Behavior Of Ln Research Articles

Convergence in Total Variation of Random Sums

Let (Xn) be a sequence of real random variables, (Tn) a sequence of random indices, and (τn) a sequence of constants such that τn→∞. The asymptotic behavior of Ln=(1/τn)∑i=1TnXi, as n→∞, is investigated when (Xn) is exchangeable and independent of (Tn). We give conditions for Mn=τn(Ln−L)⟶M in distribution, where L and M are suitable random variables. Moreover, when (Xn) is i.i.d., we find constants an and bn such that supA∈B(R)|P(Ln∈A)−P(L∈A)|≤an and supA∈B(R)|P(Mn∈A)−P(M∈A)|≤bn for every n. In particular, Ln→L or Mn→M in total variation distance provided an→0 or bn→0, as it happens in some situations.

On the frequency–voltage dependent electrical and dielectric profiles of the Al/(Zn-PVA)/p-Si structures

The frequency effect on the dielectric features of Zn doped polymer interlayered metal–semiconductor (MS) structure has been investigated by admittance measuring methods. As a function of frequency and voltage, the parameters such as dielectric constant (e′), dielectric loss (e″), dielectric loss tangent (tanδ), and ac electrical conductivity (σac) have been calculated. The values of e′, e″ and tanδ were decreased with frequency increment for each applied bias. The decrement at e′ and e″ by frequency increase indicated that the interfacial dipoles have not enough time to orient themselves in the alternate field direction. While the M′ value increase with frequency and reach a maximum, M″ displays a peak where its position shifts to higher frequency with increasing applied bias. The ln(σac) vs ln(ω) plot of the structure at 6 V has two linear regions with different slopes. Such behavior of ln(σac) vs ln(ω) plot reveals that there are two distinct conduction mechanisms in the Al/(0.07Zn-doped PVA)/p-Si MPS type SBDs at room temperature.

The investigation of dielectric properties and ac conductivity of Au/GO-doped PrBaCoO nanoceramic/n-Si capacitors using impedance spectroscopy method

Graphene oxide-doped praseodymium barium cobalt oxide (GO-doped PrBaCoO) nanoceramic was used an interfacial layer for the purpose of increasing the capacitance in Au/n-Si metal–semiconductor (MS) structures. The frequency and voltage dependence of dielectric constant (ε′), dielectric loss (ε″), loss tangent (tanδ), the real and imaginary parts of electric modulus (M′ and M″) and ac electrical conductivity (σac) of Au/GO-doped PrBaCoO nanoceramic/n-Si capacitors were investigated in detail by impedance spectroscopy method in the wide frequency range of 1kHz to 1MHz at room temperature. Experimental results showed that ε′–V plot has two distinct peaks that are located at about 0 and 2V, respectively, at low frequencies, but the first peak disappears at high frequencies. While the value of M′ increase with increasing frequency M″ shows a peak and the peak position shifts to higher frequency with increasing applied voltage. Such peak behavior can be attributed to the particular distribution of interface states located between Au and interfacial layer and to the interfacial polarization. It can be concluded that the interfacial polarization and the charges at interface can easily follow ac signal at low frequencies. In addition, the ln(σac) vs ln(ω) plot of the capacitor for 3V has two linear regions (I and II) with different slopes which correspond to low and high frequency ranges, respectively. Such behavior of ln(σac) vs ln(ω) plot indicated that there are two different conduction mechanisms in the Au/GO-doped PrBaCoO nanoceramic/n-Si capacitor at room temperature.

Frequency and voltage dependence of dielectric properties and electric modulus in Au/PVC + TCNQ/p-Si structure at room temperature

Au/PVC + TCNQ/p-Si structure was fabricated and real and imaginary parts of the dielectric constant (ɛ′, ɛ″), loss tangent (tanδ), and the real and imaginary parts of the electric modulus (M′, M″) and ac conductivity (σac) of this structure have been investigated in wide frequency a range of 1 kHz–5 MHz at room temperature. All of these parameters were found strong function of frequency and voltage especially in the inversion and depletion regions at low frequencies due to interfacial polarization and charges at interface states (Nss). The decrease in ɛ′ and ɛ″ with increasing frequency indicated that the interfacial dipoles have less time to orient themselves in the direction of the alternate field. While the value of M′ increase with increasing frequency and reach a maximum, M″ shows a peak and the peak position shifts to higher frequency with increasing applied voltage. The ln(σac) vs ln(ω) plot of the structure for 0.5 V has three linear regions (I, II and III) with different slopes which correspond to low, intermediate and high frequency ranges, respectively. Such behavior of ln(σac) vs ln(ω) plot indicated that there are three different conduction mechanisms in the Au/PVC + TCNQ/p-Si structure at room temperature.

Schottky barrier diode parameters of Ag/MgPc/p-Si structure

An Ag /Pc/p- Si Schottky barrier (SB) diode was fabricated. The current-voltage (I-V), capacitance-voltage (C-V) and conductance-voltage (G-V) measurements were carried out to determine the characteristic parameters such as barrier height, ideality factor and series resistance of the SB diode. The non-linear behavior of ln (I) vs. ln (V) and ln (I/V) vs. V1/2 plots indicated that the thermoionic emission theory can be applied to evaluate junction parameters for the investigated SB diode rather than space-charge limited conduction (SCLC) mechanism and bulk-limited Poole–Frenkel emission. The bulk doping concentration NB and fixed oxide charges Nf was determined from the measured high frequency C-V curve and was found to be 9.5 × 1014 cm-3 and 2.3 × 1013 cm-2, respectively. The values of barrier height obtained from Norde's function were compared with those from the forward bias current-voltage characteristic, and it was seen that there was a good agreement between barrier heights from both methods.

Aggregation in a one-dimensional stochastic gas model with finite polynomial moments of particle speeds

We consider a one-dimensional system of auto-gravitating sticky particles with random initial speeds and describe the process of aggregation in terms of the largest cluster size Ln at any fixed time prior to the critical time. We study the asymptotic behavior of Ln for the warm gas, i.e., for a system of particles with nonzero initial speeds vi(0) = ui, where (ui) is a family of i.i.d. random variables with mean zero, unit variance, and finite pth moment E(|ui|p) < ∞, p ≥ 2, and obtain sharp lower and upper bounds for Ln(t). Bibliography: 17 titles.

Mechanism of hopping conduction in new CeO 2–B 2O 3 semiconducting glasses

CeO 2–B 2O 3 glasses having a broad range of compositions, prepared by a press-quenching method from glass melts, were studied for DC conductivity. The conductivity at 583 K (1000/ T=1.715 K −1), ln σ 583, increases by about 16% in the composition regime 20–50 mol% CeO 2 while in the composition range 50–60 mol% CeO 2, ln σ 583 decreases by about 28%. The behavior of ln σ 583 with composition can be interpreted in terms of the changes in the high-temperature activation energy W and the hopping distance, R. Between 20 and 50 mol% CeO 2, increasing the mechanical strength and cross-linking of the glass network results in decreasing the polaron hopping energy, W H. At higher concentrations, the breaking of the 3D network observed to be probable for these glasses may increase the disorder energy, W D. The conduction mechanism is found to be non-adiabatic in nature for glasses investigated. Mott's model for the small polaron hopping conduction between nearest-neighbors gives unreasonable values for the Ce–Ce distance and the phonon frequency of the lattice vibrations. The increase in the conductivity with temperature can be interpreted in terms of the Schnakenberg model for optical multiphonon assisted hopping process at high temperatures and single optical phonon process at the lower ones. This model gives reasonable values for the phonon frequency of the lattice vibrations, the polaron hopping energy, and slightly higher values of W D.

Extraction of Lanthanides with N,N′‐Dimethyl‐N,N′‐diphenyl‐malonamide and ‐3,6‐dioxaoctanediamide

The extraction properties of the trivalent lanthanides (Ln(III)) with the bidentate N,N′‐dimethyl‐N,N′‐diphenyl‐malonamide (MA) and the tetradentate N,N′‐dimethyl‐N,N′‐diphenyl‐3,6‐dioxaoctanediamide (DOODA) were investigated. These diamides formed by coupling two amide groups with methylene and/or ether groups are bidentate for the MA and tetradentate for the DOODA. By adding a previous data regarding the tridentate N,N′‐dimethyl‐N,N′‐diphenyl‐diglycolamide (DGA), these extraction results enabled us systematically study an effect of number of oxygen donor on its extraction behavior of Ln(III). The change in the distribution ratios (Ds) of Lu(III) with an increase in the HNO3 concentration is greater than that of La(III) in both the MA and DOODA systems. Therefore, the relationship between the D and atomic number, i.e., the lanthanide pattern, changes with the HNO3 concentration: the Ds decrease with an increasing atomic number at lower HNO3 concentrations. The Ds of the lighter Ln(III) are similar to the Ds of the heavier Ln(III) at higher HNO3 concentrations. The number of the extractant in the extracted species for La(III) and Lu(III) obtained from slope analysis at 4 M HNO3 in the MA system are about 3, while those in the DOODA system are quite different, i.e., 2 for La(III) and 1.5–3 for Lu(III). The comparison of the extractability of Ln(III) by MA, DOODA, and DGA shows that the magnitude of the Ds is in the sequence of MA < DOODA ≪ DGA. This suggests the introduction of one ether oxygen atom to the principal chain in the diamides leads to a good extractability for the Ln(III) from HNO3 solution.

Complex formation of divalent lanthanides and actinides

This paper reports new data on the behaviour of Ln 2+, An 2+, and Sr 2+ in different systems. The data, obtained in this study, allowed us to compare the behaviour of 4f and 5f elements relative to one another and their analogue, strontium.

Decomposition behavior of Ln2Mn4/3W2/3O7 (Ln = Eu and Er) in reducing atmosphere and their thermodynamic properties

Decomposition behavior of Ln2Mn4/3W2/3O7 (Ln = Eu and Er) in reducing atmosphere at 1273 K was determined. These compounds decomposed to LnMnO3 and Ln2MnWO7 at PO2 = 10−8.46 atm for Ln = Eu and 10−7.46 atmosphere for Ln = Er, respectively. Decomposition product Eu2MnWO7 decomposed to Eu2MnWO6 at PO2 = 10−15.67 atm, while Er2MnWO7 decomposed to Er2O3, MnO, and W less than 10−17 atm. The standard Gibbs free energy changes of decomposition for Eu2Mn4/3W2/3O7, Eu2MnWO7, and Er2Mn4/3W2/3O7 at 1273 K were determined to be 34.4 kJ · mol−1, 191.9 kJ · mol−1, and 44.8 kJ · mol−1, respectively. The standard Gibbs free energy changes of formation of Er2Mn4/3W2/3O7 and Er2MnWO7 were also determined to be −2429.5 and −2463.2 kJ · mol−1 at 1273 K, respectively.

Polynomial interpolation in points equidistributed on the unit circle

Abstract : Let Ln(f; z) be the polynomial of degree at most n-1 found by interpolation in the distinct points znk = ei nk, k = 1, ..., n, to a function f given on z = 1. It is known that a nece sary and sufficient condition that nlim Ln(f; z) = f(z), z 1, for all f analytic n z 1, is that nk be equidistributed on 0, 2 . In nonanalytic cases, convergence has been established when znk is an n-th root of unity, b t the behavior of Ln with other spacings of the interpolation points is not clear. It is here proved that if nk, k = 1, ..., n, are independent random variables each with a uniform probability distribution and if f satisfies certain mild smoothness restrictions on z = 1, then where Ln is found by interpolation to f in the random points znk = ei nk. A simple example is constructed involving an equidistributed sample seq ence nk for w ich Ln(f; z) diverges to infinity at each point z, z < 1, for at least one function f continuous on z 1. (Author)