Complex networks constructed from irrational number sequences

In this paper, we construct (d, r) networks from sequences of different irrational numbers. In detail, segment an irrational number sequence of length M into groups of d digits which represent the nodes while two consecutive groups overlap by r digits (r = 0,1,...,d-1), and the undirected edges indicate the adjacency between two consecutive groups. (3, r) and (4, r) networks are respectively constructed from 14 different irrational numbers and their topological properties are examined. By observation, we find that network topologies change with different values of d, r and even sequence length M instead of the types of irrational numbers, although they share some similar features with traditional random graphs. We make a further investigation to explain these interesting phenomena and propose the identical-degree random graph model. The results presented in this paper provide some insight into distributions of irrational number digits that may help better understanding of the nature of irrational numbers.

Satellite Constellation Design for Complex Coverage

Most traditional satellite constellation design methods are associated with a simple zonal or global, continuous or discontinuous coverage connected with a visibility of points on the Earth's surface. A new geometric approach for more complex coverage of a geographic region is proposed. Full and partial coverage of regions is considered. It implies that, at any time, the region is completely or partially within the instantaneous access area of a satellite of the constellation. The key idea of the method is a two-dimensional space application for maps of the satellite constellation and coverage requirements. The space dimensions are right ascension of ascending node and argument of latitude. Visibility requirements of each region can be presented as a polygon and satellite constellation as a uniform moving grid. At any time, at least one grid vertex must belong to the polygon. The optimal configuration of the satellite constellation corresponds to the maximum sparse grid. The method is suitable for continuous and discontinuous coverage. In the last case, a vertex belonging to the polygon should be examined with a revisit time. Examples of continuous coverage for a space communication network and of the United States are considered. Examples of discontinuous coverage are also presented.

The design structure system - A method for managing the design of complex systems

Systems design involves the determination of interdependent variables. Thus the precedence ordering for the tasks of determining these variables involves circuits. Circuits require planning decisions abut how to iterate and where to use estimates. Conventional planning techniques, such as critical path, do not deal with these problems. Techniques are shown in this paper which acknowledge these circuits in the design of systems. These techniques can be used to develop an effective engineering plan, showing where estimates are to be used, how design iterations and reviews are handled, and how information flows during the design work.

Exact description of a cylindrically symmetrical complex-argument Laguerre-Gauss beam

Based on the perturbative series representation of a complex-source-point spherical wave an expression for cylindrically symmetrical complex-argument Laguerre-Gauss beams of radial order n is derived. This description acquires the accuracy up to any order of diffraction angle, and its first three corrected terms are in accordance with those given by Seshadri [Opt. Lett. 27, 1872 (2002)] based on the virtual source method. Numerical results show that on the beam axis the number of orders of nonvanishing nonparaxial corrections is equal to n. Meanwhile a higher radial mode number n leads to a smaller convergent domain of radius. (C) 2008 Optical Society of America.

Multiple energy transfers in rare earth complex-doped SiO2 spheres

Silica spheres doped with Eu(TTFA)(3) and/or Sm(TTFA)(3) were synthesized by using the modified Stober method. The transmission electron microscope image reveals that the hybrid spheres have smooth surfaces and an average diameter of about 210 nm. Fluorescence spectrometer was used to analyze the fluorescence properties of hybrid spheres. The results show that multiple energy transfer processes are simultaneously achieved in the same samples co-doped with Eu (TTFA)(3) and Sm(TTFA)(3), namely between the ligand and Eu3+ ion, the ligand and Sm3+ ion, and Sm3+ ion and Eu3+, ion. Energy transfer of Sm3+-> Eu3+, in the hybrid spheres leads to fluorescence enhancement of Eu3+ emission by approximately an order of magnitude. The lifetimes of the hybrid spheres were also measured.

Optical properties of a novel neodymium pentafluoropropionate binuclear complex

A novel neodymium pentafluoropropionate binuclear complex, Nd(C(2)F(5)COO)(3)Dipy (Dipy: 2,2'-dipyridyl), was synthesized and characterized by single-crystal X-ray diffraction. At a concentration of 0.2 M in DMSO-d(6), the Judd-Ofelt parameters (Omega(2), Omega(4), Omega(6)) were calculated from the UV-Vis spectrum. According to the small value of Omega(2) and the zero splitting energy of (4)F/(3/2) level, a symmetric ligand field of the complex was confirmed in DMSO-d(6). Strong emission of the complex in DMSO-d(6) at 1057 nm with a decay time about 1.3 mu s were detected when excited at 800 nm pumped by a laser diode. The stimulated emission cross-section of (4)F(3/2) -> (4)I(11/2) fluorescence transition was 2.36 x 10 (20) cm(2) and comparable with some laser glasses, which indicated good radiative properties of this neodymium pentafluoropropionate binuclear complex in liquid matrix. (c) 2008 Elsevier B.V. All rights reserved.

Design and performance of a complex-coupled DFB laser with sampled grating

A complex-coupled DFB laser with sampled grating has been designed and fabricated. The method uses the + 1 st order reflection of the sampled grating for laser single-mode operation. The typical threshold current of the sampled grating based DFB laser is 25 mA, and the optical output is about 10 mW at the injected current of 100 mA. The lasing wavelength of the device is 1.5385μm, which is the +1 st order wavelength of the sampled grating.

1.3 mu m InGaAsP/InP strained layer multi-quantum-well complex-coupled distributed feedback laser

1.3 mu m strained-layer multi-quantum wells complex-coupled distributed feedback lasers with a wide temperature range of 20 to 100 degrees C are reported. The low threshold current of 10mA and high single-facet slope efficiency of 0.3mW/mA were obtained for an as cleaved device. The single mode yield was as high as 80%.