Fault tolerance in FFT arrays: Time redundancy approaches

Fault tolerance in VLSI/WSI FFT arrays acquires relevance when defects and run-time faults become significant, due to large dimensions of processors and arrays. Then, both restructuring to overcome end-of-production defects and reconfiguration to overcome run-time faults are required, to achieve the dual purposes of higher yield and higher reliability.Adopting as basic FFT network the two-dimensions array that directly corresponds to the FFT flow graph, the usual structure redundancy techniques tailored for two-dimensions arrays reconfiguration are not well applicable, since the limited locality of this network leads to relevant area increase due to the augmented interconnection structure.In this paper,time redundancy is suggested as a viable alternative for the two-dimensions FFT array; two different solutions are presented, one based oninter-stage reconfiguration, the other one adoptingintra-state reconfiguration, both allowing for survival to multiple faults with limited increase of network complexity and very small hard-core sections. As usual in many time redundancy methods, both approaches result in a processing speed equal to half the processing speed granted by an ideal, fault-free device.Reliability and survival ratios to multiple faults are evaluated for the two cases, taking into account also the area increments necessary for fault tolerance. The reliability evaluations allow for a direct comparison of the two solutions.     

Integrability of det▽u and Evolutionary Wente''s Problem Associated to Heat Operator

In this note, the authors resolve an evolutionary Wente's problem associated to heat equation, where the special integrability of det▽u for u ∈ H1(R2,R2) is used.     

Polarization inscription in ferroelectric (111) PZT and (100) SBT films

Ferroelectric thin films form an equilibrium domain structure compatible with their respective crystallographic symmetry. In tetragonal (111) PZT, 90° domains prevail; in (pseudo-tetragonal) (100) SBT both 90° and 180° domains are present. The size of 90° domains has been measured for e.g., PZT as slabs of 15 nm width. Domain size is a result of stress minimization in the film during the paraelectric (PE) → ferroelectric (FE) transition. A precise and regular domain pattern for (111) PZT and (100) SBT films has been investigated in detail by TMSFM. Single domains can be addressed mechanically with the tip of an AFM. Such single domain switching corresponds to a data storage density of 200 Gbit/inch². Applications of ferroelectric and high- paraelectric materials for e.g., non-volatile data storage replacing DRAM devices or as sensors in infrared cameras are increasingly becoming popular.     

Spectral and voltammetric studies on titanium substituted Keggin-type heteropolyanions

Bonding and redox properties of mono- and dititanium substituted 12-heteropolytungsto-phosphates and their complexes with bivalent Mn, Co, Ni and Cu are studied by UV-Vis, ESR and cyclicvoltammetric techniques. The heteropoly blue analogue [Ti^IIITi^IVW₁₀PO₄₀]⁸⁻ is unstable and its presence in solution is proved by optical and ESR spectroscopy. ESR results reveal that the odd electron is trapped on the titanium atom at 77 K. The optical electronegativity of Ti(III) in this heteropoly blue is estimated to be 2.4 from the intervalence charge transfer (IVCT) bands. X-ray powder diffraction results show that the complexes K₅M^II[Ti₂W₁₀PO₄₀].xH₂O(M^II = Cu or Mn) are isomorphous with K₇[Ti₂W₁₀PO₄₀].6H₂O. Electronic spectroscopy indicates very high symmetry around the bivalent metal ion M in the K₅M^II[Ti₂W₁₀PO₄₀].xH₂O complexes. This high symmetry is confirmed in K₅Cu[Ti₂W₁₀PO₄₀] by the observation of dynamic Jahn-Teller (JT) distortion at 300 K and static JT distortion at 77 K.     

Turing determinacy and the continuum hypothesis

From the hypothesis that all Turing closed games are determined we prove: (1) the Continuum Hypothesis and (2) every subset of ₁ is constructible from a real.     

Microbial Transformation of Sesquiterpenes, (−)‐Ambrox® and (+)‐Sclareolide

The microbial transformation of (?)‐Ambrox^® ( 1 ), a perfumery sesquiterpene, by a number of fungi, by means of standard two‐stage‐fermentation technique, afforded ambrox‐1α‐ol ( 2 ), ambrox‐1α,11α‐diol ( 3 ), ambrox‐1α,6α‐diol ( 4 ), ambrox‐1α,6α,11α‐triol ( 5 ), ambrox‐3‐one ( 6 ), ambrox‐3β‐ol ( 7 ), ambrox‐3β,6β‐diol ( 8 ), 13,14,15,16‐tetranorlabdane‐3,8,12‐triol ( 9 ), and sclareolide ( 10 ) (Schemes 1 and 2). Further incubation of compound 10 with Cunninghamella elegans afforded 3‐oxosclareolide ( 11 ), 3β‐hydroxysclareolide ( 12 ), 2α‐hydroxysclareolide ( 13 ), 2α,3β‐dihydroxysclareolide ( 14 ), 1α,3β‐dihydroxysclareolide ( 15 ), and 3β‐hydroxy‐8‐episclareolide ( 16 ) (Scheme 3). Metabolites 2 – 5, 12, 13 , and 16 were found to be new compounds. The major transformations include a reaction path involving hydroxylation, ether‐bond cleavage and inversion of configuration. Metabolites 11 – 16 of sclareolide showed significant phytotoxicity (Table 1). The structures of the metabolites were characterized on the basis of spectroscopic techniques.     

Pinacol-Pinacolone Rearrangement of 1, 2-Di-(p-methoxyphenyl)-ethane-1, 2-diol and Bis-(4-methoxyphenyl)-acetaldehyde in Acid Media

1, 2-Di-(p-methoxyphenyl)-ethane-1, 2-diol gave in acid media bis-(4-methoxy-phenyl)-acetaldehyde, 4-4′-dimethoxy-deoxybenzoin, and 1, 2-di-(p-methoxyphenyl)-ethylene oxide; their respective yields being influenced by at least 3 factors: (i) the acid, (ii) its concentration, and (iii) the reaction period. Bis-(4-methoxyphenyl)-acetaldehyde rearranged to the deoxybenzoin in boiling sulfuric (50%) or phosphoric (75%) acids (w/w), and to two isomeric 1, 2-diacetoxy-1, 2-di-(p-methoxyphenyl) ethanes when it was heated with acetic anhydride. The mechanisms of these reactions are discussed.     

Analysis of neem oils by LC–MS and degradation kinetics of azadirachtin-A in a controlled environment

Since it was first isolated, the oil extracted from seeds of neem (Azadirachtin indica A juss) has been extensively studied in terms of its efficacy as an insecticide. Several industrial formulations are produced as emulsifiable solutions containing a stated titer of the active ingredient azadirachtin-A (AZ-A). The work reported here is the characterization of a formulation of this insecticide marketed under the name of Neem-azal T/S and kinetic studies of the major active ingredient of this formulation. We initially performed liquid–liquid extraction to isolate the neem oil from other ingredients in the commercial mixture. This was followed by a purification using flash chromatography and semi-preparative chromatography, leading to ¹³C NMR identification of structures such as azadirachtin-A, azadirachtin-B, and azadirachtin-H. The neem extract was also characterized by HPLC–MS using two ionization sources, APCI (atmospheric pressure chemical ionization) and ESI (electrospray ionization) in positive and negative ion modes of detection. This led to the identification of other compounds present in the extract—azadirachtin-D, azadirachtin-I, deacetylnimbin, deacetylsalannin, nimbin, and salannin. The comparative study of data gathered by use of the two ionization sources is discussed and shows that the ESI source enables the largest number of structures to be identified. In a second part, kinetic changes in the main product (AZ-A) were studied under precise conditions of pH (2, 4, 6, and 8), temperature (40 to 70 °C), and light (UV, dark room and in daylight). This enabled us to determine the degradation kinetics of the product (AZ-A) over time. The activation energy of the molecule (75±9 kJ mol^–1) was determined by examining thermal stability in the range 40 to 70 °C. The degradation products of this compound were identified by use of HPLC–MS and HPLC–MS–MS. The results enabled proposal of a chemical degradation reaction route for AZ-A under different conditions of pH and temperature. The data show that at room temperature and pH between 4 and 5 the product degrades into two preferential forms that are hydrolyzed to a single product over time and as a function of pH change.