Codes over \mathbb{F}_3 + u\mathbb{F}_3 and Improvements to the Bounds on Ternary Linear Codes

New ternary linear codeswith parameters [208, 8, 127], [150, 10, 85],[160, 10, 91], [170, 10, 97], [180,10, 103], and [190, 10, 110], are found whichimprove the known lower bound on the maximum possible minimumHamming distance. These codes are constructed from codes over via a Gray map.     

Mixed-Metal Cluster Chemistry. 27. Coupling of Diphenylbuta-1,3-diyne and CO at Tungsten–Triiridium Cluster Cores

Reactions of WIr₃(CO)₁₁(-C₅H₄R) (R=H, Me) and excess diphenylbuta-1,3-diyne in refluxing toluene afford a large number of products in each case, one of which has been identified as [WIr₃{ ₄- ⁷-C(Ph)C(C CPh)C(Ph)CC(H)CC₆H₄ C(O)-2}(CO)₇(-C₅H₄R)] [R=H (10 %) (1), Me (6 %)] by a single-crystal X-ray diffraction study of 1. The structure of 1 reveals a unique ten-electron-donating ligand which has formed from combination of two diphenylbuta-1,3-diyne units and one carbonyl group, addition of the latter having presumably proceeded by orthometallation of one phenyl group, followed by formal insertion of the carbonyl into the Ir-phenyl linkage. Crystal data for 1.CH₂Cl₂: space group P2₁/n, a = 8.6081(1)Å, b = 39.3638(5)Å, c = 12.3935(2)Å, = 100.4889(5)°, V = 4129.33(10)ų, Z = 4, R = 0.030, R _w = 0.026 for 4982 reflections [I > 2.00(I)]     

Aleksandrov reflection and nonlinear evolution equations,I: The n-sphere and n-ball

We consider the (degenerate) parabolic equationu _t =G(u + ug, t) on then-sphereS ⁿ . This corresponds to the evolution of a hypersurface in Euclidean space by a general function of the principal curvatures, whereu is the support function. Using a version of the Aleksandrov reflection method, we prove the uniform gradient estimate ¦u(·,t)¦ <C, whereC depends on the initial conditionu(·, 0) but not ont, nor on the nonlinear functionG. We also prove analogous results for the equationu _t =G(u +cu, ¦x¦,t) on then-ballB ⁿ , wherec ₂(B ⁿ ).     

Cubic nonlinear optical properties of platinum-terminated polyynediyl chains

The wavelength dependence of the cubic nonlinearity of ligated platinum-terminated polyynes trans, trans-{(p-MeC6H4)3P}2(p-MeC6H4)Pt(C[triple bond]C)n Pt(p-C6H4Me){P(p-C6H4Me)3}2 (n = 3-6, 8, 10, 12) has been examined by femtosecond Z-scan studies in the wavelength range 520-1500 nm and the results rationalized by density functional theory calculations on the model complexes trans, trans-(H3P)2(C6H5)Pt(C[triple bond]C)n Pt(C6H5)(PH3)2 (n = 2-8, 10, 12). Although the final states for one- and two-photon transitions are not the same in these centrosymmetric molecules, the Z-scan studies reveal coincidences in one-photon absorption with features in the frequency dependencies of both real and imaginary parts of the cubic hyperpolarizability, as well as inflections in the frequency dependencies of the real part of gamma that correspond to resonances in the imaginary part of gamma. The theoretical studies suggest that the linear absorption spectra are dominated by X(1)A g --> n(1)B(3u) transitions, with the first state of B(3u) symmetry playing a steadily diminishing role upon oligoyne chain lengthening. The theoretical studies also predict a red-shift of two-photon absorption (TPA) profile with increasing conjugation length, and a significant enhancement on proceeding from the shortest to the longest chromophore, trends that are observed experimentally. The experimental low-energy TPA maxima for these complexes can be approximated by a simple Gaussian profile. The sp-carbon chain-length dependence of linear and nonlinear absorption maxima enable an estimate (neglecting saturation) of 660 and 1000 nm for the infinite carbon chain, carbyne.     

Secure OFDM with Peak-to-Average Power Ratio Reduction Using the Spectral Phase of Chaotic Signals

In this paper, a new physical layer security technique is proposed for Orthogonal Frequency Division Multiplexing (OFDM) communication systems. The security is achieved by modifying the OFDM symbols using the phase information of chaos in the frequency spectrum. In addition, this scheme reduces the Peak to Average Power Ratio (PAPR), which is one of the major drawbacks of OFDM. The Selected Mapping (SLM) technique for PAPR reduction is employed to exploit the random characteristics of chaotic sequences. The reduction with this algorithm is shown to be similar to that of other SLM schemes, but it has lower computational complexity and side information does not have to be sent to the receiver. The security of this technique stems from the noise like behavior of chaotic sequences and their dependence on the initial conditions of the chaotic generator (which are used as the key). Even a slight difference in the initial conditions will result in a different phase sequence, which prevents an eavesdropper from recovering the transmitted OFDM symbols.     

Turbulence quantification and sediment resuspension in an oscillating grid chamber

An oscillating grid chamber has been developed to study sediment suspension, desorption of compounds from the resuspended sediment, and air–water mass transfer. The chamber is designed to allow researchers to study desorption of contaminants from cohesive sediments and the flux of those contaminants to the vapor phase. The chamber uses a single vertically oscillating grid driven by a DC motor and closed-loop controller. Sediment to be studied is placed in the bottom of the chamber and entrained into the water column by the turbulence generated by the oscillating grid. A two-component laser Doppler velocimeter (LDV) was used to measure the turbulent velocity field inside the chamber. Detailed mapping of the turbulent kinetic energy (TKE) produced by this grid arrangement was compared with established grid-stirred systems. At distances closer to the grid than two grid bar spacings, large lateral gradients exist in the TKE. The suspension of cohesive sediments was also studied using this chamber. Steady-state suspended sediment concentrations were achieved within 30 min for a variety of turbulence levels. By adjusting the grid operating parameters, the TKE can be set to simulate the turbulence found either at the bed or free surface in open-channel flow systems. With some care, the oscillating grid chamber can be used as a simple laboratory analogue to study various environmental processes within the flow or at either the sediment–water or air–water interface.     

Near-Extremal Formally Self-Dual Even Codes of Lengths 24 and 32

The weight enumerator of a formally self-dual even code is obtained by the Gleason theorem. Recently, Kim and Pless gave some restrictions on the possible weight enumerators of near-extremal formally self-dual even codes of length divisible by eight. In this paper, the weight enumerators for which there is a near-extremal formally self-dual even code are completely determined for lengths 24 and 32, by constructing new near-extremal formally self-dual codes. We also give a classification of near- extremal double circulant codes of lengths 24 and 32. Communicated by: P. Fitzpatrick     

On circulant self-dual codes over small fields

We construct self-dual codes over small fields with q = 3, 4, 5, 7, 8, 9 of moderate length with long cycles in the automorphism group. With few exceptions, the codes achieve or improve the known lower bounds on the minimum distance of self-dual codes.      

On the permutation groups of cyclic codes

We classify the permutation groups of cyclic codes over a finite field. As a special case, we find the permutation groups of non-primitive BCH codes of prime length. In addition, the Sylow p-subgroup of the permutation group is given for many cyclic codes of length p ^m . Several examples are given to illustrate the results.