Some new reflection principles for Maxwell's equations are first established, which are then applied to derive two novel identifiability results in inverse electromagnetic obstacle scattering problems with polyhed...Some new reflection principles for Maxwell's equations are first established, which are then applied to derive two novel identifiability results in inverse electromagnetic obstacle scattering problems with polyhedral scatterers.展开更多
Using the properties of theta-series and Schwarz reflection principle, a proof for Riemann hypothesis (RH) is directly presented and the first ten nontrivial zeros are easily obtained. From now on RH becomes Riemann T...Using the properties of theta-series and Schwarz reflection principle, a proof for Riemann hypothesis (RH) is directly presented and the first ten nontrivial zeros are easily obtained. From now on RH becomes Riemann Theorem (RT) and all its equivalent results and the consequences assuming RH are true.展开更多
We propose an approach for recognizing the pose and surface material of diverse objects,leveraging diffuse reflection principles and data fusion.Through theoretical analysis and the derivation of factors influencing d...We propose an approach for recognizing the pose and surface material of diverse objects,leveraging diffuse reflection principles and data fusion.Through theoretical analysis and the derivation of factors influencing diffuse reflection on objects,the method concentrates on and exploits surface information.To validate the feasibility of our theoretical research,the depth and active infrared intensity data obtained from a single time-of-flight camera are initially combined.Subsequently,these data undergo processing using feature extraction and lightweight machine-learning techniques.In addition,an optimization method is introduced to enhance the fitting of intensity.The experimental results not only visually showcase the effectiveness of our proposed method in accurately detecting the positions and surface materials of targets with varying sizes and spatial locations but also reveal that the vast majority of the sample data can achieve a recognition accuracy of 94.8%or higher.展开更多
In this paper we study the function , for z∈C. We derive a functional equation that relates G(z) and G(1−z) for all z∈C, and we prove: 1) that G and the Riemann zeta function ζ have exactly the same zeros in the cr...In this paper we study the function , for z∈C. We derive a functional equation that relates G(z) and G(1−z) for all z∈C, and we prove: 1) that G and the Riemann zeta function ζ have exactly the same zeros in the critical region D:= {z∈C:ℜz∈(0,1)};2) the Riemann hypothesis, i.e., that all of the zeros of G in D are located on the critical line := {z∈D:ℜz =1/2};and that 3) all the zeros of the Riemann zeta function located on the critical line are simple.展开更多
In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory of Reflected Backward Stochastic Differential Equations （RBSDEs）. We will establish the d...In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory of Reflected Backward Stochastic Differential Equations （RBSDEs）. We will establish the dynamic programming principle for the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper and the lower Hamilton-Jacobi-Bettman-Isaacs equations with obstacles, respectively. The method differs significantly from those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove a new estimate for RBSDEs being sharper than that in the paper of E1 Karoui, Kapoudjian, Pardoux, Peng and Quenez （1997）, which turns out to be very useful because it allows us to estimate the LP-distance of the solutions of two different RBSDEs by the p-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs equation with obstacle.展开更多
Jr. Stocks[4] discussed lattice paths from （0, 0, 0） to （n, n, n） with diagonal steps under some restrictions. In this note, we give simpler formulas for the main results in [4], andextend them to a general case.
Dynamic fund protection provides a guarantee that the account value of the investor never drops below a barrier over the investment period.In order to reduce the downside risk taken by vendors,Han,et al.(2016)proposed...Dynamic fund protection provides a guarantee that the account value of the investor never drops below a barrier over the investment period.In order to reduce the downside risk taken by vendors,Han,et al.(2016)proposed a chained dynamic fund protection(CDFP),whose protection is activated only if the value of basic fund reaches a predefined upper protection line.Motivated by them,we consider a new CDFP plan under a stochastic interest rate environment.The explicit pricing formula for a CDFP is obtained when the protection lines are proportional to a zero-coupon bond.Furthermore,the authors present some numerical results for the value of CDFP at time 0 to show how the model parameters impact the value of CDFP.展开更多
We isolate several classes of stationary sets of [κ]ω and investigate implications among them. Under a large cardinal assumption, we prove a structure theorem for stationary sets.
基金supported by NSF grant,FRG DMS 0554571supported substantially by Hong Kong RGC grant (Project 404407)partially by Cheung Kong Scholars Programme through Wuhan University,China.
文摘Some new reflection principles for Maxwell's equations are first established, which are then applied to derive two novel identifiability results in inverse electromagnetic obstacle scattering problems with polyhedral scatterers.
文摘Using the properties of theta-series and Schwarz reflection principle, a proof for Riemann hypothesis (RH) is directly presented and the first ten nontrivial zeros are easily obtained. From now on RH becomes Riemann Theorem (RT) and all its equivalent results and the consequences assuming RH are true.
基金supported by the Shaanxi Province Innovation Talent Promotion Program-Science and Technology Innovation Team(Grant No.2023-CX-TD-03).
文摘We propose an approach for recognizing the pose and surface material of diverse objects,leveraging diffuse reflection principles and data fusion.Through theoretical analysis and the derivation of factors influencing diffuse reflection on objects,the method concentrates on and exploits surface information.To validate the feasibility of our theoretical research,the depth and active infrared intensity data obtained from a single time-of-flight camera are initially combined.Subsequently,these data undergo processing using feature extraction and lightweight machine-learning techniques.In addition,an optimization method is introduced to enhance the fitting of intensity.The experimental results not only visually showcase the effectiveness of our proposed method in accurately detecting the positions and surface materials of targets with varying sizes and spatial locations but also reveal that the vast majority of the sample data can achieve a recognition accuracy of 94.8%or higher.
文摘In this paper we study the function , for z∈C. We derive a functional equation that relates G(z) and G(1−z) for all z∈C, and we prove: 1) that G and the Riemann zeta function ζ have exactly the same zeros in the critical region D:= {z∈C:ℜz∈(0,1)};2) the Riemann hypothesis, i.e., that all of the zeros of G in D are located on the critical line := {z∈D:ℜz =1/2};and that 3) all the zeros of the Riemann zeta function located on the critical line are simple.
基金supported by the Agence Nationale de la Recherche (France), reference ANR-10-BLAN 0112the Marie Curie ITN "Controlled Systems", call: FP7-PEOPLE-2007-1-1-ITN, no. 213841-2+3 种基金supported by the National Natural Science Foundation of China (No. 10701050, 11071144)National Basic Research Program of China (973 Program) (No. 2007CB814904)Shandong Province (No. Q2007A04),Independent Innovation Foundation of Shandong Universitythe Project-sponsored by SRF for ROCS, SEM
文摘In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory of Reflected Backward Stochastic Differential Equations （RBSDEs）. We will establish the dynamic programming principle for the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper and the lower Hamilton-Jacobi-Bettman-Isaacs equations with obstacles, respectively. The method differs significantly from those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove a new estimate for RBSDEs being sharper than that in the paper of E1 Karoui, Kapoudjian, Pardoux, Peng and Quenez （1997）, which turns out to be very useful because it allows us to estimate the LP-distance of the solutions of two different RBSDEs by the p-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs equation with obstacle.
基金the Natural Science Foundation of Education Department of Jiangsu Province (02KJB52005).
文摘Jr. Stocks[4] discussed lattice paths from （0, 0, 0） to （n, n, n） with diagonal steps under some restrictions. In this note, we give simpler formulas for the main results in [4], andextend them to a general case.
基金supported by the NSF of Jiangsu Province under Grant No.BK20170064the NNSF of China under Grant No.11771320+2 种基金Qing Lan Project of Jiangsu Provincethe scholarship of Jiangsu Overseas Visiting Scholar Programthe Graduate Innovation Program of USTS(SKCX18-Y06)
文摘Dynamic fund protection provides a guarantee that the account value of the investor never drops below a barrier over the investment period.In order to reduce the downside risk taken by vendors,Han,et al.(2016)proposed a chained dynamic fund protection(CDFP),whose protection is activated only if the value of basic fund reaches a predefined upper protection line.Motivated by them,we consider a new CDFP plan under a stochastic interest rate environment.The explicit pricing formula for a CDFP is obtained when the protection lines are proportional to a zero-coupon bond.Furthermore,the authors present some numerical results for the value of CDFP at time 0 to show how the model parameters impact the value of CDFP.
基金the Coalition for National Science Funding (Grant No. 10571168)the GACR (Grant Nos. 201/02/857 and 201-03-0933)+2 种基金the GAAV (Grant No. IAA 100190509)NSF (Grant No.DMS-0071437)visiting appointments at Chinese Academy of Sciences in Beijing and National University of Singapore
文摘We isolate several classes of stationary sets of [κ]ω and investigate implications among them. Under a large cardinal assumption, we prove a structure theorem for stationary sets.
