FFT-based algorithms for the string matching with mismatches problem

The string matching with mismatches problem requires finding the Hamming distance between a pattern P of length m and every length m substring of text T with length n. Fischer and Paterson's FFT-based algorithm solves the problem without error in O(σnlogm), where σ is the size of the alphabet Σ [SIAM–AMS Proc. 7 (1973) 113–125]. However, this in the worst case reduces to O(nmlogm). Atallah, Chyzak and Dumas used the idea of randomly mapping the letters of the alphabet to complex roots of unity to estimate the score vector in time O(nlogm) [Algorithmica 29 (2001) 468–486]. We show that the algorithm's score variance can be substantially lowered by using a bijective mapping, and specifically to zero in the case of binary and ternary alphabets. This result is extended via alphabet remappings to deterministically solve the string matching with mismatches problem with a constant factor of 2 improvement over Fischer–Paterson's method.     

How to Build Robust Shared Control Systems

Previous researchers have designed shared control schemes with a view to minimising the likelihood that participants will conspire to perform an unauthorised act. But, human nature being what it is, systems inevitably fail; so shared control schemes should also be designed so that the police can identify conspirators after the fact. This requirement leads us to search for schemes with sparse access structures. We show how this can be done using ideas from coding theory. In particular, secret sharing schemes based on geometric codes whose dual [n,k,d] codes have d and n as their only nonzero weights are suitable. We determine their access structures and analyse their properties. We have found almost all of them, and established some relations among codes, designs and secret-sharing schemes.     

Dimensional variation in production of high-aspect-ratio micro-pillars array by micro powder injection molding

Micro powder injection molding (μPIM) is one of the potential processes for the mass production of metallic microstructures and micro components. Here, μPIM is the miniaturization of conventional PIM, which involves four processing steps: mixing, injection molding, debinding and sintering. This paper looks into the feasibility and effectiveness of μPIM as a key mass production process for the fabrication of metallic micro components. For it to be an effective re-production process, it is imperative to examine how well parts can be duplicated/fabricated from a master mold. In this work, the dimensional variation of high-aspect-ratio micro-pillars arrays, in particular the dimensional shrinkage, global warpage, and surface roughness at each stage of the μPIM process for a range of molding pressures, are quantified and compared in detail. The sensitivity of the dimensional variation of the microstructures to the packing pressure is reported. The mechanism behind the dimensional variation is analyzed. PACS 81.20.Ev; 81.20.Hy; 81.70.Fy; 07.60.Ly; 81.05.-t     

On the asymptotic stability ofθ-methods for delay differential equations

Stability regions of -methods for the linear delay differential test equations

Magydardiendiol,diterpenoid with a new skeleton from magydaris panacifolia (umbelliferae).

Three new diterpenoids with a substituted α-cyclogeraniol skeleton have been isolated from the umbelliferae $\text{Magydaris panacifolia}$ (Vahl) Lange, for which the names of magydar-2,13-dien-11,17-diol, $\text{1}$, magydar-2,10 (20), 13-trien-17-ol, $\text{2}$, and magydar-2,10(20), 13-trien-17-yl acetate, $\text{3}$, are proposed. The structures of these substances have been deduced from spectroscopic and chemical data.     

Minor components with the γ-cyclogeranil geraniol skeleton from Bellardia trixago (L.) all.

Trixagol 1 and fourteen derivatives with the skeleton of γ-cyclogeranil geraniol were isolated from Bellardia trixago, the structures were determined by spectroscopic methods and confirmed by partial synthesis. Furthermore. 3,4-dihydro-γ-ionone, α-ambrinol, β-sitosterol and three flavonoids 5-O-demethyl tangeretin, 5-hydroxy auranetin and 3′-methoxy calycopterin were also isolated.     

Single-ion activities and Mn(Hg)/Mn(II) reactions in aqueous solutions of alkaline-earth chlorides

Combined thermodynamic and kinetic studies have yielded convenient single-ion activity coefficients for manganese(II), alkaline-earth, and chloride ions and standard exchange currents for the two steps of the Mn(Hg)/Mn(II) electrode in 0.005 M MnCl₂+0.495 M MeCl₂ (for Me=Mg, Ca, Sr, Ba, and Mn) at 25°C. The results indicate that the fall in mean ionic activity coefficient for the alkaline-earth chlorides along the sequence from magnesium to barium is carried to a larger extent by the cation than by the anion, that also the activity coefficient for the minority cation Mn(II) falls along this sequence, and that other than activity-coefficient effects on the Mn(Hg)/Mn(II) reactions appear only with barium ions, which retard the reactions additionally. The results are discussed with emphasis on ionic interactions and double-layer effects.     

Photoinitiated carbonylation with [(11)C]carbon monoxide using amines and alkyl iodides

Photoinitiated radical carbonylation with [(11)C]carbon monoxide at low concentration was employed in syntheses of carbonyl-(11)C-labeled amides using alkyl iodides and amines as precursors. Eleven (11)C-amides were synthesized in up to 74% decay-corrected radiochemical yields with reaction times of 400 s and with up to 95% conversion of carbon monoxide. Starting with 26.3 GBq of [(11)C]carbon monoxide, 10.6 GBq of 1-cyclohexane [(11)C]carbonyl-4-phenyl-piperazine (15) was obtained within 35 min from the end of bombardment (33 microA) and with a specific radioactivity of 192 GBq/micromol at the same time point. The influence of solvents was investigated. The described procedure extends the range of accessible labeling methods. The method may also be useful for preparation of (13)C- and (14)C-substituted compounds.