Publisher Correction to:Strongly Coupled 2D Transition Metal Chalcogenide‑MXene‑Carbonaceous Nanoribbon Heterostructures with Ultrafast Ion Transport for Boosting Sodium/Potassium Ions Storage

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Quantitative determination of the critical points of Mott metal–insulator transition in strongly correlated systems

Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points.

Strongly Gain Coupled DFB Laser Monolithically Integrated with a Self Alignment Spot Size Converter

A new type strongly gain coupled (GC) DFB laser and a new type self alignment spot size converter (SA SSC) are proposed and successfully fabricated.The strongly GC DFB laser is monolithically integrated with the SA SSC with three step epitaxies.A high single mode yield and large side mode suppression ratio is obtained from the strongly GC DFB laser.A near circle far field pattern is obtained by using the SA SSC.

The Growth Theorem for Strongly Starlike Mappings of Order α on Bounded Starlike Circular Domains

The authors obtain the growth and covering theorems for strongly starlike mappings of order α on bounded starlike circular domains.This kind of domain discussed is rather general,since the domain must be starlike if exists a normalized biholomorphic starlike mapping on it.

The solutions of the strongly nonlocal spatial solitons with several types of nonlocal response functions

The fundamental and second order strongly nonlocal solitons of the nonlocal nonlinear Schrodinger equation for several types of nonlocal responses are calculated by Ritz＇s variational method. For a specific type of nonlocal response, the solutions of the strongly nonlocal solitons with the same beam width but different degrees of nonlocality are identical except for an amplitude factor. For a nonlocal case where the nonlocal response function decays in direct proportion to the mth power of the distance near the source point, the power and the phase constant of the strongly nonlocal soliton are in inverse proportion to the （m ＋ 2）th power of its beam width.

Extensions of strongly π-regular general rings

The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.

Generalized system for strongly g-r-pseudomonotonic nonlinear variational inequalities in Hilbert spaces

The approximation solvability of a generalized system for strongly g-r- pseudomonotonic nonlinear variational inequalities in Hilbert spaces is studied based on the convergence of the projection method. The results presented in this paper improve, generalize and unify some recent results in the literature.

Lensless ghost imaging through the strongly scattering medium

Lensless ghost imaging has attracted much interest in recent years due to its profound physics and potential applications. In this paper we report studies of the robust properties of the lensless ghost imaging system with a pseudo-thermal light source in a strongly scattering medium. The effects of the positions of the strong medium on the ghost imaging are investigated. In the lensless ghost imaging system, a pseudo-thermal light is split into two correlated beams by a beam splitter. One beam goes to a charge-coupled detector camera, labeled as CCD2. The other beam goes to an object and then is collected in another charge-coupled detector camera, labeled as CCD1, which serves as a bucket detector. When the strong medium, a pane of ground glass disk, is placed between the object and CCD1, the bucket detector, the quality of ghost imaging is barely affected and a good image could still be obtained. The quality of the ghost imaging can also be maintained, even when the ground glass is rotating, which is the strongest scattering medium so far. However, when the strongly scattering medium is present in the optical path from the light source to CCD2 or the object, the lensless ghost imaging system hardly retrieves the image of the object. A theoretical analysis in terms of the second-order correlation function is also provided.

AN ITERATIVE PROCESS FOR FINDING APPROXIMATE SOLUTIONS TO NONLINEAR EQUATIONS OF STRONGLY ACCRETIVE OPERATORS

In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. We prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator frow X to X, or to the unique fixed point of T when T is a Lipschitzian and strictly pseudocontractive mapping from a nonempty closed convex subset K of X into itself. Our results are the extension and improvements of the earlier and recent results in this field.

Development and Application of a High-Performance Triangular Shell Element and an Explicit Algorithm in OpenSees for Strongly Nonlinear Analysis

The open-source finite element software,OpenSees,is widely used in the earthquake engineering community.However,the shell elements and explicit algorithm in OpenSees still require further improvements.Therefore,in this work,a triangular shell element,NLDKGT,and an explicit algorithm are proposed and implemented in OpenSees.Specifically,based on the generalized conforming theory and the updated Lagrangian formulation,the proposed NLDKGT element is suitable for problems with complicated boundary conditions and strong nonlinearity.The accuracy and reliability of the NLDKGT element are validated through typical cases.Furthermore,by adopting the leapfrog integration method,an explicit algorithm in OpenSees and a modal damping model are developed.Finally,the stability and efficiency of the proposed shell element and explicit algorithm are validated through the nonlinear time-history analysis of a highrise building.

J-clean and Strongly J-clean Rings

Let R be a ring and J（R） the Jacobson radical. An element a of R is called（strongly） J-clean if there is an idempotent e ∈ R and w ∈ J（R） such that a = e ＋ w（and ew = we）. The ring R is called a（strongly） J-clean ring provided that every one of its elements is（strongly） J-clean. We discuss, in the present paper,some properties of J-clean rings and strongly J-clean rings. Moreover, we investigate J-cleanness and strongly J-cleanness of generalized matrix rings. Some known results are also extended.

Uniquely strongly clean triangular matrix rings

An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of R is uniquely strongly clean. The uniquely strong cleanness of the triangular matrix ring is studied. Let R be a local ring. It is shown that any n × n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J（R） ≈Z2.

Notes on Strongly n-Gorenstein Projective, Injective and Flat Modules

In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.

Carboniferous ridge subduction in the Xingmeng Orogenic Belt:Constraints from geochronological,geochemical,and Sr-Nd-Hf isotopic analysis of strongly peraluminous granites and gabbro-diorites in the Xilinhot micro-continent

The Xingmeng Orogenic Belt evolved through a long-lived orogeny involving multiple episodes of subduction and accretion.However,there is a debate on its tectonic evolution during the Late Paleozoic.Here,we report geochemical,geochronological,and isotopic data from strongly peraluminous granites and gabbro-diorites from the Sunidzuoqi-Xilinhot region.Zircon U-Pb ages suggest that the intrusive rocks were emplaced during the Early Carboniferous(333-322 Ma).The granites exhibit geochemical characteristics similar to S-type granites,with high SiO_(2)(72.34-76.53 wt.%),Al_(2)O_(3)(12.45-14.65 wt.%),and A/CNK(1.07-1.16),but depleted Sr,Nb,and Ta contents.They exhibit positiveε_(Nd)(t)andε_(Hf)(t)values(-0.3 to 2.8 and 2.7-5.7,respectively)and young Nd and Hf model ages(T_(DM2)(Nd)=853-1110 Ma and T_(DM2)(Hf)=975-1184 Ma),suggesting that they may be the partial melting products of heterogeneous sources with variable proportions of pelite,psammite,and metabasaltic rocks.The meta-gabbro-diorites from the Maihantaolegai pluton have low SiO_(2)(47.06-53.49 wt.%)and K_2O(0.04-0.99 wt.%)contents,and demonstrate slight light rare earth element(REE)depletion in the chondritenormalized REE diagrams.They have high zirconε_(Hf)(t)values(14.41-17.34)and young Hf model ages(T_(DM2)(Hf)=230-418 Ma),indicating a more depleted mantle source.The variations of the Sm/Yb and La/Sm ratios can thus be used to assess the melting degree of the mantle source from 5%to 20%,suggesting a quite shallow mantle melting zone.We propose that the petrogenesis and distribution of the strongly peraluminous granites and gabbro-diorites,as well as the tectonic architecture of the region,can be explained by a ridge subduction model.Based on these results,and previous studies,we suggest a southward ridge subduction model for the Sunidzuoqi-Xilinhot region.

Coefficient Estimates for a Subclass of Bi-univalent Strongly Quasi-starlike Functions

The aim of this paper is to establish the Fekete-Szego inequality for a subclass of bi-univalent strongly quasi-starlike functions which is defined in the open unit disk. Furthermore, the coefficients a2 and a3 for functions in this new subclass are estimated.

A high order energy preserving scheme for the strongly coupled nonlinear Schr¨odinger system

A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the soliton evolution of the strongly coupled Schrōdinger system. Numerical results show that the high order energy preserving scheme can well simulate the soliton evolution, moreover, it preserves the discrete energy of the strongly coupled nonlinear Schrōdinger system exactly.

High-codimensional static bifurcations of strongly nonlinear oscillator

The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied. We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introducing the undetermined fundamental frequency into the computation in the complex normal form. To discuss the static bifurcation, the bifurcation problem is described as a 3-codimensional unfolding with Z2 symmetry on the basis of singularity theory. The transition set and bifurcation diagrams for the singularity are presented, while the stability of the zero solution is studied by using the eigenvalues in various parameter regions.

Coexistence of a Strongly Coupled Prey-predator Model for Holling's Type Ⅲ

In this paper, the two-species prey-predator Lotka-Volterra model with the Holling＇s type III is discussed. By the method of coupled upper and lower solutions and its associated monotone iterations, the existence of solutions for a strongly coupled elliptic system with homogeneous of Dirchlet boundary conditions is derived. These results show that this model admits at least one coexistence state if across-diffusions are weak.

A NEW METHOD FOR THE PERIODIC SOLUTION OF STRONGLY NONLINEAR SYSTEMS

A new method for the periodic solution of strongly nonlinear system is given. By using this method, the existance and stability of the periodic solution can be decided, and the approximate expression of the periodic solution can also be found.

Propagation properties and radiation force of circular Airy Gaussian vortex beams in strongly nonlocal nonlinear medium

We study the abruptly autofocusing and autodefocusing properties of the circular Airy Gaussian vortex(CAi GV)beams in strongly nonlocal nonlinear medium for the first time through numerical simulations.The magnitude of topological charges and the position of the vortex could change not only the light spot pattern but also the intensity contrast.Meanwhile,we can change the position of the autofocusing and autodefocusing planes by changing the parameter of the incident beam.Furthermore,we can control the peak intensity contrast through choosing properly the truncation factor.As for the radiation force,we study the gradient and the scattering forces of CAi GV beams on Rayleigh dielectric sphere.Our analyses demonstrate that the radiation force can be enhanced by choosing proper parameters of CAi GV beams.