Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs

A novel technique, based on the pseudo-random properties of certain graphs known as expanders, is used to obtain novel simple explicit constructions of asymptotically good codes. In one of the constructions, the expanders are used to enhance Justesen codes by replicating, shuffling, and then regrouping the code coordinates. For any fixed (small) rate, and for a sufficiently large alphabet, the codes thus obtained lie above the Zyablov bound. Using these codes as outer codes in a concatenated scheme, a second asymptotic good construction is obtained which applies to small alphabets (say, GF(2)) as well. Although these concatenated codes lie below the Zyablov bound, they are still superior to previously known explicit constructions in the zero-rate neighborhood

Analytical two-center integrals over Slater geminal functions

We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing a inhomogeneous fourth-order ordinary differential equation that is obeyed by the master integral, the simplest integral with inverse powers of all interparticle distances. To solve this equation it was necessary to introduce a new family of special functions which are defined through their series expansions around regular singular points of the differential equation. To increase the power of the interparticle distances under the sign of the integral we developed a family of open-ended recursion relations. A handful of special cases of the integrals is also analysed with some remarks on simplifications that occur. Additionally, we present some numerical examples of the master integral that validate the usefulness and correctness of the key equations derived in this paper. In particular, we compare our results with the calculations based on the series expansion of the exp(-\gamma r12) term in the master integral.Comment: 28 pages, 0 figures, 7 table

UV-B induced damage and recovery processes in apple leaves as assessed by LIF and PAM fluorescence techniques

The capability of laser-induced chlorophyll fluorescence (LIF) and pulse-amplitude-modulated (PAM) fluorescence technique as well as RED/NIR-light reflection measurements for detection and quantification of UV-B induced damages was evaluated in greenhouse experiments with apple seedlings (Malus domestica Borkh.). Photosynthetic recovery from short-term UV-B stress was assessed during 7 days after UV-B treatment with the PAM fluorometer. The exposure of apple leaves to UV-B doses in the range of 10-26 W m-2 for 180 minutes (UV-BBE dose = 5.4-14 kJ m-2) affected neither chlorophyll content nor leaf reflection. Although UV-B damage was not visually evident 2 hours after irradiation, it could be detected by PAM and LIF fluorescence techniques with equivalent success. The intensity of LIF, estimated as the integral of fluorescence spectrum, was reduced after UV-B irradiation by 19-30%. A stronger decrease in F686 compared to F740 fluorescence resulted in significantly lower F686/F740 values in all UV-B treatments.Apple leaves displayed a strong and significant reduction in maximum fluorescence (Fm) and a slightly increase in ground fluorescence (Fo) 2 hours after UV-B treatment, as documented by PAM fluorescence measurement. Negative linear regressions between investigated UV-B doses and selected PAM parameters were found with determination coefficients (R2) of 0.50 for Fv, 0.48 for Fv/Fm, and 0.58 for Fv/Fo. Among the PAM and LIF parameters tested, the Fv/Fo ratio appeared most sensitive for detection of UV-B induced damages displaying greatest changes and strongest correlation with the applied UV-B doses. PAM fluorescence images of apple leaves visualised an enhanced spatial heterogeneity of photosynthetic activity with increasing UV-B dose. The disturbance in photosynthetic functionality was followed by a continuous recovery process as indicated by restoring Fo and Fm parameters. A decline in maximum photochemical efficiency Fv/Fm from 0.80 to 0.72 and 0.43 after exposure to 20 W m-2 for 240 and 360 minutes (UV-BBE = 14.4 and 21.6 kJ m-2), respectively, was followed by recovery at 7 x 10-4 and 5 x 10-3 units per hour during the first 48 hours after UV-B treatment. The recovery curves of Fm, Fv, Fv/Fm and Fv/Fo parameters during a week after UV-B irradiation were well fitted with exponential rise to maximum function, such as: y = yo + a (1 - e-bx). However, within 7 days after exposure to UV-B light, apple leaves displayed 14% or 4% lower Fm, and 5% or 1% lower Fv/Fm values compared with control plants, indicating only a partial recovery from photoinhibition and irreversible damages in PSII

Improvement of Mg uptake of grapevine by use of rapeseed oil ethoxylates for foliar application of Mg

To improve the uptake of foliar-applied Mg a new group of toxicological and ecotoxicological harmless surfactants (rapeseed oil ethoxylates) with an average of 5 (Agnique RSO 5®), 10 (Agnique RSO 10®), 30 (Agnique RSO 30®) and 60 (Agnique RSO 60®) units of ethylene oxide (EO) was evaluated as adjuvants for a MgSO4 and Mg(NO3) formulation. The impact of the surfactants on Mg penetration was studied using astomatous cuticular membranes isolated from mature tomato fruit. The biological efficacy of a formulation, containing castor oil, ionic and non-ionic surfactants with and without addition of RSO 5 was investigated in two vineyards at the Moselle valley, cvs Riesling and Regent. Especially RSO 5-surfactant increased Mg penetration through isolated cuticles. Under field conditions, Mg application enhanced significantly the Mg content in leaves. The Mg level in bunch stems merely increased when formulated 'Bittersalz' was applied. 'Magnisal' and formulated 'Magnisal' reduced markedly Mg deficiency symptoms in leaves and increased Mg content in leaves of cv. Regent.

Error probability and error stream properties in channel with slow Rician fading, Journal of Telecommunications and Information Technology, 2003, nr 4

In a radio communication channel wave parameters fluctuate randomly. The signal envelope undergoes deep fades. When binary information is transmitted through such a channel, fading causes random variation of probabilities of error associated with the detection of individual elementary signals, which produces a clustering of errors. The paper presents an analytical description of the probability of bit error in the channel with very slow Rician fading and Gaussian noise for noncoherent and coherent detection. Digital systems employing error detection or error correction coding are generally based on the transmission of blocks of N sequential bits. Expressions are given for the probability of n errors occurring in N bits (weighted spectrum of errors) and the probability of more than n errors in a block of N bits (block error probability) for noncoherent frequency shift keying (NCFSK). Also the calculations are presented graphically

Structure-dependent optical properties of Au/Ag irradiated TiN thin films

Titanium nitride (TiN) is an attractive alternative for modern and future photonic applications, as its optical properties can be engineered over a wide spectral range. In this study, we have used sequential implantation of gold and silver ions with varying ion fluence, as well as subsequent annealing, in order to modify the optical and plasmonic properties of TiN thin films and correlated this to their structural properties. Our investigations show that the columnar structure of the TiN films is partially destroyed upon implantation, but metallic Au and Ag nanoparticles are formed. The irradiation further induces a reduction of the lattice constant as well as changes the TiN stoichiometry and grain size. From the optical point of view, the implanted films possess less metallicity with increasing Ag fluence and losses several times lower than the as-deposited film, which can be correlated with the deficiency of nitrogen and additional defects. Subsequent annealing partially recovered the destroyed columnar structure, and the films become more metallic where the optical losses are much smaller in comparison to the as-implanted situation, being comparable to those of pure Au and Ag. In this way, by varying the implantation fluence of silver ions properly while keeping the gold fluence constant, we were able to optimize experimental parameters in such a way to ensure the formation of TiN with desirable optical performances

Inequivalent representations of commutator or anticommutator rings of field operators and their applications

Hamiltonian of a system in quantum field theory can give rise to infinitely many partition functions which correspond to infinitely many inequivalent representations of the canonical commutator or anticommutator rings of field operators. This implies that the system can theoretically exist in infinitely many Gibbs states. The system resides in the Gibbs state which corresponds to its minimal Helmholtz free energy at a given range of the thermodynamic variables. Individual inequivalent representations are associated with different thermodynamic phases of the system. The BCS Hamiltonian of superconductivity is chosen to be an explicit example for the demonstration of the important role of inequivalent representations in practical applications. Its analysis from the inequivalent representations' point of view has led to a recognition of a novel type of the superconducting phase transition.Comment: 25 pages, 6 figure

Ground-state properties of rutile: electron-correlation effects

Electron-correlation effects on cohesive energy, lattice constant and bulk compressibility of rutile are calculated using an ab-initio scheme. A competition between the two groups of partially covalent Ti-O bonds is the reason that the correlation energy does not change linearly with deviations from the equilibrium geometry, but is dominated by quadratic terms instead. As a consequence, the Hartree-Fock lattice constants are close to the experimental ones, while the compressibility is strongly renormalized by electronic correlations.Comment: 1 figure to appear in Phys. Rev.