Minimal quadratic residue cyclic codes of length 2 n

LetF be a finite field of prime power orderq(odd) and the multiplicative order ofq modulo 2 ⁿ (n>1) be ?(2 ⁿ )/2. Ifn>3, thenq is odd number(prime or prime power) of the form 8m±3. Ifq=8m?3, then the ring $$R_{2^n } = F\left[ x \right]/< x^{2^n } - 1 > $$ has 2n primitive idempotents. The explicit expressions for these primitive idempotents are obtained and the minimal QR cyclic codes of length 2 ⁿ generated by these idempotents are completely described. Ifq=8m+3 then the expressions for the 2n?1 primitive idempotents ofR ₂ ⁿ are obtained. The generating polynomials and the upper bounds of the minimum distance of minimal QR cyclic codes generated by these 2n?1 idempotents are also obtained. The casen=2, 3 is dealt separately.     

Pump-induced nonlinear refractive-index change in erbium- and ytterbium-doped fibers: theory and experiment

A 980-nm pump-induced nonlinear refractive-index (n2) change in erbium-doped (20-m) and ytterbium-doped (20-m) fibers has been measured at 1064 nm by time-delayed photorefractive beam coupling in a co-propagating and counterpropagating geometry. It was found that n2 decreases at the wavelength of the probe beam when the pump beam is present. We present a semiclassical theory based on a four-state system that accounts for the pump-induced change of n2. Both theoretical and experimental results show that a significant index change, of the order of 10%, can be obtained for cw pump powers as small as 10 mW.     

Biochemical characterization of metastatic lymph nodes of breast cancer patients by in vitro 1H magnetic resonance spectroscopy: a pilot study

Using one-dimensional (1D) and two-dimensional (2D) proton nuclear magnetic resonance (NMR) methods, the perchloric acid extract of involved (n = 11) and noninvolved (n = 12) axillary lymph nodes (ALN) of breast cancer patients was investigated. Resonances from 40 metabolites such as lactate (Lac), glucose, several amino acids (alanine, lysine, glutamic acid, glutamine, etc.), nucleotides (adenosine triphosphate, guanosine triphosphate, uridine triphosphate, uridine monophosphate, etc.), membrane metabolites [glycerophosphocholine (GPC), phosphocoline (PC), phosphoethanolamine (PE), choline] were unambiguously assigned in both the involved and noninvolved ALN. The concentration of PC/GPC (p = 0.002) was significantly higher in the involved compared to noninvolved nodes. In addition, the concentration of glycolytic product Lac (p = 0.0001) was also found to be significantly higher in involved nodes. Increased concentration of membrane metabolites PC/GPC may be attributed to increased membrane synthesis in malignant cells and, therefore, suggests the presence of metastatic cells in lymph nodes. The higher concentration of Lac is indicative of the presence of malignant cells that derive energy via anaerobic glycolytic pathway. Present results demonstrate the potentials of in vitro proton NMR in detecting malignant cells in ALN and such studies may have an important bearing in determining the prognosis of breast cancer patients.     

Structural defects cause TiO2-based photocatalysts to be active in visible light

Oxidation of TiO or Ti2O3 led to the formation of TiO2 with activity in visible light much higher than when TiN was used as a precursor, pointing out the importance of oxygen defects/vacancies for extension of activity of TiO2 into the visible region.     

New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers

The nonlinear refractive index n2 of silica fiber (24 m) and erbium-doped fiber (10 m) is measured to within an accuracy of 5% by use of time-delayed photorefractive beam coupling of intense 53-ps, 1.064-microm pulses that experience self-phase modulation in the fibers. The resultant induced grating autocorrelation response yields a value of n2/A(eff) and a calibration standard for the fiber. A phase shift of the order of 0.19pi can be detected and is limited only by laser amplitude fluctuations. A unique advantage of this technique is its ability to measure n2 accurately in short lengths (z < or = 25 m) of fiber, whereas other approaches typically use much longer lengths of fiber (z > or = 100 m).     

Skeletal muscle metabolism in Duchenne muscular dystrophy (DMD): an in-vitro proton NMR spectroscopy study

The metabolic differences in the skeletal muscle of patients with Duchenne muscular dystrophy (DMD) and normal subjects (controls) were investigated using in-vitro high-resolution proton NMR spectroscopy. In all, 56 metabolites were unambiguously identified in the perchloric acid extract of muscle tissue using one- and two-dimensional NMR. The concentrations of glycolytic substrate glucose (Glc; p < 0.05), gluconeogenic amino acids such as glutamine (Gln; p < 0.05) and alanine (Ala; p < 0.05) and the glycolytic product lactate (Lac; p < 0.05) were statistically significantly lower in DMD patients as compared to controls. A significant reduction in the concentrations of total creatine (TCr; p < 0.05), glycerophosphoryl choline + phosphoryl choline + carnitine (GPC/PC/Car; p < 0.05), choline (Cho; p < 0.05) and acetate (Ace; p < 0.05) was also observed in these patients. Decrease in the level of glucose may be attributed to the reduction in the concentrations of gluconeogenic substrates or membrane abnormalities in degenerated muscle of DMD patients. Lower levels of choline containing compounds indicate membrane abnormalities. Decrease in the concentration of lactate in the muscle of DMD patients may be due to the reduction in anaerobic glycolytic activity or lower substrate concentration. The decrease in the concentration of acetate may reflect reduced transport of fatty acids into mitochondria due to decreased concentration of carnitine in DMD patients. Kreb's cycle intermediate alpha-ketoglutarate was observed only in the diseased muscle, which is suggestive of predominant oxidative metabolism for energy generation.     

Carbon dioxide induced separation of ionic liquids and water

Both hydrophobic and hydrophilic room-temperature ionic liquids can be separated from aqueous solutions with relatively low-pressure gaseous carbon dioxide.     

Characterisation of plasticized PMMA based solid polymer electrolytes

Polymer electrolyte films prepared from poly (methyl methacrylate) and LiAsF₆ with different concentrations of plasticizer (DBP) are described. The formation of polymer-salt complexes has been confirmed by XRD and FTIR spectral studies. The temperature dependence of the conductivity of the polymer films obeys the VTF relation. Values of conductivities of the polymer complexes are presented and discussed.     

Cyclodehydration of 1,4-butanediol catalyzed by metal(IV) phosphates

Metal(IV) phosphates of tin, zirconium and titanium in different morphological forms, viz. amorphous, calcined and crystalline, have been used as catalysts for selective cyclodehydration of 1,4-butanediol to tetrahydrofuran. A comparative study of the three catalysts for the above reaction has been carried out to understand the effect of their composition and morphology on the catalytic activity.