Local cohomology modules of a smooth \mathbb{Z}-algebra have finitely many associated primes

Let R be a commutative Noetherian ring that is a smooth \(\mathbb {Z}\) -algebra. For each ideal \(\mathfrak {a}\) of R and integer k, we prove that the local cohomology module \(H^{k}_{\mathfrak {a}}(R)\) has finitely many associated prime ideals. This settles a crucial outstanding case of a conjecture of Lyubeznik asserting this finiteness for local cohomology modules of all regular rings.     

Approximations to m‐Colored Complete Infinite Hypergraphs

Given an edge coloring of a graph with a set of m colors, we say that the graph is exactly m‐colored if each of the colors is used. In 1999, Stacey and Weidl, partially resolving a conjecture of Erickson from 1994, showed that for a fixed natural number and for all sufficiently large k, there is a k‐coloring of the complete graph on such that no complete infinite subgraph is exactly m‐colored. In the light of this result, we consider the question of how close we can come to finding an exactly m‐colored complete infinite subgraph. We show that for a natural number m and any finite coloring of the edges of the complete graph on with m or more colors, there is an exactly ‐colored complete infinite subgraph for some satisfying ; this is best possible up to the additive constant. We also obtain analogous results for this problem in the setting of r‐uniform hypergraphs. Along the way, we also prove a recent conjecture of the second author and investigate generalizations of this conjecture to r‐uniform hypergraphs.     

Highly Efficient Organosulfur and Lithium-Metal Hosts Enabled by C@Fe3N Sponge

Lithium-organosulfur (Li-OS) batteries, despite possessing high theoretical specific capacity, encounter a few practical challenges, including unsatisfactory lifespan and low active material utilization under realistic conditions. Here, diisoropyl xanthogen polysulfide (DIXPS) has been selected as a model organosulfur compound to investigate the practical feasibility of Li-OS batteries under realistic conditions. A well-designed freestanding carbon sponge decorated with Fe₃N nanoparticles (C@Fe₃N) is introduced into the Li-OS cells as a scaffold for both Li and DIXPS. The lithiophilic property of the C@Fe₃N host guides uniform lithium deposition at the anode, and the catalysis of the DIXPS conversion reaction promotes the kinetics at the cathode. Impressively, the synergistic effect of C@Fe₃N leads to an extremely stable cycling performance over 1 000 cycles in a Li-OS full cell under realistic conditions.     

Azo calix[4]arene based neodymium(III)-selective PVC membrane sensor

We found that the PVC membrane, containing azo calix[4]arene is a suitable ionophore, exhibited a Nernstian response for neodymium (Nd³⁺) ions (with slope of 19.8 ± 0.2 mV decade⁻¹ for the triply charged ion) over a wide linear range of 4.0 × 10⁻⁸ to 1.0 × 10⁻¹ mol L⁻¹ with a detection limit 1.0 × 10⁻⁸ mol L⁻¹, a relatively fast response time, in the whole concentration range (<10 s), and a considerable life time at least for four months in the pH range of 4.0-8.0. Furthermore, the electrode revealed high selectivity with respect to all the common alkali, alkaline earth, transition and heavy metal ions, including the members of the lanthanide family other than Nd³⁺. Concerning its applications, it was effectively employed for the determination of neodymium ions in industrial waste water as well as in lake water.     

Design,synthesis, pharmacological evaluation and DNA interaction studies of binuclear Pt(II) complexes with pyrazolo[1,5‐a]pyrimidine scaffold

Substituted pyrazolo[1,5‐a]pyrimidine ligands were synthesized by cyclization, using 3‐(thiophen‐2‐yl)‐1H‐pyrazol‐5‐amine with substituted enones (3‐phenyl‐1‐(pyridin‐2‐yl)prop‐2‐en‐1‐one) in presence of KOH and DMF as solvent to form cyclic aromatic compounds. The substituted pyrazolo[1,5‐a] pyrimidine based binuclear Pt^II complexes containing neutral tetradentated ligands have general formula [Pt₂(5a–5f)Cl₄], (where, (5a ‐5f) = pyrazolo[1,5‐a] pyrimidine ligand). This compounds were characterized by physicochemical and spectroscopic method like elemental analyses, UV‐Visible, FT‐IR, EDX, TGA, molar conductivity, magnetic susceptibility measurements, mass spectroscopy, ¹H and ¹³C NMR method. The square planar geometry was predicted by electronic spectral study. All Pt^II compounds were evaluated by antimicrobial assay, in vitro brine shrimp assay, in vivo cellular level bioassay using S. Pombe cells and anti‐tuberculosis study. LC₅₀ (50% lethal concentration) values of compounds are observed between 6.450 ‐ 102.07 μg/mL. UV‐vis absorption titration, competitive displacement assay, molecular docking and viscosity measurement were carried out to examine the binding type and binding strength of complexes. The binding studies suggest partial intercalative binding mode of the complexes and the observed binding constant (K_b) values are found in the order of 6d > 6b > 6c > 6a > 6e > 6 f. The anti‐proliferative cytotoxicity of the synthesized Pt^II complexes (6a‐6f) were tested against the HCT‐116 (Human Colorectal Carcinoma) cancer cell line.     

Detailed physicochemical and thermochemical investigation of Upper Assam oil shale

Journal of Thermal Analysis and Calorimetry - The present work provides a detailed characterization and kinetic study of oil shale of Upper Assam, India. The physicochemical characteristics of oil...     

Synthesis of metal-based nanofluids and their thermo-hydraulic performance in compact heat exchanger with multi-louvered fins working under laminar conditions

Present experimental investigation incorporates characterization of Al nanopowder, synthesis of Al/water nanofluids, and effect of these nanofluids on thermal performance of compact heat exchanger. Al nanoparticles are characterized using TEM and XRD. Al/water nanofluid is prepared by dispersing metal basis aluminium nanoparticles of average 100 nm size into double distilled water at two different particle volume concentrations of 0.1 and 0.2%. The nanofluids are prepared by two-step method and cetyl trimethyl ammonium bromide surfactant is used to stabilize the nanofluid. Thermo-physical properties of nanofluids at two different concentrations and their variation with fluid temperature are measured experimentally. It is examined that thermal conductivity, viscosity, and density of the nanofluid increased with the increase of volume concentrations. Furthermore, by increasing the fluid temperature, thermal conductivity is intensified, while the viscosity and density are decreased. Heat transfer parameters are strong functions of these thermo-physical properties. Therefore, comprehensive findings on heat transfer coefficient, Nusselt number, colburn factor, friction factor, and effectiveness are determined experimentally for prepared nanofluids passing under laminar conditions through single-pass cross-flow compact heat exchanger attached with multi-louvered fins.

     

On a nonlinear renewal equation with diffusion

In this paper, we consider a nonlinear age structured McKendrick–von Foerster population model with diffusion term. Here we prove existence and uniqueness of the solution of the equation. We consider a particular type of nonlinearity in the renewal term and prove Generalized Relative Entropy type inequality. Longtime behavior of the solution has been addressed for both linear and nonlinear versions of the equation. In linear case, we prove that the solution converges to the first eigenfunction with an exponential rate. In nonlinear case, we have considered a particular type of nonlinearity that is present in the mortality term in which we can predict the longtime behavior. Copyright © 2015 John Wiley & Sons, Ltd.     

WikiArtVectors: Style and Color Representations of Artworks for Cultural Analysis via Information Theoretic Measures

With the increase in massive digitized datasets of cultural artefacts, social and cultural scientists have an unprecedented opportunity for the discovery and expansion of cultural theory. The WikiArt dataset is one such example, with over 250,000 high quality images of historically significant artworks by over 3000 artists, ranging from the 15th century to the present day; it is a rich source for the potential mining of patterns and differences among artists, genres, and styles. However, such datasets are often difficult to analyse and use for answering complex questions of cultural evolution and divergence because of their raw formats as image files, which are represented as multi-dimensional tensors/matrices. Recent developments in machine learning, multi-modal data analysis and image processing, however, open the door for us to create representations of images that extract important, domain-specific features from images. Art historians have long emphasised the importance of art style, and the colors used in art, as ways to characterise and retrieve art across genre, style, and artist. In this paper, we release a massive vector-based dataset of paintings (WikiArtVectors), with style representations and color distributions, which provides cultural and social scientists with a framework and database to explore relationships across these two vital dimensions. We use state-of-the-art deep learning and human perceptual color distributions to extract the representations for each painting, and aggregate them across artist, style, and genre. These vector representations and distributions can then be used in tandem with information-theoretic and distance metrics to identify large-scale patterns across art style, genre, and artist. We demonstrate the consistency of these vectors, and provide early explorations, while detailing future work and directions. All of our data and code is publicly available on GitHub.     

Highly efficient implementation of pseudospectral time‐dependent density‐functional theory for the calculation of excitation energies of large molecules

We have developed and implemented pseudospectral time‐dependent density‐functional theory (TDDFT) in the quantum mechanics package Jaguar to calculate restricted singlet and restricted triplet, as well as unrestricted excitation energies with either full linear response (FLR) or the Tamm–Dancoff approximation (TDA) with the pseudospectral length scales, pseudospectral atomic corrections, and pseudospectral multigrid strategy included in the implementations to improve the chemical accuracy and to speed the pseudospectral calculations. The calculations based on pseudospectral time‐dependent density‐functional theory with full linear response (PS‐FLR‐TDDFT) and within the Tamm–Dancoff approximation (PS‐TDA‐TDDFT) for G2 set molecules using B3LYP/6‐31G*^* show mean and maximum absolute deviations of 0.0015 eV and 0.0081 eV, 0.0007 eV and 0.0064 eV, 0.0004 eV and 0.0022 eV for restricted singlet excitation energies, restricted triplet excitation energies, and unrestricted excitation energies, respectively; compared with the results calculated from the conventional spectral method. The application of PS‐FLR‐TDDFT to OLED molecules and organic dyes, as well as the comparisons for results calculated from PS‐FLR‐TDDFT and best estimations demonstrate that the accuracy of both PS‐FLR‐TDDFT and PS‐TDA‐TDDFT. Calculations for a set of medium‐sized molecules, including C_n fullerenes and nanotubes, using the B3LYP functional and 6‐31G^** basis set show PS‐TDA‐TDDFT provides 19‐ to 34‐fold speedups for C_n fullerenes with 450–1470 basis functions, 11‐ to 32‐fold speedups for nanotubes with 660–3180 basis functions, and 9‐ to 16‐fold speedups for organic molecules with 540–1340 basis functions compared to fully analytic calculations without sacrificing chemical accuracy. The calculations on a set of larger molecules, including the antibiotic drug Ramoplanin, the 46‐residue crambin protein, fullerenes up to C₅₄₀ and nanotubes up to 14×(6,6), using the B3LYP functional and 6‐31G^** basis set with up to 8100 basis functions show that PS‐FLR‐TDDFT CPU time scales as N^2.05 with the number of basis functions. © 2016 Wiley Periodicals, Inc.