Semismooth Newton Methods for Solving Semi-Infinite Programming Problems

In this paper we present some semismooth Newton methods for solving the semi-infinite programming problem. We first reformulate the equations and nonlinear complementarity conditions derived from the problem into a system of semismooth equations by using NCP functions. Under some conditions a solution of the system of semismooth equations is a solution of the problem. Then some semismooth Newton methods are proposed for solving this system of semismooth equations. These methods are globally and superlinearly convergent. Numerical results are also given.     

Surface‐Bound Cucurbit[8]uril Catenanes on Magnetic Nanoparticles Exhibiting Molecular Recognition

We demonstrate the preparation of surface‐bound cucurbit[8]uril (CB[8]) catenanes on silica nanoparticles (NPs), where CB[8] was employed as a tethered supramolecular “handcuff” to selectively capture target guest molecules. In this catenane, CB[8] was threaded onto a methyl viologen (MV²⁺) axle and immobilized onto silica NPs. The formation of CB[8] catenanes on NPs were confirmed by UV/Vis titration experiments and lithographic characterization, demonstrating a high density of CB[8] on the silica NPs surface, 0.56 nm^?2. This CB[8] catenane system exhibits specific molecular recognition towards certain aromatic molecules such as perylene bis(diimide), naphthol and aromatic amino acids, and thus it can act as a nanoscale molecular receptor for target guests. Furthermore, we also demonstrate its use as an efficient and recyclable nano‐platform for peptide separation. By embedding magnetic NPs inside silica NPs, separation could be achieved by simply applying an external magnetic field. Moreover, the peptides captured by the catenanes could be released by reversible single‐electron reduction of MV²⁺. The entire process demonstrated high recoverability.     

ON THE STATISTICAL MECHANICS OF PROBABILISTIC MODELS OF NEURAL NETWORKS

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Controlling the structure and photophysics of fluorophore dimers using multiple cucurbit[8]uril clampings

A modular strategy has been employed to develop a new class of fluorescent molecules, which generates discrete, dimeric stacked fluorophores upon complexation with multiple cucurbit[8]uril macrocycles. The multiple constraints result in a “static” complex (remaining as a single entity for more than 30 ms) and facilitate fluorophore coupling in the ground state, showing a significant bathochromic shift in absorption and emission. This modular design is surprisingly applicable and flexible and has been validated through an investigation of nine different fluorophore cores ranging in size, shape, and geometric variation of their clamping modules. All fluorescent dimers evaluated can be photo-excited to atypical excimer-like states with elongated excited lifetimes (up to 37 ns) and substantially high quantum yields (up to 1). This strategy offers a straightforward preparation of discrete fluorophore dimers, providing promising model systems with explicitly stable dimeric structures and tunable photophysical features, which can be utilized to study various intermolecular processes.

Dimerisation of a wide range of fluorophores through multiple CB[8] clampings leads to constrained intracomplex motion and distinct photophysical properties.     

Quantitative Supramolecular Heterodimerization for Efficient Energy Transfer

The challenge of quantitatively forming self‐assembled heterodimers without other equilibrium by‐products is overcome through self‐sorting favored by the introduction of designed shape‐complementary moieties. Such a supramolecular strategy based on cucurbit[8]uril‐directed dimerization is further applied to generate hetero‐chromophore dimers quantitatively, leading to efficient energy transfer (>85 %) upon photoexcitation.     

A nonnegativity preserving algorithm for multilinear systems with nonsingular ℳ ${\mathcal M}$ -tensors

Numerical Algorithms - This paper addresses multilinear systems of equations which arise in various applications such as data mining and numerical partial differential equations. When the...     

Bolaamphiphiles bearing bipyridine as mesogenic core: rational exploitation of molecular architectures for controlled self-assembly

A bolaamphiphile (5,5-B2NBr8) bearing a functional bipyridine moiety as the mesogenic core is reported for the first time. 5,5-B2NBr8 was found to self-assemble into uniform fibrous structure in aqueous solution, when the concentration was higher than cmc. Analogues of 5,5-B2NBr8 with structural differences in chain length, headgroup, mesogenic core, and substituted position were synthesized, elucidating that small variances of the molecular structure could lead to dramatic changes of the resulting assemblies. For example, compound 4,4-B2NBr8 showed only spherical colloidal aggregates rather than fibers as 5,5-B2NBr8 did, while the only difference between them was the position at which the alkyl chains were attached onto bipyridine. A probable model for the fibrous structure of 5,5-B2NBr8 was proposed. Moreover, exploiting the coordination capacity of bipyridine, assembly and disassembly of 5,5-B2NBr8 could be reversibly controlled through the addition of EDTA and Cu(II), respectively.     

Reversible algorithm of simulating multivariate densities with multi-hump

To simulate a multivariate density with multi-hump, Markov chain Monte Carlo method encounters the obstacle of escaping from one hump to another, since it usually takes extraordinately long time and then becomes practically impossible to perform. To overcome these difficulties, a reversible scheme to generate a Markov chain, in terms of which the simulated density may be successful in rather general cases of practically avoiding being trapped in local humps, was suggested.     

The symmetry of diffusions and the circulations of their projection processes

The projection process along a simple closed smooth curve of a nonexplosive diffusion process on a cornplete Riemannian manifold is defined in probabilistic way. The winding numbers of the pmjection process are clockwise and counterclockwise given. The symmetry of the diffusion process is shown to be equivalent to that for any closed smooth curve. the long time average winding numbers of the projection process in two different directions are equal. Project supported by the National Natural Science Foundation of China (Grant No. 19571045) and the Doctoral Prcgram Foundation of Institution of Higher Education and 863 Program.