Let X^H = {X^H（8）,8∈ R^N1} and XK = {X^K（t）,t ∈R^2} be two independent anisotropic Gaussian random fields with values in R^d with indices H = （H1,... ,HN1） ∈ （0, 1）^N1, K = （K1,..., KN2）∈ （0, 1）^N2, r...Let X^H = {X^H（8）,8∈ R^N1} and XK = {X^K（t）,t ∈R^2} be two independent anisotropic Gaussian random fields with values in R^d with indices H = （H1,... ,HN1） ∈ （0, 1）^N1, K = （K1,..., KN2）∈ （0, 1）^N2, respectively. Existence of intersections of the sample paths of XH and XK is studied. More generally, let E1 R^N1, E2 R^N2 and F R^d be Borel sets. A necessary condition and a sufficient condition for P{（X^H（E1） ∩ X^K（E2）） ∩ F ≠ Ф} 〉 0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 x E2 x F in the metric space （R^N1＋N2＋d, ρ） are proved, whereρ is a metric defined in terms of H and K. These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets.展开更多
Under the influence of an applied magnetic field(MF), the eigenenergies and the eigenfunctions of the ground and the first excited states(GFES) are obtained by using a variational method of the Pekar type(VMPT) in a s...Under the influence of an applied magnetic field(MF), the eigenenergies and the eigenfunctions of the ground and the first excited states(GFES) are obtained by using a variational method of the Pekar type(VMPT) in a strong electron-LO-phonon coupling asymmetrical Gaussian potential quantum well(AGPQW). This AGPQW system may be employed as a two-level qubit. The numerical results have indicated(i) that when the electron situates in the superposition state of the GFES, we obtain the time evolution and the coordinate change of the electron probability density in the AGPQW,(ii) that due to the presence of the asymmetrical potential in the growth direction of the AGPQW, the probability density shows double-peak configuration, whereas there is only one peak if the confinement is a two dimensional symmetric one in the xy plane of the AGPQW,(iii) that the oscillatory period is a decreasing function of the cyclotron frequency of the MF, the height of the AGPQW and the polaron radius,(iv) and that as the range of the confinement potential(RCP) decreases the oscillatory period will decrease firstly and then increase and it will take a minimum when R =-0.234 nm.展开更多
Stochastic Quantum Space (SQS) theory is a new version of unified field theory based on three fundamental postulations: Gaussian Probability Postulation, Prime Numbers Postulation, Vacuon Postulation. It build a frame...Stochastic Quantum Space (SQS) theory is a new version of unified field theory based on three fundamental postulations: Gaussian Probability Postulation, Prime Numbers Postulation, Vacuon Postulation. It build a framework with theoretical results agree with many experimental data well. For more information, please refer to the PDF.展开更多
To improve the recognition ability of communication jamming signals,Siamese Neural Network-based Open World Recognition(SNNOWR)is proposed.The algorithm can recognize known jamming classes,detect new(unknown)jamming c...To improve the recognition ability of communication jamming signals,Siamese Neural Network-based Open World Recognition(SNNOWR)is proposed.The algorithm can recognize known jamming classes,detect new(unknown)jamming classes,and unsupervised cluseter new classes.The network of SNN-OWR is trained supervised with paired input data consisting of two samples from a known dataset.On the one hand,the network is required to have the ability to distinguish whether two samples are from the same class.On the other hand,the latent distribution of known class is forced to approach their own unique Gaussian distribution,which is prepared for the subsequent open set testing.During the test,the unknown class detection process based on Gaussian probability density function threshold is designed,and an unsupervised clustering algorithm of the unknown jamming is realized by using the prior knowledge of known classes.The simulation results show that when the jamming-to-noise ratio is more than 0d B,the accuracy of SNN-OWR algorithm for known jamming classes recognition,unknown jamming detection and unsupervised clustering of unknown jamming is about 95%.This indicates that the SNN-OWR algorithm can make the effect of the recognition of unknown jamming be almost the same as that of known jamming.展开更多
The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" ...The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" alt="" /><img src="Edit_bdd10470-9b63-4b2d-9cec-636969547ca5.png" width="90" height="22" alt="" /><span style="white-space:normal;">and <img src="Edit_e9cd6876-e2b8-45cf-ba17-391f054679b4.png" width="90" height="21" alt="" /></span>where <span style="white-space:nowrap;"><em>α</em>,<span style="white-space:nowrap;"><em>η</em></span><em></em></span> and <span style="white-space:nowrap;"><em>β</em></span> are real or complex constants are evaluated in terms of the confluent hypergeometric function <sub>1</sub><em>F</em><sub>1</sub> and the hypergeometric function <sub>1</sub><em>F</em><sub>2</sub>. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">1</sub> and <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">2</sub>. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (<span style="white-space:nowrap;"><em>x</em><sup>2</sup></span>) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.展开更多
Reconstruction of Quaternary environments,late Cenozoic geodynamics and evaluation of volcanic hazards,all depend on the precise delineation of eruptive stages.In recent years,laser 40Ar/39Ar dating methods have been ...Reconstruction of Quaternary environments,late Cenozoic geodynamics and evaluation of volcanic hazards,all depend on the precise delineation of eruptive stages.In recent years,laser 40Ar/39Ar dating methods have been widely used for dating young volcanic rocks,given their stable automated testing process,very low background level and high sensitivity,which meet the requirements for precise dating of young samples.This paper applied high-precision laser 40Ar/39Ar dating to the main volcanic units in the Tengchong area and obtained ages in the range of 0.025–5.1 Ma using conventional data processing methods.However,conventional dating highlighted issues related to very low radiogenic 40Ar content,accidental errors and poor data stability,which led to huge age deviations.Moreover,lacking a unified timescale,conventional methods were unable to strictly define the stages of the Tengchong volcanic eruptions,leading to ongoing controversy.In this study,we applied a Gaussian mathematical model to deal with all 378 original ages from 13 samples.An apparent age-probability diagram,consisting of three independent waveforms,have been obtained.The corresponding isochron ages of these three waveforms suggest there were three volcanic eruptive stages,namely during the Pliocene(3.78±0.04 Ma),early Middle Pleistocene(0.63±0.03 Ma)and late Middle Pleistocene to early Late Pleistocene(0.139±0.005 Ma).These results accurately define eruptive stages in the Tengchong area.展开更多
In this paper,we are concerned with the asymptotic behavior,as u→∞,of P{sup_t∈|0,T|X_u(t)>u},where X_u(t),t∈|0,T|,u>0 is a family of centered Gaussian processes with continuous trajectories.A key application...In this paper,we are concerned with the asymptotic behavior,as u→∞,of P{sup_t∈|0,T|X_u(t)>u},where X_u(t),t∈|0,T|,u>0 is a family of centered Gaussian processes with continuous trajectories.A key application of our findings concerns P{sup_t∈|0,T|(X(t)+g(t))>u},as u→∞,for X a centered Gaussian process and g some measurable trend function.Further applications include the approximation of both the ruin time and the ruin probability of the Brownian motion risk model with constant force of interest.展开更多
基金supported by Zhejiang Provincial Natural Science Foundation of China(Grant No. Y6100663)National Science Foundation of US (Grant No. DMS-1006903)
文摘Let X^H = {X^H（8）,8∈ R^N1} and XK = {X^K（t）,t ∈R^2} be two independent anisotropic Gaussian random fields with values in R^d with indices H = （H1,... ,HN1） ∈ （0, 1）^N1, K = （K1,..., KN2）∈ （0, 1）^N2, respectively. Existence of intersections of the sample paths of XH and XK is studied. More generally, let E1 R^N1, E2 R^N2 and F R^d be Borel sets. A necessary condition and a sufficient condition for P{（X^H（E1） ∩ X^K（E2）） ∩ F ≠ Ф} 〉 0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 x E2 x F in the metric space （R^N1＋N2＋d, ρ） are proved, whereρ is a metric defined in terms of H and K. These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets.
基金Supported by the National Science Foundation of China under Grant No.11464034
文摘Under the influence of an applied magnetic field(MF), the eigenenergies and the eigenfunctions of the ground and the first excited states(GFES) are obtained by using a variational method of the Pekar type(VMPT) in a strong electron-LO-phonon coupling asymmetrical Gaussian potential quantum well(AGPQW). This AGPQW system may be employed as a two-level qubit. The numerical results have indicated(i) that when the electron situates in the superposition state of the GFES, we obtain the time evolution and the coordinate change of the electron probability density in the AGPQW,(ii) that due to the presence of the asymmetrical potential in the growth direction of the AGPQW, the probability density shows double-peak configuration, whereas there is only one peak if the confinement is a two dimensional symmetric one in the xy plane of the AGPQW,(iii) that the oscillatory period is a decreasing function of the cyclotron frequency of the MF, the height of the AGPQW and the polaron radius,(iv) and that as the range of the confinement potential(RCP) decreases the oscillatory period will decrease firstly and then increase and it will take a minimum when R =-0.234 nm.
文摘Stochastic Quantum Space (SQS) theory is a new version of unified field theory based on three fundamental postulations: Gaussian Probability Postulation, Prime Numbers Postulation, Vacuon Postulation. It build a framework with theoretical results agree with many experimental data well. For more information, please refer to the PDF.
基金supported by the National Natural Science Foundation of China(U19B2016)Zhejiang Provincial Key Lab of Data Storage and Transmission Technology,Hangzhou Dianzi University。
文摘To improve the recognition ability of communication jamming signals,Siamese Neural Network-based Open World Recognition(SNNOWR)is proposed.The algorithm can recognize known jamming classes,detect new(unknown)jamming classes,and unsupervised cluseter new classes.The network of SNN-OWR is trained supervised with paired input data consisting of two samples from a known dataset.On the one hand,the network is required to have the ability to distinguish whether two samples are from the same class.On the other hand,the latent distribution of known class is forced to approach their own unique Gaussian distribution,which is prepared for the subsequent open set testing.During the test,the unknown class detection process based on Gaussian probability density function threshold is designed,and an unsupervised clustering algorithm of the unknown jamming is realized by using the prior knowledge of known classes.The simulation results show that when the jamming-to-noise ratio is more than 0d B,the accuracy of SNN-OWR algorithm for known jamming classes recognition,unknown jamming detection and unsupervised clustering of unknown jamming is about 95%.This indicates that the SNN-OWR algorithm can make the effect of the recognition of unknown jamming be almost the same as that of known jamming.
文摘The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" alt="" /><img src="Edit_bdd10470-9b63-4b2d-9cec-636969547ca5.png" width="90" height="22" alt="" /><span style="white-space:normal;">and <img src="Edit_e9cd6876-e2b8-45cf-ba17-391f054679b4.png" width="90" height="21" alt="" /></span>where <span style="white-space:nowrap;"><em>α</em>,<span style="white-space:nowrap;"><em>η</em></span><em></em></span> and <span style="white-space:nowrap;"><em>β</em></span> are real or complex constants are evaluated in terms of the confluent hypergeometric function <sub>1</sub><em>F</em><sub>1</sub> and the hypergeometric function <sub>1</sub><em>F</em><sub>2</sub>. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">1</sub> and <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">2</sub>. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (<span style="white-space:nowrap;"><em>x</em><sup>2</sup></span>) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.
基金supported by the Geological Survey Project of the China Geological Survey Bureau(Grant No.1212113013700).
文摘Reconstruction of Quaternary environments,late Cenozoic geodynamics and evaluation of volcanic hazards,all depend on the precise delineation of eruptive stages.In recent years,laser 40Ar/39Ar dating methods have been widely used for dating young volcanic rocks,given their stable automated testing process,very low background level and high sensitivity,which meet the requirements for precise dating of young samples.This paper applied high-precision laser 40Ar/39Ar dating to the main volcanic units in the Tengchong area and obtained ages in the range of 0.025–5.1 Ma using conventional data processing methods.However,conventional dating highlighted issues related to very low radiogenic 40Ar content,accidental errors and poor data stability,which led to huge age deviations.Moreover,lacking a unified timescale,conventional methods were unable to strictly define the stages of the Tengchong volcanic eruptions,leading to ongoing controversy.In this study,we applied a Gaussian mathematical model to deal with all 378 original ages from 13 samples.An apparent age-probability diagram,consisting of three independent waveforms,have been obtained.The corresponding isochron ages of these three waveforms suggest there were three volcanic eruptive stages,namely during the Pliocene(3.78±0.04 Ma),early Middle Pleistocene(0.63±0.03 Ma)and late Middle Pleistocene to early Late Pleistocene(0.139±0.005 Ma).These results accurately define eruptive stages in the Tengchong area.
基金supported by Swiss National Science Foundation (Grant No. 200021166274)the National Science Centre (Poland) (Grant No. 2015/17/B/ST1/01102) (2016–2019)
文摘In this paper,we are concerned with the asymptotic behavior,as u→∞,of P{sup_t∈|0,T|X_u(t)>u},where X_u(t),t∈|0,T|,u>0 is a family of centered Gaussian processes with continuous trajectories.A key application of our findings concerns P{sup_t∈|0,T|(X(t)+g(t))>u},as u→∞,for X a centered Gaussian process and g some measurable trend function.Further applications include the approximation of both the ruin time and the ruin probability of the Brownian motion risk model with constant force of interest.
