Pure tetrahedral quadruple systems with index two

An oriented tetrahedron defined on four vertices is a set of four cyclic triples with the property that any ordered pair of vertices is contained in exactly one of the cyclic triples. A tetrahedral quadruple system of order $n$ with index $\lambda$, denoted by ${\text{TQS}}_{\lambda }\left(n\right)$, is a pair $\left(X,\mathrm{?}\right)$, where $X$ is an $n$‐set and $\mathrm{?}$ is a set of oriented tetrahedra (blocks) such that every cyclic triple on $X$ is contained in exactly $\lambda$ members of $\mathrm{?}$. A ${\text{TQS}}_{\lambda }\left(n\right)$ is pure if there do not exist two blocks with the same vertex set. When $\lambda =1$, the spectrum of a pure TQS $\left(n\right)$ has been completely determined by Ji. In this paper, we show that there exists a pure ${\text{TQS}}_2\left(n\right)$ if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$. A corollary is that a simple ${\text{QS}}_4\left(n\right)$ also exists if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$.     

Time-dependent Ginzburg–Landau equations for multi-gap superconductors

We numerically solve the time-dependent Ginzburg–Landau equations for two-gap superconductors using the finite-element technique. The real-time simulation shows that at low magnetic field, the vortices in small-size samples tend to form clusters or other disorder structures. When the sample size is large, stripes appear in the pattern. These results are in good agreement with the previous experimental observations of the intriguing anomalous vortex pattern, providing a reliable theoretical basis for the future applications of multi-gap superconductors.     

Comprehensive Profiling by Non-targeted Stable Isotope Tracing Capillary Electrophoresis-Mass Spectrometry: A New Tool Complementing Metabolomic Analyses of Polar Metabolites

Mass spectrometry (MS) driven metabolomics is a frequently used tool in various areas of life sciences; however, the analysis of polar metabolites is less commonly included. In general, metabolomic analyses lead to the detection of the total amount of all covered metabolites. This is currently a major limitation with respect to metabolites showing high turnover rates, but no changes in their concentration. Such metabolites and pathways could be crucial metabolic nodes (e.g., potential drug targets in cancer metabolism). A stable-isotope tracing capillary electrophoresis–mass spectrometry (CE-MS) metabolomic approach was developed to cover both polar metabolites and isotopologues in a non-targeted way. An in-house developed software enables high throughput processing of complex multidimensional data. The practicability is demonstrated analyzing [U-¹³C]-glucose exposed prostate cancer and non-cancer cells. This CE-MS-driven analytical strategy complements polar metabolite profiles through isotopologue labeling patterns, thereby improving not only the metabolomic coverage, but also the understanding of metabolism.     

Functionalized Silver-Ion-Mediated α-dC/β-dC Hybrid Base Pairs with Exceptional Stability: α-d-5-Iodo-2′-Deoxycytidine and Its Octadiynyl Derivative in Metal DNA

Silver-mediated α-dC–Ag⁺–β-dC hybrid base pairs decorated with 5-iodo- or 5-octadiynyl residues are well accommodated in duplex DNA. A strong T_m increase and favorable thermodynamic data for duplex DNA were observed after addition of silver ions. The phenomenon is particularly obvious when both nucleobases of the base pairs are functionalized. Neither the position of the base pair, nor the type of 5-substituent had a negative influence. On the contrary, functionalization of conventional silver-mediated β-dC–Ag⁺–β-dC homo base pairs showed a negative impact induced by the bulky substituents. To this end, cytosine modified 12-mer oligodeoxynucleotides were prepared by solid-phase synthesis employing new α-anomeric 2′-deoxycytidine phosphoramidites. A multigram scale synthesis was developed for 5-iodo-α-d -2′-deoxycytidine ( 1 ) employing the direct glycosylation of cytosine with Hoffer's α-d -halogenose followed by separation of anomeric DMT nucleosides. Regarding base-pair stability and functionalization silver-mediated α/β-dC hybrid base pairs were found to be superior to β/β-dC homo pairs. According to their extraordinary properties, they might find applications in DNA diagnostics, material science, or nanotechnology.     

Boundedness of semilinear Duffing equations at resonance in a critical situation

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation $\ddot{x}+n^{2}x+g(x)=p(t)$ with the critical situation that $|{\int }_0^{2\pi }p(t)e^{?int}dt|=2|g(+\infty )?g(?\infty )|$ on g and p, where $n\in {\mathbb{N}}^{+}$, $p(t)$ is periodic and $g(x)$ is bounded.     

Microtextures Induced by Nanosecond Laser on Ni–Co Alloy Coatings

Ni–Co alloys have a wide range of applications in various fields owning to their excellent physical, chemical, and mechanical properties. In this paper, we prepare Ni–Co alloy coatings on 316L stain steel surfaces by electroplating. We present a novel approach utilizing a nanosecond laser to induce microtextures on Ni–Co alloy coatings. We study experimentally the effects of laser power and scanning rate on the surface morphologies of Ni–Co alloy coatings. The results indicate that the shape and size of induced microtextures can be controlled by the laser power and scanning rate. The size of grains increases with increase in the work current of the laser (WCL) at a certain scanning rate. With the WCL constant, the size of grains decreases with increase in scanning rate while their average height increases. It is a simple and easily-controlled method for the fabrication of microstructures on Ni–Co alloy coatings, which has promising applications in investigations of the properties of microtextured surfaces, such as friction, adhesion, and wetting.     

Real-time phase measurement and correction of dynamic multimode beam using a single spatial light modulator

In this Letter,a novel system for adaptively correcting the phase of a dynamic multimode beam is proposed.While using merely one spatial light modulator,the phase measurement of the first-order diffraction pattern and the correction of the zeroth diffraction order are simultaneously realized.The real-time experimental result is obtained at a control rate of 10 Hz.The power-in-the-bucket value is improved from 38.5%to 61.8%,even with fundamental mode content that is consistently below 30%.To the best of our knowledge,this is the first implementation of real-time adaptive correction of the entire multimode beam.     

Crosslinked poly(ethylene oxide) containing siloxanes fabricated through thiol‐ene photochemistry

Homogenous amphiphilic crosslinked polymer films comprising of poly(ethylene oxide) and polysiloxane were synthesized utilizing thiol‐ene “ click ” photochemistry. A systematic variation in polymer composition was Carried out to obtain high quality films with varied amount of siloxane and poly(ethylene oxide). These films showed improved gas separation performance with high gas permeabilities with good CO₂/N₂ selectivity. Furthermore, the resulting films were also tested for its biocompatibility, as a carrier media which allow human adult mesenchymal stem cells to retain their capacity for osteoblastic differentiation after transplantation. The obtained crosslinked films were characterized using differential scanning calorimetry, dynamic mechanical analysis, thermogravimetric analysis, FTIR, Raman‐IR , and small angle X‐ray scattering. The synthesis ease and commercial availability of the starting materials suggests that these new crosslinked polymer networks could find applications in wide range of applications. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1548–1557     

Convergence of the viscosity solution of non-autonomous Hamilton-Jacobi equations

In this paper,we investigate the non-autonomous Hamilton-Jacobi equation ■ where H is 1-periodic with respect to t and M is a compact Riemannian manifold without boundary.We obtain the viscosity solution denoted by T_(t_0)~tφ(x) and show T_(t_0)~tφ(x) converges uniformly to a time-periodic viscosity solution u~*(x,t) of ?_tu+H(t,x,?_xu,u)=0.