A new terahertz dispersive device designed for single-shot spectral measurements of broadband terahertz pulses is proposed. With two-dimensional quasi-randomly distributed element design, the device exhibits approxima...A new terahertz dispersive device designed for single-shot spectral measurements of broadband terahertz pulses is proposed. With two-dimensional quasi-randomly distributed element design, the device exhibits approximately the dispersive property of single-order diffraction in far field. Its far-field diffraction pattern is experimentally verified employing a continuous terahertz source centered at 2.52 THz and a pyroelectric focal-plane-array camera, which is in good agreement with the numerical result. The device provides a new approach for direct single-shot spectral measurements of broadband terahertz waves.展开更多
A digital camera measuring system has been used successfully to measure the space fluctuation behaviors of Induced Dielectric Barrier Discharge (IDBD) plasma at atmospheric pres- sure. The experimental results showed ...A digital camera measuring system has been used successfully to measure the space fluctuation behaviors of Induced Dielectric Barrier Discharge (IDBD) plasma at atmospheric pres- sure. The experimental results showed that: (1) The uniformity of electron temperature in space depends on discharge condition and structure of web electrode. For a certain web electrode the higher the discharge voltage is, the more uniform distribution of electron temperature in space will be. For a certain discharge the finer and denser the holes on web electrode are, the more uniform distribution of electron temperature in space will be (2). Digital camera is an available equipment to measure some behaviors of the plasma working at atmospheric pressure.展开更多
To ensure the performance of the optical system, the machining accuracy of lens with long focal lengths is required to ensure the image quality. A new method for lens transmission wavefront power spectral density (PSD...To ensure the performance of the optical system, the machining accuracy of lens with long focal lengths is required to ensure the image quality. A new method for lens transmission wavefront power spectral density (PSD) in mid-frequency domain measurement using binary phase computer-generated hologram (CGH) is presented. This technique is widely applicable and is particularly useful for measuring large-size lenses with long focal lengths. A comparison experiment of the CGH measurement with results from a Fizeau sphere interferometry method is carried out to verify the accuracy and convenience of the measurement. Furthermore, measurement uncertainty due to CGH fabrication process is analysed. Analysis of the CGH test showed the overall accuracy of less than 1 nm RMS for a sphere lens with over 30 m focal length and Φ410 mm clear aperture. CGH can provide reference spheres with high precision, in the meantime greatly shorten air space, thus reducing the effect of vibration and air turbulence, therefore is of great importance for lens transmission wavefront PSD measurement. The realization of high precision, high efficiency and nondestructive testing of long focal-lens wavefront PSD ensure the ultra-precision and certainty level of machining, hence improving the comprehensive performance of the optical system.展开更多
General Research Institute for Non-ferrous Metals in cooperation with Changchun Instituteof Optical and Fine Mechanics prepared an automatic measurement instrument for spectral re-sponse test of solar cells. This inst...General Research Institute for Non-ferrous Metals in cooperation with Changchun Instituteof Optical and Fine Mechanics prepared an automatic measurement instrument for spectral re-sponse test of solar cells. This instrument having enough accuracy can measure at AM1.5 condi-tion. It meets the needs for measurement of spectral response for silicon, gallium arsenide solarcells.展开更多
The self-affine measure μM,Dassociated with an iterated function system{φd(x)=M(x + d)}is uniquely determined. It only depends upon an expanding matrix M and a finite digit set D. In the present paper we give some s...The self-affine measure μM,Dassociated with an iterated function system{φd(x)=M(x + d)}is uniquely determined. It only depends upon an expanding matrix M and a finite digit set D. In the present paper we give some sufficient conditions for finite and infinite families of orthogonal exponentials. Such research is necessary to further understanding the non-spectral and spectral of μM,D. As an application,we show that the L~2(μM,D) space has infinite families of orthogonal exponentials on the generalized three Sierpinski gasket. We then consider the spectra of a class of self-affine measures which extends several known conclusions in a simple manner.展开更多
This paper reports that a new plasma generator at atmospheric pressure, which is composed of two homocentric cylindrical all-metal tubes, successfully generates a cold plasma jet. The inside tube electrode is connecte...This paper reports that a new plasma generator at atmospheric pressure, which is composed of two homocentric cylindrical all-metal tubes, successfully generates a cold plasma jet. The inside tube electrode is connected to ground, the outside tube electrode is connected to a high-voltage power supply, and a dielectric layer is covered on the outside tube electrode. When the reactor is operated by low-frequency (6 kHz-20 kHz) AC supply in atmospheric pressure and argon is steadily fed as a discharge gas through inside tube electrode, a cold plasma jet is blown out into air and the plasma gas temperature is only 25-30℃. The electric character of the discharge is studied by using digital real-time oscilloscope (TDS 200-Series), and the discharge is capacitive. Preliminary results are presented on the decontamination of E.colis bacteria and Bacillus subtilis bacteria by this plasma jet, and an optical emission analysis of the plasma jet is presented in this paper. The ozone concentration generated by the plasma jet is 1.0× 10^16cm^-3 which is acquired by using the ultraviolet absorption spectroscopy.展开更多
A system for measuring terahertz spectrum is proposed based on optical interferometer theory, and is experimentally demonstrated by using a backward-wave oscillator as the terahertz source. A high-resolution, high-pre...A system for measuring terahertz spectrum is proposed based on optical interferometer theory, and is experimentally demonstrated by using a backward-wave oscillator as the terahertz source. A high-resolution, high-precision interferometer is constructed by using a pyroelectric detector and a chopper. The results show that the spectral resolution is better than 1 GHz and the relative error of frequency is less than 3%. The terahertz energy density distribution is calculated by an inverse Fourier transform and tested to verify the feasibility of the interferometric approach. Two kinds of carbon-fiber composites are imaged. The results confirm that the interferometer is useful for transmission imaging of materials with different thickness values.展开更多
The laser frequency could be linked to an radio frequency through an external cavity by the combination of Pound-Drever-Hall and Devoe-Brewer locking techniques.A stable and tunable optical frequency at wavelength of ...The laser frequency could be linked to an radio frequency through an external cavity by the combination of Pound-Drever-Hall and Devoe-Brewer locking techniques.A stable and tunable optical frequency at wavelength of 1.5μm obtained by a cavity with high finesse of 96000 and a fiber laser has been demonstrated,calibrated by a commercial optical frequency comb.The locking performances have been analyzed by in-loop and out-loop noises,indicating that the absolute frequency instability could be down to 50 kHz over 1 s and keep to less than 110 kHz over 2.5 h.Then,the application of this stabilized laser to the direct absorption spectroscopy has been performed.With the help of balanced detection,the detection sensitivity,in terms of optical density,can reach to 9.4×10^(-6).展开更多
The diffusion attenuation coefficient for downwelling irradiance, Kd (490), is an important optical parameter of seawater. The optical property, Kd (490), around Nansha Islands in the South China Sea was analyzed base...The diffusion attenuation coefficient for downwelling irradiance, Kd (490), is an important optical parameter of seawater. The optical property, Kd (490), around Nansha Islands in the South China Sea was analyzed based on optical data profiles measured with SPMR ( SeaWiFS Profiling Multichannel Radiometer ) and SMSR ( SeaWiFS Multichannel Surface Reference ) instrument in April and May, 1999. The results show that Kd (490) is closely correlated with chlorophyll-a concentration, Cchl.a, and that the vertical distribution of Kd (490) shows the strong stratification of the water column in this area. Kd (490) has a similar vertical co-variation as KL (490), the diffusive attenuation coefficient for upwelling radiance. Both coefficients increase with depth in the upper layer, where KL (490) is greater than Kd (490); and after a depth, approximatively at the chlorophyll maximum, they decrease with depth, with the former being smaller than the latter.展开更多
In this study the probable seismic behavior of skewed bridges with continuous decks under earthquake excitations from different directions is investigated. A 45° skewed bridge is studied. A suite of 20 records is...In this study the probable seismic behavior of skewed bridges with continuous decks under earthquake excitations from different directions is investigated. A 45° skewed bridge is studied. A suite of 20 records is used to perform an Incremental Dynamic Analysis (IDA) for fragility curves. Four different earthquake directions have been considered: -45°, 0°, 22.5, 45°. A sensitivity analysis on different spectral intensity measures is presented; efficiency and practicality of different intensity measures have been studied. The fragility curves obtained indicate that the critical direction for skewed bridges is the skew direction as well as the longitudinal direction. The study shows the importance of finding the most critical earthquake in understanding and predicting the behavior of skewed bridges.展开更多
It is extensively approved that Channel State Information(CSI) plays an important role for synergetic transmission and interference management. However, pilot overhead to obtain CSI with enough precision is a signific...It is extensively approved that Channel State Information(CSI) plays an important role for synergetic transmission and interference management. However, pilot overhead to obtain CSI with enough precision is a significant issue for wireless communication networks with massive antennas and ultra-dense cell. This paper proposes a learning- based channel model, which can estimate, refine, and manage CSI for a synergetic transmission system. It decomposes the channel impulse response into multiple paths, and uses a learning-based algorithm to estimate paths' parameters without notable degradation caused by sparse pilots. Both indoor measurement and outdoor measurement are conducted to verify the feasibility of the proposed channel model preliminarily.展开更多
The integration of an inertial navigation system(INS) and a celestial navigation system(CNS) has the superiority of high autonomy. However, its reliability and accuracy are permanently impaired under poor observation ...The integration of an inertial navigation system(INS) and a celestial navigation system(CNS) has the superiority of high autonomy. However, its reliability and accuracy are permanently impaired under poor observation conditions. To address this issue, the present paper proposes a tightly coupled INS/CNS/spectral redshift(SRS) integration framework based on the spectral redshift error measurement. In the proposed method, a spectral redshift error measurement equation is investigated and embedded in the traditional tightly coupled INS/CNS integrated navigation system to achieve better anti-interference under complicated circumstances. Subsequently, the inaccurate redshift estimation from the low signal-to-noise ratio spectrum is considered in the integrated system, and an improved chi-square test-based covariance estimation method is incorporated in the federated Kalman filter, allowing to deal with measurement outliers caused by the inaccurate redshift estimation but not influencing the effect of other correct redshift measurements in suppressing the error of the navigation parameter on the filtering solution. Simulations and comprehensive analyses demonstrate that the proposed tightly coupled INS/CNS/SRS integrated navigation system can effectively handle outliers and outages under hostile observation conditions, resulting in improved performance.展开更多
In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-...In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-order asymptotics of the spectral risk measure of portfolio loss is also presented.In order to illustrate the derived results,a numerical example with Monte Carlo simulation is carried out.展开更多
Let M=ρ^(-1)I∈Mn(R)be an expanding matrix with 0<|ρ|<1 and D■Z^(n)be a finite digit set with O∈D and Z(mD)■Z(mD)■Z(mD)∪{0}■m^(-1)z^(n)for a prime m,where Z(mD):=(Ede emi(a)=O),LetμM.D be theassociateds...Let M=ρ^(-1)I∈Mn(R)be an expanding matrix with 0<|ρ|<1 and D■Z^(n)be a finite digit set with O∈D and Z(mD)■Z(mD)■Z(mD)∪{0}■m^(-1)z^(n)for a prime m,where Z(mD):=(Ede emi(a)=O),LetμM.D be theassociatedsel-simiar measure defined by M.DO)-ZaeDμM,D(M()-d).In this paper,the necessary and sufficient conditions for L2(μM,D)to admit infinite orthogonal exponential functions are given.Moreover,by using the order theory of polynomial,we estimate the number of orthogonal exponential functions for all cases that L^(2)(μM,D)does not admit infinite orthogonal exponential functions.展开更多
An improved method, called Alternative Spectral Rotation (ASR) measure, for predicting protein coding regions in rice DNA has been developed. The method is based on the Spectral Rotation (SR) measure proposed by Kotla...An improved method, called Alternative Spectral Rotation (ASR) measure, for predicting protein coding regions in rice DNA has been developed. The method is based on the Spectral Rotation (SR) measure proposed by Kotlar and Lavner, and its accuracy is higher than that of the SR measure and the Spectral Content (SC) measure proposed by Tiwari et al. In order to increase the identifying accuracy, we chose three di?erent coding characters, namely the asymmetric, purine, and stop-codon variables as parameters, and an approving result was presented by the method of Linear Discriminant Analysis (LDA).展开更多
Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,...Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,0)^(t),(1,0)^(t),(0,1)^(t)}is the Sierpinski digit.We prove that there exists a setΛ⊂ℝ2 such that the family{e2πi〈λ,x〉:λ∈Λ} is an orthonormal basis of L^(2)(μ{A_(n),n≥1})if and only if 1/3(1,-1)A_(n)∈Z^(2)for n≥2 under some metric conditions on A_(n).展开更多
基金Project supported by the Foundation of Science and Technology Development of China Academy of Engineering Physics(Grant No.2011B0102023)the Foundation of Plasma Physics Laboratory(Grant No.9140C680304110C6806)
文摘A new terahertz dispersive device designed for single-shot spectral measurements of broadband terahertz pulses is proposed. With two-dimensional quasi-randomly distributed element design, the device exhibits approximately the dispersive property of single-order diffraction in far field. Its far-field diffraction pattern is experimentally verified employing a continuous terahertz source centered at 2.52 THz and a pyroelectric focal-plane-array camera, which is in good agreement with the numerical result. The device provides a new approach for direct single-shot spectral measurements of broadband terahertz waves.
基金This work was supported by National Natural Science Foundation of China No.19775010.
文摘A digital camera measuring system has been used successfully to measure the space fluctuation behaviors of Induced Dielectric Barrier Discharge (IDBD) plasma at atmospheric pres- sure. The experimental results showed that: (1) The uniformity of electron temperature in space depends on discharge condition and structure of web electrode. For a certain web electrode the higher the discharge voltage is, the more uniform distribution of electron temperature in space will be. For a certain discharge the finer and denser the holes on web electrode are, the more uniform distribution of electron temperature in space will be (2). Digital camera is an available equipment to measure some behaviors of the plasma working at atmospheric pressure.
文摘To ensure the performance of the optical system, the machining accuracy of lens with long focal lengths is required to ensure the image quality. A new method for lens transmission wavefront power spectral density (PSD) in mid-frequency domain measurement using binary phase computer-generated hologram (CGH) is presented. This technique is widely applicable and is particularly useful for measuring large-size lenses with long focal lengths. A comparison experiment of the CGH measurement with results from a Fizeau sphere interferometry method is carried out to verify the accuracy and convenience of the measurement. Furthermore, measurement uncertainty due to CGH fabrication process is analysed. Analysis of the CGH test showed the overall accuracy of less than 1 nm RMS for a sphere lens with over 30 m focal length and Φ410 mm clear aperture. CGH can provide reference spheres with high precision, in the meantime greatly shorten air space, thus reducing the effect of vibration and air turbulence, therefore is of great importance for lens transmission wavefront PSD measurement. The realization of high precision, high efficiency and nondestructive testing of long focal-lens wavefront PSD ensure the ultra-precision and certainty level of machining, hence improving the comprehensive performance of the optical system.
文摘General Research Institute for Non-ferrous Metals in cooperation with Changchun Instituteof Optical and Fine Mechanics prepared an automatic measurement instrument for spectral re-sponse test of solar cells. This instrument having enough accuracy can measure at AM1.5 condi-tion. It meets the needs for measurement of spectral response for silicon, gallium arsenide solarcells.
基金supported by National Natural Science Foundation of China(Grant No.11101334)
文摘The self-affine measure μM,Dassociated with an iterated function system{φd(x)=M(x + d)}is uniquely determined. It only depends upon an expanding matrix M and a finite digit set D. In the present paper we give some sufficient conditions for finite and infinite families of orthogonal exponentials. Such research is necessary to further understanding the non-spectral and spectral of μM,D. As an application,we show that the L~2(μM,D) space has infinite families of orthogonal exponentials on the generalized three Sierpinski gasket. We then consider the spectra of a class of self-affine measures which extends several known conclusions in a simple manner.
文摘This paper reports that a new plasma generator at atmospheric pressure, which is composed of two homocentric cylindrical all-metal tubes, successfully generates a cold plasma jet. The inside tube electrode is connected to ground, the outside tube electrode is connected to a high-voltage power supply, and a dielectric layer is covered on the outside tube electrode. When the reactor is operated by low-frequency (6 kHz-20 kHz) AC supply in atmospheric pressure and argon is steadily fed as a discharge gas through inside tube electrode, a cold plasma jet is blown out into air and the plasma gas temperature is only 25-30℃. The electric character of the discharge is studied by using digital real-time oscilloscope (TDS 200-Series), and the discharge is capacitive. Preliminary results are presented on the decontamination of E.colis bacteria and Bacillus subtilis bacteria by this plasma jet, and an optical emission analysis of the plasma jet is presented in this paper. The ozone concentration generated by the plasma jet is 1.0× 10^16cm^-3 which is acquired by using the ultraviolet absorption spectroscopy.
基金supported by the National Natural Science Foundation of China(Grant Nos.61377109 and 11374007)
文摘A system for measuring terahertz spectrum is proposed based on optical interferometer theory, and is experimentally demonstrated by using a backward-wave oscillator as the terahertz source. A high-resolution, high-precision interferometer is constructed by using a pyroelectric detector and a chopper. The results show that the spectral resolution is better than 1 GHz and the relative error of frequency is less than 3%. The terahertz energy density distribution is calculated by an inverse Fourier transform and tested to verify the feasibility of the interferometric approach. Two kinds of carbon-fiber composites are imaged. The results confirm that the interferometer is useful for transmission imaging of materials with different thickness values.
基金supported by the National Key R&D Program of China(Grant No.2017YFA0304203)the National Natural Science Foundation of China(Grant Nos.61875107,61905136,61905134,62175139)+1 种基金Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi,China(Grant No.2019L0062)Opening Foundation of Key Laboratory of Laser&Infrared System(Shandong University)。
文摘The laser frequency could be linked to an radio frequency through an external cavity by the combination of Pound-Drever-Hall and Devoe-Brewer locking techniques.A stable and tunable optical frequency at wavelength of 1.5μm obtained by a cavity with high finesse of 96000 and a fiber laser has been demonstrated,calibrated by a commercial optical frequency comb.The locking performances have been analyzed by in-loop and out-loop noises,indicating that the absolute frequency instability could be down to 50 kHz over 1 s and keep to less than 110 kHz over 2.5 h.Then,the application of this stabilized laser to the direct absorption spectroscopy has been performed.With the help of balanced detection,the detection sensitivity,in terms of optical density,can reach to 9.4×10^(-6).
基金This work was jointly supported by project KZCX2-202 from CAS the project of 818-06-03 from national 863 program and project 97-926-07 of national special program for science and technology.
文摘The diffusion attenuation coefficient for downwelling irradiance, Kd (490), is an important optical parameter of seawater. The optical property, Kd (490), around Nansha Islands in the South China Sea was analyzed based on optical data profiles measured with SPMR ( SeaWiFS Profiling Multichannel Radiometer ) and SMSR ( SeaWiFS Multichannel Surface Reference ) instrument in April and May, 1999. The results show that Kd (490) is closely correlated with chlorophyll-a concentration, Cchl.a, and that the vertical distribution of Kd (490) shows the strong stratification of the water column in this area. Kd (490) has a similar vertical co-variation as KL (490), the diffusive attenuation coefficient for upwelling radiance. Both coefficients increase with depth in the upper layer, where KL (490) is greater than Kd (490); and after a depth, approximatively at the chlorophyll maximum, they decrease with depth, with the former being smaller than the latter.
文摘In this study the probable seismic behavior of skewed bridges with continuous decks under earthquake excitations from different directions is investigated. A 45° skewed bridge is studied. A suite of 20 records is used to perform an Incremental Dynamic Analysis (IDA) for fragility curves. Four different earthquake directions have been considered: -45°, 0°, 22.5, 45°. A sensitivity analysis on different spectral intensity measures is presented; efficiency and practicality of different intensity measures have been studied. The fragility curves obtained indicate that the critical direction for skewed bridges is the skew direction as well as the longitudinal direction. The study shows the importance of finding the most critical earthquake in understanding and predicting the behavior of skewed bridges.
基金supported by National Basic Research Program of China (NO 2012CB316002)China’s 863 Project (NO 2014AA01A703)+2 种基金National Major Projec (NO. 2014ZX03003002-002)Program for New Century Excellent Talents in University (NCET-13-0321)Tsinghua University Initiative Scientific Research Program (2011THZ02-2)
文摘It is extensively approved that Channel State Information(CSI) plays an important role for synergetic transmission and interference management. However, pilot overhead to obtain CSI with enough precision is a significant issue for wireless communication networks with massive antennas and ultra-dense cell. This paper proposes a learning- based channel model, which can estimate, refine, and manage CSI for a synergetic transmission system. It decomposes the channel impulse response into multiple paths, and uses a learning-based algorithm to estimate paths' parameters without notable degradation caused by sparse pilots. Both indoor measurement and outdoor measurement are conducted to verify the feasibility of the proposed channel model preliminarily.
基金supported by the National Natural Science Foundation of China(Grant Nos.42004021&41904028)the Shenzhen Science and Technology Program(Grant No.JCYJ20210324121602008)the Shaanxi Natural Science Basic Research Project,China(Grant No.2022-JM313)。
文摘The integration of an inertial navigation system(INS) and a celestial navigation system(CNS) has the superiority of high autonomy. However, its reliability and accuracy are permanently impaired under poor observation conditions. To address this issue, the present paper proposes a tightly coupled INS/CNS/spectral redshift(SRS) integration framework based on the spectral redshift error measurement. In the proposed method, a spectral redshift error measurement equation is investigated and embedded in the traditional tightly coupled INS/CNS integrated navigation system to achieve better anti-interference under complicated circumstances. Subsequently, the inaccurate redshift estimation from the low signal-to-noise ratio spectrum is considered in the integrated system, and an improved chi-square test-based covariance estimation method is incorporated in the federated Kalman filter, allowing to deal with measurement outliers caused by the inaccurate redshift estimation but not influencing the effect of other correct redshift measurements in suppressing the error of the navigation parameter on the filtering solution. Simulations and comprehensive analyses demonstrate that the proposed tightly coupled INS/CNS/SRS integrated navigation system can effectively handle outliers and outages under hostile observation conditions, resulting in improved performance.
基金supported by the Important Natural Science Foundation of Colleges and Universities of Anhui Province under Grant No.KJ2020A0122the Scientific Research Start-up Foundation of Hefei Normal University。
文摘In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-order asymptotics of the spectral risk measure of portfolio loss is also presented.In order to illustrate the derived results,a numerical example with Monte Carlo simulation is carried out.
基金Supported by the NNSF of China(Grant Nos.12071125,12001183 and 11831007)the Hunan Provincial NSF(Grant Nos.2020JJ5097 and 2019JJ20012)the SRF of Hunan Provincial Education Department(Grant No.19B117)。
文摘Let M=ρ^(-1)I∈Mn(R)be an expanding matrix with 0<|ρ|<1 and D■Z^(n)be a finite digit set with O∈D and Z(mD)■Z(mD)■Z(mD)∪{0}■m^(-1)z^(n)for a prime m,where Z(mD):=(Ede emi(a)=O),LetμM.D be theassociatedsel-simiar measure defined by M.DO)-ZaeDμM,D(M()-d).In this paper,the necessary and sufficient conditions for L2(μM,D)to admit infinite orthogonal exponential functions are given.Moreover,by using the order theory of polynomial,we estimate the number of orthogonal exponential functions for all cases that L^(2)(μM,D)does not admit infinite orthogonal exponential functions.
文摘An improved method, called Alternative Spectral Rotation (ASR) measure, for predicting protein coding regions in rice DNA has been developed. The method is based on the Spectral Rotation (SR) measure proposed by Kotlar and Lavner, and its accuracy is higher than that of the SR measure and the Spectral Content (SC) measure proposed by Tiwari et al. In order to increase the identifying accuracy, we chose three di?erent coding characters, namely the asymmetric, purine, and stop-codon variables as parameters, and an approving result was presented by the method of Linear Discriminant Analysis (LDA).
基金supported by the National Natural Science Foundation of China (Grant Nos. 12371087, 11971109,11971194, 11672074 and 12271185)supported by the program for Probability and Statistics:Theory and Application (Grant No. IRTL1704)+1 种基金the program for Innovative Research Team in Science and Technology in Fujian Province University (Grant No. IRTSTFJ)supported by Guangdong NSFC (Grant No. 2022A1515011124)
文摘Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,0)^(t),(1,0)^(t),(0,1)^(t)}is the Sierpinski digit.We prove that there exists a setΛ⊂ℝ2 such that the family{e2πi〈λ,x〉:λ∈Λ} is an orthonormal basis of L^(2)(μ{A_(n),n≥1})if and only if 1/3(1,-1)A_(n)∈Z^(2)for n≥2 under some metric conditions on A_(n).