Low-density short-duration pulsed current-assisted aging treatment was applied to the Ti-6Al-4V-0.5Mo-0.5Zr alloy subjected to different solution treatments.The results show that numerous α_(p) phases redissolve into...Low-density short-duration pulsed current-assisted aging treatment was applied to the Ti-6Al-4V-0.5Mo-0.5Zr alloy subjected to different solution treatments.The results show that numerous α_(p) phases redissolve into the new β phase during the pulsed current-assisted aging process,and then the newly formed β phase is mainly transformed into the β_(t) phase,with occasional transition to new α_(p) phase,leading to a remarkable grain refinement,especially for the lamellarαs phases.In comparison to conventional aging treatment,the pulsed current-assisted aging approach achieves a significant enhancement in strength without degrading ductility,yielding an excellent mechanical property combination:a yield strength of 932 MPa,a tensile strength of 1042 MPa,and an elongation of 12.2%.It is primarily ascribed to the increased fraction of β_(t) phases,the obvious grain refinement effect,and the slip block effect induced by the multiple-variantαs colonies distributed within β_(t) phases.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:...AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:Totally 716 eyes of 716 patients with primary open angle glaucoma(POAG)with at least 5 reliable 24-2 test results and 2y of follow-up were selected.The functional GEE model was used to detect perimetric progression in the training dataset(501 eyes).In the testing dataset(215 eyes),progression was evaluated the functional GEE model,mean deviation(MD)and visual field index(VFI)rates of change,Advanced Glaucoma Intervention Study(AGIS)and Collaborative Initial Glaucoma Treatment Study(CIGTS)scores,and pointwise linear regression(PLR).RESULTS:The proposed method showed the highest proportion of eyes detected as progression(54.4%),followed by the VFI rate(34.4%),PLR(23.3%),and MD rate(21.4%).The CIGTS and AGIS scores had a lower proportion of eyes detected as progression(7.9%and 5.1%,respectively).The time to detection of progression was significantly shorter for the proposed method than that of other algorithms(adjusted P≤0.019).The VFI rate displayed moderate pairwise agreement with the proposed method(k=0.47).CONCLUSION:The functional GEE model shows the highest proportion of eyes detected as perimetric progression and the shortest time to detect perimetric progression in patients with POAG.展开更多
In this article, based on the Taylor expansions of generating functions and stepwise refinement procedure, authors suggest a algorithm for finding the Lie and high (generalized) symmetries of partial differential equa...In this article, based on the Taylor expansions of generating functions and stepwise refinement procedure, authors suggest a algorithm for finding the Lie and high (generalized) symmetries of partial differential equations (PDEs). This algorithm transforms the problem having to solve over-determining PDEs commonly encountered and difficulty part in standard methods into one solving to algebraic equations to which one easy obtain solution. so, it reduces significantly the difficulties of the problem and raise computing efficiency. The whole procedure of the algorithm is carried out automatically by using any computer algebra system. In general, this algorithm can yields many more important symmetries for PDEs.展开更多
This paper is devoted to investigating the solutions of refinement equations of the form Ф（x）=∑α∈Z^s α（α）Ф（Mx-α）,x∈R^s,where the vector of functions Ф = （Ф1,… ,Фr）^T is in （L1（R^s））^r, α =（...This paper is devoted to investigating the solutions of refinement equations of the form Ф（x）=∑α∈Z^s α（α）Ф（Mx-α）,x∈R^s,where the vector of functions Ф = （Ф1,… ,Фr）^T is in （L1（R^s））^r, α =（α（α））α∈Z^s is an infinitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim n→∞ M^-n =0, with m = detM. Some properties about the solutions of refinement equations axe obtained.展开更多
In this paper we will first prove that the nontrivial L p solutions of the vector refinement equation exist if and only if the corresponding subdivision scheme with a suitable initial function converges in L p...In this paper we will first prove that the nontrivial L p solutions of the vector refinement equation exist if and only if the corresponding subdivision scheme with a suitable initial function converges in L p without assumption of the stability of the solutions. Then we obtain a characterization of the convergence of the subdivision scheme in terms of the mask. This gives a complete answer to the existence of L p solutions of the refinement equation and the convergence of the corresponding subdivision schemes.展开更多
In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondl...In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.展开更多
Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay di...Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.展开更多
A local refinement hybrid scheme(LRCSPH-FDM)is proposed to solve the two-dimensional(2D)time fractional nonlinear Schrodinger equation(TF-NLSE)in regularly or irregularly shaped domains,and extends the scheme to predi...A local refinement hybrid scheme(LRCSPH-FDM)is proposed to solve the two-dimensional(2D)time fractional nonlinear Schrodinger equation(TF-NLSE)in regularly or irregularly shaped domains,and extends the scheme to predict the quantum mechanical properties governed by the time fractional Gross-Pitaevskii equation(TF-GPE)with the rotating Bose-Einstein condensate.It is the first application of the purely meshless method to the TF-NLSE to the author’s knowledge.The proposed LRCSPH-FDM(which is based on a local refinement corrected SPH method combined with FDM)is derived by using the finite difference scheme(FDM)to discretize the Caputo TF term,followed by using a corrected smoothed particle hydrodynamics(CSPH)scheme continuously without using the kernel derivative to approximate the spatial derivatives.Meanwhile,the local refinement technique is adopted to reduce the numerical error.In numerical simulations,the complex irregular geometry is considered to show the flexibility of the purely meshless particle method and its advantages over the grid-based method.The numerical convergence rate and merits of the proposed LRCSPH-FDM are illustrated by solving several 1D/2D(where 1D stands for one-dimensional)analytical TF-NLSEs in a rectangular region(with regular or irregular particle distribution)or in a region with irregular geometry.The proposed method is then used to predict the complex nonlinear dynamic characters of 2D TF-NLSE/TF-GPE in a complex irregular domain,and the results from the posed method are compared with those from the FDM.All the numerical results show that the present method has a good accuracy and flexible application capacity for the TF-NLSE/GPE in regions of a complex shape.展开更多
The pursuit of Ag-based alloys with both high strength and toughness has posed a longstanding chal-lenge.In this study,we investigated the cluster strengthening and grain refinement toughening mecha-nisms in fully oxi...The pursuit of Ag-based alloys with both high strength and toughness has posed a longstanding chal-lenge.In this study,we investigated the cluster strengthening and grain refinement toughening mecha-nisms in fully oxidized AgMgNi alloys,which were internally oxidized at 800℃ for 8 h under an oxy-gen atmosphere.We found that Mg-O clusters contributed to the hardening(138 HV)and strengthening(376.9 MPa)of the AgMg alloy through solid solution strengthening effects,albeit at the expense of duc-tility.To address this limitation,we introduced Ni nanoparticles into the AgMg alloy,resulting in signifi-cant grain refinement within its microstructure.Specifically,the grain size decreased from 67.2μm in the oxidized AgMg alloy to below 6.0μm in the oxidized AgMgNi alloy containing 0.3 wt%Ni.Consequently,the toughness increased significantly,rising from toughness value of 2177.9 MJ m^(-3) in the oxidized AgMg alloy to 6186.1 MJ m^(-3) in the oxidized AgMgNi alloy,representing a remarkable 2.8-fold enhancement.Furthermore,the internally oxidized AgMgNi alloy attained a strength of up to 387.6 MPa,comparable to that of the internally oxidized AgMg alloy,thereby demonstrating the successful realization of concurrent strengthening and toughening.These results collectively offer a novel approach for the design of high-performance alloys through the synergistic combination of cluster strengthening and grain refinement toughening.展开更多
Ammonia and nitric acid,versatile industrial feedstocks,and burgeoning clean energy vectors hold immense promise for sustainable development.However,Haber–Bosch and Ostwald processes,which generates carbon dioxide as...Ammonia and nitric acid,versatile industrial feedstocks,and burgeoning clean energy vectors hold immense promise for sustainable development.However,Haber–Bosch and Ostwald processes,which generates carbon dioxide as massive by-product,contribute to greenhouse effects and pose environmental challenges.Thus,the pursuit of nitrogen fixation through carbon–neutral pathways under benign conditions is a frontier of scientific topics,with the harnessing of solar energy emerging as an enticing and viable option.This review delves into the refinement strategies for scale-up mild photocatalytic nitrogen fixation,fields ripe with potential for innovation.The narrative is centered on enhancing the intrinsic capabilities of catalysts to surmount current efficiency barriers.Key focus areas include the in-depth exploration of fundamental mechanisms underpinning photocatalytic procedures,rational element selection,and functional planning,state-of-the-art experimental protocols for understanding photo-fixation processes,valid photocatalytic activity evaluation,and the rational design of catalysts.Furthermore,the review offers a suite of forward-looking recommendations aimed at propelling the advancement of mild nitrogen photo-fixation.It scrutinizes the existing challenges and prospects within this burgeoning domain,aspiring to equip researchers with insightful perspectives that can catalyze the evolution of cutting-edge nitrogen fixation methodologies and steer the development of next-generation photocatalytic systems.展开更多
Due to the low content of alloying elements and the lack of effective nucleation sites,the fusion zone(FZ)of tungsten inert gas(TIG)welded AZ31 alloy typically exhibits undesirable coarse columnar grains,which can res...Due to the low content of alloying elements and the lack of effective nucleation sites,the fusion zone(FZ)of tungsten inert gas(TIG)welded AZ31 alloy typically exhibits undesirable coarse columnar grains,which can result in solidification defects and reduced mechanical properties.In this work,a novel welding wire containing MgO particles has been developed to promote columnar-to-equiaxed transition(CET)in the FZ of TIG-welded AZ31 alloy.The results show the achievement of a fully equiaxed grain structure in the FZ,with a significant 71.9%reduction in grain size to 41 μm from the original coarse columnar dendrites.Furthermore,the combination of using MgO-containing welding wire and pulse current can further refine the grain size to 25.6 μm.Microstructural analyses reveal the homogeneous distribution of MgO particles in the FZ.The application of pulse current results in an increase in the number density of MgO(1-2 μm)from 5.16 × 10^(4) m^(-3) to 6.18 × 10^(4) m^(-3).The good crystallographic matching relationship between MgO and α-Mg matrix,characterized by the orientation relationship of[11(2)0]α-Mg//[0(1)1]MgO and(0002)_(α-Mg)//(111)_(MgO),indicates that the MgO particles can act as effective nucleation sites for α-Mg to reduce nucleation undercooling.According to the Hunt criteria,the critical temperature gradient for CET is greatly enhanced due to the significantly increased number density of MgO nucleation sites.In addition,the correlation with the thermal simulation results reveals a transition in the solidification conditions within the welding pool from the columnar grain zone to the equiaxed grain zone in the CET map,leading to the realization of CET.The exceptional grain refinement has contributed to a simultaneous improvement in the strength and plasticity of welded joints.This study presents a novel strategy for controlling equiaxed microstructure and optimizing mechanical properties in fusion welding or wire and arc additive manufacturing of Mg alloy components.展开更多
Background:Enzyme fragility remains a major challenge in research and applications.Free enzymes are highly unstable,inactivated by heat,acid,alkali,or organic solvents,and often lose activity even under optimal storag...Background:Enzyme fragility remains a major challenge in research and applications.Free enzymes are highly unstable,inactivated by heat,acid,alkali,or organic solvents,and often lose activity even under optimal storage conditions.Limiting their use in cosmetics.Few commercial products combine acids and enzymes effectively.Objective:To investigate the physicochemical properties,in vitro exfoliation efficacy,and effects on facial skin parameters of a supramolecular acid-enzyme complex(SAE)composed of mandelic acid(MAN),betaine(BET),and composite enzymes(CE;papain and bromelain),thereby establishing a theoretical foundation for cosmetic applications.Methods:The supramolecular structure was characterized using Fourier transform infrared(FTIR)spectroscopy and proton nuclear magnetic resonance(1H NMR)spectroscopy.Dissolution experiments were conducted to compare the solubility of SAE and CE in aqueous solutions.Enzymatic activity assays evaluated the stabilizing effect of supramolecular deep eutectic technology on enzymes.In vitro exfoliation tests assessed acid-enzyme synergy in keratin removal.A 4-week clinical trial evaluated the efficacy of a 2%SAE essence aqueous solution on facial skin parameters.Results:Dissolution experiments confirmed that supramolecular deep eutectic technology significantly improved enzyme solubility.Enzymatic activity tests demonstrated that this technology effectively preserved protease activity,substantially enhancing its practical applicability.Furthermore,in vitro exfoliation efficacy tests revealed that this technology strengthened the synergistic interaction between acids and enzymes and exhibited superior stratum corneum-removing capability of the SAE.In clinical evaluations of efficacy,after 7 days of using the essence containing SAE,the formulation significantly enhanced cheek gloss(+8.08%),while reducing comedones volume(-16.25%).after 28 days,significantly enhanced cheek hydration(+25.0%,SCH),gloss(+15.93%),and smoothness(−7.78%SEsm),while reducing TEWL(−6.86%),sebum(−15.54%),roughness(+16.24%SEr),and pore metrics(volume:−39.98%;count:−30.64%),and decreased comedones(blackheads:−70.33%;Whiteheads:−52.42%;all p<0.05).Conclusion:The supramolecular acid-enzyme complex demonstrates enhanced stability,improved solubility,and superior exfoliation efficacy compared to free enzymes.Clinical results further confirm its multifunctional benefits,including enhancing skin hydration,sebum regulation,barrier repair,pore refinement,and comedolytic effects.This study provides both theoretical and practical foundations for developing stable acid-enzyme combinations in dermatological applications.展开更多
High cracking susceptibility of Al-Li alloys with Ti/Ce B6addition is thoroughly suppressed in laser powder bed fusion(LPBF)processing of Ti/Ce co-modified 2195 alloys at relatively high scan speeds,while the cracking...High cracking susceptibility of Al-Li alloys with Ti/Ce B6addition is thoroughly suppressed in laser powder bed fusion(LPBF)processing of Ti/Ce co-modified 2195 alloys at relatively high scan speeds,while the cracking suppression mechanism and phase formation in these composites are not clarified.In this work,microstructure evolution and mechanical performance of the LPBF-fabricated Ti/Ce co-modified 2195 are investigated to reveal their cracking suppression and strengthening mechanisms.The results show that apparent grain refinement of the composites is ascribed to high supercooling from rapid formation of constitutional supercooling zone in front of solid–liquid interfaces by high-Q-value Ti solute,and heterogeneous nucleation of in situ formed Al3Ti and Al11Ce3precipitates.Their synergistic interactions promote formation of fine equiaxed grains and thus inhibit crack initiation.The composites exhibit high microhardness of 100±5HV0.2,nano-hardness of 1.6±0.1 GPa and elastic modulus of 97±3 GPa,where the elastic modulus increases by 27%and 31%compared to those of LPBF-processed and conventionally manufactured 2195 alloys,respectively.A tensile strength of 336 MPa and an elongation of 3%are obtained from in-situ synchrotron X-ray diffraction measurement.The improved properties are derived from grain refinement and Orowan strengthening.Based on the optimal processing parameter and composition,a bracket component filled with lattice structures is designed and manufactured with good manufacturing quality and processing accuracy.展开更多
To investigate the effect of microstructure evolution on corrosion behavior and strengthening mechanism of Mg-1Zn-1Ca(wt.%)alloys,as-cast Mg-1Zn-1Ca alloys were performed by equal channel angular pressing(ECAP)with 1 ...To investigate the effect of microstructure evolution on corrosion behavior and strengthening mechanism of Mg-1Zn-1Ca(wt.%)alloys,as-cast Mg-1Zn-1Ca alloys were performed by equal channel angular pressing(ECAP)with 1 and 4 passes.The corrosion behavior and mechanical properties of alloys were investigated by optical microscopy(OM),scanning electron microscopy(SEM),electron backscatter diffraction(EBSD),electrochemical tests,immersion tests and tensile tests.The results showed that mechanical properties improved after ECAP 1 pass;however,the corrosion resistance deteriorated due to high-density dislocations and fragmented secondary phases by ECAP.In contrast,synchronous improvement in the mechanical properties and corrosion resistance was achieved though grain refinement after ECAP 4 passes;fine grains led to a significant improvement in the yield strength,ultimate tensile strength,elongation,and corrosion rate of 103 MPa,223 MPa,30.5%,and 1.5843 mm/a,respectively.The enhanced corrosion resistance was attributed to the formation of dense corrosion product films by finer grains and the barrier effect by high-density grain boundaries.These results indicated that Mg-1Zn-1Ca alloy has a promising potential for application in biomedical materials.展开更多
In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error...In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.展开更多
This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ...This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.展开更多
Three types of NdFeB magnets with the same composition and different grain sizes were prepared,and then the grain boundary diffusion was conducted using metal Tb under the same technical parameters.The effect of grain...Three types of NdFeB magnets with the same composition and different grain sizes were prepared,and then the grain boundary diffusion was conducted using metal Tb under the same technical parameters.The effect of grain size on the grain boundary diffusion process and properties of sintered NdFeB magnets was investigated.The diffusion process was assessed using X-ray diffractometer,field emission scanning electron microscope,and electron probe microanalyzer.The magnetic properties of the magnet before and after diffusion were investigated.The results show that the grain refinement of the magnet leads to higher Tb utilization efficiency and results in higher coercivity at different temperatures.It can be attributed to the formation of a deeper and more complete core-shell structure,resulting in better magnetic isolation and higher anisotropy of the Nd_(2)Fe_(14)B grains.This work may shed light on developing high coercivity with low heavy rare earth elements through grain refinement.展开更多
In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system w...In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.展开更多
基金National Key Research and Development Program of China(2021YFB3700801)。
文摘Low-density short-duration pulsed current-assisted aging treatment was applied to the Ti-6Al-4V-0.5Mo-0.5Zr alloy subjected to different solution treatments.The results show that numerous α_(p) phases redissolve into the new β phase during the pulsed current-assisted aging process,and then the newly formed β phase is mainly transformed into the β_(t) phase,with occasional transition to new α_(p) phase,leading to a remarkable grain refinement,especially for the lamellarαs phases.In comparison to conventional aging treatment,the pulsed current-assisted aging approach achieves a significant enhancement in strength without degrading ductility,yielding an excellent mechanical property combination:a yield strength of 932 MPa,a tensile strength of 1042 MPa,and an elongation of 12.2%.It is primarily ascribed to the increased fraction of β_(t) phases,the obvious grain refinement effect,and the slip block effect induced by the multiple-variantαs colonies distributed within β_(t) phases.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金Supported by the Korea Health Technology R&D Project through the Korea Health Industry Development Institute(KHIDI),funded by the Ministry of Health&Welfare,Republic of Korea(No.HR20C0026)the National Research Foundation of Korea(NRF)(No.RS-2023-00247504)the Patient-Centered Clinical Research Coordinating Center,funded by the Ministry of Health&Welfare,Republic of Korea(No.HC19C0276).
文摘AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:Totally 716 eyes of 716 patients with primary open angle glaucoma(POAG)with at least 5 reliable 24-2 test results and 2y of follow-up were selected.The functional GEE model was used to detect perimetric progression in the training dataset(501 eyes).In the testing dataset(215 eyes),progression was evaluated the functional GEE model,mean deviation(MD)and visual field index(VFI)rates of change,Advanced Glaucoma Intervention Study(AGIS)and Collaborative Initial Glaucoma Treatment Study(CIGTS)scores,and pointwise linear regression(PLR).RESULTS:The proposed method showed the highest proportion of eyes detected as progression(54.4%),followed by the VFI rate(34.4%),PLR(23.3%),and MD rate(21.4%).The CIGTS and AGIS scores had a lower proportion of eyes detected as progression(7.9%and 5.1%,respectively).The time to detection of progression was significantly shorter for the proposed method than that of other algorithms(adjusted P≤0.019).The VFI rate displayed moderate pairwise agreement with the proposed method(k=0.47).CONCLUSION:The functional GEE model shows the highest proportion of eyes detected as perimetric progression and the shortest time to detect perimetric progression in patients with POAG.
文摘In this article, based on the Taylor expansions of generating functions and stepwise refinement procedure, authors suggest a algorithm for finding the Lie and high (generalized) symmetries of partial differential equations (PDEs). This algorithm transforms the problem having to solve over-determining PDEs commonly encountered and difficulty part in standard methods into one solving to algebraic equations to which one easy obtain solution. so, it reduces significantly the difficulties of the problem and raise computing efficiency. The whole procedure of the algorithm is carried out automatically by using any computer algebra system. In general, this algorithm can yields many more important symmetries for PDEs.
基金Supported by the National Natural Science Foundation of China (10071071)
文摘This paper is devoted to investigating the solutions of refinement equations of the form Ф（x）=∑α∈Z^s α（α）Ф（Mx-α）,x∈R^s,where the vector of functions Ф = （Ф1,… ,Фr）^T is in （L1（R^s））^r, α =（α（α））α∈Z^s is an infinitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim n→∞ M^-n =0, with m = detM. Some properties about the solutions of refinement equations axe obtained.
文摘In this paper we will first prove that the nontrivial L p solutions of the vector refinement equation exist if and only if the corresponding subdivision scheme with a suitable initial function converges in L p without assumption of the stability of the solutions. Then we obtain a characterization of the convergence of the subdivision scheme in terms of the mask. This gives a complete answer to the existence of L p solutions of the refinement equation and the convergence of the corresponding subdivision schemes.
基金Supported by National Natural Science Foundation of China(12101482)Postdoctoral Science Foundation of China(2022M722604)+2 种基金General Project of Science and Technology of Shaanxi Province(2023-YBSF-372)The Natural Science Foundation of Shaan Xi Province(2023-JCQN-0016)Shannxi Mathmatical Basic Science Research Project(23JSQ042)。
文摘In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.
文摘Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11501495,51779215,and 11672259)the Postdoctoral Science Foundation of China(Grant Nos.2015M581869 and 2015T80589)the Jiangsu Government Scholarship for Overseas Studies,China(Grant No.JS-2017-227)。
文摘A local refinement hybrid scheme(LRCSPH-FDM)is proposed to solve the two-dimensional(2D)time fractional nonlinear Schrodinger equation(TF-NLSE)in regularly or irregularly shaped domains,and extends the scheme to predict the quantum mechanical properties governed by the time fractional Gross-Pitaevskii equation(TF-GPE)with the rotating Bose-Einstein condensate.It is the first application of the purely meshless method to the TF-NLSE to the author’s knowledge.The proposed LRCSPH-FDM(which is based on a local refinement corrected SPH method combined with FDM)is derived by using the finite difference scheme(FDM)to discretize the Caputo TF term,followed by using a corrected smoothed particle hydrodynamics(CSPH)scheme continuously without using the kernel derivative to approximate the spatial derivatives.Meanwhile,the local refinement technique is adopted to reduce the numerical error.In numerical simulations,the complex irregular geometry is considered to show the flexibility of the purely meshless particle method and its advantages over the grid-based method.The numerical convergence rate and merits of the proposed LRCSPH-FDM are illustrated by solving several 1D/2D(where 1D stands for one-dimensional)analytical TF-NLSEs in a rectangular region(with regular or irregular particle distribution)or in a region with irregular geometry.The proposed method is then used to predict the complex nonlinear dynamic characters of 2D TF-NLSE/TF-GPE in a complex irregular domain,and the results from the posed method are compared with those from the FDM.All the numerical results show that the present method has a good accuracy and flexible application capacity for the TF-NLSE/GPE in regions of a complex shape.
基金supported by the National Natural Science Foundation of China(Nos.51977027 and 51967008)the Scientific and Technological Project of Yunnan Precious Metals Lab-oratory(Nos.YPML-2023050250 and YPML-2022050206).
文摘The pursuit of Ag-based alloys with both high strength and toughness has posed a longstanding chal-lenge.In this study,we investigated the cluster strengthening and grain refinement toughening mecha-nisms in fully oxidized AgMgNi alloys,which were internally oxidized at 800℃ for 8 h under an oxy-gen atmosphere.We found that Mg-O clusters contributed to the hardening(138 HV)and strengthening(376.9 MPa)of the AgMg alloy through solid solution strengthening effects,albeit at the expense of duc-tility.To address this limitation,we introduced Ni nanoparticles into the AgMg alloy,resulting in signifi-cant grain refinement within its microstructure.Specifically,the grain size decreased from 67.2μm in the oxidized AgMg alloy to below 6.0μm in the oxidized AgMgNi alloy containing 0.3 wt%Ni.Consequently,the toughness increased significantly,rising from toughness value of 2177.9 MJ m^(-3) in the oxidized AgMg alloy to 6186.1 MJ m^(-3) in the oxidized AgMgNi alloy,representing a remarkable 2.8-fold enhancement.Furthermore,the internally oxidized AgMgNi alloy attained a strength of up to 387.6 MPa,comparable to that of the internally oxidized AgMg alloy,thereby demonstrating the successful realization of concurrent strengthening and toughening.These results collectively offer a novel approach for the design of high-performance alloys through the synergistic combination of cluster strengthening and grain refinement toughening.
基金financially supported by the National Natural Science Foundation of China(No.21675131)the Volkswagen Foundation(Freigeist Fellowship No.89592)+1 种基金the Natural Science Foundation of Chongqing(No.2020jcyj-zdxmX0003,CSTB2023NSCQ-MSX0924)the National Research Foundation,Singapore,and A*STAR(Agency for Science Technology and Research)under its LCER Phase 2 Programme Hydrogen&Emerging Technologies FI,Directed Hydrogen Programme(Award No.U2305D4003).
文摘Ammonia and nitric acid,versatile industrial feedstocks,and burgeoning clean energy vectors hold immense promise for sustainable development.However,Haber–Bosch and Ostwald processes,which generates carbon dioxide as massive by-product,contribute to greenhouse effects and pose environmental challenges.Thus,the pursuit of nitrogen fixation through carbon–neutral pathways under benign conditions is a frontier of scientific topics,with the harnessing of solar energy emerging as an enticing and viable option.This review delves into the refinement strategies for scale-up mild photocatalytic nitrogen fixation,fields ripe with potential for innovation.The narrative is centered on enhancing the intrinsic capabilities of catalysts to surmount current efficiency barriers.Key focus areas include the in-depth exploration of fundamental mechanisms underpinning photocatalytic procedures,rational element selection,and functional planning,state-of-the-art experimental protocols for understanding photo-fixation processes,valid photocatalytic activity evaluation,and the rational design of catalysts.Furthermore,the review offers a suite of forward-looking recommendations aimed at propelling the advancement of mild nitrogen photo-fixation.It scrutinizes the existing challenges and prospects within this burgeoning domain,aspiring to equip researchers with insightful perspectives that can catalyze the evolution of cutting-edge nitrogen fixation methodologies and steer the development of next-generation photocatalytic systems.
基金supported by the National Natural Science Foundation of China(No.51871155).
文摘Due to the low content of alloying elements and the lack of effective nucleation sites,the fusion zone(FZ)of tungsten inert gas(TIG)welded AZ31 alloy typically exhibits undesirable coarse columnar grains,which can result in solidification defects and reduced mechanical properties.In this work,a novel welding wire containing MgO particles has been developed to promote columnar-to-equiaxed transition(CET)in the FZ of TIG-welded AZ31 alloy.The results show the achievement of a fully equiaxed grain structure in the FZ,with a significant 71.9%reduction in grain size to 41 μm from the original coarse columnar dendrites.Furthermore,the combination of using MgO-containing welding wire and pulse current can further refine the grain size to 25.6 μm.Microstructural analyses reveal the homogeneous distribution of MgO particles in the FZ.The application of pulse current results in an increase in the number density of MgO(1-2 μm)from 5.16 × 10^(4) m^(-3) to 6.18 × 10^(4) m^(-3).The good crystallographic matching relationship between MgO and α-Mg matrix,characterized by the orientation relationship of[11(2)0]α-Mg//[0(1)1]MgO and(0002)_(α-Mg)//(111)_(MgO),indicates that the MgO particles can act as effective nucleation sites for α-Mg to reduce nucleation undercooling.According to the Hunt criteria,the critical temperature gradient for CET is greatly enhanced due to the significantly increased number density of MgO nucleation sites.In addition,the correlation with the thermal simulation results reveals a transition in the solidification conditions within the welding pool from the columnar grain zone to the equiaxed grain zone in the CET map,leading to the realization of CET.The exceptional grain refinement has contributed to a simultaneous improvement in the strength and plasticity of welded joints.This study presents a novel strategy for controlling equiaxed microstructure and optimizing mechanical properties in fusion welding or wire and arc additive manufacturing of Mg alloy components.
文摘Background:Enzyme fragility remains a major challenge in research and applications.Free enzymes are highly unstable,inactivated by heat,acid,alkali,or organic solvents,and often lose activity even under optimal storage conditions.Limiting their use in cosmetics.Few commercial products combine acids and enzymes effectively.Objective:To investigate the physicochemical properties,in vitro exfoliation efficacy,and effects on facial skin parameters of a supramolecular acid-enzyme complex(SAE)composed of mandelic acid(MAN),betaine(BET),and composite enzymes(CE;papain and bromelain),thereby establishing a theoretical foundation for cosmetic applications.Methods:The supramolecular structure was characterized using Fourier transform infrared(FTIR)spectroscopy and proton nuclear magnetic resonance(1H NMR)spectroscopy.Dissolution experiments were conducted to compare the solubility of SAE and CE in aqueous solutions.Enzymatic activity assays evaluated the stabilizing effect of supramolecular deep eutectic technology on enzymes.In vitro exfoliation tests assessed acid-enzyme synergy in keratin removal.A 4-week clinical trial evaluated the efficacy of a 2%SAE essence aqueous solution on facial skin parameters.Results:Dissolution experiments confirmed that supramolecular deep eutectic technology significantly improved enzyme solubility.Enzymatic activity tests demonstrated that this technology effectively preserved protease activity,substantially enhancing its practical applicability.Furthermore,in vitro exfoliation efficacy tests revealed that this technology strengthened the synergistic interaction between acids and enzymes and exhibited superior stratum corneum-removing capability of the SAE.In clinical evaluations of efficacy,after 7 days of using the essence containing SAE,the formulation significantly enhanced cheek gloss(+8.08%),while reducing comedones volume(-16.25%).after 28 days,significantly enhanced cheek hydration(+25.0%,SCH),gloss(+15.93%),and smoothness(−7.78%SEsm),while reducing TEWL(−6.86%),sebum(−15.54%),roughness(+16.24%SEr),and pore metrics(volume:−39.98%;count:−30.64%),and decreased comedones(blackheads:−70.33%;Whiteheads:−52.42%;all p<0.05).Conclusion:The supramolecular acid-enzyme complex demonstrates enhanced stability,improved solubility,and superior exfoliation efficacy compared to free enzymes.Clinical results further confirm its multifunctional benefits,including enhancing skin hydration,sebum regulation,barrier repair,pore refinement,and comedolytic effects.This study provides both theoretical and practical foundations for developing stable acid-enzyme combinations in dermatological applications.
基金supported by the National Natural Science Foundation of China(Nos.52205382,52225503)National Key Research and Development Program(No.2023YFB4603300)+3 种基金Key Research and Development Program of Jiangsu Province(Nos.BE2022069,BZ2024019)National Natural Science Foundation of China for Creative Research Groups(No.51921003)International Joint Laboratory of Sustainable Manufacturing,Ministry of Education and the Fundamental Research Funds for the Central Universities(NG2024014)Postgraduate Research&Practice Innovation Program of NUAA(xcxjh20230616)。
文摘High cracking susceptibility of Al-Li alloys with Ti/Ce B6addition is thoroughly suppressed in laser powder bed fusion(LPBF)processing of Ti/Ce co-modified 2195 alloys at relatively high scan speeds,while the cracking suppression mechanism and phase formation in these composites are not clarified.In this work,microstructure evolution and mechanical performance of the LPBF-fabricated Ti/Ce co-modified 2195 are investigated to reveal their cracking suppression and strengthening mechanisms.The results show that apparent grain refinement of the composites is ascribed to high supercooling from rapid formation of constitutional supercooling zone in front of solid–liquid interfaces by high-Q-value Ti solute,and heterogeneous nucleation of in situ formed Al3Ti and Al11Ce3precipitates.Their synergistic interactions promote formation of fine equiaxed grains and thus inhibit crack initiation.The composites exhibit high microhardness of 100±5HV0.2,nano-hardness of 1.6±0.1 GPa and elastic modulus of 97±3 GPa,where the elastic modulus increases by 27%and 31%compared to those of LPBF-processed and conventionally manufactured 2195 alloys,respectively.A tensile strength of 336 MPa and an elongation of 3%are obtained from in-situ synchrotron X-ray diffraction measurement.The improved properties are derived from grain refinement and Orowan strengthening.Based on the optimal processing parameter and composition,a bracket component filled with lattice structures is designed and manufactured with good manufacturing quality and processing accuracy.
基金financially supported by the National Natural Science Foundation of China(No.52374395)the Natural Science Foundation of Shanxi Province,China(Nos.20210302123135,202303021221143)+5 种基金the Scientific and Technological Achievements Transformation Guidance Special Project of Shanxi Province,China(Nos.202104021301022,202204021301009)the Central Government Guided Local Science and Technology Development Projects,China(No.YDZJSX20231B003)the Ministry of Science and Higher Education of the Russian Federation for financial support under the Megagrant(No.075-15-2022-1133)the National Research Foundation(NRF)grant funded by the Ministry of Science and ICT of Korea through the Research Institute of Advanced Materials(No.2015R1A2A1A01006795)the China Postdoctoral Science Foundation(No.2022M710541)the Research Project supported by Shanxi Scholarship Council of China(No.2022-038)。
文摘To investigate the effect of microstructure evolution on corrosion behavior and strengthening mechanism of Mg-1Zn-1Ca(wt.%)alloys,as-cast Mg-1Zn-1Ca alloys were performed by equal channel angular pressing(ECAP)with 1 and 4 passes.The corrosion behavior and mechanical properties of alloys were investigated by optical microscopy(OM),scanning electron microscopy(SEM),electron backscatter diffraction(EBSD),electrochemical tests,immersion tests and tensile tests.The results showed that mechanical properties improved after ECAP 1 pass;however,the corrosion resistance deteriorated due to high-density dislocations and fragmented secondary phases by ECAP.In contrast,synchronous improvement in the mechanical properties and corrosion resistance was achieved though grain refinement after ECAP 4 passes;fine grains led to a significant improvement in the yield strength,ultimate tensile strength,elongation,and corrosion rate of 103 MPa,223 MPa,30.5%,and 1.5843 mm/a,respectively.The enhanced corrosion resistance was attributed to the formation of dense corrosion product films by finer grains and the barrier effect by high-density grain boundaries.These results indicated that Mg-1Zn-1Ca alloy has a promising potential for application in biomedical materials.
文摘In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.
基金Supported by National Science Foundation of China(11971027,12171497)。
文摘This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.
基金Key Research and Development Program of Shandong Province(2021CXGC010310)Shandong Province Science and Technology Small and Medium Sized Enterprise Innovation Ability Enhancement Project(2023TSGC0287,2024TSGC0519)+1 种基金Shandong Provincial Natural Science Foundation(ZR2022ME222)National Natural Science Foundation of China(51702187)。
文摘Three types of NdFeB magnets with the same composition and different grain sizes were prepared,and then the grain boundary diffusion was conducted using metal Tb under the same technical parameters.The effect of grain size on the grain boundary diffusion process and properties of sintered NdFeB magnets was investigated.The diffusion process was assessed using X-ray diffractometer,field emission scanning electron microscope,and electron probe microanalyzer.The magnetic properties of the magnet before and after diffusion were investigated.The results show that the grain refinement of the magnet leads to higher Tb utilization efficiency and results in higher coercivity at different temperatures.It can be attributed to the formation of a deeper and more complete core-shell structure,resulting in better magnetic isolation and higher anisotropy of the Nd_(2)Fe_(14)B grains.This work may shed light on developing high coercivity with low heavy rare earth elements through grain refinement.
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802).
文摘In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.
