Some Remarks on the Convergence of Sequences of Functions of Polynomial Type in W p 1 (G) Spaces

Author(s):  
V. P. Il’in
2021 ◽  
Vol 40 (3) ◽  
pp. 5517-5526
Author(s):  
Ömer Kişi

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.


Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-19
Author(s):  
Jingxia Wang ◽  
Qingchun Yu

Karst is a central focus in the field of carbonate reservoir geology. Fracture dissolution enlargement is an important mechanism for the formation of high-quality reservoirs. This study performed four carbonate fracture dissolution enlargement (CFDE) experiments under a confining pressure of 20 MPa, and temperatures ranged from 40 to 60°C. CO2-saturated deionized water was injected into artificial carbonate fractures at approximately 11.5 ml/h for 96, 208, 216, and 216 hours. The water flowing out of the fractures was sampled every 8 h to monitor the concentration of Ca2+. SEM photomicrographs and 3D laser scanning images were taken before and after the CFDE experiments to observe the dissolution process of the fracture surfaces. After the CFDE experiment, the hydraulic apertures (Bh) of sample 1 (S1), sample 3 (S3), and sample 4 (S4) were enlarged by 3.4, 1.4, and 1.2 times, respectively. The aperture of sample 2 (S2) was slightly reduced in the early stage of the experiment. The experimental results of this study demonstrate that Bh can be divided into three categories as a function of time: S type, logarithmic type, and polynomial type. The laboratory dissolution rate of S1, S2, S3, and S4 were 2.50 × 10−6, 3.11 × 10−6, 2.70 × 10−6, and 3.04 × 10−6 mol/m2/s. The pattern of fracture dissolution is closely related to the Peclet and Damkohler numbers. The dissolution processes of high Peclet and Damkohler numbers lead to a pattern of obvious channelization. The Peclet and Damkohler numbers of the S3 CFDE experiment were the highest, and the channelizing dissolution is the most notable in S3 of the four fractures. A dissolution process at low temperature has a higher Peclet number and thus leads to obvious channelizing dissolution. Mineral heterogeneities in the rock also play a significant role in channelizing dissolution. A preferential channel typically develops in places where bioclasts are accumulated or the calcite veins are distributed.


2013 ◽  
Vol 554-557 ◽  
pp. 2440-2452 ◽  
Author(s):  
Hirotaka Kano ◽  
Jiro Hiramoto ◽  
Toru Inazumi ◽  
Takeshi Uemori ◽  
Fusahito Yoshida

Yoshida-Uemori model (Y-U model) can be used with any types of yield functions. The calculated stress strain response will be, however, different depending on the chosen yield function if the yield function and the effective strain definition are inappropriate. Thus several modifications to Y-U model were proposed in the 10th International Conference on Technology of Plasticity. It was ascertained that in the modified Y-U model, the same set of material parameters can be used with von Mises, Hill’s 1948, and Hill’s 1990 yield function. In this study, Yld2000-2d and Yoshida’s 6th-order polynomial type 3D yield function were examined and it was clarified that the same set of Y-U parameters can be used with these yield functions.


2004 ◽  
Vol 41 (A) ◽  
pp. 231-238
Author(s):  
N. H. Bingham ◽  
H. R. Nili Sani

The paper studies convergence of sequences of negatively associated random variables under various summability methods. The results extend previously known results for independence and complement known results forϕ-mixing.


2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
M. De la Sen

This paper discusses the properties of convergence of sequences to limit cycles defined by best proximity points of adjacent subsets for two kinds of weak contractive cyclic maps defined by composite maps built with decreasing functions with either the so-calledr-weaker Meir-Keeler orr,r0-stronger Meir-Keeler functions in generalized metric spaces. Particular results about existence and uniqueness of fixed points are obtained for the case when the sets of the cyclic disposal have a nonempty intersection. Illustrative examples are discussed.


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