Conformal upper bounds for the eigenvalues of the Laplacian and Steklov problem

In this paper, we find upper bounds for the eigenvalues of the Laplacian in the conformal class of a compact Riemannian manifold (M,g). These upper bounds depend only on the dimension and a conformal invariant that we call “min-conformal volume”. Asymptotically, these bounds are consistent with the Weyl law and improve previous results by Korevaar and Yang and Yau. The proof relies on the construction of a suitable family of disjoint domains providing supports for a family of test functions. This method is interesting for itself and powerful. As a further application of the method we obtain an upper bound for the eigenvalues of the Steklov problem in a domain with C¹ boundary in a complete Riemannian manifold in terms of the isoperimetric ratio of the domain and the conformal invariant that we introduce.     

An easily accessible Re-based catalyst for the selective conversion of methanol: evidence for an unprecedented active site structure through combined operando techniques

Heterogeneous Re/SiO(2) catalysts prepared using a one pot sol-gel synthesis were found to display high activity in the direct, selective methanol conversion to methylal, which is correlated to an unprecedented rhenium oxide structure.     

An Improved Hybrid Adjoint Method in External Aerodynamics Using Variational Technique for the Boundary Integral Based Optimal Objective Function Gradient

An improved hybrid adjoint method to the viscous, compressible Reynold-Averaged Navier-Stokes Equation (RANS) is developed for the computation of objective function gradient and demonstrated for external aerodynamic design optimization. In this paper, the main idea is to extend the previous coupling of the discrete and continuous adjoint method by the grid-node coordinates variation technique for the computation of the variation in the gradients of flow variables. This approach in combination with the Jacobian matrices of flow fluxes refrained the objective function from field integrals and coordinate transformation matrix. Thus, it opens up the possibility of employing the hybrid adjoint method to evaluate the subsequent objective function gradient analogous to many shape parameters, comprises of only boundary integrals. This avoids the grid regeneration in the geometry for every surface perturbation in a structured and unstructured grid. Hence, this viable technique reduces the overall CPU cost. Moreover, the new hybrid adjoint method has been successfully applied to the computation of accurate sensitivity derivatives. Finally, for the investigation of the presented numerical method, simulations are carried out on NACA0012 airfoil in a transonic regime and its accuracy and effectiveness related to the new gradient equation have been verified with the Finite Difference Method (FDM). The analysis reveals that the presented methodology for the optimization provides the designer with an indispensable CPU-cost effective tool to reshape the complex geometry airfoil surfaces, useful relative to the state-of-the-art, in a less computing time.     

Selected Reactions of Diethyl (E)‐1‐(bromomethyl)‐2‐cyanovinylphosphonate with Secondary and Tertiary Amines

An easy regio‐ and stereoselective synthesis of new nitrogenous molecules 2a–e was successfully realized via an effective coupling reaction of diethyl (E)‐1‐(bromomethyl)‐2‐cyanovinylphosphonate 1 with various secondary amines in methanol. Hence, the use of less and more bulky secondary amines gives rise, respectively, to the successive (S_N2′) substitution–isomerization and (S_N2) substitution derivatives 2a–c and 2d–e . Moreover, the addition of tertiary amines to 1 in the same reaction conditions, leads exclusively to the rearranged vinyl ether 3 in good yields.     

Immunoassays Based on Surface-Enhanced Fluorescence using Gap-Plasmon-Tunable Ag Bilayer Nanoparticle Films

A novel gap-plasmon-tunable Ag bilayer nanoparticle film for immunoassays is demonstrated. Different from a traditional Ag monolayer nanoparticle film, a desired number of polyelectrolyte (PEL) layers are deposited on the nanoparticles before the self-assembly of a second Ag nanoparticle layer. Interestingly, by controlling the number of the PEL interlayers, the gap plasmon between the two Ag nanoparticle layers can be tuned across the visible spectral range. The ability of the presented Ag bilayer nanoparticle films in fluorescence enhancement has been examined experimentally. A maximal enhancement of around 15.4 fold was achieved when 7 layers of polyelectrolyte were used. When this optimal Ag bilayer nanoparticle film was applied to fluorescence immunoassay, a performance with approximately 3.3-fold enhancement was obtained compared with that performed on a traditional glass substrate. The experimental results suggest that the presented gap-plasmon tunable Ag bilayer nanoparticle films have great potential in fluorescence-based immunoassays. The method of the bilayer-film construction presented here also provides new insights into the rational design of the plasmonic substrates.     

Efficient Synthesis of New 2H‐Chromene Retinoids Hybrid Derivatives by Suzuki Cross‐coupling Reactions

In an attempt to improve anticancer activity, a series of retinoids–chromene hybrids was described. The novel heterocyclic chromene–retinoids hybrid including oxygen as a heteroatom in a six‐membered cyclic ring (2H‐chromene or 2H‐1‐benzopyran) was designed and synthesized by introducing different groups such as an aromatic or styrylphenyl ring in 6‐position of 2H‐chromene. These novel compounds were synthesized by using the efficient cascades one‐pot process involving Wittig–Horner–Emmons reaction and Suzuki–Miyaura cross‐coupling pallado‐catalyzed reactions with 60% to 90% overall yields. These new compounds were tested against glioblastoma multiforme brain cancer, medulloblastoma, neuroblastoma cell lines, and breast cancer MCF‐7 cell lines. Two of them exhibited an appreciable anti‐tumor activity in the low micromolar range, which opens new perspectives for therapeutic application on humans.     

An approximation of the analytical solution of the Jeffery-Hamel flow by decomposition method

Many researchers have been interested in application of mathematical methods to find analytical solutions of nonlinear equations and for this purpose, new methods have been developed. Since most of fluid mechanics problems due to boundary layer are strongly nonlinear, so analytical solution of them is confronted with some difficulty. In this Letter, the Jeffery-Hamel flow—a nonlinear equation of 3rd order—is studied by Adomian decomposition method. After introducing Adomian decomposition method and the way of obtaining Adomian's polynomial, we solved the problem for divergent and convergent channels. Finally, velocity distribution and shear stress constant is depicted at various Reynolds numbers and comparing our results with some earlier works illustrated their excellent accuracy.     

Thiourea Derivatives,Simple in Structure but Efficient Enzyme Inhibitors and Mercury Sensors

In this study six unsymmetrical thiourea derivatives, 1-isobutyl-3-cyclohexylthiourea (1), 1-tert-butyl-3-cyclohexylthiourea (2), 1-(3-chlorophenyl)-3-cyclohexylthiourea (3), 1-(1,1-dibutyl)-3-phenylthiourea (4), 1-(2-chlorophenyl)-3-phenylthiourea (5) and 1-(4-chlorophenyl)-3-phenylthiourea (6) were obtained in the laboratory under aerobic conditions. Compounds 3 and 4 are crystalline and their structure was determined for their single crystal. Compounds 3 is monoclinic system with space group P2₁/n while compound 4 is trigonal, space group R³:H. Compounds (1–6) were tested for their anti-cholinesterase activity against acetylcholinesterase and butyrylcholinesterase (hereafter abbreviated as, AChE and BChE, respectively). Potentials (all compounds) as sensing probes for determination of deadly toxic metal (mercury) using spectrofluorimetric technique were also investigated. Compound 3 exhibited better enzyme inhibition IC₅₀ values of 50, and 60 µg/mL against AChE and BChE with docking score of −10.01, and −8.04 kJ/mol, respectively. The compound also showed moderate sensitivity during fluorescence studies.     

Dissolution of Cellulose and Lignin with Biobased Ionic Liquids

Journal of Solution Chemistry - Choline-based ionic liquids, involving various alkyl chains lengths and carboxylates derived from biobased acids, have been synthetized with high yields through a...     

A switchable ionic liquid with polarity swing-assisted regeneration properties used for the preconcentration of cadmium in biological samples

In the present study the cadmium (Cd) was determined in serum samples of psoriatic patients. The severity of psoriasis was evaluated according to criteria based on standard clinical diagnosis using Psoriasis Area Severity Index (PASI) score. In present study, an innovative tunable green solvent system based microextraction (TSS-ME) was applied for the enrichment of Cd in acid digested serum samples prior to determination with flame atomic absorption spectrometry. The hydrophobic complex of Cd-ammonium pyrrolidine thiocarbamate was extracted in a tunable solvent system which was prepared from a polybasic amine (N, N, N′, N′-tetramethyl-1, 4-diaminobutane), decanol and water system. The tunable green solvent system (TSS) which has zero ionic strength was converted to homogeneous monophasic polar hydrophilic phase via exposure to CO₂ at different pressure and time duration. Then hydrophobic enriched Cd- ammonium pyrrolidine thiocarbamate was back extracted, using HNO₃ (0.1 to 0.5 mol L⁻¹) then the second round of TSS-ME was applied. The acidic aqueous phase enrich with analyte was separated from tunable solvent. The separated TSS was easily reused for up to 10 time for preconcentration purposes without loss of its enrichment character. The smoker and nonsmoker psoriatic patients at PASI >10, have two to three folds higher Cd levels in serum samples than healthy persons.