Hubbard model on the triangular lattice: spiral order and spin liquid

We investigate the half-filled Hubbard model on an isotropic triangular lattice with the variational cluster approximation. By decreasing the on-site repulsion U (or equivalently increasing pressure) we go from a phase with long-range, three-sublattice, spiral magnetic order, to a nonmagnetic Mott insulating phase--a spin liquid--and then, for U less or similar to 6.7t, to a metallic phase. Clusters of sizes 3, 6, and 15 with open boundary conditions are used in these calculations, and an extrapolation to infinite size is argued to lead to a disordered phase at U = 8t, but to a spiral order at U greater or similar to 12.     

Some Properties of Certain Subgroups of Tensor Squares of p-Groups

Let G be a finite p-group of order p ⁿ and ?(G) be the subgroup of the tensor square of G generated by all symbols x ? x, for all x in G. In the present article, we construct an upper bound for the order of ?(G) and any extra special p-group. It is also shown that ?(G) ? ?(G/G′). Using our result, we obtain the explicit structure of the tensor square of G and π₃ SK(G, 1). Finally, the structure of G will be characterized when the bound is attained.     

Some new extensions of Edelstein-Suzuki-type fixed point theorem to G-metric and G-cone metric spaces

In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 (1962), 74–79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.     

Rarefaction effects in thermally-driven microflows

Rarefied gas flow in a parallel-plate micro-channel is considered, where a streamwise constant temperature gradient is applied in the channel walls. An analytical approach to the problem is conducted based on linearized and semi-linearized forms of the regularized 13-moment equations (R13 equations), which are a set of macroscopic transport equations for rarefied gases at the super-Burnett order. Typical nonequilibrium effects at the boundary, i.e., velocity slip, temperature jump, and formation of Knudsen boundary layers are investigated. Nonlinear contributions lead to temperature, density, and normal stress profiles across the channel which are not reported elsewhere in literature.     

Strong Convergence of a Split Common Fixed Point Problem

In this article, we present a new general algorithm for solving the split common fixed point problem in an infinite dimensional Hilbert space, which is to find a point which belongs to the common fixed point of a family of quasi-nonexpansive mappings such that its image under a linear transformation belongs to the common fixed point of another family of quasi-nonexpansive mappings in the image space. We establish the strong convergence for the algorithm to find a unique solution of the variational inequality, which is the optimality condition for the minimization problem. The algorithm and its convergence results improve and develop previous results in this field.     

New fixed point theorems for $${\alpha}$$-$${H\Theta}$$HΘ-contractions in ordered metric spaces

Recently, Jleli and Samet [J. Inequal. Appl. (2014), 2014:38] introduced and studied a new contraction to prove a generalization of the Banach contraction principle. In this paper, we introduce the concept of \({\alpha}\)-\({H\Theta}\)-contraction with respect to a general family of functions H and we establish Jleli–Samet-type fixed point results in metric and ordered metric spaces. As an application of our results we deduce Suzuki-type fixed point results for \({H\Theta}\)-contractions. We also derive certain fixed and periodic point results for orbitally continuous generalized \({\Theta}\)-contractions. Moreover, we present an illustrative example to highlight the obtained improvements.     

A Hydrogel Microneedle Assay Combined with Nucleic Acid Probes for On-Site Detection of Small Molecules and Proteins

Point-of-care testing (POCT) of clinical biomarkers is critical to health monitoring and timely treatment, yet biosensing assays capable of detecting biomarkers without the need for costly external equipment and reagents are limited. Blood-based assays are, specifically, challenging as blood collection is invasive and follow-upprocessing is required. Here, we report a versatile assay that employs hydrogel microneedles (HMNs) to extract interstitial fluid (ISF), in a minimally invasive manner integrated with graphene oxide-nucleic acid (GO.NA)-based fluorescence biosensor to sense the biomarkers of interest in situ. The HMN-GO.NA assay is supplemented with a portable detector, enabling a complete POCT procedure. Our system could successfully measure four clinically important biomarkers (glucose, uric acid (UA), insulin, and serotonin) ex vivo, in addition, to accurately detecting glucose and UA in vivo.     

A new and efficient one-pot procedure for the synthesis of 2-styrylquinolines

A one-pot combination of a modified Friedländer annulation and a Knoevenagel condensation provides 2-styrylquinolines in good to excellent yields. A variety of substrates are reacted in one-pot in the presence of 1-methylimidazolium trifluoroacetate ([Hmim]TFA).     

Super-resolution and Raman chemical imaging: from multiple low resolution images to a high resolution image

Imaging in Raman spectroscopy is a valuable tool for analytical chemistry. Although molecular characterization at micron level is achieved for many applications, it usually fails producing chemical images of micron size samples as expected in chemical, environmental and biological analysis. The aim of the work is to introduce the potential of super-resolution in vibrational spectroscopic imaging. This original chemometrics approach uses several low resolution images of the same sample in order to retrieve a higher resolution chemical image. It is thus possible to overcome in a certain way some physical and instrumentals limitations. To illustrate the methodology, sub-micronic details of a Si/Au sample are retrieved from low resolution images with different super-resolution algorithms. The better results are obtained with Iterative L2/Bilateral Total Variation regularization method. The use of a regularization procedure gives also better results since its first property is to preserve edges during the reconstruction of the super-resolved image. This concept of chemical image data processing should open new analytical opportunities.