scholarly journals On weighted Lebesgue function type sums

2007 ◽  
Vol 146 (2) ◽  
pp. 243-251
Author(s):  
Ying Guang Shi
1990 ◽  
Vol 55 (1-2) ◽  
pp. 135-141
Author(s):  
P. Vértesi

Machines ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 150
Author(s):  
Andrei Marius Mihalache ◽  
Gheorghe Nagîț ◽  
Laurențiu Slătineanu ◽  
Adelina Hrițuc ◽  
Angelos Markopoulos ◽  
...  

3D printing is a process that has become widely used in recent years, allowing the production of parts with relatively complicated shapes from metallic and non-metallic materials. In some cases, it is challenging to evaluate the ability of 3D printers to make fine details of parts. For such an assessment, the printing of samples showing intersections of surfaces with low angle values was considered. An experimental plan was designed and materialized to highlight the influence of different factors, such as the thickness of the deposited material layer, the printing speed, the cooling and filling conditions of the 3D-printed part, and the thickness of the sample. Samples using areas in the form of isosceles triangles with constant height or bases with the same length, respectively, were used. The mathematical processing of the experimental results allowed the determination of empirical mathematical models of the power-function type. It allowed the detection of both the direction of actions and the intensity of the influence exerted by the input factors. It is concluded that the strongest influence on the printer’s ability to produce fine detail, from the point of view addressed in the paper, is exerted by the vertex angle, whose reduction leads to a decrease in printing accuracy.


Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1409
Author(s):  
Jiawen Li ◽  
Yi Zhang ◽  
Zhenghong Jin

In this paper, the Singular-Polynomial-Fuzzy-Model (SPFM) approach problem and impulse elimination are investigated based on sliding mode control for a class of nonlinear singular system (NSS) with impulses. Considering two numerical examples, the SPFM of the nonlinear singular system is calculated based on the compound function type and simple function type. According to the solvability and the steps of two numerical examples, the method of solving the SPFM form of the nonlinear singular system with (and without) impulse are extended to the more general case. By using the Heine–Borel finite covering theorem, it is proven that a class of nonlinear singular systems with bounded impulse-free item (BIFI) properties and separable impulse item (SII) properties can be approximated by SPFM with arbitrary accuracy. The linear switching function and sliding mode control law are designed to be applied to the impulse elimination of SPFM. Compared with some published works, a human posture inverted pendulum model example and Example 3.2 demonstrate that the approximation error is small enough and that both algorithms are effective. Example 3.3 is to illustrate that sliding mode control can effectively eliminate impulses of SPFM.


2021 ◽  
Vol 37 ◽  
pp. 318-326
Author(s):  
Yuzhen Zhao ◽  
Dike Hu ◽  
Song Wu ◽  
Xinjun Long ◽  
Yongshou Liu

Abstract In this paper, the dynamics of axially functionally graded (AFG) conical pipes conveying fluid are analyzed. The materials are distributed along the conical pipe axis as a volume fraction function. Either the elastic modulus or the density of the AFG conical pipe is assumed to vary from the inlet to the outlet. The governing equation of the AFG conical pipe is derived using the Hamiltonian principle and solved by the differential quadrature method. The effects of the volume fraction index, volume fraction function type and reduction factor on the natural frequency and critical velocity are analyzed. It is found that for a power function volume fraction type, the natural frequency and critical velocity increase with increasing volume fraction index and clearly increase when the volume fraction index is within the range (0, 10). For an exponential function volume fraction type, the natural frequency and critical velocity change rapidly within the range (−10, 10), besides the above range the relationship between the natural frequency, critical velocity and volume fraction index is approximate of little change. The natural frequency and critical velocity decrease linearly with increasing reduction factor.


2021 ◽  
pp. 0271678X2110103
Author(s):  
Nao Hatakeyama ◽  
Miyuki Unekawa ◽  
Juri Murata ◽  
Yutaka Tomita ◽  
Norihiro Suzuki ◽  
...  

A variety of brain cells participates in neurovascular coupling by transmitting and modulating vasoactive signals. The present study aimed to probe cell type-dependent cerebrovascular (i.e., pial and penetrating arterial) responses with optogenetics in the cortex of anesthetized mice. Two lines of the transgenic mice expressing a step function type of light-gated cation channel (channelrhodopsine-2; ChR2) in either cortical neurons (muscarinic acetylcholine receptors) or astrocytes (Mlc1-positive) were used in the experiments. Photo-activation of ChR2-expressing astrocytes resulted in a widespread increase in cerebral blood flow (CBF), extending to the nonstimulated periphery. In contrast, photo-activation of ChR2-expressing neurons led to a relatively localized increase in CBF. The differences in the spatial extent of the CBF responses are potentially explained by differences in the involvement of the vascular compartments. In vivo imaging of the cerebrovascular responses revealed that ChR2-expressing astrocyte activation led to the dilation of both pial and penetrating arteries, whereas ChR2-expressing neuron activation predominantly caused dilation of the penetrating arterioles. Pharmacological studies showed that cell type-specific signaling mechanisms participate in the optogenetically induced cerebrovascular responses. In conclusion, pial and penetrating arterial vasodilation were differentially evoked by ChR2-expressing astrocytes and neurons.


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