In this paper, the random Euler and random Runge-Kutta of the second order methods are used in solving random differential initial value problems of first order. The conditions of the mean square convergence of the nu...In this paper, the random Euler and random Runge-Kutta of the second order methods are used in solving random differential initial value problems of first order. The conditions of the mean square convergence of the numerical solutions are studied. The statistical properties of the numerical solutions are computed through numerical case studies.展开更多
To the Riemann hypothesis, we investigate first the approximation by step-wise Omega functions Ω(u) with commensurable step lengths u0 concerning their zeros in corresponding Xi functions Ξ(z). They are periodically...To the Riemann hypothesis, we investigate first the approximation by step-wise Omega functions Ω(u) with commensurable step lengths u0 concerning their zeros in corresponding Xi functions Ξ(z). They are periodically on the y-axis with period proportional to inverse step length u0. It is found that they possess additional zeros off the imaginary y-axis and additionally on this axis and vanish in the limiting case u0 → 0 in complex infinity. There remain then only the “genuine” zeros for Xi functions to continuous Omega functions which we call “analytic zeros” and which lie on the imaginary axis. After a short repetition of the Second mean-value (or Bonnet) approach to the problem and the derivation of operational identities for Trigonometric functions we give in Section 8 a proof for the position of these genuine “analytic” zeros on the imaginary axis by construction of a contradiction for the case off the imaginary axis. In Section 10, we show by a few examples that monotonically decreasing of the Omega functions is only a sufficient condition for the mentioned property of the positions of zeros on the imaginary axis but not a necessary one.展开更多
Based on the continuous development of motion capture technology for ordinary video images, unmarked optical motion capture has become the fastest human posture recognition technology. Compared with other technical pr...Based on the continuous development of motion capture technology for ordinary video images, unmarked optical motion capture has become the fastest human posture recognition technology. Compared with other technical products, Google’s 3D human body recognition framework—Mediapipe is the most mature representative in this field. However, Mediapipe also has many defects in the detection of 3D human posture. In this paper, firstly, to solve the problem of inaccurate detection of human posture by Mediapipe, the accuracy of 2D human posture detection is improved through the speed threshold correction method for each joint;According to the problem that the monocular camera can not detect the depth Z value in the human posture data accurately, the Z value of the joint point is corrected for the human tilt angle through statistics;Then, according to the inaccurate recognition of Z value caused by large body posture, the accurate correction of Z value of human posture under different body posture is realized by normalizing the simulation proportion of each body limb;Finally, in order to solve the problem of jitter, lag problem and periodic noise in multiple frames caused by the speed change of human joints, one euro filtering and mean filtering of joint data are carried out. This paper verifies that the accuracy of 3D human posture detection based on the improved Mediapipe is more than 90% through the multi-pose recognition test for people of different heights, weights, ages and gender.展开更多
A sharper asymptotic formula for the mean value sum from xmodq*L′(σ+it,X)L′(1-σ-it,X)1(where the summation is over all primitive Dirichlet characters mod q and 0<σ<1) is derived by using the analytic method...A sharper asymptotic formula for the mean value sum from xmodq*L′(σ+it,X)L′(1-σ-it,X)1(where the summation is over all primitive Dirichlet characters mod q and 0<σ<1) is derived by using the analytic method and the estimate of character sums.展开更多
文摘In this paper, the random Euler and random Runge-Kutta of the second order methods are used in solving random differential initial value problems of first order. The conditions of the mean square convergence of the numerical solutions are studied. The statistical properties of the numerical solutions are computed through numerical case studies.
文摘To the Riemann hypothesis, we investigate first the approximation by step-wise Omega functions Ω(u) with commensurable step lengths u0 concerning their zeros in corresponding Xi functions Ξ(z). They are periodically on the y-axis with period proportional to inverse step length u0. It is found that they possess additional zeros off the imaginary y-axis and additionally on this axis and vanish in the limiting case u0 → 0 in complex infinity. There remain then only the “genuine” zeros for Xi functions to continuous Omega functions which we call “analytic zeros” and which lie on the imaginary axis. After a short repetition of the Second mean-value (or Bonnet) approach to the problem and the derivation of operational identities for Trigonometric functions we give in Section 8 a proof for the position of these genuine “analytic” zeros on the imaginary axis by construction of a contradiction for the case off the imaginary axis. In Section 10, we show by a few examples that monotonically decreasing of the Omega functions is only a sufficient condition for the mentioned property of the positions of zeros on the imaginary axis but not a necessary one.
文摘Based on the continuous development of motion capture technology for ordinary video images, unmarked optical motion capture has become the fastest human posture recognition technology. Compared with other technical products, Google’s 3D human body recognition framework—Mediapipe is the most mature representative in this field. However, Mediapipe also has many defects in the detection of 3D human posture. In this paper, firstly, to solve the problem of inaccurate detection of human posture by Mediapipe, the accuracy of 2D human posture detection is improved through the speed threshold correction method for each joint;According to the problem that the monocular camera can not detect the depth Z value in the human posture data accurately, the Z value of the joint point is corrected for the human tilt angle through statistics;Then, according to the inaccurate recognition of Z value caused by large body posture, the accurate correction of Z value of human posture under different body posture is realized by normalizing the simulation proportion of each body limb;Finally, in order to solve the problem of jitter, lag problem and periodic noise in multiple frames caused by the speed change of human joints, one euro filtering and mean filtering of joint data are carried out. This paper verifies that the accuracy of 3D human posture detection based on the improved Mediapipe is more than 90% through the multi-pose recognition test for people of different heights, weights, ages and gender.
基金Project supported by the National Natural Science Foundation of China.
文摘A sharper asymptotic formula for the mean value sum from xmodq*L′(σ+it,X)L′(1-σ-it,X)1(where the summation is over all primitive Dirichlet characters mod q and 0<σ<1) is derived by using the analytic method and the estimate of character sums.
