Size control and quantum confinement in Cu2ZnSnS4 nanocrystals

Starting with metal dithiocarbamate complexes, we synthesize colloidal Cu(2)ZnSnS(4) (CZTS) nanocrystals with diameters ranging from 2 to 7 nm. Structural and Raman scattering data confirm that CZTS is obtained rather than other possible material phases. The optical absorption spectra of nanocrystals with diameters less than 3 nm show a shift to higher energy due to quantum confinement.     

Quantum confinement in silver selenide semiconductor nanocrystals

We prepare Ag(2)Se nanocrystals with average diameters between 2.7 and 10.4 nm that exhibit narrow optical absorption features in the near to mid infrared. We demonstrate that these features are broadly tunable due to quantum confinement. They provide the longest wavelength absorption peaks (6.5 μm) yet reported for colloidal nanocrystals.     

Improving the Data Augmentation Algorithm in the Two-Block Setup

The data augmentation (DA) approach to approximate sampling from an intractable probability density f_X is based on the construction of a joint density, f_{X, Y}, whose conditional densities, f_X|Y and f_Y|X, can be straightforwardly sampled. However, many applications of the DA algorithm do not fall in this “single-block” setup. In these applications, X is partitioned into two components, X = (U, V), in such a way that it is easy to sample from f_Y|X, f_{U|V, Y}, and f_{V|U, Y}. We refer to this alternative version of DA, which is effectively a three-variable Gibbs sampler, as “two-block” DA. We develop two methods to improve the performance of the DA algorithm in the two-block setup. These methods are motivated by the Haar PX-DA algorithm, which has been developed in previous literature to improve the performance of the single-block DA algorithm. The Haar PX-DA algorithm, which adds a computationally inexpensive extra step in each iteration of the DA algorithm while preserving the stationary density, has been shown to be optimal among similar techniques. However, as we illustrate, the Haar PX-DA algorithm does not lead to the required stationary density f_X in the two-block setup. Our methods incorporate suitable generalizations and modifications to this approach, and work in the two-block setup. A theoretical comparison of our methods to the two-block DA algorithm, a much harder task than the single-block setup due to nonreversibility and structural complexities, is provided. We successfully apply our methods to applications of the two-block DA algorithm in Bayesian robit regression and Bayesian quantile regression. Supplementary materials for this article are available online.     

Switching wetting morphologies in triangular grooves

Static wetting morphologies in grooves with triangular cross section are studied here. Using the electrowetting effect, we can switch between different equilibrium morphologies and transport liquid along prefabricated grooves. The particular filling and drainage behavior in triangular grooves is discussed in terms of the groove geometry.     

Study of magnetotransport in double-layered La1.4Ca1.6Mn2O7 manganite: Presence of nano-ferromagnetic domains in paramagnetic matrix

Double-layered manganite La_1.4Ca_1.6Mn₂O₇ has been synthesized using the solid-state reaction method. It had a metal-to-insulator transition at temperature T_M1≈127 K. The temperature dependence of ac susceptibility showed a broad ferromagnetic transition. The two-dimensional (2D)-ferromagnetic ordering temperature (T_C2) was observed as ≈245 K. The temperature dependence of its low-field magnetoresistance has been studied. The low-field magnetoresistance of double-layered manganite, in the temperature regions between T_M1 and T_C2, has been found to follow 1/T⁵. The observed behaviour of temperature dependence of resistivity and low-field magnetoresistance has been explained in terms of two-phase model where ferromagnetic domains exist in the matrix of paramagnetic regions in which spin-dependent tunneling of charge carriers occurs between the ferromagnetic correlated regions. Based on the two-phase model, the dimension of these ferromagnetic domains inside the paramagnetic matrix has been estimated as ∼12 Å.     

Serre’s modularity conjecture (I)

This paper is the first part of a work which proves Serre’s modularity conjecture. We first prove the cases \(p\not=2\) and odd conductor, and p=2 and weight 2, see Theorem 1.2, modulo Theorems 4.1 and 5.1. Theorems 4.1 and 5.1 are proven in the second part, see Khare and Wintenberger (Invent. Math., doi: 10.1007/s00222-009-0206-6, 2009). We then reduce the general case to a modularity statement for 2-adic lifts of modular mod 2 representations. This statement is now a theorem of Kisin (Invent. Math., doi: 10.1007/s00222-009-0207-5, 2009).     

Vector spaces as unions of proper subspaces

In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of partitioning V into subspaces.     

Current-induced effect on resistivity and magnetoresistance of La0.67Ba0.33MnO3 manganite

The influence of dc biasing current on temperature dependence of resistivity and low-field magnetoresistance (MR) of La_0.67Ba_0.33MnO₃ bulk sample is reported. A prominent finding is the change in resistivity around the insulator-to-metal transition temperature (T_IM) and the change in MR around the ferromagnetic transition temperature (T_C). The decrease in MR around T_C at higher biasing current indicates a strong interaction between carrier spin and spin of Mn ions resulting in a higher alignment of Mn ion spins. Change in resistivity around T_IM is interpreted in the framework of percolative conduction model based on the mixed phase of itinerant electrons and localized magnetic polarons.     

Conditional Entropy and the Rokhlin Metric on an Orthomodular Lattice with Bayessian State

The present paper deals with the study of conditional entropy and its properties in a quantum space (L,s), where L is an orthomodular lattice and s is a Bayessian state on L. First, we obtained a pseudo-metric on the family of all partitions of the couple (B,s), where B is a Boolean algebra and s is a state on B. This pseudo-metric turns out to be a metric (called the Rokhlin metric) by using a new notion of s-refinement and by identifying those partitions of (B,s) which are s-equivalent. The present theory has then been extended to the quantum space (L,s), where L is an orthomodular lattice and s is a Bayessian state on L. Applying the theory of commutators and Bell inequalities, it is shown that the couple (L,s) can be equivalently replaced by a couple (B,s ₀), where B is a Boolean algebra and s ₀ is a state on B.