An efficient construction of period-2 bulbs in the cubic Mandelbrot set with parametric boundaries

A parametric boundary equation is established for the principal period-2 bulb in the cubic Mandelbrot set. Using its geometry, an efficient escape-time algorithm which reduces the construction time for the period-2 bulbs in the cubic Mandelbrot set is introduced and the implementation graphic results display the fascinating fractal beauty     

Biphotonic recording effect of polarization gratings based on dye-doped liquid crystal films

This study investigates a holographic recording effect of biphotonic polarization gratings (BPGs) written on dye-doped liquid crystal (DDLC) films. One linearly polarized green light (λ_G = 514.5 nm) and a polarization-modulated interference pattern formed by two mutually coherent orthogonal (±45° with respect to the polarization of the green light) polarized red lights simultaneously excite the DDLC films to generate a BPG. The formation of BPGs depends primarily on the dichroism of the dye molecules and a sequence of mechanisms: photoisomerization, anisotropic adsorption and inhibition of dye adsorption. The cis-isomer absorbance-modulated distribution associated with the red polarization-modulation pattern induces the dye adsorption-modulated pattern, in turn, yielding the permanent BPG which generates a modulated twisted nematic (TN) structure pattern in the sample. It is found that each BPG is verified to be electrically switchable and thermally erasable. The switching time is in the order of milliseconds. Additionally, the recording time to form a BPG decreases with increasing intensity of the green pump beam.     

Bimodal fission in binary and ternary spontaneous fission of 252Cf

The hot bimodal fission of ²⁵²Cf is reexamined with new high-statistics data. We constructed a γ-γ-γ coincidence cube for binary fission and LCP-gated γ-γ matrix for ternary fission. By identifying the secondary fission fragments from their γ-ray transitions, we measured the yields for various fission splits. The normal neutron yield distribution is found to be Gaussian for Xe-Ru. However, the binary fission split of Ba-Mo is found to exhibit a bimodal neutron distribution with the “hot mode” corresponding to ≈3.1% of the total yield. In α ternary fission, the first measurements of yields for specific fission splits are presented. The Te-α-Ru and Xe-α-Mo neutron yields fit well with a single mode, but the Ba-α-Zr split shows evidence for an enhanced hot mode with an intensity of ≈13.8% of the normal mode. The text was submitted by the authors in English.     

Annealing effect on soft magnetic properties and magnetoimpedance of Finemet Fe73.5Si13.5B9Nb3Au1 alloy

Effect of annealing on the soft magnetic properties of Fe_73.5Si_13.5B₉Nb₃Au₁ amorphous ribbon has been investigated by means of structure examination, magnetoimpedance ratio (MIR) and incremental permeability ratio (PR) spectra measured in the frequency range of 1–10 MHz at a fixed current of 10 mA X-ray diffraction analysis showed that the as-cast sample was amorphous and it became nanocrystalline under a proper heat treatment. When annealing amorphous alloy at 530 °C for 30, 60, 90 min, soft magnetic properties have been improved drastically. Among the samples investigated, the sample annealed at 530 °C for 90 min showed the softest magnetic behavior. The MIR and PR curves revealed the desirable changes in anisotropy field depending upon annealing.     

Analysis of the manufacturing lead time in a production system with non-renewal batch input,threshold policy and post-operation

In this paper, we analyze the manufacturing lead time in a production system with BMAP (Batch Markovian Arrival process) input and post-operation operated under the N-policy. We use the factorization principle to derive the waiting time distribution (hence the manufacturing lead time) and the mean performance measures. A numerical example is provided.     

Recent changes in A-level Mathematics: is the availability and uptake of mechanics declining yet more?

In the past 6 years changes have occurred in GCE A-levels. Inparticular, there have been several major changes in A-levelMathematics courses. As engineering students are usually requiredto have studied A-level Mathematics, or its equivalent, thesechanges have had an effect on their prior mathematical knowledge.Moreover, engineering students traditionally obtained a goodgrounding in mechanics as part of their A-level Mathematicsqualification. However, mechanics, which was once included inthe core syllabus, is now optional. This article investigatesthe current availability and uptake of mechanics modules withinA-level Mathematics courses in schools. Comparisons are drawnbetween these results and results of a survey of schools in2004 and surveys of first year engineering students conductedin 2004 and 2005. It is found that there is a decline in theavailability of mechanics modules and the uptake of more thanone mechanics module has also decreased. The implications ofthese findings for engineering educators are discussed.     

Studies on calcium‐containing poly(urethane ether)s

The calcium salt of mono(hydroxyethoxyethyl)phthalate [Ca(HEEP)₂] was synthesized by the reaction of diethylene glycol, phthalic anhydride, and calcium acetate. Calcium‐containing poly(urethane ether)s (PUEs) were synthesized by the reaction of hexamethylene diisocyanate (HMDI) or tolylene 2,4‐diisocyanate (TDI) with a mixture of Ca(HEEP)₂ and poly(ethylene glycol) (PEG₃₀₀ or PEG₄₀₀) with di‐n‐butyltin dilaurate as a catalyst. A series of calcium‐containing PUEs of different compositions were synthesized with Ca(HEEP)₂/PEG₃₀₀ (or PEG₄₀₀)/diisocyanate (HMDI or TDI) molar ratios of 2:2:4, 3:1:4, and 1:3:4 so that the coating properties of the PUEs could be studied. Blank PUEs without calcium‐containing ionic diols were also prepared by the reaction of PEG₃₀₀ or PEG₄₀₀ with HMDI or TDI. The PUEs were well characterized by Fourier transform infrared, ¹H and ¹³C NMR, solid‐state cross‐polarity/magic‐angle‐spinning ¹³C NMR, viscosity, solubility, and X‐ray diffraction studies. The thermal properties of the polymers were also studied with thermogravimetric analysis and differential scanning calorimetry. The PUEs were applied as top coats on acrylic‐coated leather, and their physicomechanical properties were also studied. The coating properties of PUEs, such as the tensile strength, elongation at break, tear strength, water vapor permeability, flexing endurance, cold crack resistance, abrasion resistance, color fastness, and adhesive strength, were better than the standard values. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2865–2878, 2003     

A lower bound for the convexity number of some graphs

Given a connected graphG, we say that a setC ?V(G) is convex inG if, for every pair of verticesx, y ∈ C, the vertex set of everyx-y geodesic inG is contained inC. The convexity number ofG is the cardinality of a maximal proper convex set inG. In this paper, we show that every pairk, n of integers with 2 ≤k ≤ n?1 is realizable as the convexity number and order, respectively, of some connected triangle-free graph, and give a lower bound for the convexity number ofk-regular graphs of ordern withn>k+1.     

A Multisensor Deconvolution Problem

Meisters and Peterson gave an equivalent condition under which the multisensor deconvolution problem has a solution when there are two convolvers, each the characteristic function of an interval. In this article we find additional conditions under which the deconvolution problem for multiple characteristic functions is solvable. We extend the result to the space of Gevrey distributions and prove that every linear operator S, fromthe space of Gevrey functions with compact support onto itself, which commutes with translations can be represented as convolution with a unique Gevrey distribution T of compact support. Finally, we find explicit formula for deconvolvers when the convolvers satisfy weaker conditions than the equivalence conditions using nonperiodic sampling method.