The Degree Preserving Spanning Tree Problem: Valid Inequalities and Branch-and-cut method

Given a connected undirected graph G, the Degree Preserving Spanning Tree Problem (DPSTP) consists in finding a spanning tree T of G that maximizes the number of vertices that have the same degree in T and in G. In this paper, we introduce Integer Programming formulations, valid inequalities and a Branch-and-cut algorithm for the DPSTP. Reinforced with new valid inequalities, the upper bounds provided by the formulation behind our Branch-and-cut method dominate previous DPSTP bounds in the literature.     

SINGLE AND DOUBLE EDGE INTERFACE CRACK SOLUTIONS FOR ARBITRARY FORMS OF MATERIAL COMBINATION

In this paper interfacial edge crack problems are considered by the application of the finite element method. The stress intensity factors are accurately determined from the ratio of crack-tip-stress value between the target given unknown and reference problems. The reference problem is chosen to produce the singular stress fields proportional to those of the given unknown problem. Here the original proportional method is improved through utilizing very refined meshes and post-processing technique of linear extrapolation. The results for a double-edge interface crack in a bonded strip are newly obtained and compared with those of a single-edge interface crack for different forms of combination of material. It is found that the stress intensity factors should be compared in the three different zones of relative crack lengths. Different from the case of a cracked homogeneous strip, the results for the double edge interface cracks are found to possibly be bigger than those for a single edge interface crack under the same relative crack length.     

A hybrid level set method for modelling detonation and combustion problems in complex geometries

We present an accurate and fast wave tracking method that uses parametric representations of tracked fronts, combined with modifications of level set methods that use narrow bands. Our strategy generates accurate computations of the front curvature and other geometric properties of the front. We introduce data structures that can store discrete representations of the location of the moving fronts and boundaries, as well as the corresponding level set fields, that are designed to reduce computational overhead and memory storage. We present an algorithm we call stack sweeping to efficiently sort and store data that is used to represent orientable fronts. Our implementation features two reciprocal procedures, a forward ‘front parameterization’ that constructs a parameterization of a front given a level set field and a backward ‘field construction’ that constructs an approximation of the signed normal distance to the front, given a parameterized representation of the front. These reciprocal procedures are used to achieve and maintain high spatial accuracy. Close to the front, precise computation of the normal distance is carried out by requiring that displacement vectors from grid points to the front be along a normal direction. For front curves in two dimensions, a cubic interpolation scheme is used, and G ¹ surface parameterization based on triangular patches is used for the three-dimensional implementation to compute the distances from grid points near the front. To demonstrate this new, high accuracy method we present validations and show examples of combustion-like applications that include detonation shock dynamics, material interface motions in a compressible multi-material simulation and the Stephan problem associated with dendrite solidification.     

Effect of spacer length on mesomorphic behaviours of chiral liquid crystal compounds containing (-)-menthyl

ABSTRACT

A homologous series of new chiral liquid crystal compounds, MnBEB (n = 4–10), was prepared by covalently linking a chiral (–)-menthyl with biphenyl-benzoate via a dicarboxylic spacer of varying length and parity. A combination of analysis methods, such as FT-IR, ¹H NMR spectra, differential scanning calorimetry (DSC), polarised optical microscopy (POM) and X-ray diffraction was carried out to systematically investigate their phase structures and phase transition behaviours. The length and parity of the flexible spacers has a profound influence on the T_m and T_c and a modest odd-even effect is observed for the chiral liquid crystal compounds MnBEB. Only compound M4BEB developed an N* phase with selectively reflection on heating and a blue phase on cooling process. In addition, increasing the length of the flexible spacers tends to narrow the temperature range of the N* phase and widen the smectic phase, moreover, the pitch becomes longer with the spacer increases.     

Nile Red and Nile Blue: Applications and Syntheses of Structural Analogues

Nile red and Nile blue are highly fluorescent and photostable organic dyes from the benzo[a]phenoxazine family. They have been used as histological stains for imaging lysosomes and lipids in vitro. The dyes’ high quantum yields and solvent‐dependent optical properties make them ideal scaffolds for the development of pH probes and local polarity indicators. Reviews of the literature in this area are scarce with only one review ever published in 2006. It has been 10 years since and the field has evolved. This review aims to expand upon topics covered by the previous reviewers and to report on recent advances in the literature. As authors, we hope to convey a sense of scope and to spark renewed interest in this useful niche of dye chemistry.     

Efficient removal of crystal violet and methylene blue from wastewater by ultrasound nanoparticles Cu-MOF in comparison with mechanosynthesis method

The present investigation reports the synthesis of CuBTC (BTC = 1,3,5-benzenetricarboxylate) metal–organic frameworks (MOFs) under solid-state conditions and ultrasound irradiation. Herein, we study uptake and release properties of crystal violet (CV) and methylene blue (MB) from ultrasound nano-CuBTC MOF in comparison with mechanosynthesis method (bulk structure). The ultrasound-assisted methods give a decrease in the surface area as calculated from the reduced nitrogen adsorption capability. In comparison, the uptake of guest molecules on ultrasound nano-CuBTC is remarkable and clearly exceeds that of bulk structure in the aqueous solution of guests. In bulk compound the channel length is increased so that the amount of adsorption is decreased a little. The small guest enters and leaves the cavity rapidly, whereas larger guests enter slowly due to their size relative to the size of the gaps in the capsule. As a result, the uptake and release of MB from CuBTC is faster than that of CV.     

List star edge coloring of k-degenerate graphs

A star edge coloring of a graph is a proper edge coloring such that every connected 2-colored subgraph is a path with at most 3 edges. Deng et al. and Bezegová et al. independently show that the star chromatic index of a tree with maximum degree $\Delta$ is at most $?\frac{3\Delta }{2}?$, which is tight. In this paper, we study the list star edge coloring of $k$-degenerate graphs. Let $c{h}_{st}^{\prime }\left(G\right)$ be the list star chromatic index of $G$: the minimum $s$ such that for every $s$-list assignment $L$ for the edges, $G$ has a star edge coloring from $L$. By introducing a stronger coloring, we show with a very concise proof that the upper bound on the star chromatic index of trees also holds for list star chromatic index of trees, i.e. $c{h}_{st}^{\prime }\left(T\right)\le ?\frac{3\Delta }{2}?$ for any tree $T$ with maximum degree $\Delta$. And then by applying some orientation technique we present two upper bounds for list star chromatic index of $k$-degenerate graphs.