Binuclear Uranium(VI) Complexes with a “Pacman” Expanded Porphyrin: Computational Evidence for Highly Unusual Bis‐Actinyl Structures

On the basis of uranyl complexes reacting with a polypyrrolic ligand (H₄L), we explored structures and reaction energies of a series of new binuclear uranium(VI) complexes using relativistic density functional theory. Full geometry optimizations on [(UO₂)₂(L)], in which two uranyl groups were initially placed into the pacman ligand cavity, led to two minimum‐energy structures. These complexes with cation–cation interactions (CCI) exhibit unusual coordination modes of uranyls: one is a T‐shaped ( T ) skeleton formed by two linear uranyls {O_exo?U₂?O_endo→U₁(?O_exo)₂}, and another is a butterfly‐like ( B ) unit with one linear uranyl coordinating side‐by‐side to a second cis‐uranyl. The CCI in T was confirmed by the calculated longest distance and lowest stretching vibrational frequency of U₂?O_endo among the four U?O bonds. Isomer B is more stable than T , for which experimental tetrameric analogues are known. The formation of B and T complexes from the mononuclear [(UO₂)(H₂L)(thf)] ( M ) was found to be endothermic. The further protonation and dehydration of B and T are thermodynamically favorable. As a possible product, we have found a trianglelike binuclear uranium(VI) complex having a O?U?O?U?O unit.     

确定聚类数目的一个准则

Aiming to provide an appropriate number K of clusters, in this paper, we propose a new criterion function - H criterion function, whose three properties have also been proved. We validate the performance of the H criterion function on one artificial dataset and three real-world datasets, and the results are almostly consistent with a previous method. The nonparametric criterion we proposed is intuitive, simple and the computational cost is acceptable.     

Monotonicity and best approximation in Orlicz-Sobolev spaces with the Luxemburg norm

Criteria for strict monotonicity, upper (lower) locally uniform monotonicity and uniform monotonicity of Orlicz-Sobolev spaces with the Luxemburg norm are given. Some applications to best approximation are presented.     

Global exponential stability analysis of Cohen–Grossberg neural network with delays

This brief presents new sufficient conditions of globally exponential stability of Cohen–Grossberg neural networks with time delays. The results are also compared with previously reported results in the literature, implying that the results obtained in this paper provide one more set of criteria for determining the global exponential stability of Cohen–Grossberg neural networks with time delays.     

Metric generalized inverse for linear manifolds and extremal solutions of linear inclusion in Banach spaces

Let X,Y be Banach spaces and M a linear manifold in X×Y={{x,y}∣x∈X,y∈Y}. The central problem which motivates many of the concepts and results of this paper is the problem of characterization and construction of all extremal solutions of a linear inclusion y∈M(x). First of all, concept of metric operator parts and metric generalized inverses for linear manifolds are introduced and investigated, and then, characterizations of the set of all extremal or least extremal solutions in terms of metric operator parts and metric generalized inverses of linear manifolds are given by the methods of geometry of Banach spaces. The principal tool in this paper is the generalized orthogonal decomposition theorem in Banach spaces.     

Complete classification of the direction loci for three-wave collinear quadratic parametric interactions in biaxial acentric crystals

One new topological classification of the phase-matching direction loci for sum/difference frequency generation in biaxial acentric crystals is presented. Based on nine fundamental axial wave constant mismatches, 12 locus indices are used to distinguish permissible direction loci. Totally 66 kinds of combined loci belonging to 30 main classes are found and categorized by a set of ternary-digit class symbols or equivalently by sequence numbers. They are well illustrated in a classification diagram, indicative of 170 possible transitions among the loci. By an analysis of the dispersion of refractive indices, the historic “optically well-behaved crystals” are redefined and improved with simplified classification diagrams and corresponding schematic stereographic projections.     

Complete rank theorem of advanced calculus and singularities of bounded linear operators

Let E and F be Banach spaces, f: U ⊂ E → F be a map of C ^r (r ⩾ 1), x ₀ ∈ U, and ft (x ₀) denote the FréLechet differential of f at x ₀. Suppose that f′(x ₀) is double split, Rank(f′(x ₀)) = ∞, dimN(f′(_{x 0})) > 0 and codimR(f′(x ₀)) s> 0. The rank theorem in advanced calculus asks to answer what properties of f ensure that f(x) is conjugate to f′(x ₀) near x ₀. We have proved that the conclusion of the theorem is equivalent to one kind of singularities for bounded linear operators, i.e., x ₀ is a locally fine point for f′(x) or generalized regular point of f(x); so, a complete rank theorem in advanced calculus is established, i.e., a sufficient and necessary condition such that the conclusion of the theorem to be held is given.      

Fluid–structure interaction analysis of flexible composite marine propellers

There is an increasing interest in the marine industry to use composites to improve the hydrodynamic and structural performance of naval structures. Composite materials have high strength-to-weight and stiffness-to-weight ratios, and the fiber orientations can be exploited to tailor the structural deformation to reduce the load and stress variations by automatically adjusting the shape of the structure. For marine propellers, the bending–twisting coupling characteristics of anisotropic composites can be exploited to passively tailor the blade rake, skew, and pitch distributions to improve propeller performance. To fully explore the advantages of composite marine propellers, a coupled boundary element (BEM) and finite element (FEM) approach is presented to study the fluid–structure interaction of flexible composite propellers in subcavitating and cavitating flows. An overview of the formulation for both the fluid and structural models is presented. Experimental validation studies are shown for two composite propellers tested at the Naval Surface Warfare Center (NSWCCD). The feasibility of passive hydroelastic tailoring of composite marine propellers is discussed.     

Monolayer and multilayer compact film formations on different substrates by physical deposition

Dissipative particle dynamics simulations are applied to investigate the monolayer and multilayer film formations on different solid substrates by physical deposition. The influences of the polymer concentration, the polymer chain length, the solvent quality, and the interactions between the polymer solution and the solid substrate surface on the film formation dynamics and the mechanism are studied in detail. The results are analyzed in terms of the thickness and the shape of the deposited film, the kinetics of phase separation in the polymer solution, and the contact angle formed between the polymer aggregations and the substrate surface. Moreover, we suggest two strategies, designing a deposition process analogous to “chemical titration” and physically blocking interlayer diffusion by a simple crosslinked network barrier, to deposit the compact monolayer and multilayer films with better quality, respectively. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 353–365, 2009     

有限维模李超代数$W(m,n,l,\underline{t})$的$\Theta$-型导子与导子超代数

本文总设$F$是$p>2$的域,我们在域$F$上构造了有限维模李超代数$W(m,n,l,\underline{t})$, 定义了$W(m,n,l,\underline{t})$的$\Theta$-型导子,进而确定了它导子超代数.