In this paper, we discuss the exponent of n-order differential equations with unbounded piecewise-constant matrix, and resolve it's solution space into the direct sum of independent subspaces on the basis of it...In this paper, we discuss the exponent of n-order differential equations with unbounded piecewise-constant matrix, and resolve it's solution space into the direct sum of independent subspaces on the basis of it's exponent. Our results are provide important basis for stability and qualitative study.展开更多
A fast and high precision spatial domain algorithm is presented for forward modeling of two-dimensional(2D)body gravity anomalies of arbitrary shape and density distribution.The new algorithm takes advantage of the co...A fast and high precision spatial domain algorithm is presented for forward modeling of two-dimensional(2D)body gravity anomalies of arbitrary shape and density distribution.The new algorithm takes advantage of the convolution properties of the expression for 2D gravity anomalies,uses a rectangular cell as a grid subdivision unit,and then 2D bodies with irregular cross-sections are approximated by a combination of 2D bodies with a rectangular cross section.The closed-form expression is used to calculate the gravitational anomalies of the combination of 2D bodies with a rectangular cross section.To improve computing effi ciency,the new algorithm uses a fast algorithm for the implementation of the Toeplitz matrix and vector multiplication.The synthetic 2D models with rectangular and circular cross-sections and constant and variable densities are designed to evaluate the computational accuracy and speed of the new algorithm.The experiment results show that the computation costs less than 6 s for a grid subdivision with 10000×10000 elements.Compared to the traditional forward modeling methods,the proposed method significantly improved computational effi ciency while guaranteeing computational accuracy.展开更多
One of the most basic characteristics of photonic crystal is frequency band gap. When defects are introduced into the periodic photonic crystal, a number of defect modes appear in the stop band. In this paper, we expl...One of the most basic characteristics of photonic crystal is frequency band gap. When defects are introduced into the periodic photonic crystal, a number of defect modes appear in the stop band. In this paper, we exploit transfer matrix method based on photonic crystal theory, and assume the sampled fiber Bragg grating as one-dimensional dual photonic crystal with a large size defect. Characteristics of the sampled fiber Bragg grating are analyzed. Experimental results show that the sampled fiber Bragg grating has many reflective peaks. Its reflectivity, center wavelength, reflective peak intervals and band width all change with the grating parameters, including grating length, duty ratio of the material with high dielectric constant, and index modulation depth and period. Results agree with the conventional couple mode theory which can be used when analyzing other characteristics of the sampled fiber Bragg grating or applying it into practice.展开更多
This paper discusses conditions under which the solution of linear system with minimal Schatten-p norm, 0 〈 p ≤ 1, is also the lowest-rank solution of this linear system. To study this problem, an important tool is ...This paper discusses conditions under which the solution of linear system with minimal Schatten-p norm, 0 〈 p ≤ 1, is also the lowest-rank solution of this linear system. To study this problem, an important tool is the restricted isometry constant （RIC）. Some papers provided the upper bounds of RIC to guarantee that the nuclear-norm minimization stably recovers a low-rank matrix. For example, Fazel improved the upper bounds to δ4Ar 〈 0.558 and δ3rA 〈 0.4721, respectively. Recently, the upper bounds of RIC can be improved to δ2rA 〈 0.307. In fact, by using some methods, the upper bounds of RIC can be improved to δ2tA 〈 0.4931 and δrA 〈 0.309. In this paper, we focus on the lower bounds of RIC, we show that there exists linear maps A with δ2rA 〉1√2 or δrA 〉 1/3 for which nuclear norm recovery fail on some matrix with rank at most r. These results indicate that there is only a little limited room for improving the upper bounds for δ2rA and δrA.Furthermore, we also discuss the upper bound of restricted isometry constant associated with linear maps A for Schatten p （0 〈 p 〈 1） quasi norm minimization problem.展开更多
Using photonic crystals (PCs), the extraction efficiency of the light-emitting diodes (LEDs) can be greatly enhanced by the effects of photonic band gap (PBG) and grating diffraction. The two theoretical methods are a...Using photonic crystals (PCs), the extraction efficiency of the light-emitting diodes (LEDs) can be greatly enhanced by the effects of photonic band gap (PBG) and grating diffraction. The two theoretical methods are also discussed. Meanwhile, we demonstrate that LEDs can achieve high extraction efficiency by employing photonic crystal as diffraction grating. PCs with square lattice of cylindrical unit cells are fabricated in GaN layer of GaN-based blue LED. We present a theoretical discussion on the extraction efficiency of PC-LED, which relies on the effective medium theory and transmission matrix method to investigate the effect of lattice constant. The results show that the extraction efficiency of the high performance LEDs can achieve 61.8% when the lattice constant is 270 nm.展开更多
The influence of the linear birefringence on magneto-optical property measurement for optical fibers is investigated theoretically and experimentally. The evolution of polarization in fibers is simulated by the Jones ...The influence of the linear birefringence on magneto-optical property measurement for optical fibers is investigated theoretically and experimentally. The evolution of polarization in fibers is simulated by the Jones matrix. To verify this theoretical model, a magneto-optical system is built to measure the input azimuth, output azimuth and ellipticity. The Faraday rotation of spun fibers with different pitches is measured. The Verdet constant increases, while the linear birefringence decreases as the pitch becomes smaller. For spun fibers with 1 mm pitch, the Verdet constant can be enhanced by about 20.7% at 660 nm, compared with that of the unspun fiber. The results indicate that smaller linear birefringence can provide more accurate Faraday rotation measurement.展开更多
文摘In this paper, we discuss the exponent of n-order differential equations with unbounded piecewise-constant matrix, and resolve it's solution space into the direct sum of independent subspaces on the basis of it's exponent. Our results are provide important basis for stability and qualitative study.
基金This work is jointly sponsored by the National Natural Science Foundation of China(No.41404106)the Scientific Research Startup Fund for Doctoral Program of Guilin University of Technology,Guangxi Natural Science Foundation Program(No.2018GXNSFBA138049)Guangxi Natural Science Foundation Program for Innovation Research Team(No.2016GXNSFGA380004).
文摘A fast and high precision spatial domain algorithm is presented for forward modeling of two-dimensional(2D)body gravity anomalies of arbitrary shape and density distribution.The new algorithm takes advantage of the convolution properties of the expression for 2D gravity anomalies,uses a rectangular cell as a grid subdivision unit,and then 2D bodies with irregular cross-sections are approximated by a combination of 2D bodies with a rectangular cross section.The closed-form expression is used to calculate the gravitational anomalies of the combination of 2D bodies with a rectangular cross section.To improve computing effi ciency,the new algorithm uses a fast algorithm for the implementation of the Toeplitz matrix and vector multiplication.The synthetic 2D models with rectangular and circular cross-sections and constant and variable densities are designed to evaluate the computational accuracy and speed of the new algorithm.The experiment results show that the computation costs less than 6 s for a grid subdivision with 10000×10000 elements.Compared to the traditional forward modeling methods,the proposed method significantly improved computational effi ciency while guaranteeing computational accuracy.
文摘One of the most basic characteristics of photonic crystal is frequency band gap. When defects are introduced into the periodic photonic crystal, a number of defect modes appear in the stop band. In this paper, we exploit transfer matrix method based on photonic crystal theory, and assume the sampled fiber Bragg grating as one-dimensional dual photonic crystal with a large size defect. Characteristics of the sampled fiber Bragg grating are analyzed. Experimental results show that the sampled fiber Bragg grating has many reflective peaks. Its reflectivity, center wavelength, reflective peak intervals and band width all change with the grating parameters, including grating length, duty ratio of the material with high dielectric constant, and index modulation depth and period. Results agree with the conventional couple mode theory which can be used when analyzing other characteristics of the sampled fiber Bragg grating or applying it into practice.
基金supported by National Natural Science Foundation of China (Grant Nos.91130009, 11171299 and 11041005)National Natural Science Foundation of Zhejiang Province in China (Grant Nos. Y6090091 and Y6090641)
文摘This paper discusses conditions under which the solution of linear system with minimal Schatten-p norm, 0 〈 p ≤ 1, is also the lowest-rank solution of this linear system. To study this problem, an important tool is the restricted isometry constant （RIC）. Some papers provided the upper bounds of RIC to guarantee that the nuclear-norm minimization stably recovers a low-rank matrix. For example, Fazel improved the upper bounds to δ4Ar 〈 0.558 and δ3rA 〈 0.4721, respectively. Recently, the upper bounds of RIC can be improved to δ2rA 〈 0.307. In fact, by using some methods, the upper bounds of RIC can be improved to δ2tA 〈 0.4931 and δrA 〈 0.309. In this paper, we focus on the lower bounds of RIC, we show that there exists linear maps A with δ2rA 〉1√2 or δrA 〉 1/3 for which nuclear norm recovery fail on some matrix with rank at most r. These results indicate that there is only a little limited room for improving the upper bounds for δ2rA and δrA.Furthermore, we also discuss the upper bound of restricted isometry constant associated with linear maps A for Schatten p （0 〈 p 〈 1） quasi norm minimization problem.
基金supported by the National Natural Science Foundation of China (No.60877047)the Natural Science Foundation of Hebei Province (No.2010002002)
文摘Using photonic crystals (PCs), the extraction efficiency of the light-emitting diodes (LEDs) can be greatly enhanced by the effects of photonic band gap (PBG) and grating diffraction. The two theoretical methods are also discussed. Meanwhile, we demonstrate that LEDs can achieve high extraction efficiency by employing photonic crystal as diffraction grating. PCs with square lattice of cylindrical unit cells are fabricated in GaN layer of GaN-based blue LED. We present a theoretical discussion on the extraction efficiency of PC-LED, which relies on the effective medium theory and transmission matrix method to investigate the effect of lattice constant. The results show that the extraction efficiency of the high performance LEDs can achieve 61.8% when the lattice constant is 270 nm.
基金supported by the National Natural Science Foundation of China(Nos.61177088,61275051,61227012,61475096,61422507 and 61520106014)the Science and Technology Commission of Shanghai Municipality of China(Nos.14511105602,14DZ1201403 and 15220721500)
文摘The influence of the linear birefringence on magneto-optical property measurement for optical fibers is investigated theoretically and experimentally. The evolution of polarization in fibers is simulated by the Jones matrix. To verify this theoretical model, a magneto-optical system is built to measure the input azimuth, output azimuth and ellipticity. The Faraday rotation of spun fibers with different pitches is measured. The Verdet constant increases, while the linear birefringence decreases as the pitch becomes smaller. For spun fibers with 1 mm pitch, the Verdet constant can be enhanced by about 20.7% at 660 nm, compared with that of the unspun fiber. The results indicate that smaller linear birefringence can provide more accurate Faraday rotation measurement.
