BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS

In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.

Delineating homogeneous domains of fractured rocks using topological manifolds and deep learning

Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural information is proposed to delineate homogeneous domains.This technique is then applied to a high and steep slope along a road.First,geological and geotechnical domains were described based on lithology,faults,and shear zones.Next,topological manifolds were used to eliminate the incompatibility between orientations and other parameters(i.e.trace length and roughness)so that the data concerning various properties of each discontinuity can be matched and characterized in the same Euclidean space.Thus,the influence of implicit combined effect in between parameter sequences on the homogeneous domains could be considered.Deep learning technique was employed to quantify abstract features of the characterization images of discontinuity properties,and to assess the similarity of rock mass structures.The results show that the technique can effectively distinguish structural variations and outperform conventional methods.It can handle multisource engineering geological information and multiple discontinuity parameters.This technique can also minimize the interference of human factors and delineate homogeneous domains based on orientations or multi-parameter with arbitrary distributions to satisfy different engineering requirements.

CONVEXITY OF THE FREE BOUNDARY FOR AN AXISYMMETRIC INCOMPRESSIBLE IMPINGING JET

This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provided that the uneven ground is concave to the fluid.

On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

Distributed Stochastic Optimization with Compression for Non-Strongly Convex Objectives

We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

MINIMIZERS OF L^(2)-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS

This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.

Spatial correlations in time and frequency domains between chlorophyll-a concentration and environmental factors in the Bohai Sea

Based on the reconstructed MODIS data and ECMWF reanalysis data from 2003 to 2021,spatial correlations between chlorophyll a(Chl a)and sea surface temperature(SST),photosynthetically available radiation(PAR),aerosol optical thickness(AOT),and wind speed(WS)in the Bohai Sea were analyzed from the perspective of time domain and frequency domain.Results indicate that the frequency domain analysis was more conducive to revealing the correlations between Chl a and environmental factors.The spatial pattern of time-domain correlations was similar to the isobaths of the Bohai Sea,which was positive in shallow waters and negative in deep waters for SST,PAR,and AOT,and was reversed for WS.Frequency-domain correlations were obtained by performing Fourier Transform and were higher than correlations in time domain.The spatial distributions indicated that the effects of SST and PAR on Chl a were greater than AOT and WS in the Bohai Sea.Additionally,cross-spectrum analysis was applied to explore the response relationships.A depth-dependent pattern was shown in correlations and time lags,indicating that the influential mechanism of environmental factors on Chl-a concentration is related to seawater depth.

Targeting neuronal PAS domain protein 2 and KN motif/ankyrin repeat domains 1:Advances in type 2 diabetes therapy

This editorial summarizes the latest literature on the roles of neuronal PAS domain protein 2 and KN motif/ankyrin repeat domain 1 in type 2 diabetes(T2D).We highlight their involvement inβ-cell dysfunction,explore their potential as therapeutic targets,and discuss the implications for new treatment strategies.We offer valuable insights into relevant gene regulation and cellular mechanisms relevant for the targeted management of T2D.

Enhancing Relational Triple Extraction in Specific Domains:Semantic Enhancement and Synergy of Large Language Models and Small Pre-Trained Language Models

In the process of constructing domain-specific knowledge graphs,the task of relational triple extraction plays a critical role in transforming unstructured text into structured information.Existing relational triple extraction models facemultiple challenges when processing domain-specific data,including insufficient utilization of semantic interaction information between entities and relations,difficulties in handling challenging samples,and the scarcity of domain-specific datasets.To address these issues,our study introduces three innovative components:Relation semantic enhancement,data augmentation,and a voting strategy,all designed to significantly improve the model’s performance in tackling domain-specific relational triple extraction tasks.We first propose an innovative attention interaction module.This method significantly enhances the semantic interaction capabilities between entities and relations by integrating semantic information fromrelation labels.Second,we propose a voting strategy that effectively combines the strengths of large languagemodels(LLMs)and fine-tuned small pre-trained language models(SLMs)to reevaluate challenging samples,thereby improving the model’s adaptability in specific domains.Additionally,we explore the use of LLMs for data augmentation,aiming to generate domain-specific datasets to alleviate the scarcity of domain data.Experiments conducted on three domain-specific datasets demonstrate that our model outperforms existing comparative models in several aspects,with F1 scores exceeding the State of the Art models by 2%,1.6%,and 0.6%,respectively,validating the effectiveness and generalizability of our approach.

Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.

Research fronts and researchers of World Journal of Psychiatry in 2023: A visualization and analysis of mapping knowledge domains

BACKGROUND In the rapidly evolving landscape of psychiatric research,2023 marked another year of significant progress globally,with the World Journal of Psychiatry(WJP)experiencing notable expansion and influence.AIM To conduct a comprehensive visualization and analysis of the articles published in the WJP throughout 2023.By delving into these publications,the aim is to deter-mine the valuable insights that can illuminate pathways for future research endeavors in the field of psychiatry.METHODS A selection process led to the inclusion of 107 papers from the WJP published in 2023,forming the dataset for the analysis.Employing advanced visualization techniques,this study mapped the knowledge domains represented in these papers.RESULTS The findings revealed a prevalent focus on key topics such as depression,mental health,anxiety,schizophrenia,and the impact of coronavirus disease 2019.Additionally,through keyword clustering,it became evident that these papers were predominantly focused on exploring mental health disorders,depression,anxiety,schizophrenia,and related factors.Noteworthy contributions hailed authors in regions such as China,the United Kingdom,United States,and Turkey.Particularly,the paper garnered the highest number of citations,while the American Psychiatric Association was the most cited reference.CONCLUSION It is recommended that the WJP continue in its efforts to enhance the quality of papers published in the field of psychiatry.Additionally,there is a pressing need to delve into the potential applications of digital interventions and artificial intelligence within the discipline.

Design,Development and Testing of the JTech Bolt for Use in Static,Quasi-Static and Dynamic Domains

Designing a rock reinforcement element requires knowledge of:geomechanical behaviour,interaction of the reinforcement element with rock mass and the element’s mechanistic response in static and dynamic environments.Using this knowledge the JTech bolt was developed and subjected to a thorough program to test,gather data and validate the bolt performance in varying domains.By conducting FE(finite element)modeling,the simulation reviews the JTech bolt design evaluating the effects of threadbar geometric variation,threadbar and nut engagement results under high stress,coating friction response and effects of thread tolerance extremes on the failure mode.These results determine safety factors,tolerances and quality management criteria.Once manufactured,in-situ system testing,laboratory and underground short encapsulation testing,resin mixing testing,double shear testing and dynamic testing at varying velocity and mass,determine the system’s capacity and effectiveness in static,quasi-static and dynamic mining environments.In this paper,the process and results are described.

Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral-Element Methods

We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.

Identification of Stability Domains for Flow Parameters in Fused Filament Fabrication Using Acoustic Emission

In Fused Filament Fabrication(FFF),the state of material flow significantly influences printing outcomes.However,online monitoring of these micro-physical processes within the extruder remains challenging.The flow state is affected by multiple parameters,with temperature and volumetric flow rate(VFR)being the most critical.The study explores the stable extrusion of flow with a highly sensitive acoustic emission(AE)sensor so that AE signals generated by the friction in the annular region can reflect the flow state more effectively.Nevertheless,the large volume and broad frequency range of the data present processing challenges.This study proposes a method that initially selects short impact signals and then uses the Fast Kurtogram(FK)to identify the frequency with the highest kurtosis for signal filtration.The results indicate that this approach significantly enhances processing speed and improves feature extraction capabilities.By correlating AE characteristics under various parameters with the quality of extruded raster beads,AE can monitor the real-time state of material flow.This study offers a concise and efficient method for monitoring the state of raster beads and demonstrates the potential of online monitoring of the flow states.

POTENTIAL SPACE ESTIMATES IN LOCAL HARDY SPACES FOR GREEN POTENTIALS IN CONVEX DOMAINS

Let Ω be a bounded convex domain in Rn(n≥3) and G(x,y) be the Green function of the Laplace operator -△on Ω Let hPT(Ω) = {f∈D'(Ω) : (?)F ∈ hP(Rn), s.t. F|Ω = f}, by the atom characterization of Local Hardy spaces in a bounded Lipschitz domain, the bound of f Ω(?)2(Gf) for every f ∈hPr(Ω) is obtained, where n/(n + 1) <p≤1.

A Prop erty of Convex Mappings on the Classical Domains

In this paper, we give a property of normalized biholomorphic convex mappings on the first, second and third classical domains: for any Z0 belongs to the classical domains,f maps each neighbourhood with the center Z0, which is contained in the classical domains,to a convex domain.

Relaxed Stability Criteria for Delayed Generalized Neural Networks via a Novel Reciprocally Convex Combination

Dear Editor,This letter examines the stability issue of generalized neural networks(GNNs) with time-varying delay based on a novel reciprocally convex combination(RCC). By considering a new matrix polynomial, the proposed novel reciprocally convex method leads to a tight bound for integral inequality combination and encompasses several existing approaches as special cases.

Domain size and charge defects affecting the polarization switching of antiferroelectric domains

The switching behavior of antiferroelectric domain structures under the applied electric field is not fully understood.In this work,by using the phase field simulation,we have studied the polarization switching property of antiferroelectric domains.Our results indicate that the ferroelectric domains nucleate preferably at the boundaries of the antiferroelectric domains,and antiferroelectrics with larger initial domain sizes possess a higher coercive electric field as demonstrated by hysteresis loops.Moreover,we introduce charge defects into the sample and numerically investigate their influence.It is also shown that charge defects can induce local ferroelectric domains,which could suppress the saturation polarization and narrow the enclosed area of the hysteresis loop.Our results give insights into understanding the antiferroelectric phase transformation and optimizing the energy storage property in experiments.

Structure and function of the membrane microdomains in osteoclasts

The cell membrane structure is closely related to the occurrence and progression of many metabolic bone diseases observed in the clinic and is an important target to the development of therapeutic strategies for these diseases.Strong experimental evidence supports the existence of membrane microdomains in osteoclasts(OCs).However,the potential membrane microdomains and the crucial mechanisms underlying their roles in OCs have not been fully characterized.Membrane microdomain components,such as scaffolding proteins and the actin cytoskeleton,as well as the roles of individual membrane proteins,need to be elucidated.In this review,we discuss the compositions and critical functions of membrane microdomains that determine the biological behavior of OCs through the three main stages of the OC life cycle.