scholarly journals Unification Theories: New Results and Examples

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 60 ◽  
Author(s):  
Florin F. Nichita

This paper is a continuation of a previous article that appeared in AXIOMS in 2018. A Euler’s formula for hyperbolic functions is considered a consequence of a unifying point of view. Then, the unification of Jordan, Lie, and associative algebras is revisited. We also explain that derivations and co-derivations can be unified. Finally, we consider a “modified” Yang–Baxter type equation, which unifies several problems in mathematics.

1930 ◽  
Vol 3 (1) ◽  
pp. 22-23
Author(s):  
F. Kirchhof

Abstract A previous article of mine entitled “Observations on Color Reactions of Rubber and Gutta-Percha” has led to the question whether intensely colored reaction products which are obtained by fusion of phenols with bromides of hydrocarbons give characteristic absorption spectra. I have carried out a few preliminary experiments on this subject, which appear to confirm my earlier point of view that the cause of the different colorations is to be found in dispersion color reactions. It is well known that when rubber bromide or gutta-percha bromide is suspended in carbon tetrachloride and is heated with phenol until the carbon tetrachloride is eliminated, a red-violet to blue fusion mixture is obtained, which gives colors of various stabilities depending upon the solvent into which the fusion mixture is dropped. Thus the blue and violet colorations in chloroform are stable for some time, but they change gradually to green and then to brown, with separation of a flocculent precipitate. Yellow-brown reaction products (hydroxyphenylhydrorubber and gutta-percha) are however obtained in the presence of catalysts (iron, aluminum chloride) or by the action of alkalies (NH3, KOH) or by pouring the blue-violet fusion mixtures into ether.


2012 ◽  
Vol 46 (2) ◽  
Author(s):  
Adriaan L. Rheeder

In ’n vorige artikel is beredeneer dat die grammaties-historiese metode van Skrifuitleg as kreatuurlike geskrif nie meer voldoende is vir alleengebruik in Skrifvertolking nie en dat dit met ander uitgangspunte aangevul moet word. In aansluiting by twee hermeneutiese uitgangspunte wat in ’n vorige artikel behandel is (Rheeder), word in hierdie artikel ’n verdere drie hermeneutiese vertrekpunte bespreek, naamlik teenkultuur, nie-wetenskaplike skopus en moreel-etiese vertolking. Die teenkulturele vertrekpunt gaan uit van die oortuiging dat outentieke getuienis in die Skrif gevind word in dit wat verskil (afwyk) van die omliggende antieke kultuur, terwyl die nie-wetenskaplike skopus vertrekpunt uit gaan van die standpunt dat wetenskaplike (of empiriese) kennis in die Bybel buite die skopus of bedoeling van die Skrif staan. Die moreel-teologiese vertolking as vertrekpunt van die standpunt uitgaan dat ’n moreel-teologiese beoordeling van liefde die keuse tussen twee konflikterende, maar beide aanvaarbare, interpretasies moet begelei. Daar word tot die gevolgtrekking gekom dat ’n etiese verstaan van die posisie van die vrou beteken dat die vrou as gelykwaardig aan die man beskou en so behandel moet word, wat beteken dat die vrou, net soos die man, tot enige amp in die kerk toegelaat mag word.Appeal to Scriptures in the formation of an ethical point of view: An ethical understanding of women in the Bible. In a previous article it was argued that the grammatical-historical method  of  Bible  exposition  was  no  longer  sufficient  as  sole  method  and  should  be supplemented with other hermeneutical points of departure. Following the discussion of two hermeneutical points in a previous article (Rheeder), this article will discuss three other hermeneutical points of departure, namely counterculture, non-scientific scope and moral-ethical interpretation. The counter-cultural point of departure is based on the belief that authentic witness in Scripture is found in that which is different (that which deviates) from the surrounding ancient culture, while a non-scientific scope starts from the view that scientific (or empirical) knowledge in the Bible is outside the scope or intent of Scripture. The point of departure of the moral-theological interpretation is the view that a moral-theological evaluation of love should inform the choice between two conflicting but mutually acceptable interpretations. It is concluded that an ethical understanding of women in the Bible means that women should be regarded and treated as equal to men, which leads to the further conclusion that all offices in the church should be open to women.


2007 ◽  
Vol 18 (10) ◽  
pp. 1113-1132
Author(s):  
ZBIGNIEW BŁOCKI

For domains in ℝn we construct the Bergman kernel on the diagonal using solutions of the Dirichlet problem. Starting from this, in a natural way we obtain an algebra 𝔸n of dimension n(n - 1)/2 + 1 over ℝ and a class of holomorphic functions valued in 𝔸n. Of course 𝔸2 is the field of complex numbers, and it turns out that 𝔸3 is the algebra of quaternions, whereas for n ≥ 4, 𝔸n is non-associative. Holomorphic functions can be written as f + ω, where f is a (real-valued) function and ω a differential 2-form such that d* ω = df and dω = 0. We investigate the main properties of the obtained objects, especially from the analytic point of view.


2006 ◽  
Vol 2006 ◽  
pp. 1-13
Author(s):  
Jan Awrejcewicz ◽  
Yuriy Pyryev

The methods of both analysis and modeling of contact bush-shaft systems exhibiting heat generation and wear due to friction are presented [3–5]. From the mathematical point of view, the considered problem is reduced to the analysis of ordinary differential equations governing the change of velocities of the contacting bodies, and to the integral Volterra-type equation governing contact pressure behavior. In the case where tribological processes are neglected, thresholds of chaos are detected using bifurcation diagrams and Lyapunov exponents identification tools. In addition, analytical Mel'nikov's method is applied to predict chaos. It is shown, among the others, that tribological processes play a stabilizing role. The following theoretical background has been used in the analysis: perturbation methods, Mel'nikov's techniques [7,8], Laplace transformations, the theory of integral equations, and various variants of numerical analysis.


2016 ◽  
Vol 2016 ◽  
pp. 1-15
Author(s):  
Qing Meng ◽  
Bin He

The generalized HD type equation is studied by using the bifurcation method of dynamical systems. From a dynamic point of view, the existence of different kinds of traveling waves which include periodic loop soliton, periodic cusp wave, smooth periodic wave, loop soliton, cuspon, smooth solitary wave, and kink-like wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given. Also, all possible exact parametric representations of the bounded waves are presented and their relations are stated.


2004 ◽  
Vol 6 (2) ◽  
pp. 56-68
Author(s):  
Haruko Sakaedani

In a previous article I have examined shifts of noun phrase forms in Qur'anic narrative texts and found that this kind of shift is strictly associated with the construction of texts and development of stories. It was also found that other categories such as voice, aspect and tense are connected with the shifts of these noun phrase forms. In the present paper I first confirm the argument made in my previous paper: that forms of noun phrases are markers of point of view in narratives. Next, the correlations between these noun phrase forms and various verb forms are inquired into, and the effect of using different noun phrase forms and verb forms in the texts is discussed. The argument is restricted to narratives because these realise textual coherence more than the early fragmentary revelations, and because the points of view in these narratives can be examined through the various persons coming into the stories. In addition, this study focuses on definite noun phrases rather than indefinite ones as, other than when they are first introduced into the texts, the referents in these stories are referred to with definite noun phrases, or more strictly speaking, a number of prophets and other famous persons are frequently introduced with definite noun phrases.


2020 ◽  
Author(s):  
Katharina Schmidt ◽  
Lucie Tajmanova ◽  
Lyudmila Khakimova

<p>Preservation of mechanically-controlled microstructures can help us to unravel the long-term stress state in geological materials. To better understand the stress state in such a microstructure, we need to quantify the processes in a coupled, chemo-mechanical, point of view. One of such a mechanically-controlled microstructure is oscillatory zoning in high-temperature metamorphic rocks. The presented example is a sharp zoned plagioclase of 150 x 200 µm size with thin compositional lamellae of 1-10 µm alternating from the core towards the rim. This microstructure is interpreted to be mechanically-controlled, since conventional diffusion failed to preserve the observed microstructure within timescales that would be reasonable from a regional geology point of view. In contrast, considering that chemical diffusion is coupled to mechanical deformation the observed zoning can be maintained over the geologically-relevant timescales.</p><p>Despite of the recent valuable progress in our understanding of these microstructures, the mechanisms controlling its evolution from slowly cooled rocks are still not complete. Here, we numerically investigate the coupled, chemo-mechanical, effect that generates oscillatory zones mechanically maintained over geologically relevant timescales. We test the possibility of modelling oscillatory zoning in minerals that is similar to the exsolution process. We apply a classical Cahn-Hilliard-type equation where we add more complexity considering the impact of deformation during the process.</p>


1990 ◽  
Vol 4 (1) ◽  
pp. 49-52
Author(s):  
Charles Fairley

As a companion to the previous article this article considers the role of licensing from the point of view of SMEs to show how the identification and uptake of licences can be improved and how licence or technology providers can help this process.


2019 ◽  
Vol 65 ◽  
pp. 294-308x ◽  
Author(s):  
Bruno Bouchard ◽  
Ki Wai Chau ◽  
Arij Manai ◽  
Ahmed Sid-Ali

We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear reaction/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching processes based algorithm of [8]. Our numerical experiments show that approximating the discontinuous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results.


Author(s):  
Daniela Maccario

In order to define teaching principles to be adopted to support learning in Mathematics and Italian in primary school classes starting from the use of Fenix Program, the research was aimed at increasing the knowledge base available through the recognition of good teaching practices from the point of view of teachers in the form of professional routines. In a previous article (Maccario, 2016) we described some findings on the criteria that you can follow in the development of teaching sequences. This article presents a further order of the results concerning the dialogic-discursive structures that represent an important dimension of teaching mediation in accordance with the operational perspective of teachers. Also in this case it is phenomenology which refers to the practical knowledge as a source to be exploited for the construction of teaching principles and scientifically based knowledge in Didactics.


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