Search Results (7)

Laterite is the predominant zonal soil in China’s southernmost tropical rainforest and monsoon forest regions, where typhoons are the primary source of precipitation. These storms pose significant risks of land and soil degradation due to heavy rainfall. In recent years, a substantial area of sloping land has been converted to agricultural use in these regions, predominantly for the cultivation of crops grown in laterite soil. These activities contribute to soil erosion, exacerbate environmental challenges, and hinder the pursuit of sustainable development. There is a paucity of research reports on the processes and mechanisms of runoff and sediment on sugarcane-cropped slopes in regions with laterite soil under heavy rainfall conditions. In this study, four different heavy rainfall scenarios of 75, 100, 125, and 150 mm/h were designed to assess the impact on sugarcane growth at four key stages and to measure the resulting effects on initial runoff time, surface runoff, and sediment yield from laterite soil slopes under controlled laboratory conditions. The results showed that the Horton model explained much of the variation in infiltration rate on the sugarcane-cropped laterite slopes. The cumulative sediment yield on the sugarcane-cropped laterite slopes followed a second-degree polynomial function. The initial runoff time, infiltration intensity, runoff intensity, and sediment yield were all linearly related to the leaf area index (LAI) and rainfall intensity on the sugarcane-cropped slope surface. The leaf area index exerted a greater influence on the initial runoff time and infiltration intensity than rainfall intensity. However, rainfall intensity exerted a greater influence on the runoff intensity and sediment yield than the leaf area index. Compared with the bare sloping land, the average sediment yield was reduced by 12.2, 33.1, 58.2, and 64.9% with the sugarcane growth stages of seedling, tillering, elongation, and maturity, respectively. Full article

The determination of the distributions of the eigenvalues associated with matrix-variate gamma and beta random variables of either type proves to be a challenging problem. Several of the approaches utilized so far yield unwieldy representations that, for instance, are expressed in terms of multiple integrals, functions of skew symmetric matrices, ratios of determinants, solutions of differential equations, zonal polynomials, and products of incomplete gamma or beta functions. In the present paper, representations of the density functions of the smallest, largest and $j^{\mathrm{th}}$ largest eigenvalues of matrix-variate gamma and each type of beta random variables are explicitly provided as finite sums when certain parameters are integers and, as explicit series, in the general situations. In each instance, both the real and complex cases are considered. The derivations initially involve an orthonormal or unitary transformation whereby the wedge products of the differential elements of the eigenvalues can be worked out from those of the original matrix-variate random variables. Some of these results also address the distribution of the eigenvalues of a central Wishart matrix as well as eigenvalue problems arising in connection with the analysis of variance procedure and certain tests of hypotheses in multivariate analysis. Additionally, three numerical examples are provided for illustration purposes. Full article

The complex Wishart distribution has ample applications in science and engineering. In this paper, we give explicit expressions for $E\left[{(tr\left(W^h\right))}^g{(tr\left(W^j\right))}^i\right]$ and $E\left[{(tr\left(W^{-h}\right))}^g{(tr\left(W^{-j}\right))}^i\right]$, respectively, for particular values of g, h, i, j, $g+h+i+j\le 5$, where W follows a complex Wishart distribution. For specific values of g, h, i, j, we first write ${(tr\left(W^h\right))}^g{(tr\left(W^j\right))}^i$ and ${(tr\left(W^{-h}\right))}^g{(tr\left(W^{-j}\right))}^i$ in terms of zonal polynomials and then by using results on integration evaluate resulting expressions. Several expected values of matrix-valued functions of a complex Wishart matrix have also been derived. Full article

Here we test the capability of the Broadcast Ephemeris Message, in both its GPS-like (Keplerian ellipse with secular and periodic perturbations) and Glonass-like (numerical integration of a 9D state vector) formats, to reproduce a corresponding precise ephemeris. We start from a daily Rinex 3.04 navigation file for multiple GNSS and the corresponding SP3 precise orbits computed by CNES (Centre National d’Etudes Spatiales) for GPS, Glonass, Galileo and CODE (Center for Orbit Determination in Europe) for Beidou, and compute broadcast ECEF coordinates and clocks. The pre-fit discrepancies are converted by least squares to corrections to the broadcast ephemeris parameters in two-hour consecutive arcs (for GPS, Galileo and Beidou) and to a set of seven Helmert parameters for the entire day, to align in origin, orientation and scale to the common GNSS IGS14 Reference Frame. The test cases suggest that the Broadcast Ephemeris Message, complemented with Reference Frame information, can reproduce the precise ephemeris and clocks with centimetric accuracy for intervals at least equal to the respective validity times, typically 2 h. The broadcast ephemeris of Glonass consists of three initial positions and velocities at epoch, three constant Lunisolar accelerations for the satellite position, and of three polynomial coefficients for the satellite clock. The 9D vector of state is numerically integrated to generate position and velocity data within the validity time (0.5 h) of the message. To test the capability of this model to reproduce the corresponding values of a precise ephemeris, the 9D vector of state and clock polynomials are adjusted until the rms (root mean squared spread) of the post-fit residuals relative to a precise orbit (CNES’s in our case) is minimum. We show in one example (one satellite for one day) that the Glonass type of message can reproduce a precise ephemeris and clock with a rms spread of 0.025 m over one-hour arcs. Volume computations on one month of data with all available satellites confirm the test results. For GPS, Glonass, Galileo and Beidou, the best fitting clock values predicted by our second order polynomials, based on a 15 min sampling, are shown to fit the corresponding high rate clocks (30 s sampling) of MGEX with zero bias and a rms spread of 0.062 ns (GPS G01), 0.023 ns (Galileo E01), 0.43 ns (Glonass R01), 0.086 ns (Beidou C07) and 0.086 ns (Beidou C12). Modifications to the GPS-like message structure and Glonass algorithm are proposed to increase the validity time by including the effect of the 3rd zonal harmonic of the Earth’s gravity field. The potential of the RTCM messages for broadcasting the improved navigation message is reviewed. Full article

We study the atmospheric structure in response to the propagation of gravity waves under nonisothermal (nonzero vertical temperature gradient), wind-shear (nonzero vertical zonal/meridional wind speed gradients), and dissipative (nonzero molecular viscosity and thermal conduction) conditions. As an alternative to the “complex wave-frequency” model proposed by Vadas and Fritts, we employ the traditional “complex vertical wave-number” approach to solving an eighth-order complex polynomial dispersion equation. The empirical neutral atmospheric models of NRLMSISE-00 and HWM93 are employed to provide mean-field properties. In response to the propagation of gravity waves, the atmosphere is driven into three sandwich-like layers: the adiabatic layer (0–130 km), the dissipation layer (130–230 km) and the pseudo-adiabatic layer (above 230 km). In the lower layer, (extended-)Hines’ mode or ordinary dissipative wave modes exist, whereas viscous dissipation and thermal conduction fail to exert perceptible influences; in the middle layer, Hines’ mode ceases to exist, and both ordinary and extraordinary dissipative wave modes flourish; in the top layer, only extraordinary wave modes survive, and dissipations affect the real part of the vertical wavenumber ( m r ) substantially; however, they contribute little to the imaginary part, which is the vertical growth rate ( m i ). We also analyze the transition of Hines’ classical mode to ordinary dissipative wave modes, describe both the upward and downward modes of gravity waves and illustrate nonisothermal and wind-shear effects on the propagation of gravity waves of different modes. Full article

Results from the theory of the generalized hypergeometric functions of matrix argument, and the related zonal polynomials, are used to develop a new approach to study the asymptotic distributions of linear functions of uniformly distributed random matrices from the classical compact matrix groups. In particular, we provide a new approach for proving the following result of D’Aristotile, Diaconis, and Newman: Let the random matrix H_n be uniformly distributed according to Haar measure on the group of n × n orthogonal matrices, and let A_n be a non-random n × n real matrix such that tr (A'_nA_n) = 1. Then, as n→∞, √n tr A_nH_n converges in distribution to the standard normal distribution. Full article

Generating functions play important roles in theory of orthogonal polynomials. In particular, it is important to consider generating functions that have symmetry. This paper is a survey on generating functions that define unitary operators. First, classical generating functions that define unitary operators are discussed. Next, group theoretical approach to generating functions that have unitarity are discussed. Full article