scholarly journals Weak Slice Regular Functions on the n-Dimensional Quadratic Cone of Octonions

2021 ◽  
Author(s):  
Xinyuan Dou ◽  
Guangbin Ren ◽  
Irene Sabadini ◽  
Ting Yang
Keyword(s):  
Complex Plane ◽  
Taylor Expansion ◽  
Complex Structure ◽  
Quadratic Cone ◽  
Axially Symmetric ◽  
Slice Regular Functions ◽  
New Class ◽  
Regular Functions ◽  
The One ◽  
Class Of Functions

AbstractIn the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the same complex structure of the complex plane), the second one makes use of stem and slice functions. So far, in the setting of several hypercomplex variables, only the second approach has been considered, i.e. the one based on stem functions. In this paper, we use instead the first definition on the so-called n-dimensional quadratic cone of octonions. These two approaches yield the same class of slice regular functions on axially symmetric slice-domains, however, they are different on other types of domains. We call this new class of functions weak slice regular. We show that there exist weak slice regular functions which are not slice regular in the second approach. Moreover, we study various properties of these functions, including a Taylor expansion.

scholarly journals A New Approach to Slice Analysis Via Slice Topology

2021 ◽  
Vol 31 (5) ◽  
Author(s):  
Xinyuan Dou ◽  
Ming Jin ◽  
Guangbin Ren ◽  
Irene Sabadini
Keyword(s):  
Taylor Expansion ◽  
Regular Function ◽  
Alternative Algebra ◽  
Representation Formula ◽  
Monogenic Functions ◽  
Slice Regular Functions ◽  
New Approach ◽  
Regular Functions ◽  
Several Variables ◽  
Slice Monogenic Functions

AbstractIn this paper we summarize some known facts on slice topology in the quaternionic case, and we deepen some of them by proving new results and discussing some examples. We then show, following Dou et al. (A representation formula for slice regular functions over slice-cones in several variables, arXiv:2011.13770, 2020), how this setting allows us to generalize slice analysis to the general case of functions with values in a real left alternative algebra, which includes the case of slice monogenic functions with values in Clifford algebra. Moreover, we further extend slice analysis, in one and several variables, to functions with values in a Euclidean space of even dimension. In this framework, we study the domains of slice regularity, we prove some extension properties and the validity of a Taylor expansion for a slice regular function.

scholarly journals Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions

2021 ◽  
Vol 8 (1) ◽  
pp. 90-113
Author(s):  
Florian-Horia Vasilescu
Keyword(s):  
Clifford Algebra ◽  
Complex Plane ◽  
Functional Calculus ◽  
Clifford Algebras ◽  
Cauchy Type ◽  
Analytic Functional ◽  
Slice Regular Functions ◽  
Regular Functions

Abstract The main purpose of this work is the construction of an analytic functional calculus for Clifford operators, which are operators acting on certain modules over Clifford algebras. Unlike in some preceding works by other authors, we use a spectrum defined in the complex plane, and also certain stem functions, analytic in neighborhoods of such a spectrum. The replacement of the slice regular functions, having values in a Clifford algebra, by analytic stem functions becomes possible because of an isomorphism induced by a Cauchy type transform, whose existence is proved in the first part of this work.

scholarly journals Spherical Coefficients of Slice Regular Functions

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Amedeo Altavilla
Keyword(s):  
Differential Equations ◽  
Regular Function ◽  
Countable Family ◽  
Slice Regular Functions ◽  
Regular Functions ◽  
Spherical Expansion ◽  
Derivatives Of

AbstractGiven a quaternionic slice regular function f, we give a direct and effective way to compute the coefficients of its spherical expansion at any point. Such coefficients are obtained in terms of spherical and slice derivatives of the function itself. Afterwards, we compare the coefficients of f with those of its slice derivative $$\partial _{c}f$$ ∂ c f obtaining a countable family of differential equations satisfied by any slice regular function. The results are proved in all details and are accompanied to several examples. For some of the results, we also give alternative proofs.

DEVELOPMENT OF A MODEL FOR DECISION SUPPORT SYSTEMS FOR MANAGING THE PROCESS OF INVESTING IN CYBERSECURITY TAKING INTO ACCOUNT MULTIFACTORIALITY

2021 ◽  
Vol 75 (3) ◽  
pp. 70-75
Author(s):  
B.E. Yagaliyeva ◽  
◽  
B.B. Akhmetov ◽  
V.A. Lakhno ◽  
G.S. Zhilkishbayeva ◽  
...  
Keyword(s):  
Information Technologies ◽  
Complex Structure ◽  
Multidimensional Space ◽  
Simulation Environment ◽  
Matlab Simulation ◽  
Program Code ◽  
New Class ◽  
Multistage Games ◽  
The Difference ◽  
Investment Process

A model for managing the investment process is proposed, based on the example of investing in cybersecurity of national scale informatization objects, taking into account the multifactorial nature of this process. The difference between this model and those previously developed is that, firstly, it considers the investment process as a complex structure, for which it is not enough to model it as a one-factor category. Second, our model is based on the solution of a bilinear multi-step quality game with several terminal surfaces. The solution is obtained within the framework of the scheme of a new class of bilinear multistage games describing the interaction of objects in a multidimensional space. Consideration of the investment process in such a setting makes it possible to adequately describe the process of searching for rational strategies of players in the course of investing in information technologies. The study made it possible to implement the program code of the model in the MatLab simulation environment.

scholarly journals Methyl phenlactonoates are efficient strigolactone analogs with simple structure

2017 ◽  
Vol 69 (9) ◽  
pp. 2319-2331 ◽  
Author(s):  
Muhammad Jamil ◽  
Boubacar A Kountche ◽  
Imran Haider ◽  
Xiujie Guo ◽  
Valentine O Ntui ◽  
...  
Keyword(s):  
Mycorrhizal Fungi ◽  
Simple Structure ◽  
Complex Structure ◽  
Arbuscular Mycorrhizal ◽  
Structural Diversity ◽  
Striga Hermonthica ◽  
Biological Processes ◽  
Structural Modifications ◽  
New Class ◽  
Agricultural Applications

abstract Strigolactones (SLs) are a new class of phytohormones that also act as germination stimulants for root parasitic plants, such as Striga spp., and as branching factors for symbiotic arbuscular mycorrhizal fungi. Sources for natural SLs are very limited. Hence, efficient and simple SL analogs are needed for elucidating SL-related biological processes as well as for agricultural applications. Based on the structure of the non-canonical SL methyl carlactonoate, we developed a new, easy to synthesize series of analogs, termed methyl phenlactonoates (MPs), evaluated their efficacy in exerting different SL functions, and determined their affinity for SL receptors from rice and Striga hermonthica. Most of the MPs showed considerable activity in regulating plant architecture, triggering leaf senescence, and inducing parasitic seed germination. Moreover, some MPs outperformed GR24, a widely used SL analog with a complex structure, in exerting particular SL functions, such as modulating Arabidopsis roots architecture and inhibiting rice tillering. Thus, MPs will help in elucidating the functions of SLs and are promising candidates for agricultural applications. Moreover, MPs demonstrate that slight structural modifications clearly impact the efficiency in exerting particular SL functions, indicating that structural diversity of natural SLs may mirror a functional specificity.

scholarly journals A note on weakly θ-continuous functions

1989 ◽  
Vol 12 (1) ◽  
pp. 9-13 ◽  
Author(s):  
M. Mrševic ◽  
I. L. Reilly
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
Topological Spaces ◽  
New Class ◽  
Weakly Continuous ◽  
Class Of Functions

Recently a new class of functions between topological spaces, called weaklyθ-continuous functions, has been introduced and studied. In this paper we show how an appropriate change of topology on the domain of a weaklyθ-continuous function reduces it to a weakly continuous function. This paper examines some of the consequences of this result.

Intermolecular Interactions of Xe Atoms Confined in One-dimensional Nanochannels of Tris(o-phenylenedioxy)cyclotriphosphazene as Studied by High-pressure 129Xe NMR

2003 ◽  
Vol 58 (12) ◽  
pp. 727-734 ◽  
Author(s):  
Hirokazu Kobayashi ◽  
Takahiro Ueda ◽  
Keisuke Miyakubo ◽  
Taro Eguchi
Keyword(s):  
High Pressure ◽  
Nmr Spectroscopy ◽  
Chemical Shift ◽  
Pressure Dependence ◽  
Average Distance ◽  
Chemical Shift Tensor ◽  
Axially Symmetric ◽  
One Dimensional ◽  
129Xe Nmr ◽  
The One

The pressure dependence of the 129Xe chemical shift tensor confined in the Tris(o-phenylenedioxy) cyclotriphosphazene (TPP) nanochannel was investigated by high-pressure 129Xe NMR spectroscopy. The observed 129Xe spectrum in the one-dimensional TPP nanochannel (0.45 nm in diameter) exhibits a powder pattern broadened by an axially symmetric chemical shift tensor. As the pressure increases from 0.02 to 7.0 MPa, a deshielding of 90 ppm is observed for the perpendicularcomponent of the chemical shift tensor δ⊥, whereas a deshielding of about 30 ppm is observed for the parallel one, δ‖. This suggests that the components of the chemical shift tensor, δ‖ and δ⊥, are mainly dominated by the Xe-wall and Xe-Xe interaction, respectively. Furthermore, the effect of helium, which is present along with xenon gas, on the 129Xe chemical shift is examined in detail. The average distance between the Xe atoms in the nanochannel is estimated to be 0.54 nm. This was found by using δ⊥ at the saturated pressure of xenon, and comparing the increment of the chemicalshift value in δ⊥ to that of a β -phenol/Xe compound.

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