Analytical solutions of refined plate theory for bending,buckling and vibration analyses of thick plates

Analytical solutions for bending, buckling, and vibration analyses of thick rectangular plates with various boundary conditions are presented using two variable refined plate theory. The theory accounts for parabolic variation of transverse shear stress through the thickness of the plate without using shear correction factor. In addition, it contains only two unknowns and has strong similarities with the classical plate theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. Equations of motion are derived from Hamilton’s principle. Closed-form solutions of deflection, buckling load, and natural frequency are obtained for rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. Comparison studies are presented to verify the validity of present solutions. It is found that the deflection, stress, buckling load, and natural frequency obtained by the present theory match well with those obtained by the first-order and third-order shear deformation theories.     

Metric regularity of a positive order for generalized equations

This paper focuses on the metric regularity of a positive order for generalized equations. More concretely, we establish verifiable sufficient conditions for a generalized equation to achieve the metric regularity of a positive order at its a given solution. The provided conditions are expressed in terms of the Fréchet coderivative/or the Mordukhovich coderivative/or the Clarke one of the corresponding multifunction formulated the generalized equation. In addition, we show that such sufficient conditions turn out to be also necessary for the metric regularity of a positive order of the generalized equation in the case where the multifunction established the generalized equation is closed and convex.     

The yin and yang of amyloid: insights from α-synuclein and repeat domain of Pmel17

Amyloid has been traditionally viewed in the context of disease. However, the emerging concept of 'functional amyloid' has taken a new direction into how we view amyloid. Recent studies have identified amyloid fibrils ranging from bacteria to humans that have a beneficial role, instead of being associated with a misfolded state that has been implicated in diseases such as Alzheimer's, Parkinson's and prion diseases. Here, we review our work on two human amyloidogenic polypeptides, one associated with Parkinson's disease, α-synuclein (α-syn), and the other important for melanin synthesis, the repeat domain (RPT) from Pmel17. Particularly, we focused our attention on spectroscopic studies of protein conformation and dynamics and their impact on α-syn amyloid formation and for RPT, we discussed the strict pH dependence of amyloid formation and its role in melanin biosynthesis.     

A front-tracking method with Catmull–Clark subdivision surfaces for studying liquid capsules enclosed by thin shells in shear flow

This paper presents a front-tracking method for studying the large deformation of a liquid capsule enclosed by a thin shell in a shear flow. The interaction between the fluid and the shell body is accomplished through an implicit immersed boundary method. An improved thin-shell model for computing the forces acting on the shell middle surface during the deformation is described in surface curvilinear coordinates and within the framework of the principle of virtual displacements. This thin-shell model takes full account of in-plane tensions and bending moments developing due to the shell thickness and a preferred three-dimensional membrane structure. The approximation of the shell middle surface is performed through the use of the Catmull–Clark subdivision surfaces. The resulting limit surface is C²-continuous everywhere except at a small number of extraordinary nodes where it retains C¹ continuity. The smoothness of the limit surface significantly improves the ability of our method in simulating capsules enclosed by hyperelastic thin shells with different shapes and physical properties. The present numerical technique has been validated by several examples including an inflation of a spherical shell and deformations of spherical, ellipsoidal and biconcave capsules in the shear flow. In addition, different types of motion such as tank-treading, swinging, tumbling and transition from tumbling to swinging have been studied over a range of shear rates, viscosity ratios and bending modulus.     

A cutting-plane algorithm for solving a weighted influence interdiction problem

We consider a two-stage defender-attacker game that takes place on a network, in which the attacker seeks to take control over (or “influence”) as many nodes as possible. The defender acts first in this game by protecting a subset of nodes that cannot be influenced by the attacker. With full knowledge of the defender’s action, the attacker can then influence an initial subset of unprotected nodes. The influence then spreads over a finite number of time stages, where an uninfluenced node becomes influenced at time t if a threshold number of its neighbors are influenced at time t?1. The attacker’s objective is to maximize the weighted number of nodes that are influenced over the time horizon, where the weights depend both on the node and on the time at which that is influenced. This defender-attacker game is especially difficult to optimize, because the attacker’s problem itself is NP-hard, which precludes a standard inner-dualization approach that is common in many interdiction studies. We provide three models for solving the attacker’s problem, and develop a tailored cutting-plane algorithm for solving the defender’s problem. We then demonstrate the computational efficacy of our proposed algorithms on a set of randomly generated instances.     

Atmospheric concentrations of sulfur dioxide, nitrogen oxides, ammonia, hydrogen chloride, nitric acid, formic and acetic acids in the south of Vietnam measured by the passive sampling method.

A passive sampling method was applied to measure the concentrations of air pollutants, such as sulfur dioxide, nitrogen oxides, ammonia, hydrogen chloride, and nitric, formic and acetic acids, in the ambient air at four test sites in the southern region of Vietnam. The monthly averages and the average concentrations of air pollutants during the period from July 2001 to September 2002 are reported here. The concentrations of air pollutants varied widely, depending on the test sites and the sampling periods. The average concentrations of sulfur dioxide in the air during the period from July 2001 to September 2002 at the four test sites were 3.3-16.9 ppb, and those of nitrogen dioxide were 5.4-12.8 ppb. The concentrations of nitrogen monoxide and hydrogen chloride were very low at all of the test sites. The observed concentrations of all of the above-mentioned pollutants were lower than those of the Vietnamese standards of air pollutants.     

Exact relaxations for parametric robust linear optimization problems

We first show that the closedness of the characteristic cone of the constraint system of a parametric robust linear optimization problem is a necessary and sufficient condition for each robust linear program with the finite optimal value to admit exact semidefinite linear programming relaxations. We then provide the weakest regularity condition that guarantees exact second-order cone programming relaxations for parametric robust linear programs.     

Highly Active Phosphine‐Free Bifunctional Iron Complex for Hydrogenation of Bicarbonate and Reductive Amination

Based on a “transition metal frustrated Lewis pair” approach, a cyclopentadienone iron tricarbonyl complex has been designed and applied in the reductive amination and hydrogenation of bicarbonate. This well‐defined phosphine‐free complex displays the best activities reported to date for an iron complex in the reduction of bicarbonate into formate and in reductive amination.