Curved traversable wormholes in (3+1)-dimensional spacetime

We present the general method of constructing curved traversable wormholes in (3+1)-d spacetime and proceed to thoroughly discuss the physics of a zero tidal force metric without cross-terms. The (3+1)-d solution is compared with the recently studied lower-dimensional counterpart, where we identify that the much richer physics—involving pressures and shear forces of the mass-energy fluid supporting the former—is attributed to the mixing of all three spatial coordinates. Our (3+1)-d universe is the lowest dimension where such nontrivial terms appear. An explicit example, the static zero tidal force (3+1)-d catenary wormhole is analysed and we show the existence of a geodesic through it supported locally by non-exotic matter, similar to the (2+1)-d version. A key difference is that positive mass-energy is used to support the entire (3+1)-d catenary wormhole, though violation of the null energy condition in certain regions is inevitable. This general approach of first constructing the geometry of the spacetime and then using the field equations to determine the physics to support it has the potential to discover new solutions in general relativity or to generalise existing ones. For instance, the metric of a time-evolving inflationary wormhole with a conformal factor can actually be geometrically constructed using our method.     

Impact of quantum–classical correspondence on entanglement enhancement by single-mode squeezing

Quantum entanglement between two field modes can be achieved through the collective squeezing of the two respective modes. If single-mode squeezing is performed prior to such a two-mode squeezing, an enhancement of entanglement production can happen. Interestingly, the occurrence of this enhancement can be implicitly linked to the local classical dynamical behavior via the paradigm of quantum–classical correspondence. In particular, the entanglement generated through quantum chaos is found to be hardly enhanced by prior squeezing, since it is bounded by the saturation value of the maximally entangled Schmidt state with fixed energy. These results illustrate that entanglement enhancement via initial squeezing can serve as a useful indicator of quantum chaotic behaviour.     

Color-encoded microcarriers based on nano-silicon dioxide film for multiplexed immunoassays

Multiplexed analysis allows researchers to obtain high-density information with minimal assay time, sample volume and cost. Currently, microcarrier or particle-based approaches for multiplexed analysis involve complicated or expensive encoding and decoding processes. In this paper, a novel optical encoding technique based on nano-silicon dioxide film is presented. Microcarriers composed of thermally grown silicon dioxide (SiO(2)) film and monocrystalline silicon (Si) substrate were fabricated. The nano-silicon dioxide film exhibited unique surface color by low-coherence interference. Hence the colors can be used for encoding at least 100 microcarriers loaded with films of different thickness. We demonstrated that color-encoded microcarriers loaded with antigens could be used for multiplexed immunoassays to detect goat anti-human IgG, goat anti-mouse IgG and goat anti-rabbit IgG, with fluorescent detection as the interrogating approach. This microcarrier-based method also exhibited improved analytical performance compared with a microarray technique. This approach will provide new opportunities for multiplexed target assay development.     

Highly regioselective and practical synthesis of 1-acyl-5-hydroxypyrazolines and 1-acyl pyrazoles from 1,2-allenic ketones and hydrazides

A mild and highly regioselective synthesis of 1-acyl-5-hydroxypyrazolines has been achieved through the condensation of 1,2-allenic ketones with hydrazides in the absence of any catalyst. Moreover, the obtained 1-acyl-5-hydroxypyrazolines can be easily transformed into 1-acyl pyrazoles under the promotion of BF₃·Et₂O. It was also found that 1-acyl pyrazoles can be produced directly from allenic ketones and hydrazides through a one-pot procedure.     

Quantum chemical topology investigation on structure, electronic properties and interaction of CuNg n + (n?=?1–3, Ng?=?He, Ne)

The structures and stabilities of title clusters have been investigated at CCSD(T) computational level. For the title systems, the geometry with high symmetry is preferred and the n?=?2 systems are more stable than its neighbors. For the Cu?CNg interaction, topological analysis of the electron density field, electron localization function, and positive local energy density represent the intermediate interaction type $ \left( {\nabla^{2}{}_{(3,\; - 1)} \rho > 0\; {\text{and}}\;E\left( r \right) < 0} \right) $ . The interaction region is located by generating reduced density gradient isosurface in the real molecular space.     

Polymerization of water-in-oil microemulsions: Methyl methacrylate,acrylic acid,and sodium acrylamidostearate

Water-in-oil (w/o) microemulsions of methyl methacrylate (MMA), acrylic acid (AA), sodium acrylamidostearate (NaAAS), and water were investigated. MMA, AA, and NaAAS could be terpolymerized in these microemulsions. For a composition of 54% MMA, 34% AA, 2% NaAAS, and 10% H₂O, polymers of high molecular weights of about 1,000,000 were obtained between 3.5 to 24% polymer conversion. The system became a transparent gel when conversion exceeded 36%. Transparent solid terpolymer containing water up to 16% were also obtained after fully polymerizations of certain compositions.     

Total chromatic number of complete r-partite graphs

Rosenfeld (1971) proved that the Total Colouring Conjecture holds for balanced complete r-partite graphs. Bermond (1974) determined the exact total chromatic number of every balanced complete r-partite graph. Rosenfeld's result had been generalized recently to complete r-partite graphs by Yap (1989). The main result of this paper is to prove that the total chromatic number of every complete r-partite graph G of odd order is Δ (G) + 1. This result gives a partial generalization of Bermond's theorem.     

Maximal points with respect to cone dominance in Banach spaces and their existence

Given a convex cone in a Banach spaceV, an examination of the cone maximal points of a setX inV (with respect to the cone dominance induced by ) with respect to their characterization and existence is undertaken. The totality of cone maximal points ofX is called the conical frontier ofX. Comparisons of the conical frontiers of related sets and corresponding to related cones are made. By relaxing the compactness requirements of the underlying setX and by assuming some cone-related weaker forms of compactness, existence theorems for cone maximal points are developed. These theorems are believed to be generalizations of the existing results in one way or another.Maximizing points onX of certain linear functionals in the dual cone * of provide natural examples of cone maximal points. Properties characterizing a maximizing point of a linear functional in *, including the generalized version of Geoffrion's characterization of proper efficiency, are compiled and proved to be valid characterizations. Functionals in * with special properties are studied. Existence theorems are also obtained for the maximizing points of these functionals.The author is indebted to Professor James V. Whittaker for helpful discussions and comments and to Professors P. S. Bullen, C. W. Clark, B. N. Moyls, and F. Y. M. Wan for their encouragement and support.