Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.     

Simulation of the nonlinear vibration of a string using the Cellular Automata based on the reflection rule

In this study, the nonlinear dynamic responses of a string are simulated using the Cellular Automata method based on the reflection rule. In the case of nonlinear systems, the velocity of wave propagation is not constant and depends on the amplitude. A new treatment of the dynamic time step is proposed for the Cellular Automata method considering the effect of the propagation velocity. As numerical examples, first, the dynamic responses of a string with linear characteristic are simulated using the Cellular Automata method. A typical resonance curve can be obtained. Second, the dynamic responses of a string with nonlinear characteristic are simulated using the proposed method. Some characteristic types of vibration can be obtained. It is concluded that the linear and nonlinear dynamic responses of a string may be obtained by simulation using the Cellular Automata method.     

Altered expression of polyhydroxyalkanoate synthase gene and its effect on poly[(R)-3-hydroxybutyrate] synthesis in recombinant Escherichia coli

Polyhydroxyalkanoate (PHA) synthase (PhaC) from Wautersia eutropha was expressed in a wide range of production level in Escherichia coli XL1-Blue cells and its effects on PhaC activity, poly[(R)-3-hydroxybutyrate] [P(3HB)] production and its molecular weights were investigated. The production level of PhaC was controlled both by the amount of chemical inducer (isopropyl-β-d-thiogalactopyranoside, IPTG) added into the medium and the use of different copy number of plasmids. In a flask experiment, as PhaC production level in the cells increased, the PhaC activity also increased in the range of low PhaC concentration. However, PhaC activity did not further increase in the range of high PhaC concentration, probably due to the formation of inclusion body in the cells. The molecular weight of P(3HB) was found to decrease with increasing PhaC activity. This trend was also verified in high cell density cultivation using 10-l jar fermentor. Furthermore, we demonstrated that the use of low copy number plasmid and appropriate induction of PhaC expression were effective in achieving both high productivity and high molecular weight of P(3HB).     

Estimation of growth rate in unidirectionally solidified multicrystalline silicon by the growth-induced striation method

Multicrystalline silicon was grown by unidirectional solidification method using the accelerated crucible rotation technique. The application of the accelerated crucible rotation technique in unidirectional solidification method induced growth striations across the axial direction of the grown crystal. This striation pattern was observed from carbon concentration distribution, obtained by using Fourier transform infrared spectroscopy. The generated striation pattern was found to be weak and discontinuous. Some striations were absent, probably due to back melting, caused during each crucible rotation. From the growth striations and applied time period in crucible rotation, the growth rate was estimated by using Fourier transformation analysis.     

Bump formation on a glass surface with a transparent coating using femtosecond laser processing

The morphology of a glass surface having a transparent coating processed with focused femtosecond laser pulses is investigated. The transparent coating is formed of poly-methyl methacrylate (PMMA). When the glass was coated with a PMMA film with a thickness of 2.8 μm, bumps were formed over a wide range of axial focus positions. The same laser pulse energy produced cavities when processing bare glass with no coating. The bumps were formed as a result of suppressing material emission from the glass surface by a shielding effect of plasma generated by ablation of the PMMA film and by physical blocking of the PMMA film. A thinner film with a thickness of 0.7 μm produced a reduced shielding effect, forming an exploded bump with a small pit at its center and debris around the periphery. PACS 44.10.+i; 61.80.Ba; 79.20.Ds     

Recursive Fermion System in Cuntz Algebra. I

Embeddings of the CAR (canonical anticommutation relations) algebra of fermions into the Cuntz algebra ?₂ (or ?_{2 d} more generally) are presented by using recursive constructions. As a typical example, an embedding of CAR onto the U(1)-invariant subalgebra of ?₂ is constructed explicitly. Generalizing this construction to the case of ?_{2 p} , an embedding of CAR onto the U(1)-invariant subalgebra of ?_{2 p} is obtained. Restricting a permutation representation of the Cuntz algebra, we obtain the Fock representation of CAR. We apply the results to embed the algebra of parafermions of order p into ?_{2 p} according to Green's ansatz. Received: 3 September 2001 / Accepted: 19 January 2002     

Novel ring transformation of thiazolidine to oxazolidine: acyl halide-promoted intramolecular rearrangement of 4(R)-hydroxymethyl-3-methyl-1,3-thiazolidine

An interesting transformation occurs during acylation of 4(R)-hydroxymethyl-3-methyl-1,3-thiazolidine when 4(R)-acylthiomethyl-3-methyl-1,3-oxazolidines are yielded: the reaction competing with O-acylation is controlled by the bulkiness of the acyl group.     

Factors affecting polyhydroxybutyrate biosynthesis in the marine photosynthetic bacteriumRhodopseudomonas sp. strain W-1S

Applied Biochemistry and Biotechnology - A marine photosynthetic bacterium,Rhodopseudomonas sp. strain W-1S, accumulated polyhydroxybutyrate (PHB) to 56% of the dry cell weight under microaerobic...     

Determination of237Np in environmental samples using inductively coupled plasma mass spectrometry

Ammonium uranates (AU) obtained by the addition of aqueous NH₄ OH to a solution of UO₂ (NO₃)₂ or the equilibrium reaction of UO₃ · 2H₂ O with the vapour over concentrated NH₄ OH have been studied by X-ray diffraction (XRD) analysis, diffuse reflectance Fourier transform infrared spectrometry (DR-FTIR) and chemical analysis. Ammonia can be present as either NH₃ or NH ₄ ⁺ . For precipitates obtained at a pH of 3.7, ammonia in the form of NH₃ is predominant. For ammonium uranate obtained by reaction over concentrated NH₄OH, most of the ammonia is bonded as NH ₄ ⁺ . The reaction mechanism and structures of the products are also discussed.