The multifractal critical phase (MCP) fundamentally differs from extended and localized phases, exhibiting delocalized distributions in both position and momentum spaces. The investigation on the MCP has largely focus...
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The multifractal critical phase (MCP) fundamentally differs from extended and localized phases, exhibiting delocalized distributions in both position and momentum spaces. The investigation on the MCP has largely focused on one-dimensional quasiperiodic systems. Here, we introduce a two-dimensional (2D) quasiperiodic model with a MCP. We present its phase diagram and investigate the characteristics of the 2D system's MCP in terms of wave packet diffusion and transport based on this model. We further investigate the movement of the phase boundary induced by the introduction of next-nearest-neighbor hopping by calculating the fidelity susceptibility. Finally, we consider how to realize our studied model in superconducting circuits. Our work opens the door to exploring MCP in 2D systems.
In this paper,we study the multiplicity and concentration of positive solutions for the following fractional Kirchhoff-Choquard equation with magnetic fields:(aε^(2s)+bε^(4 s-3)[u]_(ε)^(2),A/ε)(-Δ)_(A/ε)^(s)u+V(...
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In this paper,we study the multiplicity and concentration of positive solutions for the following fractional Kirchhoff-Choquard equation with magnetic fields:(aε^(2s)+bε^(4 s-3)[u]_(ε)^(2),A/ε)(-Δ)_(A/ε)^(s)u+V(x)u=ε^(-α)(Iα*F(|u|^(2)))f(|u|^(2))u in R^(3).Hereε>0 is a small parameter,a,b>0 are constants,s E(0,1),(-Δ)As is the fractional magnetic Laplacian,A:R^(3)→R^(3) is a smooth magnetic potential,Iα=Γ(3-α/2)/2απ3/2Γ(α/2)·1/|x|^(α) is the Riesz potential,the potential V is a positive continuous function having a local minimum,and f:R→R is a C^(1) subcritical *** some proper assumptions regarding V and f,we show the multiplicity and concentration of positive solutions with the topology of the set M:={x∈R^(3):V(x)=inf V}by applying the penalization method and LjusternikSchnirelmann theory for the above equation.
We classify all Polish semigroup topologies on the symmetric inverse monoid IN on the natural numbers N. This result answers a question of Elliott et al. There are countably infinitely many such topologies. Under cont...
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In the rapidly advancing field of genomics, the identification of Single Nucleotide Polymorphisms (SNPs) plays a crucial role in understanding complex phenotypic *** study introduces "PentaPen", an innovativ...
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Undergraduate science, technology, engineering, and mathematics (STEM) experiences have academic, psychological, and social challenges that require additional support to navigate. This article explains the implementat...
Electrical impedance tomography (EIT) is a non-invasive imaging method for recovering the internal conductivity of a physical body from electric boundary measurements. EIT combined with machine learning has shown prom...
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In an attempt to optimize computation resources for unsupervised learning techniques, including k-means and k- means++, different methods of parallelization are proposed depending on the scale of business and demands....
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作者：
Mohamed A. MabrokMathematics Program
Department of Mathematics Statistics and Physics College of Arts and Sciences Qatar University P.O. box 2713 Doha Qatar
In this paper, we consider the problem of robust stabilization of linear time-invariant systems with respect to unmodeled dynamics and structure uncertainties. To that end, we first present a methodology to find the n...
In this paper, we consider the problem of robust stabilization of linear time-invariant systems with respect to unmodeled dynamics and structure uncertainties. To that end, we first present a methodology to find the nearest negative imaginary system for a given non-negative imaginary system. Then, we employ this result to construct a near optimal linear quadratic Gaussian controller achieving desired performance measures. The problem is formulated using port-Hamiltonian method and the required conditions are defined in terms of linear matrix inequalities. The technique is presented using fast gradient method to solve the problem systematically. The designed controller satisfies a negative imaginary property and guarantees a robust feedback loop. The effectiveness of the approach is demonstrated by simulation on a numerical example.
Diagnosability is an important parameter to measure the fault tolerance of a multiprocessor system. If we only care about the state of a node, instead of doing the global diagnosis, Hsu and Tan proposed the idea of lo...
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We prove an entropy version of van der Corput’s difference theorem: the entropy of a sequence is equal to the entropy of its differences. This reveals a potential correspondence between the theory of uniform distribu...
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