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.     

Effect of different electronic properties on 9-aryl-substituted BMVC derivatives for new fluorescence probes

We have previously illustrated that the electron donor of carbazole moiety and the electron acceptor of methyl pyridinium cation in 3,6-bis(1-methyl-4-vinylpyridinium) carbazole diiodide (BMVC) molecule could form an intramolecular charge-transfer state. The intramolecular twist of the vinyl group in bridging the donor and acceptor plays an important role in the BMVC fluorescence. Here, we have synthesized three 9-aryl-substituted BMVC derivatives with different electronic properties for the design of the second generation of fluorescence probes. The steady-state solvatochromic studies show no appreciable change to the charge transfer of BMVC by substituting an anisole electron-donating group at 9-position of BMVC. However, substituting a 9-nitrobenzyl electron-withdrawing group in BMVC could restrict the charge transfer in the excited state. Moreover, the increase of the fluorescence yields of 9-anisole BMVC and 9-phenyl BMVC upon interaction with DNA is even higher than that in glycerol, while the fluorescence yield of 9-nitrobenzyl BMVC upon interaction with DNA is much lower than that in glycerol. Although 9-nitrobenzyl BMVC is a good G-quadruplex stabilizer, substituting an electron-withdrawing group at 9-position of BMVC is not recommended for the design of fluorescence probes. On the other hand, co-localization between 9-phenyl BMVC and MitoTracker Red in the merged image of cells indicates that the 9-phenyl BMVC is a potential fluorescent mitochondrial probe.     

'Living' controlled in situ gelling systems: thiol-disulfide exchange method toward tailor-made biodegradable hydrogels

A 'living' controlled hydrogel formation method was first reported to create loose and compact in situ biodegradable hydrogels. The method executed under mild reaction conditions can conveniently tailor the hydrogel properties, and it has the potential to develop into a powerful tool for the design, synthesis, and self-assembly of novel tailor-made biomaterials and drug delivery systems.     

Synthesis of Lewis a and Lewis X Pentasaccharides Based on N-Trichloroethoxycarbonyl Protection 1

Abstract

Thexyldimethylsilyl 4,6-O-benzylidene-2-deoxy-2-trichloroethoxycarbonylamino-β-D- glucopyranoside (4), having the 3-hydroxy group unprotected, is a versatile starting material for the synthesis of glucosamine containing oligosaccharides. Thus, reaction with galactosyl donor 5 or fucosyl donor 6 afforded the desired β(1-3)- and α(1-3)-linked disaccharides 7 and 8, respectively, in high yields. Reductive opening of the benzylidene moieties in 7 and 8 gave access to the 4-hydroxy groups in 9 and 10. Ensuing fucosylation of 9 or galactosylation of 10 led to Lewis A (Le^a) and Lewis X (Le^x) trisaccharide building blocks 13 and 14, respectively. Their transformation into glycosyl donors 19 and 20 and subsequent reaction with 3b-O-unprotected lactose derivative 23 as acceptor furnished the Le^a? and Le^x pentasaccharide precursors 24 and 25. Exchange of the N-trichloroethoxycarbonyl group for an N-acetyl group and removal of the O-benzyl and O-acetyl protective groups afforded the desired Le^a? and Le^x? pentasaccharides 1 and 2.

     

Search for magnetic fields due to anyons in high-T c superconductors

We have searched for anomalous internal magnetic fields in highT _c materials which are predicted to occur in anyon and flux phase models of superconductivity. The magnitude, anisotropy and temperature dependence of the observed fields inc-axis oriented samples of sintered YBa₂CuO₃O₇ and of thick-film Bi₂Sr₂CaCu₂O₈ are consistent with a conventional nuclear dipolar origin. An upper limit of ≲0.08 mT is set for any anomalous magnetic fields along thec-axis atμ ⁺ sites in bulk CuO₂ superconductors.     

Growth of Ge nanofilms using electrochemical atomic layer deposition, with a "bait and switch" surface-limited reaction

Ge nanofilms were deposited from aqueous solutions using the electrochemical analog of atomic layer deposition (ALD). Direct electrodeposition of Ge from an aqueous solution is self-limited to a few monolayers, depending on the pH. This report describes an E-ALD process for the growth of Ge films from aqueous solutions. The E-ALD cycle involved inducing a Ge atomic layer to deposit on a Te atomic layer formed on Ge, via underpotential deposition (UPD). The Te atomic layer was then reductively stripped from the deposit, leaving the Ge and completing the cycle. The Te atomic layer was bait for Ge deposition, after which the Te was switched out, reduced to a soluble telluride, leaving the Ge (one "bait and switch" cycle). Deposit thickness was a linear function of the number of cycles. Raman spectra indicated formation of an amorphous Ge film, consistent with the absence of a XRD pattern. Films were more stable and homogeneous when formed on Cu substrates, than on Au, due to a larger hydrogen overpotential, and the corresponding lower tendency to form bubbles.     

Novel carbohydrate-based bifunctional organocatalysts for nucleophilic addition to nitroolefins and imines

Glucosamine has been selected as a cheap and readily available chiral scaffold for the synthesis of a series of novel enantiomerically pure bifunctional organocatalysts bearing a tertiary amino group in proximity to a (thio)urea group. The catalytic behaviour of these compounds, both as neutral and N-protonated species, was investigated using the addition of acetylacetone to β-nitrostyrene as a model reaction. Under optimized experimental conditions, chemical yields up to 93% and enantioselectivities up to 89% were obtained. Semiempirical (AM1) computational studies allowed to find a theoretical rationale for the chemical and stereochemical behaviour of the catalyst of choice. These catalysts were also preliminarily investigated as promoters in the addition of diethyl malonate to the N-Boc imine of benzaldehyde, affording the product in up to 81% ee.