Nonlinear critical problems for the biharmonic operator with Hardy potential

2014 ◽  
Vol 54 (1) ◽  
pp. 365-396 ◽  
Author(s):  
Lorenzo D’Ambrosio ◽  
Enrico Jannelli
Keyword(s):  
Biharmonic Operator ◽  
Hardy Potential ◽  
Critical Problems

Eigenvalues for a class of singular problems involving p(x)-Biharmonic operator and q(x)-Hardy potential

2019 ◽  
Vol 9 (1) ◽  
pp. 1130-1144 ◽  
Author(s):  
Abdelouahed El Khalil ◽  
Mohamed Laghzal ◽  
My Driss Morchid Alaoui ◽  
Abdelfattah Touzani
Keyword(s):  
Eigenvalue Problem ◽  
Real Number ◽  
Distance Function ◽  
Positive Real Number ◽  
Nonlinear Eigenvalue Problem ◽  
Biharmonic Operator ◽  
Hardy Potential ◽  
Positive Real ◽  
Singular Problems ◽  
Rellich Inequality

Abstract In this paper, we consider the nonlinear eigenvalue problem: $$\begin{array}{} \displaystyle \begin{cases} {\it\Delta}(|{\it\Delta} u|^{p(x)-2}{\it\Delta} u)= \lambda \frac{|u|^{q(x)-2}u}{{\delta(x)}^{2q(x)}} \;\; \mbox{in}\;\; {\it\Omega}, \\ u\in W_0^{2,p(x)}({\it\Omega}), \end{cases} \end{array}$$ where Ω is a regular bounded domain of ℝN, δ(x) = dist(x, ∂Ω) the distance function from the boundary ∂Ω, λ is a positive real number, and functions p(⋅), q(⋅) are supposed to be continuous on Ω satisfying $$\begin{array}{} \displaystyle 1 \lt \min_{\overline{{\it\Omega} }}\,q\leq \max_{\overline{{\it\Omega}}}\,q \lt \min_{\overline{{\it\Omega} }}\,p \leq \max_{\overline{{\it\Omega}}}\,p \lt \frac{N}{2} \mbox{ and } \max_{\overline{{\it\Omega}}}\,q \lt p_2^*:= \frac{Np(x)}{N-2p(x)} \end{array}$$ for any x ∈ Ω. We prove the existence of at least one non-decreasing sequence of positive eigenvalues. Moreover, we prove that sup Λ = +∞, where Λ is the spectrum of the problem. Furthermore, we give a proof of positivity of inf Λ > 0 provided that Hardy-Rellich inequality holds.

A simplified method of emulsion coating and development for quantitative electron microscopic radioautography

1978 ◽  
Vol 36 (2) ◽  
pp. 64-65
Author(s):  
K. Yoshida ◽  
F. Murata ◽  
S. Ohno ◽  
T. Nagata
Keyword(s):  
Mass Production ◽  
Identical Condition ◽  
Microscopic Level ◽  
Electron Microscopic Level ◽  
Electron Microscopic ◽  
Simplified Method ◽  
Complicated Process ◽  
Critical Problems ◽  
Electron Microscopic Radioautography ◽  
Quantitative Radioautography

IntroductionSeveral methods of mounting emulsion for radioautography at the electron microscopic level have been reported. From the viewpoint of quantitative radioautography, however, there are many critical problems in the procedure to produce radioautographs. For example, it is necessary to apply and develop emulsions in several experimental groups under an identical condition. Moreover, it is necessary to treat a lot of grids at the same time in the dark room for statistical analysis. Since the complicated process and technical difficulties in these procedures are inadequate to conduct a quantitative analysis of many radioautographs at once, many factors may bring about unexpected results. In order to improve these complicated procedures, a simplified dropping method for mass production of radioautographs under an identical condition was previously reported. However, this procedure was not completely satisfactory from the viewpoint of emulsion homogeneity. This paper reports another improved procedure employing wire loops.

Coal mining-disturbed land reclamation laws

2020 ◽  
pp. 15-26
Author(s):  
T. V. Galanina ◽  
M. I. Baumgarten ◽  
T. G. Koroleva
Keyword(s):  
Large Scale ◽  
Land Reclamation ◽  
Mining Industry ◽  
Development Program ◽  
Soil Disturbance ◽  
Open Pit ◽  
Open Pit Mining ◽  
Disturbed Land ◽  
Critical Problems ◽  
Production Output

Large-scale mining disturbs wide areas of land. The development program for the mining industry, with an expected considerable increase in production output, aggravates the problem with even vaster territories exposed to the adverse anthropogenic impact. Recovery of mining-induced ecosystems in the mineral-extracting regions becomes the top priority objective. There are many restoration mechanisms, and they should be used in integration and be highly technologically intensive as the environmental impact is many-sided. This involves pollution of water, generation of much waste and soil disturbance which is the most typical of open pit mining. Scale disturbance of land, withdrawal of farming land, land pollution and littering are critical problems to the solved in the first place. One of the way outs is highquality reclamation. This article reviews the effective rules and regulations on reclamation. The mechanism is proposed for the legal control of disturbed land reclamation on a regional and federal level. Highly technologically intensive recovery of mining-induced landscape will be backed up by the natural environment restoration strategy proposed in the Disturbed Land Reclamation Concept.

Inhibiting Factors of Cost Performance in UAE Construction Projects

2020 ◽  
Vol 11 (2) ◽  
Author(s):  
Ahmed Salem Ahmed Marey Alhammadi ◽  
◽  
Aftab Hameed Memon ◽  
Keyword(s):  
Construction Industry ◽  
Construction Projects ◽  
Past Research ◽  
Cost Overrun ◽  
Index Method ◽  
Cost Performance ◽  
Factors Affecting ◽  
Inhibiting Factors ◽  
Critical Problems ◽  
Structured Questionnaire

UAE construction industry frequently faces poor cost performance which commonly known as cost overrun problem. This problem is resulted from several factors and it is important to identify these cost overrun factors in order to avoid and minimize it. Hence, this paper focused on determined the relevancy of factors affecting cost performance in construction projects of UAE. Through a review of past research works conducted globally, 27 factors of cost overrun were listed and used for developing a structured questionnaire. A survey was conducted with 33 practitioners from client, consultant and contractors organizations involved in handling construction projects in UAE. The respondents were requested to state their perception regarding the relevancy of each of the factors that was perceived in context with cost overrun issue using 5-points Likert scale. The responses were analysed using average index method and the results found that all the 27 factors are relevant with construction industry of UAE in causing cost overrun. These factors can be used for further investigation to uncover critical problems of cost overrun.

Some Critical Problems of Botnets

2012 ◽  
Vol 35 (6) ◽  
pp. 1192 ◽  
Author(s):  
Tian-Zuo WANG ◽  
Huai-Min WANG ◽  
Bo LIU ◽  
Pei-Chang SHI
Keyword(s):  
Critical Problems

‘Wisselbare Woorde’

2018 ◽  
Author(s):  
Carrol Clarkson
Keyword(s):  
South Africa ◽  
Freedom Of Expression ◽  
The Other ◽  
Frantz Fanon ◽  
Politics Of Representation ◽  
Black Consciousness ◽  
Nadine Gordimer ◽  
Contact Zones ◽  
Critical Problems ◽  
Ethics And Politics

Carrol Clarkson’s chapter wrestles with the contentious question of Coetzee’s relation to the Black Consciousness Movement in South Africa of the 1970s and early 1980s, which took its philosophical bearings from Frantz Fanon and found expression in the writings of Steve Biko. Clarkson focuses on the ways in which Coetzee departed from the ideas about writing and resistance that were circulating in his contemporary South Africa, particularly as articulated by novelist Nadine Gordimer. Clarkson discusses two related literary-critical problems: an ethics and politics of representation, and an ethics and politics of address, showing how Coetzee explores a tension between freedom of expression and responsibility to the other. In the slippage from saying to addressing we are led to further thought about modes and sites of consciousness—and hence accountabilities—in the interlocutory contact zones of the post-colony. The chapter invites a sharper appreciation of what a postcolonial philosophy might be.

scholarly journals Multiple positive solutions for nonlocal elliptic problems involving the Hardy potential and concave–convex nonlinearities

2020 ◽  
pp. 2050008
Author(s):  
Shaya Shakerian
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Variational Approach ◽  
Nehari Manifold ◽  
Multiple Positive Solutions ◽  
Hardy Potential ◽  
Smooth Bounded Domain ◽  
Existence And Multiplicity ◽  
The Nehari Manifold

In this paper, we study the existence and multiplicity of solutions for the following fractional problem involving the Hardy potential and concave–convex nonlinearities: [Formula: see text] where [Formula: see text] is a smooth bounded domain in [Formula: see text] containing [Formula: see text] in its interior, and [Formula: see text] with [Formula: see text] which may change sign in [Formula: see text]. We use the variational methods and the Nehari manifold decomposition to prove that this problem has at least two positive solutions for [Formula: see text] sufficiently small. The variational approach requires that [Formula: see text] [Formula: see text] [Formula: see text], and [Formula: see text], the latter being the best fractional Hardy constant on [Formula: see text].

ExypnoSteganos - A smarter approach to steganography

2021 ◽  
pp. 1-12
Author(s):  
Gaurav Sarraf ◽  
Anirudh Ramesh Srivatsa ◽  
MS Swetha
Keyword(s):  
Neural Network ◽  
Deep Learning ◽  
Data Compression ◽  
Building Block ◽  
Communication Techniques ◽  
Systems Security ◽  
Learning Technique ◽  
Critical Problems ◽  
Sporadic Cases ◽  
Compressed Data

With the ever-rising threat to security, multiple industries are always in search of safer communication techniques both in rest and transit. Multiple security institutions agree that any systems security can be modeled around three major concepts: Confidentiality, Availability, and Integrity. We try to reduce the holes in these concepts by developing a Deep Learning based Steganography technique. In our study, we have seen, data compression has to be at the heart of any sound steganography system. In this paper, we have shown that it is possible to compress and encode data efficiently to solve critical problems of steganography. The deep learning technique, which comprises an auto-encoder with Convolutional Neural Network as its building block, not only compresses the secret file but also learns how to hide the compressed data in the cover file efficiently. The proposed techniques can encode secret files of the same size as of cover, or in some sporadic cases, even larger files can be encoded. We have also shown that the same model architecture can theoretically be applied to any file type. Finally, we show that our proposed technique surreptitiously evades all popular steganalysis techniques.

scholarly journals Potential antifungal effects of silver nanoparticles (AgNPs) of different sizes against phytopathogenic Fusarium oxysporum f. sp. radicis-lycopersici (FORL) strains

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
Ilgin Akpinar ◽  
Muammer Unal ◽  
Taner Sar
Keyword(s):  
Silver Nanoparticles ◽  
Fusarium Oxysporum ◽  
Antifungal Agents ◽  
New Technology ◽  
Economic Loss ◽  
Phytopathogenic Fungi ◽  
Growth Media ◽  
Mycelium Growth ◽  
Antifungal Effects ◽  
Critical Problems

AbstractFusarium species are the primary fungal pathogen affecting agricultural foodstuffs both in crop yield and economic loss. Due to these problems, control of phytopathogenic fungi has become one of the critical problems around the World. Nanotechnology is a new technology with potential in many fields, including agriculture. This study focused on determining potential effects of silver nanoparticles (AgNPs) with different nanosizes (3, 5, 8 and 10 nm) and at different concentrations (12.5–100 ppm) against phytopathogenic Fusarium oxysporum f. sp. radicis-lycopersici (FORL) strains. The maximum antifungal activity was achieved by decreasing nanosize and increasing concentration of AgNPs. Mycelium growth abilities were decreased about 50%, 75% and 90% by AgNPs treatment with 3 nm sizes at 25 ppm, 37.5 ppm and 50 ppm concentrations, respectively. The productivity of fungal biomass in the liquid growth media was found to be too limited at the 25–37.5 ppm of AgNPs concentrations with all sizes. In addition, both septation number and dimensions of micro- and macroconidia were found to be gradually decreased with the application of silver nanoparticles. This work showed that the low concentration of AgNPs could be used as potential antifungal agents and applied for control of phytopathogens.

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