Global infimum of strictly convex quadratic functions with bounded perturbations

The problem of minimizing [(f)\tilde]=f+p{\tilde f=f+p} over some convex subset of a Euclidean space is investigated, where f(x) = x ^T Ax + b ^T x is strictly convex and |p| is only assumed to be bounded by some positive number s. It is shown that the function [(f)\tilde]{\tilde f} is strictly outer γ-convex for any γ > γ*, where γ* is determined by s and the smallest eigenvalue of A. As consequence, a γ*-local minimal solution of [(f)\tilde]{\tilde f} is its global minimal solution and the diameter of the set of global minimal solutions of [(f)\tilde]{\tilde f} is less than or equal to γ*. Especially, the distance between the global minimal solution of f and any global minimal solution of [(f)\tilde]{\tilde f} is less than or equal to γ*/2. This property is used to prove a roughly generalized support property of [(f)\tilde]{\tilde f} and some generalized optimality conditions.     

A new sinusoidal shear deformation theory for bending,buckling, and vibration of functionally graded plates

A new sinusoidal shear deformation theory is developed for bending, buckling, and vibration of functionally graded plates. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed sinusoidal shear deformation theory contains only four unknowns and has strong similarities with classical plate theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton’s principle. The closed-form solutions of simply supported plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the bending, buckling, and vibration responses of functionally graded plates.     

Control of Metal–Organic Framework Crystallization by Metastable Intermediate Pre‐equilibrium Species

There is an increasing amount of interest in metal–organic frameworks (MOFs) for a variety of applications, from gas sensing and separations to electronics and catalysis. However, the mechanisms by which they crystallize remain poorly understood. Herein, an important new insight into MOF formation is reported. It is shown that, prior to network assembly, crystallization intermediates in the canonical ZIF‐8 system exist in a dynamic pre‐equilibrium, which depends on the reactant concentrations and the progress of reaction. Concentration can, therefore, be used as a synthetic handle to directly control particle size, with potential implications for industrial scale‐up and gas sorption applications. These findings enable the rationalization of apparent contradictions between previous studies of ZIF‐8 and opens up new opportunities for the control of crystallization in network solids more generally.     

Synthesis and Magnetic Characteristics of Neodymium Ferrite Powders with Perovskite Structure

Russian Journal of Applied Chemistry - Nanopowders of neodymium ferrite with perovskite structure were synthesized by co-precipitation precipitation via hydrolysis of iron(III) and neodymium(III)...     

The electronic properties and electron transport of sawtooth penta-graphene nanoribbon under uniaxial strain: ab-initio study

ABSTRACT

The electronic properties and electron transport of a sawtooth penta-graphene nanoribbon (SSPGNR) under uniaxial strains are theoretically studied by density-functional theory (DFT) in combination with the non-equilibrium Green's function formalism. We investigated the electronic structures and the current–voltage (I–V) characteristics of the SSPGNRs under a sequence of uniaxial strains in range from 10% compression to 10% stretch. In this strained range, carbon atoms still keep a pentagon network, but with the changing bond lengths. The C–C bond lengths change almost linearly with the tolerable strain. The value of the band gap of SSPGNRs can be depicted as a parabola under uniaxial strain. Our calculations show that the current is monotonous increase with compressive strain at the same applied bias voltage. In case of tensile strain, the variable rule of the current is different that it increases at first and decrease later. The fundamental physical properties (band structure, I–V characteristic) of SSPGNRs seem to be more sensitive to compressive strain than the stretch strain. The current intensity of the compressive-SSPGNR is by 2 orders of magnitude compared to that of the tensile-SSPGNR at the same strain in range from 6% to 10%. The results obtained from our calculations are beneficial to practical applications of these strained structures in SSPGNRs-based electromechanical devices.     

Mechanically Activated Solid-State Radical Polymerization and Cross-Linking via Piezocatalysis

Piezocatalysis offers a means to transduce mechanical energy into chemical potential, harnessing physical force to drive redox reactions. Working in the solid state, we show here that piezoelectric BaTiO₃ nanoparticles can transduce mechanical load into a flux of reactive radical species capable of initiating solid state free radical polymerization. Activation of a BaTiO₃ powder by ball milling, striking with a hammer, or repeated compressive loading generates highly reactive hydroxyl radicals (⋅OH), which readily initiate radical chain growth and crosslinking of solid acrylamide, acrylate, methacrylate and styrenic monomers. Control experiments indicate a critical role for chemisorbed water on the BaTiO₃ nanoparticle surface, which is oxidized to ⋅OH via mechanoredox catalysis. The force-induced production of radicals by compressing dry piezoelectric materials represents a promising new route to harness mechanical energy for solid state radical synthesis.     

Chemical constituents from the leaves of Manglietia phuthoensis and their effects on osteoblastic MC3T3-E1 cells

Two new phenyl glycosides, mangliesides A and B (1, 2), a new ionol glycoside, manglieside C (3), two new lignan glycosides, mangliesides D and E (4, 5), were isolated from the leaves of Manglietia phuthoensis, along with two known lignans, 3-methoxymagnolol (6) and obovatol (7). Their structures were established by means of 1D and 2D NMR, electrospray ionization (ESI)-MS and HR-ESI-MS experiments. Among them, compounds 2 and 5 significantly (p<0.05) increased the growth and differentiation of osteoblastic MC3T3-E1 cells in vitro.