scholarly journals Multiplicative Dirac System

2021 ◽  
Author(s):  
Tuba Gulsen ◽  
◽  
Emrah Yılmaz ◽  
Sertac Goktas ◽  
◽  
...  
Keyword(s):  
Asymptotic Estimates ◽  
Dirac System ◽  
Algebraic Structures ◽  
Fundamental Properties ◽  
Multiplicative Calculus

We define a Dirac system in multiplicative calculus by some algebraic structures. Asymptotic estimates for eigenfunctions of the multiplicative Dirac system are obtained. Eventually, some fundamental properties of the multiplicative Dirac system are examined in detail.

scholarly journals A New Type of Sturm-Liouville Equation in the Non-Newtonian Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Sertac Goktas
Keyword(s):  
Liouville Equation ◽  
Spectral Properties ◽  
Liouville Problem ◽  
Mathematical Physics ◽  
Asymptotic Estimates ◽  
One Dimensional ◽  
Multiplicative Calculus ◽  
New Type ◽  
Sturm Liouville ◽  
The One

In mathematical physics (such as the one-dimensional time-independent Schrödinger equation), Sturm-Liouville problems occur very frequently. We construct, with a different perspective, a Sturm-Liouville problem in multiplicative calculus by some algebraic structures. Then, some asymptotic estimates for eigenfunctions of the multiplicative Sturm-Liouville problem are obtained by some techniques. Finally, some basic spectral properties of this multiplicative problem are examined in detail.

scholarly journals On the Theory of Left/Right Almost Groups and Hypergroups with their Relevant Enumerations

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1828
Author(s):  
Christos G. Massouros ◽  
Naveed Yaqoob
Keyword(s):  
Neutral Element ◽  
Algebraic Structures ◽  
Fundamental Properties ◽  
Algebraic Properties ◽  
Left And Right ◽  
Definition Of ◽  
The Right ◽  
Weak Commutativity

This paper presents the study of algebraic structures equipped with the inverted associativity axiom. Initially, the definition of the left and the right almost-groups is introduced and afterwards, the study is focused on the more general structures, which are the left and the right almost-hypergroups and on their enumeration in the cases of order 2 and 3. The outcomes of these enumerations compared with the corresponding in the hypergroups reveal interesting results. Next, fundamental properties of the left and right almost-hypergroups are proved. Subsequently, the almost hypergroups are enriched with more axioms, like the transposition axiom and the weak commutativity. This creates new hypercompositional structures, such as the transposition left/right almost-hypergroups, the left/right almost commutative hypergroups, the join left/right almost hypergroups, etc. The algebraic properties of these new structures are analyzed and studied as well. Especially, the existence of neutral elements leads to the separation of their elements into attractive and non-attractive ones. If the existence of the neutral element is accompanied with the existence of symmetric elements as well, then the fortified transposition left/right almost-hypergroups and the transposition polysymmetrical left/right almost-hypergroups come into being.

Metastable Defects in the Amorphous Silicon-Germanium Alloys

2003 ◽  
Vol 762 ◽  
Author(s):  
J. David Cohen
Keyword(s):  
Amorphous Silicon ◽  
Silicon Germanium ◽  
Dangling Bonds ◽  
Annealing Behavior ◽  
Fundamental Properties ◽  
Silicon Materials ◽  
Salient Features ◽  
The Individual ◽  
Amorphous Silicon Germanium ◽  
Silicon Germanium Alloys

AbstractThis paper first briefly reviews a few of the early studies that established some of the salient features of light-induced degradation in a-Si,Ge:H. In particular, I discuss the fact that both Si and Ge metastable dangling bonds are involved. I then review some of the recent studies carried out by members of my laboratory concerning the details of degradation in the low Ge fraction alloys utilizing the modulated photocurrent method to monitor the individual changes in the Si and Ge deep defects. By relating the metastable creation and annealing behavior of these two types of defects, new insights into the fundamental properties of metastable defects have been obtained for amorphous silicon materials in general. I will conclude with a brief discussion of the microscopic mechanisms that may be responsible.

Fundamental Properties of Nanocellulose

2014 ◽  
Vol 68 (8) ◽  
pp. 837-840
Author(s):  
Tsuguyuki Saito ◽  
Yuri Kobayashi ◽  
Shuji Fujisawa ◽  
Chun-Nan Wu ◽  
Akira Isogai
Keyword(s):  
Fundamental Properties

Fundamental Properties of Surface Modified Pulp Sheet

2018 ◽  
Vol 72 (7) ◽  
pp. 715-720
Author(s):  
Yukinori Kobayashi ◽  
Yasutomo Noishiki ◽  
Manabu Yamamoto
Keyword(s):  
Fundamental Properties ◽  
Surface Modified

FUNDAMENTAL PROPERTIES OF ELECTRICAL WIRING TOROIDAL CURRENT STRUCTURES.

2019 ◽  
Vol 1 (61) ◽  
pp. 13-17
Author(s):  
E.A. Grigoriev
Keyword(s):  
Fundamental Properties ◽  
Electrical Wiring

SOME ALGEBRAIC STRUCTURES ON MAX-MAX, MIN-MIN COMPOSITIONS OVER INTUITIONISTIC FUZZY MATRICES

2020 ◽  
Vol 9 (8) ◽  
pp. 5683-5691
Author(s):  
T. Muthuraji ◽  
K. Lalitha
Keyword(s):  
Algebraic Structures ◽  
Intuitionistic Fuzzy
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