Mathematical formulas describing the sequences of the periodic table

Mathematical formulas describing all of the sequences of the chemical elements are derived from double tetrahedron face‐centered cubic lattice model. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Nontrivial periodic solution of a stochastic epidemic model with seasonal variation

In this paper, we consider a stochastic SIR epidemic model with seasonal variation. First, we obtain the threshold of our model which determines whether the epidemic occurs or not. In the case of persistence, we prove that there is a nontrivial positive periodic solution.     

Shear to longitudinal mode conversion via second harmonic generation in a two-dimensional microscale granular crystal

Shear to longitudinal mode conversion via second harmonic generation is studied theoretically and computationally for plane waves in a two-dimensional, adhesive, hexagonally close-packed microscale granular medium. The model includes translational and rotational degrees of freedom, as well as normal and shear contact interactions. We consider fundamental frequency plane waves in all three linear modes, which have infinite spatial extent and travel in one of the high-symmetry crystal directions. The generated second harmonic waves are longitudinal for all cases. For the lower transverse–rotational mode, an analytical expression for the second harmonic amplitude, which is derived using a successive approximations approach, reveals the presence of particular resonant and antiresonant wave numbers, the latter of which is prohibited if rotations are not included in the model. By simulating a lattice with adhesive contact force laws, we study the effectiveness of the theoretical analysis for non-resonant, resonant, and antiresonant cases. This work is suitable for the analysis of microscale and statically compressed macroscale granular media, and should inspire future studies on nonlinear two- and three-dimensional granular systems in which interparticle shear coupling and particle rotations play a significant role.     

登陆艇光学对中方法及LED引导光源设计

设计了基于引导光源颜色/相对位置的登陆艇光学对中方法,登陆艇驾驶员通过不同颜色引导光源间的相对位置判断其是否偏航以及偏航的程度,从而提高登陆艇快速入舱的精度和安全.引导光源以横纵向90°视场角的光束对最远200m海面进行均匀照明,采用CREE XPE型号的LED,通过改进的网格映射法设计自由曲面透镜以获得要求的矩形照明光场,仿真与实验结果表明,所设计的LED引导光源可以满足登陆艇光学对中系统的照明要求.     

Existence solutions for second order Hamiltonian systems

We study the existence of periodic solutions for a second order non-autonomous dynamical system containing variable kinetic energy terms. Subquadratic problems and superquadratic problems are both considered.     

A rigorous lower bound for the stability regions of the quadratic map

We establish a lower bound on the measure of the set of stable parameters a for the quadratic map Q_a(x)=ax(1−x). For these parameters, we prove that Q_a either has a single stable periodic orbit or a period-doubling bifurcation. From this result, we also obtain a non-trivial upper bound on the set of stochastic parameters for Q_a.     

Choice of optimal exposures in photographing the earth’s surface by multispectral photographic equipment

An analysis of radiation fluxes entering the image plane of the spectral channels of multispectral photographic equipment (MSPE) used in photographing the earth’s surface from space, the illumination intensity levels created by these fluxes, and the degree of blackening of photographic materials depending on the exposure has been carried out. The method of selecting the optimal values for the exposure time in photographing various classes of the earth’s surface in each spectral channel of MSPE is proposed. Using the spectra of brightness, measured from aboard the orbital Salyut-7 and Mir stations, evaluations of the optimal exposure time of the basic classes of the earth’s surface depending on optical parameters of the MSPE were made. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 1, pp. 111–116, January–February, 2000.     

Solar sail orbits at the Earth–Moon libration points

Solar sail technology offer new capabilities for the analysis and design of space missions. This new concept promises to be useful in overcoming the challenges of moving throughout the solar system. In this paper, novel families of highly non-Keplerian orbits for solar sail spacecraft at linear order are investigated in the Earth–Moon circular restricted three-body problem, where the third body is a solar sail. In particular, periodic orbits near the collinear libration points in the Earth–Moon system will be explored along with their applications. The dynamics are completely different from the Earth–Sun system in that the sun line direction constantly changes in the rotating frame but rotates once per synodic lunar month. Using an approximate, first-order analytical solution to the nonlinear nonautonomous ordinary differential equations, periodic orbits can be constructed that are displaced above the plane of the restricted three-body system. This new family of orbits have the property of ensuring visibility of both the lunar far-side and the equatorial regions of the Earth, and can enable new ways of performing lunar telecommunications.     

Global exponential stability of periodic solution of neural network with variable coefficients and time-varying delays

By using the continuation theorem of Mawhin’s coincidence degree theory and some inequality techniques, some new sufficient conditions are obtained ensuring existence and global exponential stability of periodic solution of neural networks with variable coefficients and time-varying delays. These results are helpful to design globally exponentially stable and oscillatory neural networks. Finally, the validity and performance of the obtained results are illustrated by two examples.