scholarly journals The motivated unmotivated: Variation, function and context

2020 ◽  
pp. 305-332
Author(s):  
Hendrik De Smet
Keyword(s):  
Variation Function

Geometric‐Mean Variation Function for H2+

1969 ◽  
Vol 50 (8) ◽  
pp. 3642-3644 ◽  
Author(s):  
Stanley R. Radel ◽  
Ronnie Gorman ◽  
Carol Cutler ◽  
Luis Kahn
Keyword(s):  
Geometric Mean ◽  
Variation Function

THE EFFECT OF THE WEYL FRACTIONAL INTEGRAL ON FUNCTIONS

Fractals ◽  
2021 ◽  
Author(s):  
XIA TING ◽  
CHEN LEI ◽  
LUO LING ◽  
WANG YONG
Keyword(s):  
Linear Relationship ◽  
Bounded Variation ◽  
Fractional Integral ◽  
Continuous Functions ◽  
Fractional Integrals ◽  
Hölder Condition ◽  
Weierstrass Function ◽  
Variation Function ◽  
Weyl Fractional Integral

This paper mainly discusses the influence of the Weyl fractional integrals on continuous functions and proves that the Weyl fractional integrals can retain good properties of many functions. For example, a bounded variation function is still a bounded variation function after the Weyl fractional integral. Continuous functions that satisfy the Holder condition after the Weyl fractional integral still satisfy the Holder condition, furthermore, there is a linear relationship between the order of the Holder conditions of the two functions. At the end of this paper, the classical Weierstrass function is used as an example to prove the above conclusion.

scholarly journals Entanglement Control of Two-Level Atoms in Dissipative Cavities

2020 ◽  
Vol 10 (4) ◽  
pp. 1510
Author(s):  
Reyad Salah ◽  
Ahmed M. Farouk ◽  
Ahmed Farouk ◽  
Mahmoud Abdel-Aty ◽  
Hichem Eleuch ◽  
...  
Keyword(s):  
Time Variation ◽  
System State ◽  
Radio Waves ◽  
Cavity Field ◽  
Mathematical Procedure ◽  
Precise Information ◽  
Variation Function ◽  
Field Decay ◽  
State Death ◽  
Degree Of Entanglement

An open quantum bipartite system consisting of two independent two-level atoms interacting nonlinearly with a two-mode electromagnetic cavity field is investigated by proposing a suitable non-Hermitian generalization of the Hamiltonian. The mathematical procedure of obtaining the corresponding wave function of the system is clearly given. Pancharatnam phase is studied to give a precise information about the required initial system state, which is related to artificial phase jumps, to control the degree of entanglement (DEM) and get the highest concurrence. We discuss the effect of time-variation coupling, and dissipation of both atoms and cavity. The effect of the time-variation function appears as frequency modulation (FM) effect in the radio waves. Concurrence rapidly reaches the disentangled state (death of entanglement) by increasing the effect of field decay. On the contrary, the atomic decay has no effect.

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