the treatment of non-well-founded objects is simple and concrete. The final coalgebra of a functor is its greatest fixedpoint.Compared with previous work (Paulson, 1995a), iterated substitutions and solutions are considered, as well as final coalgebras defined with respect to parameters. The disjoint sum construction is replaced by a smoother treatment of urelements that simplifies many of the derivations.The theory facilitates machine implementation of recursive definitions by letting both inductive and coinductive definitions be represented as fixed points. It has already been applied to the theorem prover Isabelle (Paulson, 1994).

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