Multivariate Polynomial Minimization and Its Application in Signal Processing

We make a conjecture that the number of isolated local minimum points of a 2n-degree or (2n+1)-degree r-variable polynomial is not greater than n ^r when n 2. We show that this conjecture is the minimal estimate, and is true in several cases. In particular, we show that a cubic polynomial of r variables may have at most one local minimum point though it may have 2^r critical points. We then study the global minimization problem of an even-degree multivariate polynomial whose leading order coefficient tensor is positive definite. We call such a multivariate polynomial a normal multivariate polynomial. By giving a one-variable polynomial majored below a normal multivariate polynomial, we show the existence of a global minimum of a normal multivariate polynomial, and give an upper bound of the norm of the global minimum and a lower bound of the global minimization value. We show that the quartic multivariate polynomial arising from broad-band antenna array signal processing, is a normal polynomial, and give a computable upper bound of the norm of the global minimum and a computable lower bound of the global minimization value of this normal quartic multivariate polynomial. We give some sufficient and necessary conditions for an even order tensor to be positive definite. Several challenging questions remain open.     

Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit

Classical optical lithography is diffraction limited to writing features of a size lambda/2 or greater, where lambda is the optical wavelength. Using nonclassical photon-number states, entangled N at a time, we show that it is possible to write features of minimum size lambda/(2N) in an N-photon absorbing substrate. This result allows one to write a factor of N2 more elements on a semiconductor chip. A factor of N = 2 can be achieved easily with entangled photon pairs generated from optical parametric down-conversion. It is shown how to write arbitrary 2D patterns by using this method.     

p‐Methoxy­benz­aldehyde benzoyl­hydrazone monohydrate

The crystal structure of the title compound, C₁₅H₁₄N₂O₂·H₂O, is in the keto tautomeric form and the configuration at the azomethine C=N double bond is E. The mol­ecule is non‐planar, with a dihedral angle of 27.3 (1)° between the aromatic rings. The crystal structure is stabilized by extensive hydrogen bonding involving the water mol­ecule and hydrazone moiety.     

Investigation of excited states of11B and7Li by means of thermal neutron capture on10B nuclei

Theγ-radiation from the¹⁰B(n,γ) reaction is studied using an unpolarized target. More accurate values for energies of transitions in¹¹B could be determined. No new levels have been found. TheQ value of this reaction: 11,454.1 (2)keV, is in agreement with earlier experiments. Also a new value for the cross section could be derived: 0.29 (4) barn, which is a factor 5 more accurate than earlier experiments. The¹⁰B(n, α)⁷ Li reaction, leading to the 478 keV state in⁷Li, is studied by means of polarized¹⁰B nuclei and polarized neutrons. The resulting anisotropy in the directional distribution of the⁷Li particles manifests itself in the Doppler broadening of the 478 keV line. Analysis of the line shape directly yields the conclusion, that the reaction proceeds for more than 96% through theJ=7/2 channel of¹¹B in case of destructive channel interference of theJ=5/2 channel. Constructive channel interference is only possible if the reaction proceeds for more than 99.5% through theJ=7/2 channel. It appeared that the outcomingα and⁷Li particles are emitted predominantly in directions perpendicular to the nuclear orientation axis.     

Efficient algorithms for machine scheduling problems with earliness and tardiness penalties

In this paper, we study the multi-machine scheduling problem with earliness and tardiness penalties and sequence dependent setup times. This problem can be decomposed into two subproblems—sequencing and timetabling. Sequencing focuses on assigning each job to a fixed machine and determine the job sequence on each machine. We call such assignment a semi-schedule. Timetabling focuses on finding an executable schedule from the semi-schedule via idle-time insertion. Sequencing is strongly NP-hard in general. Although timetabling is polynomial-time solvable, it can become a computational bottleneck if the procedure is executed many times within a larger framework. This paper makes two contributions. We first propose a quantum improvement to the computational efficiency of the timetabling algorithm. We then apply it within a squeaky wheel optimization framework to solve the sequencing and overall problem. Finally, we demonstrate the strength of our proposed algorithms by experiments.     

Growth rate determination of heterogeneous microbial population in swine manure

The effect of manure concentration on the growth of the heterogeneous microbial population under batch condition was studied. Four manure concentrations were used in the study. The dehydrogenase activity was used as a measure of the active biomass in the manure. The chemical oxygen demand test was used to measure the change in organic material caused by biological activities. The growth curve of the heterogeneous microbial population in swine manure was essentially similar to that of a pure culture grown batchwise in that it had the four principle phases: lag, exponential growth, stationary, and death. The exponential growth phase followed a diauxic growth pattern. High concentration of manure had an inhibitory effect on the microbial growth. Manure diluted less than 1:3 (manure:water) depressed the specific growth rate of the microbial population.     

Characterization of Acacia mangium polyflavonoid tannins by MALDI-TOF mass spectrometry and CP-MAS C NMR

The MALDI-TOF mass spectrometry (MS) and solid state CP-MAS ¹³C Nuclear Magnetic Resonance (NMR) spectroscopic technique were introduced to characterize Acacia mangium tannin (condensed tannins). The MALDI-TOF MS illustrated a series of peaks corresponding to oligomers of condensed tannins of up to 11 flavonoid units (3200 Da). A. mangium condensed tannins were found to consist predominantly of prorobinetinidin combined with profisetinidin and prodelphinidin. Both the MALDI-TOF mass spectra and the solid state CP-MAS ¹³C NMR indicated that the A. mangium tannins obtained from Kudat, had an almost completely linear structure; In addition, Lembah Beringin, consist of “angular” polymer structure; and Tawau, has included “twice-angular” polymer structures present in oligomers type of up to 7 flavonoid units. The high degree of polymerization of linear, angular type, twice-angular structures and longer oligomer (3200 Da) chains have not been observed in previous studies of condensed tannins. The spectra also indicated that A. mangium tannins are more heavily branched and have higher degree of polymerization (>7.0) compared to commercial mimosa (A. mearnsii) tannin (4.9). Because tannins are phenolic, it was expected that they can be used to replace phenol-formaldehyde (PF) adhesives.     

Challenges associated with the synthesis of unusual o-carboxamido stilbenes by the Heck protocol: Intriguing substituent effects, their toxicological and chemopreventive implications

The syntheses of fourteen unusual o-carboxamido stilbenes by the Heck protocol revealed surprising complexity related to intriguing substituent effects with mechanistic implications. The unexpected cytotoxic and chemopreventive properties also seem to be substituent dependent. For example, although stilbene 15d (with a 4-methoxy substituent) showed cytotoxicity on HT29 colon cancer cells with an IC(50) of 4.9 μM, the 3,4-dimethoxy derivative (15c) is inactive. It is interesting to observe that the 3,5-dimethoxy derivative (15e) showed remarkable chemopreventive activity in WRL-68 fetal hepatocytes, surpassing the gold standard, resveratrol. The resveratrol concentration needed to be 5 times higher than that of 15e to produce comparable elevation of NQO1.     

Evaporative Preconcentration of Fluorescent Protein Samples in Capillary Based Microplates

The preconcentration of analytes is important in biochemical analysis as it offers the ability to detect for trace species, and increase signal-to-noise ratios when using optical sensing on fluorophores. A strong advantage of the evaporation technique lies in its ability to operate without the need of any energy source; albeit major challenges exist on how to increase the surface area exposure to air for heightened evaporation, ensure no further increases once specified analyte concentrations have been achieved, and not needing any intervening membranes. We demonstrate here that the droplet creation and retraction approach in capillary based microplates offers such abilities whilst at the same time facilitating mixing.