Linkage and Codes on Complete Intersections

This note is meant to be an introduction to cohomological methods and their use in the theory of error-correcting codes. In particular we consider evaluation codes on a complete intersection. The dimension of the code is determined by the Koszul complex for X² and a lower bound for the minimal distance is obtained through linkage. By way of example our result fits the well-known formula for the minimal distance of the Generalized Reed-Muller code. Keywords:Liason, Linkage, Complete intersections, Error-correcting codes, Generalized Reed-Muller codesPart of this work was done while visiting Institut de Mathématique de Luminy, 163 avenue de Luminy, Case 907, 13288 Marseille CEDEX 9, France     

The Dual Code of some Reed-Muller type Codes

The dual code of some Reed-Muller type codes arising from the Veronese variety and Complete Intersections is determined. An example is given to illustrate the main result. Keywords:Reed-Muller type codes, Dual codes, Veronese variety, Complete intersection.     

Relationship between deposition and recrystallization textures of copper and chromium electrodeposits

The 100, 111 and 110 textures of copper electrodeposits obtained from copper sulfate baths changed to the 100, 100 and textures, respectively, after recrystallization. The textures of chromium electrodeposits obtained from the standard Sargent bath remained unchanged after recrystallization. The results are in agreement with the prediction of the strain energy release maximization model, in which the recrystallized grains orient themselves so that their minimum elastic modulus direction can be parallel to the absolute maximum internal stress direction due to dislocations in the non-recrystallized grains.     

Theoretical estimation of the effect of interfacial energy on the mechanical strength of spinodally decomposed alloys

New interfaces are produced on the slip plane when a crystal with continuous composition fluctuation arising from spinodal decomposition is deformed by slip. In this work, the energy of such interfaces is evaluated for both modulated and mottled structures, and their effects on slip behaviour are discussed. It is concluded that the contribution of this interfacial energy is large enough to account for the age-hardening concomitant with spinodal decomposition.     

On the mechanism of feathery crystallisation of aluminium

The growth of twinned crystals of aluminium on solidification is discussed with reference to the structure of the growing tip. It is shown that one must differentiate between two types of 112 growth directions in the twin boundary. Normally, all the tips grow in the same type of 112 growth direction and this particular type may give the tip a favourable shape, possibly by producing a sharp edge. If a tip is growing in a less favourable 112 direction, the favourable type can be established by the twins changing sides. This is observed to occur regularly in the continuous casting method according to Hunter. The re-entrant edge mechanism is not supported by the present results.     

The Interplay of Electronic and Nuclear Magnetism in PtFe x at Milli-, Micro-, and Nanokelvin Temperatures

We have measured ac susceptibility, nuclear magnetic resonance, and nuclear heat capacity of two PtFe _x samples with concentrations of magnetic impurities x = 11 ppm and 41 ppm at magnetic fields (0 ± 0.05) mTB248 mT. The susceptibility data have been measured at temperatures of 0.3 KT100 mK, no hint for nuclear magnetic ordering could be detected to a temperature of 0.3 K. The nuclear heat capacity data taken at 1.4 KT10 mK show enhanced values which scale with x at low polarization. This effect is described by a model assuming an internal magnetic field caused by the impurities. No indication for nuclear magnetic ordering could be detected to 1.4 K. The nuclear magnetic resonance experiments have been performed on these samples at 0.8 KT0.5 mK and 2.5 mTB22.8 mT as well as on three other samples with x = 5, 10, 31 ppm in a different setup at 40 KT0.5 mK and at 5.4 mTB200 mT. Spin-lattice and effective spin-spin relaxation times ₁and ₂ ^* of ¹⁹⁵ Pt strongly depend on x and on the external magnetic field. No temperature dependence of ₁and ₂ ^* could be detected and the NMR data, too, give no hint for nuclear magnetic ordering to 0.8 K.     

Flow of a heated ferrofluid over a stretching sheet in the presence of a magnetic dipole

Summary The flow of a viscous ferrofluid over a stretching sheet in the presence of a magnetic dipole is considered. The fluid momentum and thermal energy equations are fomulated as a five-parameter problem, and the influence of the magneto-thermomechanical coupling is explored numerically. It is concluded that the primary effect of the magnetic field is to decelerate the fluid motion as compared to the hydrodynamic case, thereby increasing the skin friction and reducing the heat transfer rate at the sheet.Nomenclature a distance - c constant - c _p specific heat at constant pressure - C _f wall friction coefficient - e 2.71828 ... - f dimensionless stream function - H magnetic field - k thermal conductivity - K constant - M magnetization - Nu _x local Nusselt number - p pressure - P dimensionless pressure - Pr Prandtl number, c _p/k - Re _x local Reynolds number, cx ²/ - T temperature - u velocity component along the sheet - v velocity component normal to the sheet - x coordinate along the sheet - y coordinate normal to the sheet - dimensionless distance - ferrohydrodynamic interaction parameter - constant - dimensionless Curie temperature - dimensionless coordinate - dimensionless temperature - viscous dissipation parameter - dynamic viscosity - ₀ permeability - dimensionless coordinate - density - shear stress - magnetic potential - stream function     

Effect of crystalline phase, orientation and temperature on the dielectric properties of poly (vinylidene fluoride) (PVDF)

The effect of crystalline phase, uniaxial drawing and temperature on the real () and imaginary () parts of the relative complex permittivity of poly (vinylidene fluoride) (PVDF) was studied in the frequency range between 10² and 10⁶ Hz. Samples containing predominantly and phases, or a mixture of these, were obtained by crystallization from a DMF solution at different temperatures. phase samples were also obtained from melt crystallization and from commercial films supplied by Bemberg Folien. Different molecular orientations were obtained by uniaxial drawing of and phase samples. The results showed that the crystalline phase exerts strong influence on the values of and , indicating that the _a relaxation process, associated with the glass transition of PVDF, is not exclsively related to the amorphous region of the polymer. An interphase region, which maintains the conformational characteristics of the crystalline regions, should influence the process decisively. The molecular orientation increased the values of for both PVDF phases and modified its dependence with temperature over the whole frequency range studied. The influence of the crystallization and molecular orientation conditions on the dc electric conductivity (_dc) were also verified. The value of _dc was slightly higher for samples crystallized from solution at the lowest temperature and decreased with draw ratio.     

Flux motion in anisotropic type-II superconductors nearH c 2 with arbitrary vortex orientation

Flux motion in anisotropic type-II superconductors near H_{c 2} is studied in the framework of the time-dependent Ginzburg-Landau (TDGL) theory for the case that the average flux densityB is oriented in an arbitrary direction relative to the principal axes of the sample. The linearized TDGL equation for a uniformly translating order parameter is solved and expressions for all elements of the flux-flow resistivity tensor _ij (including the off-diagonal Hall elements) are obtained. The diagonal elements _ii show the angular scaling property that _ii(B) = _ii(B/H_{c 2}(, ø)), whereas the Hall elements _ij (i j) have additional angular dependences that are not contained in H_c2. For the case that the normal state Hall elements _ij ⁽ⁿ⁾ B _k with i j k, the ratios _ij/ _ij ⁽ⁿ⁾ are functions of B/H_c2 (, ) only.     

Influence of calcination and sintering temperatures on the structure of (Pb1 − xBax )ZrO3

(Pb1–xBax)ZrO3 powders are synthesized below 800 °C for x 0.25 using a semi-wet route involving solid-state thermochemical reaction in a mixture of ZrO2 and (Pb1–xBax)CO3. The (Pb1–xBax)CO3 precursors were obtained by a forced coprecipitation technique. These powders can be sintered to achieve nearly 99% of the theoretical density at 1050 °C, which is 200 to 300 °C lower than that employed for the solid state route. The structure of as-calcined powder is orthorhombic for x 0.10 and rhombohedral for 0.25 > x 0.35, whereas the two phases coexist for 0.15 x 0.25. The structure of sintered material is orthorhombic for 0 x 0.10, rhombohedral for 0.20 x 0.30, and cubic for x 0.35, whereas orthorhombic and rhombohedral phases coexist at x = 0.15. The difference in the structure of the as-calcined and sintered powders is discussed in terms of particle size effect and chemical homogenisation of Ba2+ in the PBZ matrix.     

Mössbauer studies of α″-Fe16N2 and α′-Fe8N films

Conversion-electron Mössbauer spectra of epitaxial -Fe₁₆N₂ and -Fe₈N films have been studied and their differences are discussed in detail. The Mössbauer spectrum of -Fe₁₆N₂ can be decomposed into three subspectra, which correspond to the 4d, 8h and 4c sites. The Mössbauer spectrum of -Fe₈N can be fitted using four spectra based on a nitrogen-atom-random-distribution model. The average hyperfine field is larger (3%) for -Fe₁₆N₂ than for -Fe₈N, which is approximately consistent with a 4.1% enhancement of the magnetic moments for -Fe₁₆N₂. The iron moments tend to locate in the film plane for -Fe₁₆N₂ and to arrange perpendicularly to the film plane for -Fe₈N.     

Investigation of Sonoluminescence Amplification under the Interaction of Ultrasonic Fields Widely Differing in Frequency

The laws of sonoluminescence generation under the interaction of ultrasonic fields widely differing in frequency have been investigated. It is shown that nonadditive amplification of the sonoluminescence is observed not only under the simultaneous action of the fields on a liquid, but also in a highfrequency field after preliminary insonification of the liquid by a lowfrequency field. The phenomenon of a longduration aftereffect of the lowfrequency field on the cavitation generated by the highfrequency field has been revealed. On the basis of the obtained results the conclusion has been drawn that the main mechanism of increasing the cavitation activity in the interacting fields is the generation of new cavitation nuclei as a result of the collapse of bubbles excited by the lowfrequency field.     

Nonlinear asymptotic theory of hypersonic flow past a circular cone

Summary The hypersonic small-disturbance theory is reexamined in this study. A systematic and rigorous approach is proposed to obtain the nonlinear asymptotic equation from the Taylor-Maccoll equation for hypersonic flow past a circular cone. Using this approach, consideration is made of a general asymptotic expansion of the unified supersonic-hypersonic similarity parameter together with the stretched coordinate. Moreover, the successive approximate solutions of the nonlinear hypersonic smalldisturbance equation are solved by iteration. Both of these approximations provide a closed-form solution, which is suitable for the analysis of various related flow problems. Besides the velocity components, the shock location and other thermodynamic properties are presented. Comparisons are also made of the zeroth-order with first-order approximations for shock location and pressure coefficient on the cone surface, respectively. The latter (including the nonlinear effects) demonstrates better correlation with exact solution than the zeroth-order approximation. This approach offers further insight into the fundamental features of hypersonic small-disturbance theory.Notation a speed of sound - H unified supersonic-hypersonic similarity parameter, - K hypersonic similarity parameter, M - M freestream Mach number - P pressure - T temperature - S entropy - u, v radial, polar velocities - V freestream velocity - shock angle - cone angle - density - density ratio, /() - ratio of specific heats - polar angle - stretched polar angle, / - (), (), () gage functions     

Energy loss distribution of charged particles in thin absorbers

Conclusions 1. For thin absorbers, the Landau theory incorporating certain above-listed corrections is a general-purpose one and is in good agreement with experiment both for heavy and light charged particles 0.01. 2. For intermediate layers (0.01 1 and 1), exact solutions are provided by the Vavilov theory [11]. 3. The numerical-analytic method of plotting the energy loss distribution function proposed in [13] is suitable for very thin ( 0.01) absorbers.Translated from Izmeritel'naya Tekhnika, No. 3, pp. 60–62, March, 1970.     

On the proximity effect in a superconductive slab bordered by metal

The first Ginzburg-Landau equation for the order parameter in the absence of magnetic fields is solved analytically for a superconducting slab of thickness 2d bordered by semi-infinite regions of normal metal at each face. The real-valued normalized wave function f=/ depends only on the transversal spatial coordinate x, normalized with respect to the coherence length of the superconductor, provided the de Gennes boundary condition df/dx=f/b is used. The closed-form solution expresses x as an elliptic integral of f, depending on the normalized parameters d and b. It is predicted theoretically that, for b< and dd_c=arctan(1/b), the proximity effect is so strong that the superconductivity is completely suppressed. In fact, in this case, the first Ginzburg-Landau equation possesses only the trivial solution f0.     

Dielectric properties of LiF single crystals

The dielectric constant,, loss, tan, and a.C. Conductivity, , of high quality single crystals of LiF have been measured in the frequency range 10² to 10⁵ Hz and in the temperature range 30 to 400° C. of LiF at 30° C is 8.3 and is frequency independent; tan was below detection level (tan<0.0001). increases slowly with temperature up to about 150° C (frequency independent region) beyond which it rises rapidly, being frequency dependent with larger values at lower frequencies. A similar behaviour is exhibited by tan . The activation energy for conduction in the high temperature region is calculated to be 0.93 eV from log against 1/T graphs. Log () against 1/T plots (where is the difference between the dielectric constant at any temperature and the value at room temperature, 30° C) yields an activation energy value of 1.0 eV in the high temperature region. This activation energy is found to be independent of frequency. This agreement between the two activation energy values, one for the a.c. conductivity and the other for the increase with temperature. This suggests that the same charge carriers are responsible for the two processes in the high temperature region.     

Microstructures of titanium-aluminides produced by laser surface alloying

The microstructures of Ti-Al layers (from 43–80 at %Al) produced by laser surface alloying of titanium substrate with a powder feed technique have been investigated. The laser processing parameters were; 1.8 kW laser power, 3 mm beam diameter, 7 mm s^–1 traverse speed, and values of powder flow rates of aluminium ranging from 0.07–0.11 g s^–1. The microstructures were dendrites of ₂ and interdendritic regions of ₂+ in the Ti-43 at %Al alloy; dendrites of either ₂ or ₂+ with interdendritic in the Ti-50 at %Al alloy; dendrites of ₂+ with interdendritic in the Ti-55 at %Al alloy; single phase in the Ti-60 at %Al alloy and TiAl₃ dendrites and Al solid solution in the interdendritic regions in the Ti-80 at %Al alloy. The microstructures were fine and comparable to those produced by other methods of rapid solidification processing. The microstructures of the Ti-50 and Ti-55 at %Al alloys were in agreement with the existence of the peritectic reactions:L + andL + , in the Ti-Al system.     

High-frequency dielectric properties of Mg-Al-Si,Ca-Al-Si and Y-Al-Si oxynitride glasses

Recently developed coaxial line techniques [1] have been used to determine, at room temperature, the values of the real () and imaginary (') parts of the dielectric constants for some Mg-Al-Si, Ca-Al-Si and Y-Al-Si oxynitride glasses over the frequency range 500 MHz to 5 GHz. The frequency dependencies of and ' are consistent with the universal law of dielectric response in that (-_t8)^(n–1) and '^(n–1) for all glass compositions; the high experimental value of the exponent (n=1.0±0.1) suggests the limiting form of lattice loss [2] situation. In this frequency range, as previously reported [3] at longer wavelengths, the addition of nitrogen increases the dielectric constant, (); in both the oxide and oxynitride glasses is also influenced by the cation, being increased with cation type in the order magnesium, yttrium, calcium as at lower frequencies.     

X-ray diffraction characterisation of low temperature plasma nitrided austenitic stainless steels

The nitrided layers produced by low temperature (400–500 °C) plasma nitriding on austenitic stainless steels, AISI 316, 304 and 321, have been characterised by X-ray diffraction, in conjunction with metallographic and chemical composition profile analysis. The thin, hard and corrosion resistant layers exhibited similar X-ray diffraction patterns, but the positions of the major diffraction peaks varied with nitriding temperature and nitrogen concentration profile. The low temperature nitrided layers are predominantly composed of a phase with a face centred cubic (fcc) structure, which is named S phase. However, the positions of the diffraction peaks from the S phase deviated in a systematic way from those for an ideal fcc lattice. Detailed analysis of the deviation suggested that very high compressive residual stresses and stacking faults were formed in the layers, resulting in a highly distorted and disordered fcc structure. The lattice parameter of the distorted and disordered S phase was found to increase with increasing nitrogen concentration.     

Simulation of the Process of Water Freezing in a Round Pipe

The problem of freezing of pure water in a round pipe is treated with due regard for convection under asymmetric thermal boundary conditions in the absence of motion along the pipe. The problem is solved numerically using the control volume approach, SIMPLER algorithm, and the enthalpy method. Results are obtained for three Grashof (Gr) and six Biot (Bi) numbers: Gr = 1.55 × 10⁶, Bi = 0.305 (0 < ), Bi = 0.044 ( < 2); Gr = 1.24 × 10⁷, Bi = 0.610 (0 < ), Bi = 0.087 ( < 2); Gr = 9.89 × 10⁷, Bi = 1.220 (0 < ), Bi = 0.174 ( < 2). The correctness of calculation of the problem disregarding free-convection flows is analyzed.