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.     

Designing an effective federal biomass program

This article addresses two questions: Has the effectiveness of the US governments federal research and development (R&;D) spending suffered from the post-1980 strategic change from freely shared and publicly owned to privately owned scientific advances? What criteria would a federal R&;D program use to design a strategy that most effectively enhances the well-being of farmers and rural communities? Several studies found that the pre-1980 US Department of Agriculture research strategy was very effective. No comparable studies have analyzed the comparative effectiveness of the post-1980 strategy of restricting access to the results of public research. Recent experience and several analytical studies suggest that to significantly enhance the health of rural economies from an expanded use of plant matter as an industrial material, federal policy should channel scientific and engineering research into small- and medium-sized production and processing technologies and should encourage farmer-owned, value-added enterprises.     

Dependence of the neodymium random laser threshold on the diameter of the pumped spot

We experimentally studied the dependence of the threshold energy density E/sub th//S in Nd/sub 0.5/La/sub 0.5/Al/sub 3/(BO/sub 3/)/sub 4/ random laser on the diameter of the pumped spot d and found that at d/spl ges/130/spl mu/m, E/sub th//S is proportional to 1/d+const. This functional dependence is different from the one commonly expected in the case of diffusion, /spl prop/1/d/sup 2/+const. However, the obtained experimental dependence does not mean the failure of the diffusion model. Calculating the mean photon's residence time /spl tau//sub res//sup p/ (which photons, making their diffusion-like random walks, spend inside the gain volume) as the function of d and further assuming that E/sub th//S/spl prop/(/spl tau//sup p//sub res/)/sup -1/, we predicted the experimentally obtained functional dependence, /spl prop/1/d+const. The major difference between our model and that of and was in the boundary conditions.     

89-GHz fT room-temperature silicon MOSFETs

The authors report the implementation of deep-submicrometer Si MOSFETs that at room temperature have a unity-current-gain cutoff frequency (f_T) of 89 GHz, for a drain-to-source bias of 1.5 V, a gate-to-source bias of 1 V, a gate oxide thickness of 40 Å, and a channel length of 0.15 μm. The fabrication procedure is mostly conventional, except for the e-beam defined gates. The speed performance is achieved through an intrinsic transit time of only 1.8 ps across the active device region     

Fast atom bombardment mass spectra of keto acid and keto ester phosphoranes

Positive-ion fast atom bombardment mass spectra of 13 keto acid and keto ester phosphoranes were examined. All compounds gave a protonated molecular ion and characteristic peaks at m/z 303, 279, 262 and 201.     

Generalized Gabor expansions of discrete-time signals in l2(Z) via biorthogonal-like sequences

In this paper, a biorthogonal-like sequences (BLS) theory and its application to the generalized Gabor expansions (equivalently, the generalized short-time Fourier transform/filterbank summation) are presented. A pair of BLS's are defined to be two sequences satisfying a biorthogonal-like condition (BLC), which is a moment equation and equivalent to a linear difference equation. We show that two collections in a Hilbert space generated by a pair of BLS's in the joint time-frequency domain are complete, either can be used as an analysis filter, and the other can be used as a synthesis filter for a generalized Gabor expansion of discrete-time signals. A sufficient and necessary condition on the existence of BLS's based on the moment equation is presented, which is simpler to use than frame theory. Given a filter generating a frame, its BLS's also generate frames. The dual frame is one of them. Given a FIR analysis/synthesis filter, there is a FIR synthesis/analysis filter if BLS's exist. The algorithm to compute FIR analysis and synthesis filters based on the linear difference equation is presented in this paper, which is simpler than frame operator     

Scanning tunnelling microscopic images of the surface ordering of the liquid crystal 4-n-octyl-4'-cyanobiphenyl

Images of the surface ordering of 4-n-octyl-4'-cyanobiphenyl, a room temperature smectic liquid crystal deposited upon graphite, have been obtained by scanning tunnelling microscopy. The microscope was operated in air using the constant-current mode. Under certain tunnelling conditions it has been possible to resolve both the aliphatic and aromatic parts of the molecule, and to observe individual benzene rings. Two previously unreported conformations have been observed: an overlapping bilayer structure with spacing 3.7 nm, and a monolayer structure with spacing 2.4 nm. The latter structure may represent the first visual evidence for a surface polar ordered structure.     

Improved bounds for sampling contingency tables

We study the problem of sampling contingency tables (nonnegative integer matrices with specified row and column sums) uniformly at random. We give an algorithm which runs in polynomial time provided that the row sums r_i and the column sums c_j satisfy r_i = Ω(n^3/2m log m), and c_j = Ω(m^3/2n log n). This algorithm is based on a reduction to continuous sampling from a convex set. The same approach was taken by Dyer, Kannan, and Mount in previous work. However, the algorithm we present is simpler and has weaker requirements on the row and column sums. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 135–146, 2002     

Synthesis and properties of polyethersulphone–polydimethyisiloxane block copolymers

High molecular weight alternating block copolymers of polyethesulphone (PES) and polydimethylsiloxane (PDMS) were prepared by the condensation of dimethylamino-terminated PDMS oligomers and hydroxy-terminated PES oligomers in 1,2-dichlorobenzene. Microphase separation of the block copolymers at exceptionally short block lengths was observed by differential scanning calorimetry (DSC) and transmission electron microscopy (TEM). The Si? O? C intersegment linkage in these materials appeared to display poor hydrolytic stability which is contrary to results obtained for other block copolymers.