scholarly journals On (L,M)-Double Fuzzy Filter Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
A. A. Abd El-Latif ◽  
H. Aygün ◽  
V. Çetkin
Keyword(s):  
Second Order ◽  
Fuzzy Filter ◽  
Topological Category ◽  
Filter Base ◽  
Fundamental Properties ◽  
Filter Structures ◽  
The Given ◽  
Order Image

We give in this paper the definitions of (L,M)-double fuzzy filter base and (L,M)-double fuzzy filter structures where L and M are strictly two-sided commutative quantales, and we also investigate the relations between them. Moreover, we propose second-order image and preimage operators of (L,M)-double fuzzy filter base and study some of its fundamental properties. Finally, we handle the given structures in the categorical aspect. For instance, we show that the category (L,M)-DFIL of (L,M)-double fuzzy filter spaces and filter maps between these spaces is a topological category over the category SET.

Measurements of second order image aberrations of a sector magnet

1981 ◽  
Vol 187 (1) ◽  
pp. 75-79 ◽  
Author(s):  
G. Moritz ◽  
U. Czok ◽  
H. Wollnik
Keyword(s):  
Second Order ◽  
Order Image

Second-order image aberration correction of double-focusing mass spectrometers by electrostatic hexapole lens

1978 ◽  
Vol 152 (2-3) ◽  
pp. 407-414 ◽  
Author(s):  
Shunroku Taya ◽  
Hiroshi Hirose ◽  
Hitoshi Tsuyama ◽  
Hisashi Matsuda
Keyword(s):  
Second Order ◽  
Aberration Correction ◽  
Mass Spectrometers ◽  
Double Focusing ◽  
Order Image

SURFACE-COVERED 1×3 GRATING WITH DIELECTRIC-METAL SLABS UNDER SECOND BRAGG INCIDENCE

2020 ◽  
Vol 27 (09) ◽  
pp. 1950201
Author(s):  
CHEN FU ◽  
BO WANG ◽  
WENHUA ZHU ◽  
KUNHUA WEN ◽  
ZIMING MENG ◽  
...  
Keyword(s):  
Incident Light ◽  
Polarized Light ◽  
Transverse Magnetic ◽  
Second Order ◽  
Bragg Angle ◽  
Efficiency Ratio ◽  
First Order ◽  
Rigorous Coupled Wave Analysis ◽  
Rigorous Coupled Wave ◽  
The Given

This paper designed a novel three-port reflective surface-covered grating with a connecting layer. The grating can be used as a splitter, and the polarized light can be divided into zero order, first order and second order. Through rigorous coupled-wave analysis, the efficiency of the three orders of diffraction light is close to 33% under the condition that the incident light at 1550 nm is incident at the second Bragg angle and the given duty cycle is 0.5. The efficiency and bandwidth of the surface-covered grating are improved compared with that of the surface-relief grating reported in the past. Especially for transverse magnetic polarized light, the beam splitting effect is more uniform, the efficiency ratio of the zeroth order to first order can reach 1.01, and the efficiency ratio of the first order to second order can reach 1.

scholarly journals Sampled-Data-Based Adaptive Group Synchronization of Second-Order Nonlinear Complex Dynamical Networks with Time-Varying Delays

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Bo Liu ◽  
Jiahui Bai ◽  
Yue Zhao ◽  
Chao Liu ◽  
Xuemin Yan ◽  
...  
Keyword(s):  
Adaptive Strategy ◽  
Second Order ◽  
Complex Dynamical Networks ◽  
Time Varying ◽  
Sampled Data ◽  
Dynamical Networks ◽  
Coupling Strengths ◽  
Simulation Results ◽  
Group Synchronization ◽  
The Given

This paper studies the adaptive group synchronization of second-order nonlinear complex dynamical networks with sampled-data and time-varying delays by designing a new adaptive strategy to feedback gains and coupling strengths. According to Lyapunov stability properties, it is shown that the agents of subgroups can converge the given synchronous states, respectively, under some conditions on the sampled period. Moreover, some simulation results are given.

Uniformly almost periodic solutions of non-linear differential equations of the second order I. General exposition

1955 ◽  
Vol 51 (4) ◽  
pp. 604-613
Author(s):  
Chike Obi
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Almost Periodic ◽  
Non Linear ◽  
Independent Variable ◽  
Linear Differential ◽  
The Given ◽  
Analytical Expressions

1·1. A general problem in the theory of non-linear differential equations of the second order is: Given a non-linear differential equation of the second order uniformly almost periodic (u.a.p.) in the independent variable and with certain disposable constants (parameters), to find: (i) the non-trivial relations between these parameters such that the given differential equation has a non-periodic u.a.p. solution; (ii) the number of periodic and non-periodic u.a.p. solutions which correspond to each such relation; and (iii) explicit analytical expressions for the u.a.p. solutions when they exist.

scholarly journals Riesz Inequality for the System of Root Functions of Second Order Ordinary Differential Operator

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Differential Operator ◽  
Sufficient Conditions ◽  
Second Order ◽  
Ordinary Differential Operator ◽  
Root Functions ◽  
Riesz Property ◽  
System Of Root Functions ◽  
The Given ◽  
Riesz Inequality

An ordinary differential operator of second order with coefficients is considered. The Riesz property of the system of root functions of the given operator is studied. The criterion of Bessel property in 2 L , of root functions system is established and use it to obtain sufficient conditions for the Riesz property of a system of normalized root functions of this operator in p L .

scholarly journals Action Function Formulation for Conservative Systems with Second-Order Lagrangian

2018 ◽  
Vol 10 (4) ◽  
pp. 50
Author(s):  
Ola Jarabah
Keyword(s):  
Lagrange Equation ◽  
Equations Of Motion ◽  
Second Order ◽  
Action Function ◽  
Time Integral ◽  
Function Formulation ◽  
Conservative Systems ◽  
The Given

The Euler Lagrange equation is studied to obtain the equations of motion for conservative systems with second order Lagrangian. The solutions of these equations are substituted in the given Lagrangian. The action function is then derived by calculating the time integral of the Lagrangian. To explain the application of our formalism two examples are discussed.

Synthesis and Optimization of Transient Performances for Underdamped Second-Order Linear System Based on the Switching Control Strategy

2012 ◽  
Author(s):  
Qingyu Su ◽  
Georgi M. Dimirovski ◽  
Jun Zhao
Keyword(s):  
Linear System ◽  
Control Strategy ◽  
Optimization Problems ◽  
Switching Control ◽  
Second Order ◽  
Order Linear ◽  
Output Response ◽  
Special Cases ◽  
Switching Control Strategy ◽  
The Given

In this paper, the synthesis and optimization problems of the transient performances, such as overshoot and setting time, of the output response with respect to a step signal for an under-damped second-order linear system are studied. The traditional control strategy and the switching control strategy are used, respectively. Our control objective is twofold: Objective 1 is to ensure that the overshoot of the system output does not violate the given safety bound and objective 2 is to ensure that the settling time is smaller than the given allowable time. The obtained results indicate that the switching control strategy has main two evident advantages: firstly, the switching proportional controllers can take advantages of both the quick response and the small overshoot of the output response. Secondly, the switching controller is always available, while the single proportional controller is available in some special cases. Finally, an example of servomotor is given to demonstrate the effectiveness of the proposed method.

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