Relative T -Injective Modules and Relative T -Flat Modules

Let T be a Wakamatsu tilting module. A module M is called (n, T)-copure injective (resp. (n, T)-copure flat) if ɛ _T ¹ (N, M) = 0 (resp. Γ₁ ^T (N, M) = 0) for any module N with T-injective dimension at most n (see Definition 2.2). In this paper, it is shown that M is (n, T)-copure injective if and only if M is the kernel of an I _n (T)-precover f: A → B with A ∈ Prod T. Also, some results on Prod T-syzygies are presented. For instance, it is shown that every nth Prod T-syzygy of every module, generated by T, is (n, T)-copure injective.     

Roughness evolution of highly ordered nanoporous anodic aluminum oxide films

In this paper, we report on the surface roughness evolution of highly ordered anodic aluminum oxide (AAO) films based on an atomic force microscopy (AFM) study. Root mean square of the surface roughness was measured on AFM images taken from highly ordered AAO films produced by two-step anodization under different conditions including electrolyte type, anodization voltage, and anodization time. Surface roughness of highly ordered AAO films increases step by step through the two-step anodizing process including electropolishing, first-step anodization, dissolution, and second-step anodization. However, increase of the surface roughness is proportional to the anodization voltage and time. The surface roughness of AAO films changes as a function of length scale until it finally approaches a maximum termed the saturation roughness. The variation of roughness of the growth of AAO could be scaled with an anomalous dynamic behavior as it saturates over a critical length scale while the saturation roughness is dependent on the anodizing time and voltage.     

Solvent-free and room temperature synthesis of thiochromans in the presence of a catalytic amount of tungstophosphoric acid

Tungstophosphoric acid catalyzed rapid and good yielding reactions of α,β-unsaturated aldehydes with arenethiols to give the corresponding 4-thioaryl-1,2,3,4-tetrahydro-1-benzothiopyrans (thiochromans) under solvent-free and room temperature conditions.     

Vibrational assignment, structure and intramolecular hydrogen bond study of 3-amino-1-phenyl-2-buten-1-one

Fourier transform infrared and Fourier transform Raman spectra of 3-amino-1-phenyl-2-buten-1-one and its deuterated analogue were recorded in the regions 400-4,000 and 150-4,000 cm(-1), respectively. Furthermore, the molecular structure and vibrational frequencies of title compound were investigated by a series of density functional theoretical, DFT, and ab initio calculations at the post-Hartree-Fock (MP2) level. Although, the calculated frequencies are generally in agreement with the observed spectra but the DFT results are in much better quantitative agreement with the observed spectra than the MP2 results. The observed wavenumbers were analyzed and assigned to different normal modes of vibration of the molecule. The calculated geometrical parameters show a strong intramolecular hydrogen bond with a N...O distance of 2.621-2.668 A. This bond length is shorter than that of its parent, 4-amino-3-penten-2-one (with two methyl groups in the beta-position), which is in agreement with spectroscopic results. The topological properties of the electron density contributions for intramolecular hydrogen bond in 3-amino-1-phenyl-2-buten-1-one and 4-amino-3-penten-2-one have been analyzed in term of the Bader theory of atoms in molecules (AIM). These results also support the stronger hydrogen bond in the title compound with respect to the parent molecule.     

A distance function for computing on finite subsets of Euclidean spaces

In practical purposes for some geometrical problems, specially the fields in common with computer science, we deal with information of some finite number of points. The problem often arises here is: “How are we able to define a plausible distance function on a finite three dimensional space?” In this paper, we define such a distance function in order to apply it to further purposes, e.g. in the field settings of transportation theory and geometry. More precisely, we present a new model for traveling salesman problem and vehicle routing problem for two dimensional manifolds in three dimensional Euclidean space, the second problem on which we focus on this line is, three dimensional triangulation.     

Weyl’s Law and Connes’ Trace Theorem for Noncommutative Two Tori

We prove the analogue of Weyl’s law for a noncommutative Riemannian manifold, namely the noncommutative two torus ${\mathbb{T}_{\theta}^{2}}$ equipped with a general translation invariant conformal structure and a Weyl conformal factor. This is achieved by studying the asymptotic distribution of the eigenvalues of the perturbed Laplacian on ${\mathbb{T}_{\theta}^{2}}$ . We also prove the analogue of Connes’ trace theorem by showing that the Dixmier trace and a noncommutative residue coincide on pseudodifferential operators of order ?2 on ${\mathbb{T}_{\theta}^{2}}$ .     

Optimal sensor array configuration in remote image formation.

Determination of optimal sensor configuration is an important issue in many remote imaging modalities, such as tomographic and interferometric imaging. In this paper, a statistical optimality criterion is defined and a search is performed over the space of candidate sensor locations to determine the configuration that optimizes the criterion over all candidates. To make the search process computationally feasible, a modified version of a previously proposed suboptimal backward greedy algorithm is used. A statistical framework is developed which allows for inclusion of several widely used image constraints. Computational complexity of the proposed algorithm is discussed and a fast implementation is described. Furthermore, upper bounds on the sum of the squared error of the proposed algorithm are derived. Connections of the method to the deterministic backward greedy algorithm for the subset selection problem are presented, and two application examples are described. Five compelling optimality criteria are considered, and their performance is investigated through numerical experiments for a tomographic imaging scenario. In all cases, it is verified that the configuration designed by the proposed algorithm performs better than wisely chosen alternatives.     

Dual Gold‐Catalyzed Cycloaromatization of Unconjugated (E)‐Enediynes

A synthesis of unconjugated (E)‐enediynes from allenyl amino alcohols is reported and their gold‐catalyzed cascade cycloaromatization to a broad range of enantioenriched substituted isoindolinones has been developed. Experimental and computational studies support the reaction proceeding via a dual‐gold σ,π‐activation mode, involving a key gold‐vinylidene‐ and allenyl‐gold‐containing intermediate.     

Decentralized Hierarchical Coded Caching Over Heterogeneous Wireless Networks with Multi-level Popularity Content

Wireless Personal Communications - Decentralized hierarchical coded caching is studied with two layers of caches which users receive their demands through intermediate helpers from a main server....