Nonlinear surface fit stability formula without any transition region for conventional breakwater design

Determining the optimum weight of the armor blocks is of vital importance in the design of conventional breakwaters. The widely used formulae in the literature include the transition region from plunging to surging waves. In this paper, it is aimed to investigate a new design formula without any transition region as an alternative to widely used Van der Meer formulae. The dimensionless parameters of Van der Meer formulae as well as newly generated variables are used as inputs. Nonlinear surface fit best subset regression model is used to find the optimum input combination that keeps the nonlinear relationships. All the input parameters, their second powers, and their two-way interactions are included in the regression analyses to obtain a nonlinear surface fit. Various goodness of fit statistics are applied to check the different perspectives of the model accuracy. It is demonstrated that the proposed model gives a realistic prediction of the stability number for critical data range. Especially for high values of stability number the proposed formula outperforms the benchmark formulae of Van der Meer and Etemad-Shahidi and Bonakdar. The other advantage is that it does not contain any transition region that depends on wave conditions. Besides, there is no need to include “number of waves” and “permeability” parameters into the equation.     

Health risk profile for terrestrial radionuclides in soil around artisanal gold mining area at Alsopag,Sudan

This study shows the assessment of radiation hazard parameters due to terrestrial radionuclides in the soil around artisanal gold mining for addressing the issue of natural radioactivity in mining areas. Hence, the levels ²³⁸U, ²³²Th, ⁴⁰K and ²²⁶Ra in soil (using gamma spectrometry), ²²²Rn in soil and ²²²Rn in air were determined. Radiation hazard parameters were then computed. These include absorbed dose D, annual effective dose E, radium equivalent activity Ra_eq, external hazard H_ex, annual gonadal dose equivalent hazard index AGDE and excess lifetime cancer risk ELCR due to the inhalation of radon (²²²Rn) and consumption of radium (²²⁶Ra) in vegetation. Uranium (²³⁸U), thorium (²³²Th) and potassium (⁴⁰K) averages were, respectively, 26, 36 and 685 Becquerel per kilogram (Bq kg^?1). Soil radon (4671 Bq m^?3) and radon in air (14.77 Bq m^?3) were found to be less than worldwide data. Nevertheless, the average ⁴⁰K concentration was 685 Bq kg^?1. This is slightly higher than the United Nations Scientific Committee on the Effects of Atomic Radiation average value of 412 Bq kg^?1. The obtained result indicates that some of the radiation hazard parameters seem unsavory. The mean value of absorbed dose rate (62.49 nGy h^?1) was slightly higher than average value of 57 nGy h^?1 (~?45% from ⁴⁰K), and that of AGDE (444 μSv year^?1) was higher than worldwide average reported value (300 μSv year^?1). This study highlights the necessity to launch extensive nationwide radiation protection program in the mining areas for regulatory control.     

Distances of Galaxies from the Apparent Size Distribution of Dark Clouds. II NGC 224, NGC 2841 and NGC 7331

The distances of three Sb galaxies NGC 224, NGC 2841 and NGC 7331 have been determined using the apparent size distribution of dark interstellar clouds in each of them. The distances of NGC 224, NGC 2841, NGC 7331 were found to be 727.7 ± 63 kpc, 8.07 ± 0.16 Mpc and 7.22 ± 0.15 Mpc, respectively.     

The construction of a seventh-order Jupiter-Saturn analytical theory

We extend the construction of the Jupiter-Saturn theory to include all the terms up to the seventh order in the masses. The Hori-Lie transformation technique is employed. The Jacobian coordinates are adopted and the theory is expressed in terms of the canonical non-singular variables of H. Poincaré.     

Is there period-activity correlation in RS CVn-type binary systems?

The rotation period-activity luminosity and the rotation period-surface activity flux correlations for the components of RS CVn-type binaries are discussed. It is argued that such correlations, although they are required by dynamo generated magnetic fields, do not represent the dominant parameter in determining the level of activity. Evidences are given that these correlations may essentially be induced by the period-radius dependence for the components of RS CVn-type binaries, and in addition, this result may well be valid for all the late-type stars (single or binary components).     

The construction of a third order secular

In this part we find out the 24 equations of secular perturbation equations for the subsystem J-S-U-N. The solution of these equations by the Lagrange-Laplace procedure and the Eigen value Eigen vector is analysed. Also we refer to Hurwitz theorem to test stability.     

The construction of a general third-order planetary theory

We review in this part the outline of a third-order general planetary theory established through Von Zeipel's method and in terms of Poincaré's canonical variables We consider our system to consist of the Sun as the primary body, one disturbed planet, and one disturbing planet.     

Determination of secular terms in general planetary theory

A method to calculate secular terms of the two parts of the planetary disturbing function— when it is expressed in terms of the true anomalies or the eccentric anomalies instead of the mean anomalies - is described. Also an alternative method is outlined.     

Fourier analysis of the light curves of eclipsing variables,XV

A new general expression for the theoretical momentsA _2m of the light curves of eclipsing systems has been presented in the form of infinite series expansion. In this expansion, the terms have been given as the product of two different polynomials which satisfy certain three-term recursion formulae, and the coefficients diminish rapidly with increasing number of terms. Thus, the numerical values of the theoretical momentsA _2m can be generated recursively up to four significant figures for any given set of eclipse elements. This can be utilized to solve the eclipse elements in two ways: (i) with an indirect method (for the procedures see Paper XIV, Kopal and Demircan, 1978), (ii) with a direct method as minimization to the observational momentsA _2m (area fitting). The procedures given in Paper XIV for obtaining the elements of any eclipsing system consisting of spherical stars have been automated by making use of the new expression for the momentsA _2m of the light curves. The theoretical functionsf ₀,f ₂,f ₄,f ₆,g ₂ andg ₄ which are the functions ofa andc ₀, have been used to solve the eclipse elements from the observed photometric data. The closed-form expressions for the functionsf ₂,f ₄ andf ₆ have also been derived (Section 3) in terms of Kopal'sI-integrals.The automated methods for obtaining the eclipse elements from one minimum alone have been tested on the light curves of YZ (21) Cassiopeiae under the spherical model assumptions. The results of these applications will be given in Section 5 which follows a brief introduction to the procedure we followed.     

Expansion of the planetary mutual distance raised to any negative power by the method of symbolic differential operators

We present a literal approach to evaluate ^–s necessary for the construction of high order planetary theories. This approach is valid to be applied on very large scale digital computers with standard Poisson series programs, for high order and high degree planetary theories. We apply the method of symbolic differential operators for single variable functions, and the binomial theorem expansions, for the evaluation of ^–s . We utilize Laplace coefficients and its derivatives to carry out the development, without dealing with Newcomb operators or Hansen's coefficients.