THE IMPLICIT CONTINUITY OF DISCONTINUOUS SYSTEMS

An example is presented to introduce the concept of implicit continuity proposed as contrasted with the explicit continuity.A sufficient and necessary condition of the implicit continuity is given and proved in forms of implicit system.This condition also offers the solution of initial values at the points where the dynamic system is discontinuous.Some discussions are contributed to the physical significance of implicit continuity.

Finite Difference Implicit Schemes to Coupled Two-Dimension Reaction Diffusion System

In this research article, two finite difference implicit numerical schemes are described to approximate the numerical solution of the two-dimension modified reaction diffusion Fisher’s system which exists in coupled form. Finite difference implicit schemes show unconditionally stable and second-order accurate nature of computational algorithm also the validation and comparison of analytical solution, are done through the examples having known analytical solution. It is found that the numerical schemes are in excellent agreement with the analytical solution. We found, second-implicit scheme is much faster than the first with good rate of convergence also we used NVIDA devices to accelerate the computations and efficiency of the algorithm. Numerical results show our proposed schemes with use of HPC (High performance computing) are very efficient and reliable.

Existence and algorithm of solutions for a system of generalized mixed implicit equilibrium problems in Banach spaces

A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.

Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium

A new system of generalized mixed implicit equilibrium problems （SGMIEP） involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem （AMEP） is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems （SGEP） is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field.

Generalized Alternating-Direction Implicit Finite-Difference Time-Domain Method in Curvilinear Coordinate System

In this paper, a novel approach is introduced towards an efficient Finite-Difference Time-Domain (FDTD) algorithm by incorporating the Alternating Direction Implicit (ADI) technique to the Nonorthogonal FDTD (NFDTD) method. This scheme can be regarded as an extension of the conventional ADI-FDTD scheme into a generalized curvilinear coordinate system. The improvement on accuracy and the numerical efficiency of the ADI-NFDTD over the conventional nonorthogonal and the ADI-FDTD algorithms is carried out by numerical experiments. The application in the modelling of the Electromagnetic Bandgap (EBG) structure has further demonstrated the advantage of the proposed method.

A Fast and Memory-Efficient Direct Rendering Method for Polynomial-Based Implicit Surfaces

Three-dimensional surfaces are typically modeled as implicit surfaces.However,direct rendering of implicit surfaces is not simple,especially when such surfaces contain finely detailed shapes.One approach is ray-casting,where the field of the implicit surface is assumed to be piecewise polynomials defined on the grid of a rectangular domain.A critical issue for direct rendering based on ray-casting is the computational cost of finding intersections between surfaces and rays.In particular,ray-casting requires many function evaluations along each ray,severely slowing the rendering speed.In this paper,a method is proposed to achieve direct rendering of polynomial-based implicit surfaces in real-time by strategically narrowing the search range and designing the shader to exploit the structure of piecewise polynomials.In experiments,the proposed method achieved a high framerate performance for different test cases,with a speed-up factor ranging from 1.1 to 218.2.In addition,the proposed method demonstrated better efficiency with high cell resolution.In terms of memory consumption,the proposed method saved between 90.94%and 99.64%in different test cases.Generally,the proposed method became more memory-efficient as the cell resolution increased.

A Simple Embedding Method for the Laplace-Beltrami Eigenvalue Problem onImplicit Surfaces

We propose a simple embedding method for computing the eigenvalues and eigenfunctions of the Laplace-Beltrami operator on implicit surfaces.The approach follows an embedding approach for solving the surface eikonal equation.We replace the differential operator on the interface with a typical Cartesian differential operator in the surface neighborhood.Our proposed algorithm is easy to implement and efficient.We will give some two-and three-dimensional numerical examples to demonstrate the effectiveness of our proposed approach.

Technologies for implicit surfaces sampling with particle systems

Point-based surface has been widely used in computer graphics for modeling, animation, visualization, simulation of liq- uid and so on. Furthermore, particle-based approach can distribute the surface sampling points and control its parameters according to the needs of the application. In this paper, we examine several kinds of algorithms presented over the last decades, with the main focus on particle sampling technologies for implicit surface. Therefore, we classify various algorithms into categories, describe main ideas behind each categories, and compare the advantages and shortcomings of the algorithms in each category.

Impaired implicit emotion regulation in patients with panic disorder:An event-related potential study on affect labeling

BACKGROUND Panic disorder(PD)involves emotion dysregulation,but its underlying mechanisms remain poorly understood.Previous research suggests that implicit emotion regulation may play a central role in PD-related emotion dysregulation and symptom maintenance.However,there is a lack of studies exploring the neural mechanisms of implicit emotion regulation in PD using neurophysiological indicators.AIM To study the neural mechanisms of implicit emotion regulation in PD with eventrelated potentials(ERP).METHODS A total of 25 PD patients and 20 healthy controls(HC)underwent clinical evaluations.The study utilized a case-control design with random sampling,selecting participants for the case group from March to December 2018.Participants performed an affect labeling task,using affect labeling as the experimental condition and gender labeling as the control condition.ERP and behavioral data were recorded to compare the late positive potential(LPP)within and between the groups.RESULTS Both PD and HC groups showed longer reaction times and decreased accuracy under the affect labeling.In the HC group,late LPP amplitudes exhibited a dynamic pattern of initial increase followed by decrease.Importantly,a significant group×condition interaction effect was observed.Simple effect analysis revealed a reduction in the differences of late LPP amplitudes between the affect labeling and gender labeling conditions in the PD group compared to the HC group.Furthermore,among PD patients under the affect labeling,the late LPP was negatively correlated with disease severity,symptom frequency,and intensity.CONCLUSION PD patients demonstrate abnormalities in implicit emotion regulation,hampering their ability to mobilize cognitive resources for downregulating negative emotions.The late LPP amplitude in response to affect labeling may serve as a potentially valuable clinical indicator of PD severity.

Analysis of The Use of Implicit Nursing Knowledge in The Teaching of Cardiovascular Internal Medicine Nursing

Objective: To explore the utilization of implicit nursing knowledge in the teaching of cardiovascular internal medicine nursing and to provide a reference for improving the quality and efficiency of cardiovascular internal medicine nursing work. Methods: Thirty-six trainee nurses working in the cardiovascular internal medicine department of our hospital from September 2022 to September 2023 were selected and randomly divided into a control group and an observation group of 18 trainees each. The control adopted the traditional teaching methods while the observation group adopted the implicit nursing knowledge in their clinical practice work. The assessment scores and teamwork ability of the two groups were analyzed and compared. Results: The performance of the observation group was better than that of the control group, and the difference between the two groups was statistically significant (P < 0.05). The teamwork ability of the observation group was significantly better than that of the control group in teamwork ability (P < 0.05). Conclusion: Implicit nursing knowledge teaching is conducive to the cultivation of high-quality nursing talents and meets the development needs of hospitals. Therefore, the importance of implicit nursing knowledge should be strengthened in the teaching of cardiovascular internal medicine nursing and it should be comprehensively organized to improve the quality of nursing services.

A-high-order Accuraqcy Implicit Difference Scheme for Solving the Equation of Parabolic Type

In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(Δt 4+Δx 4) It can be easily solved by double sweeping method.

基于Implicit Wendroff差分格式的汽车线束导线串扰时域瞬态响应分析

介绍了一种具有Implicit Wendroff差分格式的时域有限差分法,将其应用于汽车线束导线串扰的时域瞬态响应分析。由于该方法包含了隐式人工粘性项,可在一定程度上削弱由空间坐标离散化而产生的间断解处的非物理性振荡现象,提高了计算结果的准确性,同时由于不受稳定性条件的限制,使其计算效率得到大幅度提高。通过应用于非均匀双导体传输线系统和均匀三导体传输线系统的数值实验可知,在保证计算精度的同时,与传统的Leapfrog差分格式和显式Lax-Wendroff差分格式进行对比,其计算效率分别提高了60%和70%左右,明显优于其他两种方法。同时,本文给出了传输线上电压和电流的时空分布三维图,直观地表示出了传输线上电压和电流与时间和空间位置的变化关系。

Implicit Learning and Explicit Learning in Second Language Vocabulary Acquisition

Implicit and explicit learning strategies of SL vocabulary acquisition are summarized based on precious studies and experiments. It is concluded that implicit learning strategies dolittlehelpto SL vocabulary acquisition, but explicit learning strategies play a very important part in SL vocabulary acquisition. Besides, an assumption is proposed: the more obvious explicit learning is in vocabulary acquisition, the more words learners can acquire. It is hoped that this research has certain implications for SL learners and teaching.

Implicit Love and Passionate Love-Contrast the Diction in "Song To Celia" by Ben Jonson and that in "The Canonization" by John Donne

Love is a permanent theme in the world's history of literature.With different dictions(choice of words),poets can portray diverse images of love,thus leaving completely distinct impression on the readers' minds.By analyzing and contrasting the diction in "Song To Celia" by Ben Jonson and that in "The Canonization" by John Donne,this essay aims to illustrate that different dramatic effects could be achieved with different choices of words in creative writing,and diction could be a representative symbol of a poet's writing style.

Implicit Knowledge, Explicit Knowledge and Interaction in the College English Teaching

In each act or process of knowledge, all components can be classified into two kinds: tacit (implicit) components and focal (explicit) components. This article, first of all introduces the terms of implicit knowledge, explicit knowledge and their distinctions in the process of English language learning and then provides interactive instruction design to improve learners' communicative competence.

A truncated implicit high-order finite-difference scheme combined with boundary conditions

In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.

A Teaching Case of Subject Clause Based on Implicit Learning

The New English curriculum criteria suggest teaching English grammar based on the students’cognitive characteristics and emotional needs,helping them discover the rules and encouraging them to master the grammar by using it.But due to the limited time in a lesson,many English teachers adopt a simple approach to teach grammar,in which students are required to memorize the rules first and then practice a lot.This approach is effec-

Implicit modeling of complex orebody with constraints of geological rules

To dynamically update the shape of orebody according to the knowledge of a structural geologist’s insight,an approach of orebody implicit modeling from raw drillhole data using the generalized radial basis function interpolant was presented.A variety of constraint rules,including geology trend line,geology constraint line,geology trend surface,geology constraint surface and anisotropy,which can be converted into interpolation constraints,were developed to dynamically control the geology trends.Combined with the interactive tools of constraint rules,this method can avoid the shortcomings of the explicit modeling method based on the contour stitching,such as poor model quality,and is difficult to update dynamically,and simplify the modeling process of orebody.The results of numerical experiments show that the 3D ore body model can be reconstructed quickly,accurately and dynamically by the implicit modeling method.

Carbody Structural Lightweighting Based on Implicit Parameterized Model

Most of recent research on carbody lightweighting has focused on substitute material and new processing technologies rather than structures. However, new materials and processing techniques inevitably lead to higher costs. Also, material substitution and processing lightweighting have to be realized through body structural profiles and locations. In the huge conventional workload of lightweight optimization, model modifications involve heavy manual work, and it always leads to a large number of iteration calculations. As a new technique in carbody lightweighting, the implicit parameterization is used to optimize the carbody structure to improve the materials utilization rate in this paper. The implicit parameterized structural modeling enables the use of automatic modification and rapid multidisciplinary design optimization （MDO） in carbody structure, which is impossible in the traditional structure finite element method （FEM） without parameterization. The structural SFE parameterized model is built in accordance with the car structural FE model in concept development stage, and it is validated by some structural performance data. The validated SFE structural parameterized model can be used to generate rapidly and automatically FE model and evaluate different design variables group in the integrated MDO loop. The lightweighting result of body-in-white （BIW） after the optimization rounds reveals that the implicit parameterized model makes automatic MDO feasible and can significantly improve the computational efficiency of carbody structural lightweighting. This paper proposes the integrated method of implicit parameterized model and MDO, which has the obvious practical advantage and industrial significance in the carbody structural lightweighting design.

AN IMPLICIT SERIES PRECISE INTEGRATION ALGORITHM FOR STRUCTURAL NONLINEAR DYNAMIC EQUATIONS

Nonlinear dynamic equations can be solved accurately using a precise integration method. Some algorithms exist, but the inversion of a matrix must be calculated for these al- gorithms. If the inversion of the matrix doesn’t exist or isn’t stable, the precision and stability of the algorithms will be afected. An explicit series solution of the state equation has been pre- sented. The solution avoids calculating the inversion of a matrix and its precision can be easily controlled. In this paper, an implicit series solution of nonlinear dynamic equations is presented. The algorithm is more precise and stable than the explicit series solution and isn’t sensitive to the time-step. Finally, a numerical example is presented to demonstrate the efectiveness of the algorithm.