Eisenstein series and an asymptotic for the K-Bessel function

The Ramanujan Journal - We produce an estimate for the K-Bessel function $$K_{r + i t}(y)$$ with positive, real argument y and of large complex order $$r+it$$ where r is bounded and $$t = y \sin...     

Capillary induced self-assembly of thin foils into 3Dstructures

Self-assembly of complex structures is common in nature. Self-assembly principles provide a promising way to fabricate three-dimensional, micro- or millimeter scale devices. In the present paper, we present a generalized analytical study of the self-folding of thin plates into deterministic 3D shapes through fluid-solid interactions. Based on the beam theory, a mechanics model is developed, incorporating the two competing components—a capillary force promoting folding and the bending rigidity of the foil that resists folding into a 3D structure. Through an equivalence argument of thin foils of different geometry, an effective folding parameter, which uniquely characterizes the driving force for folding, has been identified. A criterion for spontaneous folding of any shaped 2D patterned foil based on the effective folding parameter is thus established. The model predictions show excellent agreement with experimental measurements made on a variety of materials, indicating that the assumptions used in the analysis arevalid.     

Raman endoscopy for in vivo differentiation between benign and malignant ulcers in the stomach

The aim of this study was to evaluate the clinical utility of an image-guided Raman endoscopy technique for in vivo differential diagnosis of benign and malignant ulcerous lesions in the stomach. A rapid-acquisition image-guided Raman endoscopy system with 785 nm laser excitation has been developed to acquire in vivo gastric tissue Raman spectra within 0.5 s during clinical gastroscopic examinations. A total of 1102 in vivo Raman spectra were acquired from 71 gastric patients, in which 924 Raman spectra were from normal tissue, 111 Raman spectra were from benign ulcers whereas 67 Raman spectra were from ulcerated adenocarcinoma. There were distinctive spectral differences in Raman spectra among normal mucosa, benign ulcers and malignant ulcers, particularly in the spectral ranges of 800-900, 1000-1100, 1245-1335, 1440-1450 and 1500-1800 cm(-1), which primarily contain signals related to proteins, DNA, lipids and blood. The malignant ulcerous lesions showed Raman signals to be mainly associated with abnormal nuclear activity and decrease in lipids as compared to benign ulcers. Partial least squares-discriminant analysis (PLS-DA) was employed to generate multi-class diagnostic algorithms for classification of Raman spectra of different gastric tissue types. The PLS-DA algorithms together with leave-one tissue site-out, cross validation technique yielded diagnostic sensitivities of 90.8%, 84.7%, 82.1%, and specificities of 93.8%, 94.5%, 95.3%, respectively, for classification of normal mucosa, benign and malignant ulcerous lesions in the stomach. This work demonstrates that image-guided Raman endoscopy technique associated with PLS-DA diagnostic algorithms has for the first time promising clinical potential for rapid, in vivo diagnosis and detection of malignant ulcerous gastric lesions at the molecular level.     

Ga(OTf)3-catalyzed direct substitution of alcohols with sulfur nucleophiles

It is reported that Ga(OTf)(3) catalyzes the direct displacement of alcohols with sulfur nucleophiles. The products are versatile intermediates that can be utilized in carbon-carbon, carbon-sulfur bond formation or used in modified Julia olefination reactions. The only byproduct generated is water.     

On the spanning fan-connectivity of graphs

Let G be a graph. The connectivity of G, κ(G), is the maximum integer k such that there exists a k-container between any two different vertices. A k-container of G between u and v, C_k(u,v), is a set of k-internally-disjoint paths between u and v. A spanning container is a container that spans V(G). A graph G is k^∗-connected if there exists a spanning k-container between any two different vertices. The spanning connectivity of G, κ^∗(G), is the maximum integer k such that G is w^∗-connected for 1≤w≤k if G is 1^∗-connected.Let x be a vertex in G and let U={y₁,y₂,…,y_k} be a subset of V(G) where x is not in U. A spanningk−(x,U)-fan, F_k(x,U), is a set of internally-disjoint paths {P₁,P₂,…,P_k} such that P_i is a path connecting x to y_i for 1≤i≤k and . A graph G is k^∗-fan-connected (or -connected) if there exists a spanning F_k(x,U)-fan for every choice of x and U with |U|=k and x∉U. The spanning fan-connectivity of a graph G, , is defined as the largest integer k such that G is -connected for 1≤w≤k if G is -connected.In this paper, some relationship between κ(G), κ^∗(G), and are discussed. Moreover, some sufficient conditions for a graph to be -connected are presented. Furthermore, we introduce the concept of a spanning pipeline-connectivity and discuss some sufficient conditions for a graph to be k^∗-pipeline-connected.     

Differences between tethered polyelectrolyte chains on bare mica and hydrophobically modified mica

This study investigates the structures of layers of amphiphilic diblock copolymers of poly(t-butyl styrene)-poly(styrene sulfonate) (PtBS-PSS) adsorbed on both the bare mica surface (hydrophilic) and an octadecyltriethoxysilane (OTE)-modified mica surface (hydrophobic). When the surface is rendered hydrophobic, the nonsoluble block exhibits stronger interaction with the surface and higher adsorbed masses are achieved. Interaction forces between two such adsorbed layers on both substrates were measured using the surface forces apparatus. The effect of salt concentration (Cs) and molecular weight (N) on the height of the self-assembled layers (L0) was examined in each case. The resulting scaling relationship is in good agreement with predictions of the brush model, L0 proportional to N(1.0) in the low-salt limit and L0N(-1) proportional to (Cs/sigma)(-0.32) in the salted regime, when adsorption takes place onto the hydrophobized mica surface. For adsorption on the bare mica surface, L0N(-0.7) proportional, variant Cs(-0.17) agrees with the scaling prediction of the sparse tethering model. The results suggest that, on the hydrophilic bare mica surface, the adsorbed amount is not high enough to form a brush structure and only very little intermolecular stretching of the tethered chains occurs; in contrast, the presence of the hydrophobic OTE layer increases the tethering density such that the polyelectrolyte chains adopt a brush conformation.     

Synthesis of hierarchical nanoporous F-doped TiO2 spheres with visible light photocatalytic activity

Hierarchical porous F-doped TiO2 microspheres exhibiting high visible light photocatalytic activity have been fabricated by a one-step low-temperature hydrothermal approach without using any templates.     

Second-order general perturbed sweeping process differential inclusion

The paper presents a study of perturbed sweeping process where the moving set depends on both the time and the state. This evolution problem is governed by second-order differential inclusions with an unbounded perturbation. Assuming that such set is prox-regular or subsmooth, we prove the existence of solutions even in the presence of a delay.     

Halogenated catechols from cycloaddition reactions of η-(2-ethoxyvinylketene)iron(0) complexes with 1-haloalkynes

1-Chloroalkynes and 1-bromohexyne undergo cycloaddition reactions with ethoxyvinylketeneiron(0) complexes to form chloro and bromocatechols. With most substituents, the halogen is incorporated ortho to the phenolic hydroxyl group regioselectively. With chloroethyne, chlorohexyne, and methyl chloropropiolate, the reverse regioselection is observed. Ab initio calculations reveal that the products are, in most cases, nearly isoenergetic, which indicates that the intermediate ketene-alkyne adduct geometry must be important in determining the product distribution.     

Microdistillation and analysis of volatiles from eight ornamental Salvia taxa

Volatile compounds from seven Salvia species and one interspecific hybrid growing at the Dallas Arboretum and Botanical Garden, Texas, US. Salvia coccinea, S. farinacea, S. greggii, S. leucantha, S. longispicata x farinacea, S. madrensis, S. roemeriana and S. splendens were investigated for their chemical compositions using a microdistillation technique. Volatiles were analyzed by gas chromatography (GC) and gas chromatography-mass spectrometry (GC/MS). One hundred and twenty seven compounds were identified representing 94.3-99.7% of the oils. The major components in each of the seven species were as follows: S. coccinea (Z)-3-hexenal (31%), viridiflorol (19%); S. farinacea 1-octen-3-ol (30%) and (Z)-3-hexenal (23%); S. greggii 1,8-cineole (22%), borneol (17%), camphene (11%) and alpha-pinene (10%); S. leucantha limonene (35%) and alpha-pinene (17%); S. longispicata x farinacea 1-octen-3-ol (50%) and (Z)-3-hexenal (24%); S. madrensis (Z)-3-hexenal (53%); S. roemeriana limonene (49%) and alpha-pinene (20%); and S. splendens (Z)-3-hexenal (36%), 2,5-dimethoxy-p-cymene (19%) and linalool (11%). The microdistillation method was fast, practical and a useful technique that enabled the isolation of the volatiles in samples when only limited quantities were available.