Oxidation of aldehydes by aqueous Ce (IV) in nitric acid

The kinetics of oxidation of acetaldehyde (at 20°, 31° and 40° C.), propionaldehyde (at 15°, 25° and 35° C.) and chloral hydrate (40°, 50° and 60° C.) by ceric nitrate in nitric acid medium [(H⁺) ≈ 0 · 5?1 · 5 M] were studied. The reactions were followed by determining rates of ceric disappearance for variations in [Ce⁴⁺], [RCHO], [H⁺], μ, temperature, etc. The stoichiometry, ΔCe⁴⁺ / Δ CH₃CHO ≈ 2 was established. The reactions were found to be 2nd Order—first order each with respect to [Ce⁴⁺] and [RCHO]. No complex formation between Ce⁴⁺ and aldehydes was observed. Neutral Ce (NO₃)₄ (H₂O)₂ and diol of the aldehyde were assumed the active species. The rate and thermodynamic data were calculated and discussed. The rates of oxidation were correlated with the structures of the aldehydes.     

Thermal expansion of ferroelectrics

Using the interference method the thermal expansion of lithium hydrazinium sulphate [Li(N₂H₅)SO₄] has been investigated in the temperature range ?170° C. to +220° C. The principal expansion coefficients along the crystallographic axes have been determined and at room temperature (25° C.) the values ofa _a,a _b anda _c are respectively 17·7, 13·5, and 43·0, ×10^?6 (°C.)^?1. The expansion coefficients are found to vary nonlinearly, and, in particular, along thec-axis the thermal expansion shows an anomalous behaviour between ?160°C. and ?60°C. and also in the neighbourhood of +130°C. These anomalies are explained as due to homomorphous transitions in which there is a reorientation of the ?NH ₊ ³ group about the N-N axis or a re-alignment of the ?NH₂ group.     

Variation of the piezo-electric constants of α-quartz with temperature

The method of finding the piezo-electric constants with the help of the variations of bond distances and bond angles on strain has been utilised in finding the variations of the piezo-electric constants ε₁₁ and ε₄₁ of α-quartz with temperature. It is found that the variations of ε₁₁ with temperature can be explained on the basis of the change of co-ordinates with temperature. At 558° C. the silicon atoms are found to occupy the same positions as they do in β-quartz. As the transition temperature is reached, the longitudinal coefficient ε₁₁ drops to zero, while the transverse coefficient ε₄₁ decreases by only 15%. The piezo-electric constant of β-quartz has been similarly determined and its value comes out to be 1·05×10⁴ for a non-ionic crystal (k=·724) and 1·45×10⁴ for an ionic crystal (k=1).     

Optical absorption of Co2+ doped NH4Cl: Phase transformation studies

The absorption spectrum of Co²⁺ doped NH₄Cl has been studied from the room temperature to the liquid nitrogen temperature. A sudden change in the spectrum is observed between 243° K and 233° K which is attributed to the phase transition in the crystal. From the observed spectrum it is suggested that Co²⁺ goes in interstitially as well as substitutionally. Both the types of centers exist at room temperature, but with decrease in temperature substitutional ions migrate to interstitial sites, the process being stimulated at the phase transformation point so that the 77° K spectrum seems to be mostly due to the interstitial centers. The 77° K spectrum is analyzed in the approximation of octahedral symmetry for interstitial ions and the band positions are fitted fairly well with B = 870 cm.^?1 Dq = 850 cm.^?1 and C = 4·4 B. A blue shift of about 100 cm.^?1 is observed for⁴T₁ (P) band at the phase transition which is attributed to the increase in Dq value with the anomalous lattice contraction at the phase transition. The decrease in the lattice parameter calculated from this blue shift is around 0·4% which is in good agreement with the results of X-ray measurements. Two possible models for the interstitial complex are examined and the one with fourfold chlorine coordination associated with two neutral water molecules at the first neighbour (NH₄)⁺ site lying along < 100> direction is suggested to be more probable.     

Raman and infrared spectra of ammonium selenate and lithium ammonium selenate

The Raman and infrared absorption spectra of (NH₄)₂ SeO₄, (ND₄)₂ SeO₄ and Li (NH₄) SeO₄ have been recorded at 300° K; while the spectra of the non-deuterated compounds have been recorded at 110° K also. (NH₄)₂ Se0₄ crystal exhibits 33 Raman lines, while LiNH₄SaO₄ shows 30 Raman lines at 300° K. Proper assignments have been given to the observed vibration frequencies. The SeO₄ ^?? ions and the (NH₄)⁺ ions are found to be highly distorted in these selenates. There is lowering of the N-H vibration frequencies due to hydrogen bonding. The present spectroscopic investigations do not reveal the existence of any phase transition in these selenates in the temperature region investigated.     

Anomalous double wave of cobalt (II) in aqueous thiocyanate medium

In neutral thiocyanate medium at low temperatures (0–5°C) cobaltous ion produced an anomalous double wave of nearly equal height. This behaviour was ascribed by earlier workers to a stepwise reduction of cobaltous ion in this medium. A study of the effects of temperature and height of the mercury column as well as the influence of the concentrations of cobalt and thiocyanate on the waves showed that the processes were controlled by chemical reaction and adsorption. It has been concluded that the first wave is a surface kinetic wave resulting from the reduction of [Co(H₂O)₄(SCN)₂] and the second step is a post-adsorption wave brought about by the adsorption of [Co(H₂O)₅SCN]⁺ species on the electrode.     

Oxidation studies

The results on the kinetics of oxidation of HCHO and some alcohols,viz.,n-propanol, allyl alcohol, cyclohexanol and benzyl alcohol by ceric nitrate in nitric acid medium in the temperature range of 10–35° C. are presented. The active form of Ce⁴⁺ during the oxidation of the above organic substrates was assumed to be the neutral Ce(NO₃)₄. The mechanism of oxidation and thermodynamic parameters for the above compounds are also given.     

Fundamental regular semigroups with inverse transversals

Let C be a regular semigroup with an inverse transversal C° and let C be generated by its idempotents. Following W. D. Munn and T. E. Hall’s idea, in this paper, a fundamental regular semigroup T _C,C° with an inverse transversal T _C,C° ^° is constructed such that the following holds. For any regular semigroup S with an inverse transversal S° and 〈E(S)〉 = C, C° = C ∩ S°, there is a homomorphism φ from S to T _C,C° such that the kernel of φ is the maximum idempotent-separating congruence on S, and φ satisfies: (1) φ| _C is a homomorphism from C onto 〈E(T _C,C°)〉 ; (2) φ| _S° is a homomorphism from S° to T _C,C° °. In particular, S is fundamental if and only if S is isomorphic to a full subsemigroup of T _C,C°. Our fundamental regular semigroup T _C,C° is isomorphic to a subsemigroup of the Hall semigroup of C but it is easier to handle. Its elements are partial transformations, and the operation—although not the usual composition—is defined by means of composition.     

Preparation and structural stability investigation of CoN/CN soft X-ray multilayers

The structural stability of heat-treated CoN/CN soft X-ray multilayers fabricated by dual-facing-target sputtering has been investigated by using complementary measurement techniques. The high temperature annealing results imply that the destructive threshold of the Co/C multilayers is improved by 100–200 degrees centigrade through doping with N. The low-angle X-ray diffraction of CoN/CN soft X-ray multilayers indicates that the period expansion of the multilayers is only 4 % at 400°C, and the interface pattern still exists even if they were annealed at 700°C. The Raman spectra analyses give the evidence that the formation of the sp³ bonding in the CN sublayers can be suppressed effectively by doping N with atoms, and thus the period expansion resulting from the changes in the density of CN layers can be decreased considerably. The X-ray photoelectron spectra analyses present the information of the existence of the strong covalent bonding betweenC andN atoms, and the ionic bonding between Co and N atoms, which can slow down the tendency of the structural relaxation. The interstitial N atoms decrease the mobility of Co atoms, and thus the fcc-Co and hcp-Co coexist even though the annealing temperature is much higher than the phase transformation temperature of 420°C, leading to the suppression of the grain growth.     

The Γ-limit of a finite-strain Cosserat model for asymptotically thin domains and a consequence for the Cosserat couple modulus μc

We study the behaviour of a geometrically exact 3D Cosserat continuum model for an asymptotically flat domain. Despite the inherent nonlinearity, the Γ-limit of a corresponding canonically rescaled problem on a domain with constant thickness can be explicitly calculated. This “membrane” limit exhibits no bending contributions scaling with h ³ (similar to classical approaches) but features a transverse shear resistance scaling with h for strictly positive Cosserat couple modulus μ_c > 0. This result is physically inacceptable for a zero-thickness “membrane” limit model. Therefore it is suggested that the physically consistent value of the Cosserat couple modulus μ_c is zero. In this case, however, the Γ-limit looses coercivity for the midsurface deformation in H ^1,2(ω , ℝ³). For numerical purposes then, a transverse shear resistance can be reintroduced, establishing coercivity. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Permanent magnet system of alpha magnetic spectrometer

Alpha magnetic spectrometer (AMS) is the first large magndtic spectrometer in space. Its precursor flioht was completed successfully in June 1998. The key part of AMS is the permanent magnet system, which was built by the lnstitute of Electric Engineering, the institute of High Energy Physics and the Chinese Academy of Launch Vehicle Technology. This system includes a permanent magnet made of high grade NdFeB and a support structure. The unique design of the permanent magnet based on the magic ring fulfills the severe requirements on the magnetic field leakage and the dipole moment for space experiments. The permanent magnet weighs about 2 tons, and provides a geometric acceptance of 0.6 m² · sr and an analyzing powerBL ² of 0.135 T · m². It works up to 40°C without demagnetization. The main structure is a thin double shell, which undergoes the strong magnetic force and torque of the permanent magnet, as well as the large load during launching and landing. The permanent magnet system fulfills the requirements from AMS, and satisfies the strict safety standards of NASA.     

Electron paramagnetic resonance of Mn2+ in (NH4)2SO4 single crystal

Electron paramagnetic resonance investigation of Mn²⁺ in (NH₄)₂SO₄ single crystal is discussed both in paraelectric and ferroelectric phases of the crystal. Mn²⁺ is found to substitute one of the two possible types (α andβ) of NH ₄ ⁺ ions and get associated with the second type of NH ₄ ⁺ vacancy, the vacancy being the second distant neighbour in thebc-plane. As The line joining Mn²⁺ substituted NH ₄ ⁺ site and NH ₄ ⁺ vacancy lies at an angle of 18° from the crystallographicb-axis in thebc-plane. As the temperature is lowered to ? 56° C the crystal becomes ferroelectric and the spectrum in the paraelectric phase splits into two from which it appears that two sets of Mn²⁺ sites which are magnetically equivalent in the paraelectric phase become inequivalent in the ferroelectric phase. The spin Hamiltonian analysis is presented for the spectrum in the paraelectric phase.     

Upper bounds for the autocorrelation coefficients of the Rudin-Shapiro polynomials

Givena _m to be them ^th correlation coefficient of the Rudin-Shapiro polynomials of degrees 2 ⁿ ? 1, ¦a _m¦ ≤ C(2 ⁿ )^3/4 and there existsk ≠ 0 such that ¦a _k¦ >D(2 ⁿ )^0.73 (C andD are universal constants). Here we show that the 0.73 is optimal in the upper bound case.     

Temperature dependence of the photoelastic behaviour of crystals—Part I

A modified form of Filon’s spectrometer method is used to study the variation of the stress-optical constants (q ₁₁-q ₁₂) andq ₄₄ of KCl, KBr, KI, LiF, MgO and NaCl in the temperature range 30° C. to 400° C. It is found that (q ₁₁-q ₁₂) andq ₄₄ generally increase numerically with the increase of temperature except those of NaCl which show a decrease. In KBr and KI,q ₄₄ first increases and then decreases numerically. The potassium halides show an interesting gradation of variation of these constants. In all the crystals studied, which are of NaCl type, the variation in (q ₁₁-q ₁₂) is greater than that inq ₄₄. Mueller’s ultrasonic method is used for measuring the ratio of strain-optical constantsp ₁₂/p ₁₁, in the temperature range 30°C. to 250°C. Combining the results obtained by these two methods, the absolute strain-optical constantsp ₁₁ andp ₁₂ have been evaluated at different temperatures. Curves are given showing the variation ofp ₁₁ andp ₁₂ with temperature. The variation ofp ₁₁ andp ₁₂ with temperature is discussed in terms of the contributions of the various factors considered by Mueller in his theory of photoelastic effect in cubic crystals.     

Synthesis and surface reactivity of phosphide nanocrystals

Gap and InP nanocrystals were synthesized from Na₃P and GaCI₃ at low temperature (80–100°C) and atmospheric pressure. The samples were characterized by XRD and TEM measurements. The surface reactivity of Gap nanocrystals was studied by heating in N₂. The weight of the nanocrystals increased at the temperature between 370°C and 480°C. It can be concluded that N, molecule was absorbed and reactivated on the surface of Gap nanocrystals. Keywords: gallium phosphide, indium phosphide, nanocrystal, surface reactivity.     

Band-dominated operators on metric measure spaces

We generalise the notion of band-dominated operators originally introduced for the space ℓ_p(ℤⁿ) to the setup of metric measure spaces and show various algebraic properties of this space of operators. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ω‐estimates related to irreducible algebraic integers

We study large values of the remainder term E_K (x) in the asymptotic formula for the number of irreducible integers in an algebraic number field K. We show that E_K (x) = Ω_± (√(x)(log x)) for certain positive constant B_K, improving in that way the previously best known estimate E_K (x) = Ω_± (x^(1/2)‐ε) for every ε > 0, due to A. Perelli and the present author. Assuming that no entire L‐function from the Selberg class vanishes on the vertical line σ = 1, we show that E_K (x) = Ω_± (√(x)(log log x)^{D (K)‐1}(log x)^‐1), supporting a conjecture raised recently by the author. In particular, it follows that the last omega estimate is a consequence of the Selberg Orthonormality Conjecture (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the stability of the Ekman boundary layer

We present a result on well-posedness and stability of the Ekman boundary layer problem in the space FM(ℝ², L²(ℝ₊)³), i.e., in the space of L²(ℝ₊)³-valued Fourier transformed finite Radon measures. In particular we obtain stability in the angle velocity of rotation, which is important in the analysis of fast oscillating singular limits. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental Investigation of thermal convection in an inclined narrow gap II

In the past decade the development in micro technology has experienced great progress, what made the knowledge of the flow behavior in small cavities fundamentally interesting. Our experimental contribution describes the measured temperature and velocity fields in a fluid containing inclined cavity with the dimensions 17 × 6 × 24 mm³ (w × d × h). Using PIV/T, we can determine the velocity and temperature distribution in the cavity simultaneously. The chamber is illuminated with a white light sheet of 1 mm. A 20% glycerin-water mixture is examined. The lower side is heated to 46.2°C, while the upper side has a constant temperature of 26°C. In this work we present the measured velocity and temperature fields of the fluid at different angles of the cavity orientation with respect to the direction of gravity in the stationary state. This is a continuation of last years presentation [1] in the sense that the temperature difference has been substantially increased. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electron spin resonance studies of the ligand exchange in cupric complexes with diethyldithiocarbamate and diethyldithiophosphate as ligands

The kinetics of ligand substitutions in the cupric complexes where a diethyldithiocarbamate (dtc^?) is replaced by a diethyldithiophosphate (dtp^?) has been studied with chloroform as solvent. The relative concentrations of the paramagnetic species produced in the reactions have been determined using electron spin resonance. The reaction studies suggest the presence of the short time equilibria: Cu (dtc)₂ + dtpH ? Cu (dtc) (dtp) + dtcH Cu (dtc) (dtp) + dtpH ? Cu (dtp)₂ + dtcH where the equilibrium constants have the value, 0.0625 and 0.00143 respectively. The equilibria are disturbed by the reaction: dtcH + dtpH → (C₂ H₅)₂ NH₂ ⁺ dtp^? + CS₂ with a rate constantk = 0.07 1. mole^?1 sec.^?1 at 26°C. Analysis of the thermodynamic parameters determined from the study of the kinetics of the reactions at various temperatures shows that dtp^? group favours more solvent and excess ligand coordination than dtc^?. This is consistent with the study of “Long time equilibrium” which indicates that Cu (dtp)₂ exists with further two weakly bonded dtpH groups in the axial positions in chloroform solutions.