On Intrinsic Bounds in the Nullstellensatz

 Let k be a field and  f ₁, . . . ,  f _s be non constant polynomials in k[X ₁, . . . , X _n ] which generate the trivial ideal. In this paper we define an invariant associated to the sequence  f ₁, . . . ,  f _s : the geometric degree of the system. With this notion we can show the following effective Nullstellensatz: if δ denotes the geometric degree of the trivial system  f ₁, . . . ,  f _s and d :=max _j  deg( f _j ), then there exist polynomials p ₁, . . . , p _s ∈k[X ₁, . . . , X _n ] such that 1=∑ _j  p _j  f _j and deg p _j   f _j ≦3n ²δd. Since the number δ is always bounded by (d+1) ^n-1 , one deduces a classical single exponential upper bound in terms of d and n, but in some cases our new bound improves the known ones. Received November 24, 1995, revised version January 19, 1996     

Truncated Gröbner Bases for Integer Programming

 The toric ideal I _A of a matrix A=(a ₁, . . . ,  a _n )∈ℤd ^× n is the kernel of the monoid algebra map π^ _A  : k[x ₁, . . . ,  x _n ]→k[t ^±1 ₁, . . . ,  t ^±1 _d ], defined as x _j ?t ^aj . It was shown in [4] that the reduced Gr?bner basis of I _A , with respect to the weight vector c, can be used to solve all integer programs minimize {cx : Ax=b, x∈ℕ ⁿ }, denoted IP _A,b,c,= , as b varies. In this paper we describe the construction of a truncated Gr?bner basis of I _A with respect to c, that solves IP _A,b,c,= for a fixed b. This is achieved by establishing the homogeneity of I _A with respect to a multivariate grading induced by A. Depending on b, the truncated Gr?bner basis may be considerably smaller than the entire Gr?bner basis of I _A with respect to c. For programs of the form maximize{cx : Ax≦b, x≦u, x∈ℕ  ⁿ } in which all data are non-negative, this algebraic method gives rise to a combinatorial algorithm presented in [17]. Received: April 10, 1995; revised version: February 6, 1996     

Synthesis of the Bi-2222 Compounds of Bi–Sr–Ln(Zr)–Cu–O (Ln = Sm,Eu, Gd,and Dy)

Bi-based superconducting compounds with the 2222 structure has been already synthesized in the Bi₂Sr₂- (Ln_1−x Ce _x )₂Cu₂O_10+y (Ln = Sm, Eu, and Gd) systems. One of the characteristics of these compounds is the existence of the fluorite-like (Ln_1−x Ce _x )₂O₂ block between two CuO₅ pyramids in the crystal structure. The tetravalent ions of Ce⁴⁺ are reported to be necessary to stabilize the 2222 structure. Recently, we have discovered that the Bi-2222 phase could be composed in the Bi₂Sr₂(Ln_2−x Zr _x )Cu₂O _z (Ln = Sm, Eu, Gd, and Dy) systems, where Zr⁴⁺ is used as a new tetravalent ion stabilizing the 2222 structure in stead of Ce⁴⁺. In the new system, nearly single 2222 phase samples have been obtained at the nominal composition of x=0.5 (Ln = Sm, Eu, and Gd) and in the range of 0.1≤x≤0.3 (Ln = Dy). Among them, the sample with Ln = Gd has the smallest resistivity at 273 K. But it is a semiconductor, and the conduction process at low temperatures is assumed to be followed by a two-dimensional VRH. The experimental results for the Gd samples with a partial substitution of Pb for Bi in the Bi₂Sr₂(Gd_2−x Zr _x )Cu₂O _z system are also reported.     

Cryptanalysis of ‘Less Short’ RSA Secret Exponents

 In some applications of RSA, it is desirable to have a short secret exponent d. Wiener [6], describes a technique to use continued fractions (CF) in a cryptanalytic attack on an RSA cryptosystem having a ‘short’ secret exponent. Let n=p ⋅ q be the modulus of the system. In the typical case that G=gcd(p−1, q−1) is small. Wiener’s method will give the secret exponent d when d does not exceed (approximately) n ^1/4. Here, we describe a general method to compute the CF-convergents of the continued fraction expansion of the same number as in Wiener (which has denominator d ⋅ G) up to the point where the denominator of the CF-convergent exceeds approximately n ^1/4. When d<n ^1/4 this technique determines d, p, and q as does Wiener’s method. For larger values of d there is still information available on the secret key. An estimate is made of the remaining workload to determine d, p and q. Roughly speaking this workload corresponds to an exhaustive search for about 2r+8 bit, where r=ln₂ d/n ^1/4. Received: September 30, 1996; revised version: March 7, 1997     

Acoustic Resonator Experiments at the Triple Point of Water: First Results for the Boltzmann Constant and Remaining Challenges

We report on two sets of isothermal acoustic measurements made with argon close to the triple point of water using a 50 mm radius, thin-walled, diamond-turned quasisphere. Our two isotherms yielded values for the Boltzmann constant, k _B, which differ by 0.9 parts in 10⁶, and have an average value of k _B = (1.380 649 6 ± 0.000 004 3) × 10⁻²³J · K⁻¹. The relative uncertainty is 3.1 parts in 10⁶, and the average value is 0.58 parts in 10⁶ below the 2006 CODATA value (Mohr et al. Rev Mod Phys 80:633, 2008), and so the values are consistent within their combined (k = 1) uncertainties.     

Bounds on the Weight Hierarchies of Extremal Non-chain Codes of Dimension 4

 The weight hierarchy of a linear [n, k; q] code C over GF(q) is the sequence (d ₁, d ₂, . . . , d _k ) where d _r is the smallest support of an r-dimensional subcode of C. An [n, k; q] code is external non-chain if for any r and s, where 1≦r<s≦k, there are no subspaces D and E, such that D⊂E, dim D=r, dim E=s, w _S (D)=d _r , and w _S (E)=d _s . Bounds on the weight hierarchies of such codes of dimension 4 are studied. Received: September 27, 1996     

Post irradiated microstructural characterization of Zr–1Nb alloy by X-ray diffraction technique and positron annihilation spectroscopy

Zr–1Nb samples were irradiated with 116 MeV O^5 + ions at different doses ranging from 5 × 10¹⁷ to 8 × 10¹⁸ O^5 +/m². X-ray diffraction line profile analysis was performed to characterize the microstructural parameters of these samples. Average domain size, microstrain and dislocation density were estimated as a function of dose. An anomaly was observed in the values of these parameters at a dose of 2 × 10¹⁸ O^5 +/m². Positron annihilation spectroscopy was used to determine the existence and nature of vacancy clusters in the samples. Isochronal annealing was carried out for a sample to study the evolution of defect clusters.     

Preparation of High-Purity Indium and Gallium via Electrotransfer in a Magnetic Field

High-purity (7N) indium and gallium are obtained via electrotransfer in melts placed in a static transverse magnetic field. The resistance ratios of the indium and gallium thus purified (25000 and 85000, respectively) are larger than in commercial grades of these metals. The magnetoresistance of liquid gallium is measured as a function of magnetic field. A multiband model for the Fermi surface of liquid gallium is proposed, which includes an electronic sphere of radius k _F ^e = 1.654 × 10⁸ cm^–1 and a spherical hole shell of thickness k = 0.5 × 10⁸ cm^–1 and radius k _F ^h = 1.114 × 10⁸ cm^–1. The model accounts for the observed magnetoresistive response of liquid gallium in a transverse magnetic field.     

Formation of nanoscale tungsten oxide structures and colouration characteristics

In this work, pH dependent evolution of tungsten oxide (WO₃) nanostructures is being reported along with physical characteristics. The synthesis was carried out via an inexpensive solvothermal cum chemical reduction route, with sodium tungstate (Na₂WO₄) and cetyl trimethyl ammonium bromide (C₁₉H₄₂NBr) as main reactants. The X-ray diffraction, together with transmission electron microscopic studies have revealed formation of regular polyhedral nanocrystalline structures and fractals as one goes from higher pH (= 5·5) to lower pH (= 2) values. The average crystallite size, as calculated through Williamson–Hall plots, was varied within 2·8–6·8 nm for different pH samples. Fourier transform infrared spectroscopy reveals in-plane bending vibration δ (W–OH), observable at ∼1630 cm^− 1 and strong stretching ν (W–O–W) located at ∼814 cm^− 1. Raman spectroscopy has divulged WO₃ Raman active optical phonon modes positioned at ∼717 and 805 cm^− 1. The thermochromic and photochromic properties of the nanoscale WO₃ sample prepared at pH = 5·5, are also highlighted.     

Oxidation Resistance and Magnetic Properties of SmCo7?x Si x Permanent Magnetic Alloys

The crystal structure, oxidation resistance, and magnetic properties of SmCo_7−x Si _x (x=0, 0.4, 0.6, and 0.9) permanent magnetic alloys were investigated systematically. It is found that the addition of silicon in the as-cast SmCo₇ ingot plays an important role in stabilizing TbCu₇ phase and improving inherent oxidation resistance. For the bulk nanocrystalline SmCo_7−x Si _x magnets, the oxidation resistance remarkably enhances but the corresponding Curie temperature T _c and maximum energy product (BH)_max exhibit a decreasing trend with the increase in Si content x. For the typical SmCo_6.4Si_0.6 nanocrystalline magnet, its final mass gain was about 1.71 mg/cm² after oxidation at 500 °C for 100 h, indicating the enhanced inherent oxidation resistance. Its T _c and (BH)_max were about 708 °C and 35.4 kJ/m³, respectively.     

Towards All Electrical Spin Injection and Detection in GaAs in a Lateral Geometry

Herein we discuss our approach to realizing all electrical spin injection and detection in GaAs. We propose a lateral geometry, with two ferromagnetic electrodes crossing an n-doped GaAs channel. AlO _x tunnel barriers are to be used in order to overcome the impedance mismatch and different widths of the two electrodes ensure different coercive fields. We present a detailed theoretical analysis of the expected magnetoresistance. Differences in behavior between lateral and vertical devices, the influence of the applied bias (electric field), and opportunities offered by different measurement geometries were explored. The MBE grown wafer consisted of 100 nm Al_0.3Ga_0.7As, acting as confinement layer, 100 nm n-doped (4 × l0¹⁷ cm⁻³) GaAs, 3 nm n⁺⁺ GaAs (10²¹ cm⁻³), to suppress Schottky barrier formation, and 1.5 nm Al. The Al was oxidized naturally in order to obtain tunnel barriers. By making use of in-situ shadow masks, a 0.1 mm wide channel is defined by covering the rest of the sample by insulating SiO₂, followed by deposition of Ta bonding pads. Finally, 500 and 1000 nm wide CoFe electrodes crossing the GaAs channel are obtained by e-beam lithography and sputtering. We show that the I–V characteristics of the CoFe/AlO _x /GaAs interface are consistent with tunneling as the main injection mechanism. However, the resistance-area (5 × 10⁹ Ω μm²) of our barriers is too high compared to the GaAs conductance (50 Ω square resistance) leading to a strong suppression of magnetoresistance. Further experiments are in progress toward optimizing barrier and channel impedance matching.     

Gravity Induced Absorption Changes in <Emphasis Type="Italic">Phycomyces blakesleanus</Emphasis> and Coleoptiles of <Emphasis Type="Italic">Zea mays</Emphasis> as Measured on the Drop Tower in Bremen (FRG)

Various spectroscopic experiments performed on the AIRBUS ZERO G in the years 2002 to 2007 clearly exhibited optical reflection changes as a result of gravitational changes (GIAC = Gravity Induced Absorption Change) in Phycomyces sporangiophores and corn coleoptiles. GIACs that occurred during flight parabolas in response to hyper- and microgravity were detected by a micro dual wavelength spectrometer (MDWS) for wavelengths pairs in the visible and the near infrared. We assume that GIACs indicate redox-changes of electron transport components such as flavins and cytochromes. Because microgravity on the AIRBUS 300 ZERO G only amounts to moderate values of ±4 ×10^− 2 g, i.e. far below sensitivity of the MDWS, we performed an experiment on the drop tower in Bremen (Germany) that generates microgravity as low as 4 ×10^− 5 g for 4.7 s. We detected small but significant GIACs during the microgravity phase, different in various specimen.     

Very Low Temperature Electronic Transport in Al-Pd-Re Quasicrystalline Alloys

Electrical resistivities of two icosahedral (I) Al-Pd-Re alloys have been measured between room temperature and mK temperatures. One quasicrystalline (QC) polygrain Al-Pd-Re sample exhibited insulating behavior in its resistivities, increasing by a factor of r=R(4 K)/R(300 K)=7.76; its room temperature resistivity was 9,890 μΩ cm. A “phenomenological” expression fitted the conductivity data well between 300 K to 0.5 K. Below 0.4 K a crossover to an activated variable-range hopping law was observed. Low temperature magnetoresistance ratio data and fits using the wave function shrinkage theory are presented. A second QC Al-Pd-Re sample had a small resistance temperature ratio r=2.12. The room temperature resistivity was extremely large, ρ(300 K)≈40,980 μΩ cm. Its conductivity could be described well using a simple temperature power law between 300 K to 20 K. Below 20 K there was a crossover to a new behavior. Below 1 K, the conductivity could be fitted using a very weakly insulating power law where σ(T)≈11.37T ^0.032 in (Ω cm)⁻¹, suggesting that this sample is located just below the metal-insulator transition. The magnetoconductivity data could not be fitted successfully using the 3D weak localization (WL) theory and inserting into it physical and realistic fitting magnitudes for the inelastic magnetic field B _in.      

Effect of an electric field applied during the solution heat treatment of the Al–Mg–Si alloy AA6022 on the subsequent natural aging kinetics

The influence of a dc electric field E = 5 kV/cm applied during the solution heat treatment (SHT) of the Al–Mg–Si alloy AA6022 at 475–552 °C on the subsequent natural aging kinetics was determined employing resistivity. It was found that the increase in the as-quenched resistivity which resulted from application of the field during SHT was retained throughout the natural aging process. An Avrami-type analysis of the natural aging kinetics gave n _avg. = 0.3 and k _avg. = 5 × 10⁻² (min⁻¹)^0.3. These values are in qualitative accord with those determined for the Al–Mg–Si–Cu alloy AA6111.     

Application of non-linear k–ω model to a turbulent flow inside a sharp U-bend

Simulation of the complex flow inside a sharp U-bend needs both refined turbulence models and higher order numerical discretization schemes. In the present study, a non-linear low-Reynolds number (low-Re) k–ω model including the cubic terms was employed to predict the turbulent flow through a square cross-sectioned U-bend with a sharp curvature, R _C/D = 0.65. In the turbulence model employed for the present study, the cubic terms are incorporated to represent the effect of extra strain-rates such as streamline curvature and three-dimensionality on both turbulence normal and shear stresses. In order to accurately predict such complex flowfields, a higher-order bounded interpolation scheme (Song et al., 1999) has been used to discretize all the transport equations. The calculated results by using both the non-linear k–ω model and the linear low-Reynolds number k–ɛ model (Launder and Sharma, 1974) have been compared with experimental data. It is shown that the present model produces satisfactory predictions of the flow development inside the sharp U-bend and well captures the characteristics of the turbulence anisotropy within the duct core region and wall sub-layer.     

Reduction of Np(V) with Fe(II) in weakly acidic solutions containing H<Subscript>2</Subscript>C<Subscript>2</Subscript>O<Subscript>4</Subscript>

The kinetics of the reaction of Np(V) with Fe(II) in dilute perchloric and nitric acid solutions containing H₂C₂O₄ was studied by spectrophotometry. In the range pH 1–2, the reaction rate is described by the equation d[Np(V)]/dt = k[Np(V)][Fe(II)][H₂C₂O₄]²[H⁺]^−1.6, k = 182 mol^−1.4 l^1.4 s⁻¹. The activation energy in the range 25–45°C is 26 kJ mol⁻¹. The reaction mechanism involves formation of Fe(II) and Np(V) oxalate complexes, followed by their reaction with the participation of the H⁺ ion.     

Computation of the relaxation and creep functions of elastomers from harmonic shear modulus

The purpose of this paper is to compute the relaxation and creep functions from the data of shear complex modulus, G ^∗(iν). The experimental data are available in the frequency window ν∈[ν_min,ν_max] in terms of the storage G′(ν) and loss G″(ν) moduli. The loss factor h( n) = \fracG"( n)G￠(n)\eta( \nu) = \frac{G'( \nu )}{G'(\nu )} is asymmetrical function. Therefore, a five-parameter fractional derivative model is used to predict the complex shear modulus, G ^∗(iν). The corresponding relaxation spectrum is evaluated numerically because the analytical solution does not exist. Thereby, the fractional model is approximated by a generalized Maxwell model and its rheological parameters (G _k ,τ _k ,N) are determined leading to the discrete relaxation spectrum G(t) valid in time interval corresponding to the frequency window of the input experimental data. Based on the deterministic approach, the creep compliance J(t) is computed on inversing the relaxation function G(t).     

A Steady-State Apparatus to Measure the Thermal Conductivity of Solids

This paper presents a steady-state apparatus to measure the thermal conductivity of solids based on the use of heat flux sensors. The uncertainty assessment of the experimental apparatus is performed in accordance with the ISO “Guide to the Expression of Uncertainty in Measurement” (GUM): the combined standard uncertainty (k = 1) with reference to the properties of Pyrex Glass CRM 039 at 20°C is ±1.9%. The standard uncertainty has also been assessed in the measurement range from 0.1 to 10W · m⁻¹ · K⁻¹. The experimental apparatus has been used to measure the certified reference material Pyrex Glass CRM 039 in the temperature range from 3.1 to 60.3°C: the standard deviation (k = 1) between the experimental measurements and the certified values is ±1.1% with a maximum deviation of 2.4%. Reasonable agreement is found between the uncertainty assessment and the experimental validation.     

Effect of cobalt substitution on magnetic and transport properties of Nd0·5Sr0·5Mn1?xCoxO3 (x = 0·1, 0·3 and 0·5)

The magnetic and transport properties of the compounds Nd_0·5Sr_0·5Mn_1-x_{{\rm 1}-{x}}Co_x_{{x}}O₃ (x = 0·1, 0·3 and 0·5), synthesized by citrate–gel route have been investigated. The spin transition in cobaltates at low temperatures affects the magnetic as well as transport properties. The irreversibility behaviour between the zero-field cooled (ZFC) and field cooled (FC) magnetization as a function of temperature becomes stronger with increasing Co content. This is understood on the basis of glassy behaviour, which becomes more robust with increasing Co substitution. The non-saturating M–H behaviour indicates strong magnetic inhomogeneities which may cause the magnetic phase separation at the nanoscopic length scale. The double exchange interaction is stronger between Mn^3 +–O^2 −–Mn^4 + as compared to Co^3 +–O^2 −–Co^4 + pairs. Co-substitution suppresses the double exchange which will lead to cluster/spin glass like behaviour as well as semiconducting features due to localization of charge carriers (mobile e_g{e}_{\rm g} electrons).     

Synthesis,growth, optical,mechanical and electrical properties of <Emphasis Type="Italic">L</Emphasis>-lysine <Emphasis Type="Italic">L</Emphasis>-lysinium dichloride nitrate (<Emphasis Type="Italic">L</Emphasis>-LLDN) single crystal

Semi-organic nonlinear optical material, L-lysine L-lysinium dichloride nitrate (2C₆H₁₅N₂O₂⁺_{2}^{+} · H⁺ · NO₃^-_{3}^{-} · 2Cl⁻) was synthesized at room temperature. Single crystals of L-LLDN were grown by slow cooling solution growth technique. The grown crystal was confirmed by powder X-ray diffraction analysis. The crystalline perfection of the grown single crystal was characterized by high-resolution X-ray diffraction (HRXRD) studies. The cut-off wavelength was determined by UV-vis transmission spectral analysis. The frequency doubling of the grown crystal was confirmed by powder second harmonic generation (SHG) measurement. The refractive index and birefringence of the crystal were determined using He–Ne laser source. Mechanical property of the crystal was determined by Vickers hardness tester. The frequency and temperature dependence of dielectric constant (ε _r), dielectric loss (tan δ) and a.c. conductivity (σ _ac) were also measured.