Definition of Derivative Function: Logical Error in Mathematics

Derivative Function ◽

Essential Value ◽

Variable Quantity ◽

Starting Point ◽

Logical Error ◽

Definition Of ◽

The critical analysis of the foundations of the differential calculus is proposed. Methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is shown that differential calculus is fictitious mathematical theory because the concept of the limiting process is the starting point for definition of the derivative function. The passage to the limit “zero” in the definition of the derivative function signifies that the variable quantity takes the only essential value “zero”. This fact leads to the following errors. (1) The definition of the derivative function is based on the violation of the necessary and sufficient condition for the validity of the relationship between the increment of the function argument and the increment of the function because the increment of the function is divided by the zero increment of the argument in the case of the limiting process. (2) The definition of the derivative function is based on the contradiction which is that the increment of the argument is both zero and not zero in the same relationship. This contradiction represents a violation of the formal-logical law of identity and of the formal-logical law of the lack of contradiction. (3) The definition of the differential of function is based on two contradictory (mutually exclusive) features: the differential of the argument is not zero while the increment of the argument in the definition of the derivative function is zero.

Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2011/164843 ◽

2011 ◽

Vol 2011 ◽

pp. 1-26 ◽

Cited By ~ 1

Author(s):

Roberto C. Raimondo

Keyword(s):

Bergman Space ◽

Toeplitz Operators ◽

Boundary Behavior ◽

Berezin Transform ◽

Planar Domain ◽

Sufficient Condition ◽

Planar Domains ◽

We study the problem of the boundedness and compactness of when and is a planar domain. We find a necessary and sufficient condition while imposing a condition that generalizes the notion of radial symbol on the disk. We also analyze the relationship between the boundary behavior of the Berezin transform and the compactness of

A generalized inversion formula for the continuous Jacobi transform

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171287000796 ◽

1987 ◽

Vol 10 (4) ◽

pp. 671-692 ◽

Cited By ~ 4

Author(s):

Ahmed I. Zayed

Keyword(s):

Analytic Function ◽

Inversion Formula ◽

Generalized Functions ◽

Generalized Function ◽

Sufficient Condition ◽

Generalized Inversion ◽

Definition Of ◽

Jacobi Transform

In this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by-product of our technique we obtain a necessary and sufficient condition for an analytic functionF(λ)inReλ>0to be the continuous Jacobi transform of a generalized function.

On the Very Idea of Civilisation

Dialogue and Universalism ◽

10.5840/du202131233 ◽

2021 ◽

Vol 31 (2) ◽

pp. 307-321

Author(s):

Luke O’Sullivan ◽

Keyword(s):

Technological Development ◽

Thomas Hobbes ◽

Alternative Definition ◽

Starting Point ◽

Western Imperialism ◽

Clash Of Civilisations ◽

Definition Of ◽

Contemporary Liberalism ◽

Relationship Of ◽

The concept of civilisation is a controversial one because it is unavoidably normative in its implications. Its historical associations with the effort of Western imperialism to impose substantive conditions of life have made it difficult for contemporary liberalism to find a definition of “civilization” that can be reconciled with progressive discourse that seeks to avoid exclusions of various kinds. But because we lack a way of identifying what is peculiar to the relationship of civilisation that avoids the problem of domination, it has tended to be conflated with other ideas. Taking Samuel Huntington's idea of a “Clash of Civilisations” as a starting point, this article argues that we suffer from a widespread confusion of civilisation with “culture,” and that we also confuse it with other ideas including modernity and technological development. Drawing on Thomas Hobbes, the essay proposes an alternative definition of civilisation as the existence of limits on how we may treat others.

Military Targeting in the Context of Self-Defence Actions

Nordic Journal of International Law ◽

10.1163/15718107-08401002 ◽

2015 ◽

Vol 84 (1) ◽

pp. 3-28 ◽

Cited By ~ 2

Author(s):

James A. Green ◽

Christopher P.M. Waters

Keyword(s):

Target Selection ◽

Jus In Bello ◽

Customary International Law ◽

Jus Ad Bellum ◽

Conceptual Clarity ◽

Starting Point ◽

Definition Of ◽

The Relationship ◽

Self Defence ◽

Selection Of

For self-defence actions to be lawful, they must be directed at military targets. The absolute prohibition on non-military targeting under the jus in bello is well known, but the jus ad bellum also limits the target selection of states conducting defensive operations. Restrictions on targeting form a key aspect of the customary international law criteria of necessity and proportionality. In most situations, the jus in bello will be the starting point for the definition of a military targeting rule. Yet it has been argued that there may be circumstances when the jus ad bellum and the jus in bello do not temporally or substantively overlap in situations of self-defence. In order to address any possible gaps in civilian protection, and to bring conceptual clarity to one particular dimension of the relationship between the two regimes, this article explores the independent sources of a military targeting rule. The aim is not to displace the jus in bello as the ‘lead’ regime on how targeting decisions must be made, or to undermine the traditional separation between the two ‘war law’ regimes. Rather, conceptual light is shed on a sometimes assumed but generally neglected dimension of the jus ad bellum’s necessity and proportionality criteria that may, in limited circumstances, have significance for our understanding of human protection during war.

On the Indispensability of Intentionality

Canadian Journal of Philosophy ◽

10.1080/00455091.1972.10716869 ◽

1972 ◽

Vol 2 (1) ◽

pp. 127-133

Author(s):

Harold Morick

Keyword(s):

Recent Literature ◽

Essential Property ◽

Sufficient Condition ◽

Conceptual Scheme ◽

Definition Of ◽

Necessary And Sufficient

In the last two decades, there has been a great deal of interest in providing an intentional criterion of the psychological. Of the various ones proferred, it seems to me that the best was the earliest, which was Chisholm’s initial criterion in his 1955 essay “Sentences about Believing.” In this present paper I first single out a basic misconception pervading the recent literature on intentionality and suggest that a consequence of this misconception has been the futile attempt to use the notion of intentionality to provide a kind of definition of “mind”; that is, to use intentionality to provide a necessary and sufficient condition for the psychological. Secondly, I point out how intentionality as captured by my own criterion is indispensable in that it is an essential property of certain particulars (persons) which are basic to our conceptual scheme and apparently basic to any conceptual scheme whatsoever.

On the Geometrical Representation of Classical Statistical Mechanics

10.26434/chemrxiv.7217819 ◽

2018 ◽

Author(s):

Georgios C. Boulougouris

Keyword(s):

Statistical Mechanics ◽

Parametric Representation ◽

Gauss Map ◽

Inner Product ◽

Thermodynamic State ◽

Classical Statistical Mechanics ◽

Geometrical Representation ◽

Definition Of ◽

Necessary And Sufficient

In this work a geometrical representation of equilibrium and near equilibrium statistical mechanics is proposed. Using a formalism consistent with the Bra-Ket notation and the definition of inner product as a Lebasque integral, we describe the macroscopic equilibrium states in classical statistical mechanics by “properly transformed probability Euclidian vectors” that point on a manifold of spherical symmetry. Furthermore, any macroscopic thermodynamic state “close” to equilibrium is described by a triplet that represent the “infinitesimal volume” of the points, the Euclidian probability vector at equilibrium that points on a hypersphere of equilibrium thermodynamic state and a Euclidian vector a vector on the tangent bundle of the hypersphere. The necessary and sufficient condition for such representation is expressed as an invertibility condition on the proposed transformation. Finally, the relation of the proposed geometric representation, to similar approaches introduced under the context of differential geometry, information geometry, and finally the Ruppeiner and the Weinhold geometries, is discussed. It turns out that in the case of thermodynamic equilibrium, the proposed representation can be considered as a Gauss map of a parametric representation of statistical mechanics.

On B- Covariant Derivative of First Order for Some Tensors in different Spaces

Journal of Mathematical Analysis and Modeling ◽

10.48185/jmam.v2i2.276 ◽

2021 ◽

Vol 2 (2) ◽

pp. 30-37

Author(s):

Alaa A. Abdallah ◽

A. A. Navlekar ◽

Kirtiwant P. Ghadle

Keyword(s):

Curvature Tensor ◽

Covariant Derivative ◽

Torsion Tensor ◽

Sufficient Condition ◽

First Order ◽

Recurrence Property ◽

In this paper, we study the relationship between Cartan's second curvature tensor $P_{jkh}^{i}$ and $(h) hv-$torsion tensor $C_{jk}^{i}$ in sense of Berwald. Moreover, we discuss the necessary and sufficient condition for some tensors which satisfy a recurrence property in $BC$-$RF_{n}$, $P2$-Like-$BC$-$RF_{n}$, $P^{\ast }$-$BC$-$RF_{n}$ and $P$-reducible-$BC-RF_{n}$.

Nilai Dasar Collaborative Governance Dalam Studi Kebijakan Publik

KOLABORASI JURNAL ADMINISTRASI PUBLIK ◽

10.26618/kjap.v6i3.2261 ◽

2020 ◽

Vol 6 (3) ◽

pp. 395-402

Author(s):

Nasrulhaq Nasrulhaq

Keyword(s):

Public Policy ◽

Resource Sharing ◽

Collaborative Governance ◽

Theoretical Studies ◽

Integrated Process ◽

Collective Leadership ◽

Essential Value ◽

Starting Point ◽

This paper examines the basic values of collaborative governance based on theoretical studies and empirical facts in an integrative manner. The starting point study of the relationship between stakeholders in each stage of public policy is increasingly complex. Based on this complexity, studies on governance also experience dynamics. The collaborative framework in governance provides a meaning that is more than just governance. Collaborative governance is a concept in public policy that has developed in the last few decades. In principle, the collaborative is different from the network as well as the partnership. There is an essential value attached to it. Henceforth, it becomes part of its characteristics. The basic values referred to are consensus orientation, collective leadership, multidirectional communication, and resource sharing. The four basic values are integrated into one integrated process in any collaborative governance action.

Artificial moral agents: an intercultural perspective

The International Review of Information Ethics ◽

10.29173/irie14 ◽

2007 ◽

Vol 7 ◽

pp. 129-134

Author(s):

Michael Nagenborg

Keyword(s):

Poor Countries ◽

Moral Agents ◽

Artificial Moral Agents ◽

Starting Point ◽

Different Types ◽

Good Starting Point ◽

Cultural Dialogue ◽

Definition Of ◽

The Impact ◽

In this paper I will argue that artificial moral agents (AMAs) are a fitting subject of intercultural information ethics because of the impact they may have on the relationship between information rich and information poor countries. I will give a limiting definition of AMAs first, and discuss two different types of AMAs with different implications from an intercultural perspective. While AMAs following preset rules might raise con-cerns about digital imperialism, AMAs being able to adjust to their user‘s behavior will lead us to the question what makes an AMA ?moral?? I will argue that this question does present a good starting point for an inter-cultural dialogue which might be helpful to overcome the notion of Africa as a mere victim.

Some results concerning frames in Banach spaces

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.38.2007.80 ◽

2007 ◽

Vol 38 (3) ◽

pp. 267-276 ◽

Cited By ~ 3

Author(s):

S. K. Kaushik

Keyword(s):

Finite Number ◽

Banach Spaces ◽

Necessary Condition ◽

Sufficient Condition ◽

Linearly Independent ◽

Banach Frame ◽

Minimal Sequence ◽

Definition Of ◽

Necessary And Sufficient

A necessary and sufficient condition for the associated sequence of functionals to a complete minimal sequence to be a Banach frame has been given. We give the definition of a weak-exact Banach frame, and observe that an exact Banach frame is weak-exact. An example of a weak-exact Banach frame which is not exact has been given. A necessary and sufficient condition for a Banach frame to be a weak-exact Banach frame has been obtained. Finally, a necessary condition for the perturbation of a retro Banach frame by a finite number of linearly independent vectors to be a retro Banach frame has been given.