Hyperbole is a very common rhetorical device which is widely used both in English and Chinese. In order to express his/her strong feelings and also to make his/her language more powerful, the writer/speaker exaggerate...Hyperbole is a very common rhetorical device which is widely used both in English and Chinese. In order to express his/her strong feelings and also to make his/her language more powerful, the writer/speaker exaggerates things on purpose. Yet in spite of the over-truth expression, employment of hyperbole does not affect the conversation flow between parties. Through an analysis of hyperbole from the perspective of pragrnatics, this article tries to explain the pragmatic functions of hyperbole.展开更多
In daily lives,people unconsciously use hyperbole to address their speech in everyday conversation,it has been an indivisible part of people's talk.And the usage of hyperbole has its own effects and functions,this...In daily lives,people unconsciously use hyperbole to address their speech in everyday conversation,it has been an indivisible part of people's talk.And the usage of hyperbole has its own effects and functions,this paper aims at searching the main effects of hyperbole in our everyday conversations,and tries to classify them as three effects or functions.First,hyperbole can reveal the essence of events.Second,it can enhance the infection of sentences and appeal to audience.Third,it can help the listeners imagine the situation the speaker described.And in this paper,through the analysis of everyday conversations,illustrated how hyperbole achieved these effects.展开更多
In this study,we systematically investigated the effect of proton concentration on the kinetics of the oxygen reduction reaction(ORR)on Pt(111)in acidic solutions.Experimental results demonstrate a rectangular hyperbo...In this study,we systematically investigated the effect of proton concentration on the kinetics of the oxygen reduction reaction(ORR)on Pt(111)in acidic solutions.Experimental results demonstrate a rectangular hyperbolic relationship,i.e.,the ORR current excluding the effect of other variables increases with proton concentration and then tends to a constant value.We consider that this is caused by the limitation of ORR kinetics by the trace oxygen concentration in the solution,which determines the upper limit of ORR kinetics.A model of effective concentration is further proposed for rectangular hyperbolic relationships:when the reactant concentration is high enough to reach a critical saturation concentration,the effective reactant concentration will become a constant value.This could be due to the limited concentration of a certain reactant for reactions involving more than one reactant or the limited number of active sites available on the catalyst.Our study provides new insights into the kinetics of electrocatalytic reactions,and it is important for the proper evaluation of catalyst activity and the study of structureperformance relationships.展开更多
Anisotropic hyperbolic phonon polaritons(PhPs)in natural biaxial hyperbolic materialα-MoO_(3) has opened up new avenues for mid-infrared nanophotonics,while active tunability ofα-MoO_(3) PhPs is still an urgent prob...Anisotropic hyperbolic phonon polaritons(PhPs)in natural biaxial hyperbolic materialα-MoO_(3) has opened up new avenues for mid-infrared nanophotonics,while active tunability ofα-MoO_(3) PhPs is still an urgent problem necessarily to be solved.In this study,we present a theoretical demonstration of actively tuningα-MoO_(3) PhPs using phase change material VO_(2) and graphene.It is observed thatα-MoO_(3) PhPs are greatly dependent on the propagation plane angle of PhPs.The insulator-to-metal phase transition of VO_(2) has a significant effect on the hybridization PhPs of theα-MoO_(3)/VO_(2) structure and allows to obtain actively tunableα-MoO_(3) PhPs,which is especially obvious when the propagation plane angle of PhPs is 900.Moreover,when graphene surface plasmon sources are placed at the top or bottom ofα-MoO_(3) inα-MoO_(3)/VO_(2)structure,tunable coupled hyperbolic plasmon-phonon polaritons inside its Reststrahlen bands(RB s)and surface plasmonphonon polaritons outside its RBs can be achieved.In addition,the above-mentionedα-MoO_(3)-based structures also lead to actively tunable anisotropic spontaneous emission(SE)enhancement.This study may be beneficial for realization of active tunability of both PhPs and SE ofα-MoO_(3),and facilitate a deeper understanding of the mechanisms of anisotropic light-matter interaction inα-MoO_(3) using functional materials.展开更多
Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f i...Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.展开更多
Relative rotation between the emitter and receiver could effectively modulate the near-field radiative heat transfer(NFRHT)in anisotropic media.Due to the strong in-plane anisotropy,natural hyperbolic materials can be...Relative rotation between the emitter and receiver could effectively modulate the near-field radiative heat transfer(NFRHT)in anisotropic media.Due to the strong in-plane anisotropy,natural hyperbolic materials can be used to construct near-field radiative modulators with excellent modulation effects.However,in practical applications,natural hyperbolic materials need to be deposited on the substrate,and the influence of substrate on modulation effect has not been studied yet.In this work,we investigate the influence of substrate effect on near-field radiative modulator based onα-MoO_(3).The results show that compared to the situation without a substrate,the presence of both lossless and lossy substrate will reduce the modulation contrast(MC)for different film thicknesses.When the real or imaginary component of the substrate permittivity increases,the mismatch of hyperbolic phonon polaritons(HPPs)weakens,resulting in a reduction in MC.By reducing the real and imaginary components of substrate permittivity,the MC can be significantly improved,reaching 4.64 forε_(s)=3 at t=10 nm.This work indicates that choosing a substrate with a smaller permittivity helps to achieve a better modulation effect,and provides guidance for the application of natural hyperbolic materials in the near-field radiative modulator.展开更多
Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagati...Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.展开更多
We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third ord...We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.展开更多
In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy ...In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary conditions.Furthermore,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO method.Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme.展开更多
Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes.Because they do ...Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes.Because they do not involve any special data structure,and do not induce savings in memory requirements,they are easily implemented on existing codes and are recommended for 1D and 2D simulations when intensive testing is required.The multilevel technique can also be applied to balance laws,but in this case,numerical errors may be induced by the technique.We present a series of numerical tests that point out that the use of monotonicity-preserving interpolatory techniques eliminates the numerical errors observed when using the usual 4-point centered Lagrange interpolation,and leads to a more robust multilevel code for balance laws,while maintaining the efficiency rates observed forhyperbolic conservation laws.展开更多
Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of ...Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of the comparable accuracy.This makes them quite attractive for several science and engineering applications.But,to the best of our knowledge,such schemes have not been extended to non-linear hyperbolic systems with non-conservative products.In this paper,we perform such an extension which improves the domain of the applicability of such schemes.The extension is carried out by writing the scheme in fluctuation form.We use the HLLI Riemann solver of Dumbser and Balsara(J.Comput.Phys.304:275-319,2016)as a building block for carrying out this extension.Because of the use of an HLL building block,the resulting scheme has a proper supersonic limit.The use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme,thus expanding its domain of the applicability.Our new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions,making it very easy for users to transition over to the present formulation.For conservation laws,the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO,with two major advantages:(i)It can capture jumps in stationary linearly degenerate wave families exactly.(i)It only requires the reconstruction to be applied once.Several examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of the accuracy for smooth multidimensional flows.Stringent Riemann problems and several novel multidimensional problems that are drawn from compressible Baer-Nunziato multiphase flow,multiphase debris flow and twolayer shallow water equations are also shown to document the robustness of the method.For some test problems that require well-balancing we have even been able to apply the scheme without any modification and obtain good results.Many useful PDEs may have stiff relaxation source terms for which the finite difference formulation of WENO is shown to provide some genuine advantages.展开更多
We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a ...We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a Riemannian version of the Adam algorithm.We show numerical simulations of these algorithms on various benchmarks.展开更多
Graph Convolutional Neural Networks(GCNs)have been widely used in various fields due to their powerful capabilities in processing graph-structured data.However,GCNs encounter significant challenges when applied to sca...Graph Convolutional Neural Networks(GCNs)have been widely used in various fields due to their powerful capabilities in processing graph-structured data.However,GCNs encounter significant challenges when applied to scale-free graphs with power-law distributions,resulting in substantial distortions.Moreover,most of the existing GCN models are shallow structures,which restricts their ability to capture dependencies among distant nodes and more refined high-order node features in scale-free graphs with hierarchical structures.To more broadly and precisely apply GCNs to real-world graphs exhibiting scale-free or hierarchical structures and utilize multi-level aggregation of GCNs for capturing high-level information in local representations,we propose the Hyperbolic Deep Graph Convolutional Neural Network(HDGCNN),an end-to-end deep graph representation learning framework that can map scale-free graphs from Euclidean space to hyperbolic space.In HDGCNN,we define the fundamental operations of deep graph convolutional neural networks in hyperbolic space.Additionally,we introduce a hyperbolic feature transformation method based on identity mapping and a dense connection scheme based on a novel non-local message passing framework.In addition,we present a neighborhood aggregation method that combines initial structural featureswith hyperbolic attention coefficients.Through the above methods,HDGCNN effectively leverages both the structural features and node features of graph data,enabling enhanced exploration of non-local structural features and more refined node features in scale-free or hierarchical graphs.Experimental results demonstrate that HDGCNN achieves remarkable performance improvements over state-ofthe-art GCNs in node classification and link prediction tasks,even when utilizing low-dimensional embedding representations.Furthermore,when compared to shallow hyperbolic graph convolutional neural network models,HDGCNN exhibits notable advantages and performance enhancements.展开更多
Utilizing graph neural networks for knowledge embedding to accomplish the task of knowledge graph completion(KGC)has become an important research area in knowledge graph completion.However,the number of nodes in the k...Utilizing graph neural networks for knowledge embedding to accomplish the task of knowledge graph completion(KGC)has become an important research area in knowledge graph completion.However,the number of nodes in the knowledge graph increases exponentially with the depth of the tree,whereas the distances of nodes in Euclidean space are second-order polynomial distances,whereby knowledge embedding using graph neural networks in Euclidean space will not represent the distances between nodes well.This paper introduces a novel approach called hyperbolic hierarchical graph attention network(H2GAT)to rectify this limitation.Firstly,the paper conducts knowledge representation in the hyperbolic space,effectively mitigating the issue of exponential growth of nodes with tree depth and consequent information loss.Secondly,it introduces a hierarchical graph atten-tion mechanism specifically designed for the hyperbolic space,allowing for enhanced capture of the network structure inherent in the knowledge graph.Finally,the efficacy of the proposed H2GAT model is evaluated on benchmark datasets,namely WN18RR and FB15K-237,thereby validating its effectiveness.The H2GAT model achieved 0.445,0.515,and 0.586 in the Hits@1,Hits@3 and Hits@10 metrics respectively on the WN18RR dataset and 0.243,0.367 and 0.518 on the FB15K-237 dataset.By incorporating hyperbolic space embedding and hierarchical graph attention,the H2GAT model successfully addresses the limitations of existing hyperbolic knowledge embedding models,exhibiting its competence in knowledge graph completion tasks.展开更多
In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyp...In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyperbolic space, which are the analogues of the geometric construction of inversions with respect to a circle on the complex plane. These results are then applied to Lorentz transformation and Einstein velocity addition to obtain geometric illustrations. We gain new insights into the relationship between special relativity and hyperbolic geometry.展开更多
Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The ...Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared.展开更多
For training the present Neural Network(NN)models,the standard technique is to utilize decaying Learning Rates(LR).While the majority of these techniques commence with a large LR,they will decay multiple times over ti...For training the present Neural Network(NN)models,the standard technique is to utilize decaying Learning Rates(LR).While the majority of these techniques commence with a large LR,they will decay multiple times over time.Decaying has been proved to enhance generalization as well as optimization.Other parameters,such as the network’s size,the number of hidden layers,drop-outs to avoid overfitting,batch size,and so on,are solely based on heuristics.This work has proposed Adaptive Teaching Learning Based(ATLB)Heuristic to identify the optimal hyperparameters for diverse networks.Here we consider three architec-tures Recurrent Neural Networks(RNN),Long Short Term Memory(LSTM),Bidirectional Long Short Term Memory(BiLSTM)of Deep Neural Networks for classification.The evaluation of the proposed ATLB is done through the various learning rate schedulers Cyclical Learning Rate(CLR),Hyperbolic Tangent Decay(HTD),and Toggle between Hyperbolic Tangent Decay and Triangular mode with Restarts(T-HTR)techniques.Experimental results have shown the performance improvement on the 20Newsgroup,Reuters Newswire and IMDB dataset.展开更多
文摘Hyperbole is a very common rhetorical device which is widely used both in English and Chinese. In order to express his/her strong feelings and also to make his/her language more powerful, the writer/speaker exaggerates things on purpose. Yet in spite of the over-truth expression, employment of hyperbole does not affect the conversation flow between parties. Through an analysis of hyperbole from the perspective of pragrnatics, this article tries to explain the pragmatic functions of hyperbole.
文摘In daily lives,people unconsciously use hyperbole to address their speech in everyday conversation,it has been an indivisible part of people's talk.And the usage of hyperbole has its own effects and functions,this paper aims at searching the main effects of hyperbole in our everyday conversations,and tries to classify them as three effects or functions.First,hyperbole can reveal the essence of events.Second,it can enhance the infection of sentences and appeal to audience.Third,it can help the listeners imagine the situation the speaker described.And in this paper,through the analysis of everyday conversations,illustrated how hyperbole achieved these effects.
基金supported by the National Natural Science Foundation of China(21972131)。
文摘In this study,we systematically investigated the effect of proton concentration on the kinetics of the oxygen reduction reaction(ORR)on Pt(111)in acidic solutions.Experimental results demonstrate a rectangular hyperbolic relationship,i.e.,the ORR current excluding the effect of other variables increases with proton concentration and then tends to a constant value.We consider that this is caused by the limitation of ORR kinetics by the trace oxygen concentration in the solution,which determines the upper limit of ORR kinetics.A model of effective concentration is further proposed for rectangular hyperbolic relationships:when the reactant concentration is high enough to reach a critical saturation concentration,the effective reactant concentration will become a constant value.This could be due to the limited concentration of a certain reactant for reactions involving more than one reactant or the limited number of active sites available on the catalyst.Our study provides new insights into the kinetics of electrocatalytic reactions,and it is important for the proper evaluation of catalyst activity and the study of structureperformance relationships.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.52204258 and 52106099)the Postdoctoral Research Foundation of China (Grant No.2023M743779)+2 种基金the Fundamental Research Funds for the Central Universities (Grant No.2022QN1017)the Key Research Development Projects in Xinjiang Uygur Autonomous Region (Grant No.2022B03003-3)the Shandong Provincial Natural Science Foundation (Grant No.ZR2020LLZ004)。
文摘Anisotropic hyperbolic phonon polaritons(PhPs)in natural biaxial hyperbolic materialα-MoO_(3) has opened up new avenues for mid-infrared nanophotonics,while active tunability ofα-MoO_(3) PhPs is still an urgent problem necessarily to be solved.In this study,we present a theoretical demonstration of actively tuningα-MoO_(3) PhPs using phase change material VO_(2) and graphene.It is observed thatα-MoO_(3) PhPs are greatly dependent on the propagation plane angle of PhPs.The insulator-to-metal phase transition of VO_(2) has a significant effect on the hybridization PhPs of theα-MoO_(3)/VO_(2) structure and allows to obtain actively tunableα-MoO_(3) PhPs,which is especially obvious when the propagation plane angle of PhPs is 900.Moreover,when graphene surface plasmon sources are placed at the top or bottom ofα-MoO_(3) inα-MoO_(3)/VO_(2)structure,tunable coupled hyperbolic plasmon-phonon polaritons inside its Reststrahlen bands(RB s)and surface plasmonphonon polaritons outside its RBs can be achieved.In addition,the above-mentionedα-MoO_(3)-based structures also lead to actively tunable anisotropic spontaneous emission(SE)enhancement.This study may be beneficial for realization of active tunability of both PhPs and SE ofα-MoO_(3),and facilitate a deeper understanding of the mechanisms of anisotropic light-matter interaction inα-MoO_(3) using functional materials.
基金supported by the Grant No.20-16367/NRPU/RD/HEC/20212021。
文摘Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.
基金Project supported by the National Natural Science Foundation of China (Grant No.52106099)the Natural Science Foundation of Shandong Province of China (Grant No.ZR2022YQ57)the Taishan Scholars Program。
文摘Relative rotation between the emitter and receiver could effectively modulate the near-field radiative heat transfer(NFRHT)in anisotropic media.Due to the strong in-plane anisotropy,natural hyperbolic materials can be used to construct near-field radiative modulators with excellent modulation effects.However,in practical applications,natural hyperbolic materials need to be deposited on the substrate,and the influence of substrate on modulation effect has not been studied yet.In this work,we investigate the influence of substrate effect on near-field radiative modulator based onα-MoO_(3).The results show that compared to the situation without a substrate,the presence of both lossless and lossy substrate will reduce the modulation contrast(MC)for different film thicknesses.When the real or imaginary component of the substrate permittivity increases,the mismatch of hyperbolic phonon polaritons(HPPs)weakens,resulting in a reduction in MC.By reducing the real and imaginary components of substrate permittivity,the MC can be significantly improved,reaching 4.64 forε_(s)=3 at t=10 nm.This work indicates that choosing a substrate with a smaller permittivity helps to achieve a better modulation effect,and provides guidance for the application of natural hyperbolic materials in the near-field radiative modulator.
文摘Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.
基金partially supported by the National Nature Science Foundation of China(12271114)the Guangxi Natural Science Foundation(2023JJD110009,2019JJG110003,2019AC20214)+2 种基金the Innovation Project of Guangxi Graduate Education(JGY2023061)the Key Laboratory of Mathematical Model and Application(Guangxi Normal University)the Education Department of Guangxi Zhuang Autonomous Region。
文摘We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.
基金supported by the NSFC grant 12101128supported by the NSFC grant 12071392.
文摘In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary conditions.Furthermore,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO method.Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme.
基金supported by Grant PID2020-117211GB-I00funded by MCIN/AEI/10.13039/501100011033+4 种基金by Grant CIAICO/2021/227funded by the Generalitat Valencianasupported by the Ministerio de Ciencia e Innovacion of Spain(Grant Ref.PID2021-125709OB-C21)funded by MCIN/AEI/10.13039/501100011033/FEDER,UEby the Generalitat Valenciana(CIAICO/2021/224).
文摘Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes.Because they do not involve any special data structure,and do not induce savings in memory requirements,they are easily implemented on existing codes and are recommended for 1D and 2D simulations when intensive testing is required.The multilevel technique can also be applied to balance laws,but in this case,numerical errors may be induced by the technique.We present a series of numerical tests that point out that the use of monotonicity-preserving interpolatory techniques eliminates the numerical errors observed when using the usual 4-point centered Lagrange interpolation,and leads to a more robust multilevel code for balance laws,while maintaining the efficiency rates observed forhyperbolic conservation laws.
基金support via NSF grants NSF-19-04774,NSF-AST-2009776,NASA-2020-1241NASA grant 80NSSC22K0628.DSB+3 种基金HK acknowledge support from a Vajra award,VJR/2018/00129a travel grant from Notre Dame Internationalsupport via AFOSR grant FA9550-20-1-0055NSF grant DMS-2010107.
文摘Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of the comparable accuracy.This makes them quite attractive for several science and engineering applications.But,to the best of our knowledge,such schemes have not been extended to non-linear hyperbolic systems with non-conservative products.In this paper,we perform such an extension which improves the domain of the applicability of such schemes.The extension is carried out by writing the scheme in fluctuation form.We use the HLLI Riemann solver of Dumbser and Balsara(J.Comput.Phys.304:275-319,2016)as a building block for carrying out this extension.Because of the use of an HLL building block,the resulting scheme has a proper supersonic limit.The use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme,thus expanding its domain of the applicability.Our new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions,making it very easy for users to transition over to the present formulation.For conservation laws,the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO,with two major advantages:(i)It can capture jumps in stationary linearly degenerate wave families exactly.(i)It only requires the reconstruction to be applied once.Several examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of the accuracy for smooth multidimensional flows.Stringent Riemann problems and several novel multidimensional problems that are drawn from compressible Baer-Nunziato multiphase flow,multiphase debris flow and twolayer shallow water equations are also shown to document the robustness of the method.For some test problems that require well-balancing we have even been able to apply the scheme without any modification and obtain good results.Many useful PDEs may have stiff relaxation source terms for which the finite difference formulation of WENO is shown to provide some genuine advantages.
基金partially supported by NSF Grants DMS-1854434,DMS-1952644,and DMS-2151235 at UC Irvinesupported by NSF Grants DMS-1924935,DMS-1952339,DMS-2110145,DMS-2152762,and DMS-2208361,and DOE Grants DE-SC0021142 and DE-SC0002722.
文摘We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a Riemannian version of the Adam algorithm.We show numerical simulations of these algorithms on various benchmarks.
基金supported by the National Natural Science Foundation of China-China State Railway Group Co.,Ltd.Railway Basic Research Joint Fund (Grant No.U2268217)the Scientific Funding for China Academy of Railway Sciences Corporation Limited (No.2021YJ183).
文摘Graph Convolutional Neural Networks(GCNs)have been widely used in various fields due to their powerful capabilities in processing graph-structured data.However,GCNs encounter significant challenges when applied to scale-free graphs with power-law distributions,resulting in substantial distortions.Moreover,most of the existing GCN models are shallow structures,which restricts their ability to capture dependencies among distant nodes and more refined high-order node features in scale-free graphs with hierarchical structures.To more broadly and precisely apply GCNs to real-world graphs exhibiting scale-free or hierarchical structures and utilize multi-level aggregation of GCNs for capturing high-level information in local representations,we propose the Hyperbolic Deep Graph Convolutional Neural Network(HDGCNN),an end-to-end deep graph representation learning framework that can map scale-free graphs from Euclidean space to hyperbolic space.In HDGCNN,we define the fundamental operations of deep graph convolutional neural networks in hyperbolic space.Additionally,we introduce a hyperbolic feature transformation method based on identity mapping and a dense connection scheme based on a novel non-local message passing framework.In addition,we present a neighborhood aggregation method that combines initial structural featureswith hyperbolic attention coefficients.Through the above methods,HDGCNN effectively leverages both the structural features and node features of graph data,enabling enhanced exploration of non-local structural features and more refined node features in scale-free or hierarchical graphs.Experimental results demonstrate that HDGCNN achieves remarkable performance improvements over state-ofthe-art GCNs in node classification and link prediction tasks,even when utilizing low-dimensional embedding representations.Furthermore,when compared to shallow hyperbolic graph convolutional neural network models,HDGCNN exhibits notable advantages and performance enhancements.
基金the Beijing Municipal Science and Technology Program(No.Z231100001323004).
文摘Utilizing graph neural networks for knowledge embedding to accomplish the task of knowledge graph completion(KGC)has become an important research area in knowledge graph completion.However,the number of nodes in the knowledge graph increases exponentially with the depth of the tree,whereas the distances of nodes in Euclidean space are second-order polynomial distances,whereby knowledge embedding using graph neural networks in Euclidean space will not represent the distances between nodes well.This paper introduces a novel approach called hyperbolic hierarchical graph attention network(H2GAT)to rectify this limitation.Firstly,the paper conducts knowledge representation in the hyperbolic space,effectively mitigating the issue of exponential growth of nodes with tree depth and consequent information loss.Secondly,it introduces a hierarchical graph atten-tion mechanism specifically designed for the hyperbolic space,allowing for enhanced capture of the network structure inherent in the knowledge graph.Finally,the efficacy of the proposed H2GAT model is evaluated on benchmark datasets,namely WN18RR and FB15K-237,thereby validating its effectiveness.The H2GAT model achieved 0.445,0.515,and 0.586 in the Hits@1,Hits@3 and Hits@10 metrics respectively on the WN18RR dataset and 0.243,0.367 and 0.518 on the FB15K-237 dataset.By incorporating hyperbolic space embedding and hierarchical graph attention,the H2GAT model successfully addresses the limitations of existing hyperbolic knowledge embedding models,exhibiting its competence in knowledge graph completion tasks.
文摘In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyperbolic space, which are the analogues of the geometric construction of inversions with respect to a circle on the complex plane. These results are then applied to Lorentz transformation and Einstein velocity addition to obtain geometric illustrations. We gain new insights into the relationship between special relativity and hyperbolic geometry.
文摘Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared.
文摘For training the present Neural Network(NN)models,the standard technique is to utilize decaying Learning Rates(LR).While the majority of these techniques commence with a large LR,they will decay multiple times over time.Decaying has been proved to enhance generalization as well as optimization.Other parameters,such as the network’s size,the number of hidden layers,drop-outs to avoid overfitting,batch size,and so on,are solely based on heuristics.This work has proposed Adaptive Teaching Learning Based(ATLB)Heuristic to identify the optimal hyperparameters for diverse networks.Here we consider three architec-tures Recurrent Neural Networks(RNN),Long Short Term Memory(LSTM),Bidirectional Long Short Term Memory(BiLSTM)of Deep Neural Networks for classification.The evaluation of the proposed ATLB is done through the various learning rate schedulers Cyclical Learning Rate(CLR),Hyperbolic Tangent Decay(HTD),and Toggle between Hyperbolic Tangent Decay and Triangular mode with Restarts(T-HTR)techniques.Experimental results have shown the performance improvement on the 20Newsgroup,Reuters Newswire and IMDB dataset.
