In this paper,we are concerned with the stability of traveling wavefronts of a Belousov-Zhabotinsky model with mixed nonlocal and degenerate diffusions.Such a system can be used to study the competition among nonlocal...In this paper,we are concerned with the stability of traveling wavefronts of a Belousov-Zhabotinsky model with mixed nonlocal and degenerate diffusions.Such a system can be used to study the competition among nonlocally diffusive species and degenerately diffusive species.We prove that the traveling wavefronts are exponentially stable,when the initial perturbation around the traveling waves decays exponentially as x→-∞,but in other locations,the initial data can be arbitrarily large.The adopted methods are the weighted energy with the comparison principle and squeezing technique.展开更多
This paper discusses the valuation of the Credit Default Swap based on a jump market, in which the asset price of a firm follows a double exponential jump diffusion process, the value of the debt is driven by a geomet...This paper discusses the valuation of the Credit Default Swap based on a jump market, in which the asset price of a firm follows a double exponential jump diffusion process, the value of the debt is driven by a geometric Brownian motion, and the default barrier follows a continuous stochastic process. Using the Gaver-Stehfest algorithm and the non-arbitrage asset pricing theory, we give the default probability of the first passage time, and more, derive the price of the Credit Default Swap.展开更多
A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where ...A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.展开更多
Structural models of credit risk are known to present vanishing spreads at very short maturities. This shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering d...Structural models of credit risk are known to present vanishing spreads at very short maturities. This shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering discontinuities of the jump type in their evolution over time. In this paper, we extend the pricing model for corporate bond and determine the default probability in jump-diffusion model to address this issue. To make the problem clearly, we first investigate the case that the firm value follows a geometric Brownian motion under similar assumptions to those in Black and Scholes（1973）, Briys and de Varenne（1997）, i.e, the default barrier is KD （t, T） and the recovery rate is （1 -w）, where D （t, T） is the price of zero coupon default free bond and w is a constant （0 〈 w 〈 1）. By changing the numeraire, we obtain the closed-form solution for both the price of bond and default probability. Further, we consider the case of jump-diffusion and suppose that a firm will go bankruptcy if its value Vt 〈 KD （t, T） and at the same time, the bondholder will receive （1 - w） vt/k By introducing the Green function of PDE with absorbing boundary and converting the problem to an II-type Volterra integral equation, we get the closed-form expressions in series form for bond price and corresponding default probability. Numerical results are presented to show the impact of different parameters to credit spread of bond.展开更多
In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and driv...In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and drive the joint distribution of the first exit time from an interval and the overshoot over the boundary at the exit time.展开更多
Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure ri...Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.展开更多
Missing values in radionuclide diffusion datasets can undermine the predictive accuracy and robustness of the machine learning(ML)models.In this study,regression-based missing data imputation method using a light grad...Missing values in radionuclide diffusion datasets can undermine the predictive accuracy and robustness of the machine learning(ML)models.In this study,regression-based missing data imputation method using a light gradient boosting machine(LGBM)algorithm was employed to impute more than 60%of the missing data,establishing a radionuclide diffusion dataset containing 16 input features and 813 instances.The effective diffusion coefficient(D_(e))was predicted using ten ML models.The predictive accuracy of the ensemble meta-models,namely LGBM-extreme gradient boosting(XGB)and LGBM-categorical boosting(CatB),surpassed that of the other ML models,with R^(2)values of 0.94.The models were applied to predict the D_(e)values of EuEDTA^(−)and HCrO_(4)^(−)in saturated compacted bentonites at compactions ranging from 1200 to 1800 kg/m^(3),which were measured using a through-diffusion method.The generalization ability of the LGBM-XGB model surpassed that of LGB-CatB in predicting the D_(e)of HCrO_(4)^(−).Shapley additive explanations identified total porosity as the most significant influencing factor.Additionally,the partial dependence plot analysis technique yielded clearer results in the univariate correlation analysis.This study provides a regression imputation technique to refine radionuclide diffusion datasets,offering deeper insights into analyzing the diffusion mechanism of radionuclides and supporting the safety assessment of the geological disposal of high-level radioactive waste.展开更多
A medical image encryption is proposed based on the Fisher-Yates scrambling,filter diffusion and S-box substitution.First,chaotic sequence associated with the plaintext is generated by logistic-sine-cosine system,whic...A medical image encryption is proposed based on the Fisher-Yates scrambling,filter diffusion and S-box substitution.First,chaotic sequence associated with the plaintext is generated by logistic-sine-cosine system,which is used for the scrambling,substitution and diffusion processes.The three-dimensional Fisher-Yates scrambling,S-box substitution and diffusion are employed for the first round of encryption.The chaotic sequence is adopted for secondary encryption to scramble the ciphertext obtained in the first round.Then,three-dimensional filter is applied to diffusion for further useful information hiding.The key to the algorithm is generated by the combination of hash value of plaintext image and the input parameters.It improves resisting ability of plaintext attacks.The security analysis shows that the algorithm is effective and efficient.It can resist common attacks.In addition,the good diffusion effect shows that the scheme can solve the differential attacks encountered in the transmission of medical images and has positive implications for future research.展开更多
The dynamics of phase separation in H–He binary systems within gas giants such as Jupiter and Saturn exhibit remarkable complexity, yet lack systematic investigation. Through large-scale machine-learning-accelerated ...The dynamics of phase separation in H–He binary systems within gas giants such as Jupiter and Saturn exhibit remarkable complexity, yet lack systematic investigation. Through large-scale machine-learning-accelerated molecular dynamics simulations spanning broad temperature-pressure-composition(2000–10000 K, 1–7 Mbar,pure H to pure He) regimes, we systematically determine self and mutual diffusion coefficients in H–He systems and establish a six-dimensional framework correlating temperature, pressure, helium abundance, phase separation degree, diffusion coefficients, and anisotropy. Key findings reveal that hydrogen exhibits active directional migration with pronounced diffusion anisotropy, whereas helium passively aggregates in response. While the conventional mixing rule underestimates mutual diffusion coefficients by neglecting velocity cross-correlations,the assumption of an ideal thermodynamic factor(Q = 1) overestimates them due to unaccounted non-ideal thermodynamic effects—both particularly pronounced in strongly phase-separated regimes. Notably, hydrogen's dual role, anisotropic diffusion and bond stabilization via helium doping, modulates demixing kinetics. Large-scale simulations(216,000 atoms) propose novel phase-separation paradigms, such as “hydrogen bubble/wisp” formation, challenging the classical “helium rain” scenario, striving to bridge atomic-scale dynamics to planetary-scale phase evolution.展开更多
The interdiffusion coefficients in Al_(0.2)CoCrFeNi,CoCrCu_(0.2)FeNi,and CoCrFeMn_(0.2)Ni high-entropy alloys were efficiently determined by combining diffusion couple experiments and high-throughput determination of ...The interdiffusion coefficients in Al_(0.2)CoCrFeNi,CoCrCu_(0.2)FeNi,and CoCrFeMn_(0.2)Ni high-entropy alloys were efficiently determined by combining diffusion couple experiments and high-throughput determination of interdiffusion coefficients(HitDIC)software at 1273−1373 K.The results show that the addition of Al,Cu,and Mn to CoCrFeNi high-entropy alloys promotes the diffusion of Co,Cr,and Fe atoms.The comparison of tracer diffusion coefficients indicates that there is no sluggish diffusion in tracer diffusion on the thermodynamic temperature scale for the present Al_(0.2)CoCrFeNi,CoCrCu_(0.2)FeNi,and CoCrFeMn_(0.2)Ni high-entropy alloys.The linear relationship between diffusion entropy and activation energy reveals that the diffusion process of atoms is unaffected by an increase in the number of components as long as the crystal structure remains unchanged.展开更多
In this paper,we propose a numerical method for solving parabolic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition.The main idea is to use traditional finite element method on se...In this paper,we propose a numerical method for solving parabolic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition.The main idea is to use traditional finite element method on semi-Cartesian mesh coupled with Newton’s method to handle nonlinearity.It is easy to implement even though variable coefficients are used in the jump condition instead of constant in previous work for elliptic interface problem.Numerical experiments show that our method is about second order accurate in the L1 norm.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12261081).
文摘In this paper,we are concerned with the stability of traveling wavefronts of a Belousov-Zhabotinsky model with mixed nonlocal and degenerate diffusions.Such a system can be used to study the competition among nonlocally diffusive species and degenerately diffusive species.We prove that the traveling wavefronts are exponentially stable,when the initial perturbation around the traveling waves decays exponentially as x→-∞,but in other locations,the initial data can be arbitrarily large.The adopted methods are the weighted energy with the comparison principle and squeezing technique.
基金Supported by The National Natural Science Foundation of China(71261015)Humanity and Social Science Youth Foundation of Education Ministry in China(10YJC630334)Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region
文摘This paper discusses the valuation of the Credit Default Swap based on a jump market, in which the asset price of a firm follows a double exponential jump diffusion process, the value of the debt is driven by a geometric Brownian motion, and the default barrier follows a continuous stochastic process. Using the Gaver-Stehfest algorithm and the non-arbitrage asset pricing theory, we give the default probability of the first passage time, and more, derive the price of the Credit Default Swap.
基金supported by the National Basic Research Program of China (973 Program, 2007CB814904)the National Natural Science Foundations of China (10921101)+2 种基金Shandong Province (2008BS01024, ZR2010AQ004)the Science Funds for Distinguished Young Scholars of Shandong Province (JQ200801)Shandong University (2009JQ004),the Independent Innovation Foundations of Shandong University (IIFSDU,2009TS036, 2010TS060)
文摘A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.
基金Supported by the National Basic Research Program of China(973 Program)(2007CB814903)
文摘Structural models of credit risk are known to present vanishing spreads at very short maturities. This shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering discontinuities of the jump type in their evolution over time. In this paper, we extend the pricing model for corporate bond and determine the default probability in jump-diffusion model to address this issue. To make the problem clearly, we first investigate the case that the firm value follows a geometric Brownian motion under similar assumptions to those in Black and Scholes（1973）, Briys and de Varenne（1997）, i.e, the default barrier is KD （t, T） and the recovery rate is （1 -w）, where D （t, T） is the price of zero coupon default free bond and w is a constant （0 〈 w 〈 1）. By changing the numeraire, we obtain the closed-form solution for both the price of bond and default probability. Further, we consider the case of jump-diffusion and suppose that a firm will go bankruptcy if its value Vt 〈 KD （t, T） and at the same time, the bondholder will receive （1 - w） vt/k By introducing the Green function of PDE with absorbing boundary and converting the problem to an II-type Volterra integral equation, we get the closed-form expressions in series form for bond price and corresponding default probability. Numerical results are presented to show the impact of different parameters to credit spread of bond.
文摘In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and drive the joint distribution of the first exit time from an interval and the overshoot over the boundary at the exit time.
基金Supported by the NNSF of China(40675023)the PHD Foundation of Guangxi Normal University.
文摘Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.
基金supported by the National Natural Science Foundation of China(No.12475340 and 12375350)Special Branch project of South Taihu Lakethe Scientific Research Fund of Zhejiang Provincial Education Department(No.Y202456326).
文摘Missing values in radionuclide diffusion datasets can undermine the predictive accuracy and robustness of the machine learning(ML)models.In this study,regression-based missing data imputation method using a light gradient boosting machine(LGBM)algorithm was employed to impute more than 60%of the missing data,establishing a radionuclide diffusion dataset containing 16 input features and 813 instances.The effective diffusion coefficient(D_(e))was predicted using ten ML models.The predictive accuracy of the ensemble meta-models,namely LGBM-extreme gradient boosting(XGB)and LGBM-categorical boosting(CatB),surpassed that of the other ML models,with R^(2)values of 0.94.The models were applied to predict the D_(e)values of EuEDTA^(−)and HCrO_(4)^(−)in saturated compacted bentonites at compactions ranging from 1200 to 1800 kg/m^(3),which were measured using a through-diffusion method.The generalization ability of the LGBM-XGB model surpassed that of LGB-CatB in predicting the D_(e)of HCrO_(4)^(−).Shapley additive explanations identified total porosity as the most significant influencing factor.Additionally,the partial dependence plot analysis technique yielded clearer results in the univariate correlation analysis.This study provides a regression imputation technique to refine radionuclide diffusion datasets,offering deeper insights into analyzing the diffusion mechanism of radionuclides and supporting the safety assessment of the geological disposal of high-level radioactive waste.
文摘A medical image encryption is proposed based on the Fisher-Yates scrambling,filter diffusion and S-box substitution.First,chaotic sequence associated with the plaintext is generated by logistic-sine-cosine system,which is used for the scrambling,substitution and diffusion processes.The three-dimensional Fisher-Yates scrambling,S-box substitution and diffusion are employed for the first round of encryption.The chaotic sequence is adopted for secondary encryption to scramble the ciphertext obtained in the first round.Then,three-dimensional filter is applied to diffusion for further useful information hiding.The key to the algorithm is generated by the combination of hash value of plaintext image and the input parameters.It improves resisting ability of plaintext attacks.The security analysis shows that the algorithm is effective and efficient.It can resist common attacks.In addition,the good diffusion effect shows that the scheme can solve the differential attacks encountered in the transmission of medical images and has positive implications for future research.
基金supported by the National University of Defense Technology Research Fund Projectthe National Natural Science Foundation of China under Grant Nos. 12047561 and 12104507+1 种基金the NSAF under Grant No. U1830206the Science and Technology Innovation Program of Hunan Province under Grant No. 2021RC4026。
文摘The dynamics of phase separation in H–He binary systems within gas giants such as Jupiter and Saturn exhibit remarkable complexity, yet lack systematic investigation. Through large-scale machine-learning-accelerated molecular dynamics simulations spanning broad temperature-pressure-composition(2000–10000 K, 1–7 Mbar,pure H to pure He) regimes, we systematically determine self and mutual diffusion coefficients in H–He systems and establish a six-dimensional framework correlating temperature, pressure, helium abundance, phase separation degree, diffusion coefficients, and anisotropy. Key findings reveal that hydrogen exhibits active directional migration with pronounced diffusion anisotropy, whereas helium passively aggregates in response. While the conventional mixing rule underestimates mutual diffusion coefficients by neglecting velocity cross-correlations,the assumption of an ideal thermodynamic factor(Q = 1) overestimates them due to unaccounted non-ideal thermodynamic effects—both particularly pronounced in strongly phase-separated regimes. Notably, hydrogen's dual role, anisotropic diffusion and bond stabilization via helium doping, modulates demixing kinetics. Large-scale simulations(216,000 atoms) propose novel phase-separation paradigms, such as “hydrogen bubble/wisp” formation, challenging the classical “helium rain” scenario, striving to bridge atomic-scale dynamics to planetary-scale phase evolution.
基金supported by the National Natural Science Foundation of China(No.52374372)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.23KJB430042)+3 种基金the Jiangsu Province Large Scientific Instruments Open Sharing Autonomous Research Filing Project,China(No.TC2023A037)the Yangzhou City−Yangzhou University Cooperation Foundation,China(No.YZ2022183)High-end Talent Support Program of Yangzhou University,China,Qinglan Project of Yangzhou University,ChinaLvyangjinfeng Talent program of Yangzhou,China.
文摘The interdiffusion coefficients in Al_(0.2)CoCrFeNi,CoCrCu_(0.2)FeNi,and CoCrFeMn_(0.2)Ni high-entropy alloys were efficiently determined by combining diffusion couple experiments and high-throughput determination of interdiffusion coefficients(HitDIC)software at 1273−1373 K.The results show that the addition of Al,Cu,and Mn to CoCrFeNi high-entropy alloys promotes the diffusion of Co,Cr,and Fe atoms.The comparison of tracer diffusion coefficients indicates that there is no sluggish diffusion in tracer diffusion on the thermodynamic temperature scale for the present Al_(0.2)CoCrFeNi,CoCrCu_(0.2)FeNi,and CoCrFeMn_(0.2)Ni high-entropy alloys.The linear relationship between diffusion entropy and activation energy reveals that the diffusion process of atoms is unaffected by an increase in the number of components as long as the crystal structure remains unchanged.
基金L.Shi’s research is supported by National Natural Science Foundation of China(No.11701569)S.Hou’s research is supported by Dr.Walter Koss Professorship made available through Louisiana Board of RegentsL.Wang’s research is supported by Science Foundations of China University of Petroleum-Beijing(No.2462015BJB05).
文摘In this paper,we propose a numerical method for solving parabolic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition.The main idea is to use traditional finite element method on semi-Cartesian mesh coupled with Newton’s method to handle nonlinearity.It is easy to implement even though variable coefficients are used in the jump condition instead of constant in previous work for elliptic interface problem.Numerical experiments show that our method is about second order accurate in the L1 norm.
