Fabrications of hollow nanocubes of Cu(2)O and Cu via reductive self-assembly of CuO nanocrystals

In this work, a template-free synthetic approach for generating single-crystalline hollow nanostructures has been described. Using the small optical band-gap cuprous oxide Cu(2)O as a model case, we demonstrate that, instead of normally known spherical aggregates, primary nanocrystalline particles can first self-aggregate into porous organized solids with a well-defined polyhedral shape according to the oriented attachment mechanism, during which chemical conversion can also be introduced. In contrast to the spherical aggregates, where the nanocrystallites are randomly joined together, the Cu(2)O nanocrystallites in the present case are well organized, maintaining a definite geometric shape and a global crystal symmetry. Due to the presence of intercrystallite space, hollowing and chemical conversion can also be carried out in order to create central space and change the chemical phase of nanostructured polyhedrons. It has been revealed that Ostwald ripening plays a key role in the solid evacuation process. Using this synthetic strategy, we have successfully prepared single-crystal-like Cu(2)O nanocubes and polycrystalline Cu nanocubes with hollow interiors. For the first time, we demonstrate that nanostructured polyhedrons of functional materials with desired interiors can be synthesized in solution via a combination of oriented attachment and Ostwald ripening processes.     

N-Heterocyclic carbene catalyzed C-glycosylation: a concise approach from Stetter reaction

Described herein is the first example of an organocatalytic approach for acylanion addition to the anomeric carbon of 2-nitroglucal using an N-heterocyclic carbene catalyst. Control over the reaction conditions gives β-selective and nitro-eliminated C-glycosides, providing opportunities to produce new classes of C-glycoside.     

Subdifferential and optimality conditions for the difference of set-valued mappings

In this paper, an existence theorem of the subgradients for set-valued mappings, which introduced by Borwein (Math Scand 48:189?C204, 1981), and relations between this subdifferential and the subdifferential introduced by Baier and Jahn (J Optim Theory Appl 100:233?C240, 1999), are obtained. By using the concept of this subdifferential, the sufficient optimality conditions for generalized D.C. multiobjective optimization problems are established. And the necessary optimality conditions, which are the generalizations of that in Gadhi (Positivity 9:687?C703, 2005), are also established. Moreover, by using a special scalarization function, a real set-valued optimization problem is introduced and the equivalent relations between the solutions are proved for the real set-valued optimization problem and a generalized D.C. multiobjective optimization problem.     

Structures and Chromaticity of Extremal 3-Colourable Sparse Graphs

 Assume that G is a 3-colourable connected graph with e(G) = 2v(G) −k, where k≥ 4. It has been shown that s ₃(G) ≥ 2 ^{k −3}, where s _r (G) = P(G,r)/r! for any positive integer r and P(G, λ) is the chromatic polynomial of G. In this paper, we prove that if G is 2-connected and s ₃(G) < 2 ^{k −2}, then G contains at most v(G) −k triangles; and the upper bound is attained only if G is a graph obtained by replacing each edge in the k-cycle C _k by a 2-tree. By using this result, we settle the problem of determining if W(n, s) is χ-unique, where W(n, s) is the graph obtained from the wheel W _n by deleting all but s consecutive spokes. Received: January 29, 1999 Final version received: April 8, 2000     

Machine Learning Approaches for Metalloproteins

Metalloproteins are a family of proteins characterized by metal ion binding, whereby the presence of these ions confers key catalytic and ligand-binding properties. Due to their ubiquity among biological systems, researchers have made immense efforts to predict the structural and functional roles of metalloproteins. Ultimately, having a comprehensive understanding of metalloproteins will lead to tangible applications, such as designing potent inhibitors in drug discovery. Recently, there has been an acceleration in the number of studies applying machine learning to predict metalloprotein properties, primarily driven by the advent of more sophisticated machine learning algorithms. This review covers how machine learning tools have consolidated and expanded our comprehension of various aspects of metalloproteins (structure, function, stability, ligand-binding interactions, and inhibitors). Future avenues of exploration are also discussed.     

Thermal Degradation Kinetics and Modeling Study of Ultra High Molecular Weight Polyethylene (UHMWP)/Graphene Nanocomposite

The incorporation of nanofillers such as graphene into polymers has shown significant improvements in mechanical characteristics, thermal stability, and conductivity of resulting polymeric nanocomposites. To this aim, the influence of incorporation of graphene nanosheets into ultra-high molecular weight polyethylene (UHMWPE) on the thermal behavior and degradation kinetics of UHMWPE/graphene nanocomposites was investigated. Scanning electron microscopy (SEM) analysis revealed that graphene nanosheets were uniformly spread throughout the UHMWPE’s molecular chains. X-Ray Diffraction (XRD) data posited that the morphology of dispersed graphene sheets in UHMWPE was exfoliated. Non-isothermal differential scanning calorimetry (DSC) studies identified a more pronounced increase in melting temperatures and latent heat of fusions in nanocomposites compared to UHMWPE at lower concentrations of graphene. Thermogravimetric analysis (TGA) and derivative thermogravimetric (DTG) revealed that UHMWPE’s thermal stability has been improved via incorporating graphene nanosheets. Further, degradation kinetics of neat polymer and nanocomposites have been modeled using equations such as Friedman, Ozawa–Flynn–Wall (OFW), Kissinger, and Augis and Bennett’s. The "Model-Fitting Method” showed that the auto-catalytic nth-order mechanism provided a highly consistent and appropriate fit to describe the degradation mechanism of UHMWPE and its graphene nanocomposites. In addition, the calculated activation energy (E_a) of thermal degradation was enhanced by an increase in graphene concentration up to 2.1 wt.%, followed by a decrease in higher graphene content.     

Generalized Invexity and Generalized Invariant Monotonicity

In this paper, several kinds of invariant monotone maps and generalized invariant monotone maps are introduced. Some examples are given which show that invariant monotonicity and generalized invariant monotonicity are proper generalizations of monotonicity and generalized monotonicity. Relationships between generalized invariant monotonicity and generalized invexity are established. Our results are generalizations of those presented by Karamardian and Schaible.     

Liouville Action and Weil-Petersson Metric on Deformation Spaces, Global Kleinian Reciprocity and Holography

We rigorously define the Liouville action functional for the finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that classical action – the critical value of the Liouville action functional, considered as a function on the quasi-Fuchsian deformation space, is an antiderivative of a 1-form given by the difference of Fuchsian and quasi-Fuchsian projective connections. This result can be considered as global quasi-Fuchsian reciprocity which implies McMullen's quasi-Fuchsian reciprocity. We prove that the classical action is a Kähler potential of the Weil-Petersson metric. We also prove that the Liouville action functional satisfies holography principle, i.e., it is a regularized limit of the hyperbolic volume of a 3-manifold associated with a quasi-Fuchsian group. We generalize these results to a large class of Kleinian groups including finitely generated, purely loxodromic Schottky and quasi-Fuchsian groups, and their free combinations.     

Higher-order generalized convexity and duality in nondifferentiable multiobjective mathematical programming

In this paper, a class of generalized convexity is introduced and a unified higher-order dual model for nondifferentiable multiobjective programs is described, where every component of the objective function contains a term involving the support function of a compact convex set. Weak duality theorems are established under generalized convexity conditions. The well-known case of the support function in the form of square root of a positive semidefinite quadratic form and other special cases can be readily derived from our results.     

Sharp Minima for Multiobjective Optimization in Banach Spaces

We study sharp minima for multiobjective optimization problems. In terms of the Mordukhovich coderivative and the normal cone, we present sufficient and or necessary conditions for existence of such sharp minima, some of which are new even in the single objective setting.This research was supported by a Central Research Grant of The Hong Kong Polytechnic University (Grant No. G-T 507). Research of the first author was also supported by the National Natural Science Foundation of PR China (Grant No. 10361008) and the Natural Science Foundation of Yunnan Province, China (Grant No. 2003A002M).