Second-order functional differential equations with past, present and future dependence

In this paper we obtain a result on existence of extremal quasisolutions and solutions for second-order functional differential equations with functional boundary conditions and past, present and future dependence. In order to do that, we develop a generalized monotone method in presence of lower and upper solutions. Some examples of application are provided too.     

Stability of sets of functional differential equations with impulse effect

In this paper, we investigate stability of sets for a class of impulsive functional differential equations by using piecewise continuous Lyapunov functions with Razumickhin techniques. Some sufficient conditions for stability of sets are established, and some known stability theorems also are generalized.     

Strong-stability-preserving 3-stage Hermite-Birkhoff time-discretization methods

Strong-stability-preserving (SSP) time-discretization methods have a nonlinear stability property that makes them particularly suitable for the integration of hyperbolic conservation laws. A collection of SSP explicit 3-stage Hermite-Birkhoff methods of orders 3 to 7 with nonnegative coefficients are constructed as k-step analogues of third-order Runge-Kutta methods, incorporating a function evaluation at two off-step points. Generally, these new methods have larger effective CFL coefficients than the hybrid methods of Huang with the same step number k. They have larger maximum scaled step sizes than hybrid methods on Burgers' equations.     

Some new almost sure results on the functional increments of the uniform empirical process

Given an observation of the uniform empirical process α_n, its functional increments α_n(u+a_n⋅)−α_n(u) can be viewed as a single random process, when u is distributed under the Lebesgue measure. We investigate the almost sure limit behaviour of the multivariate versions of these processes as n→∞ and a_n↓0. Under mild conditions on a_n, a convergence in distribution and functional limit laws are established. The proofs rely on a new extension of the usual Poissonisation tools for the local empirical process.     

Uniform asymptotic stability of impulsive discrete systems with time delay

This paper studies impulsive discrete systems with time delay. Some novel criteria on uniform asymptotic stability are established by using the method of Lyapunov functions and the Razumikhin-type technique. Examples are presented to illustrate the criteria.     

Design of experiments on 135 cloned poplar trees to map environmental influence in greenhouse

To find and ascertain phenotypic differences, minimal variation between biological replicates is always desired. Variation between the replicates can originate from genetic transformation but also from environmental effects in the greenhouse. Design of experiments (DoE) has been used in field trials for many years and proven its value but is underused within functional genomics including greenhouse experiments. We propose a strategy to estimate the effect of environmental factors with the ultimate goal of minimizing variation between biological replicates, based on DoE. DoE can be analyzed in many ways. We present a graphical solution together with solutions based on classical statistics as well as the newly developed OPLS methodology.In this study, we used DoE to evaluate the influence of plant specific factors (plant size, shoot type, plant quality, and amount of fertilizer) and rotation of plant positions on height and section area of 135 cloned wild type poplar trees grown in the greenhouse. Statistical analysis revealed that plant position was the main contributor to variability among biological replicates and applying a plant rotation scheme could reduce this variation.     

Enhanced mechanical performance and biological evaluation of a PLGA coated β-TCP composite scaffold for load-bearing applications

Porous β-tricalcium phosphate (β-TCP) has been used for bone repair and replacement in clinics due to its excellent biocompatibility, osteoconductivity, and biodegradability. However, the application of β-TCP has been limited by its brittleness. Here, we demonstrated that an interconnected porous β-TCP scaffold infiltrated with a thin layer of poly(lactic-co-glycolic acid) (PLGA) polymer showed improved mechanical performance compared to an uncoated β-TCP scaffold while retaining its excellent interconnectivity and biocompatibility. The infiltration of PLGA significantly increased the compressive strength of β-TCP scaffolds from 2.90 to 4.19 MPa, bending strength from 1.46 to 2.41 MPa, and toughness from 0.17 to 1.44 MPa, while retaining an interconnected porous structure with a porosity of 80.65%. These remarkable improvements in the mechanical properties of PLGA-coated β-TCP scaffolds are due to the combination of the systematic coating of struts, interpenetrating structural characteristics, and crack bridging. The in vitro biological evaluation demonstrated that rat bone marrow stromal cells (rBMSCs) adhered well, proliferated, and expressed alkaline phosphatase (ALP) activity on both the PLGA-coated β-TCP and the β-TCP. These results suggest a new strategy for fabricating interconnected macroporous scaffolds with significantly enhanced mechanical strength for potential load-bearing bone tissue regeneration.     

The Rearrangement of 2,2‐Diphenyl‐1‐[(E)‐2‐phenylethenyl]cyclopropane to 3,4,4‐Triphenylcyclopent‐1‐ene: a DFT Analysis

A computational study on the rearrangement of 2,2‐diphenyl‐1‐[(E)‐2‐phenylethenyl]cyclopropane ( 1 ) is presented, using density functional theory (DFT), (U)B3LYP with the 6‐31G* basis set (DFT1) and (U)M05‐2X with the 6‐311+G** basis set (DFT2). In agreement with a biradical character of the transition structure (TS) or intermediate, the potential‐energy hypersurface is lowered by the influence of three conjugated Ph groups. Surprisingly, two conformations of the geminal diphenyl group (different twist angles) induce two different minimum‐energy pathways for the rearrangement. Independent of the functional used, the first hypersurface harbors true biradical intermediates, whereas the second energy surface is a flat, slightly ascending slope from the starting material to the TS. The functional (U)M05‐2X with the basis set 6‐311+G** provides realistic energies which seem to be close to experiment. The activation energy for racemization of enantiomers of 1 is lower than that of rearrangement by 2.5 kcal mol^?1, in agreement with experiment.     

Synthesis of glycopolymers via click reactions

This mini-review describes recent work in the field of glycopolymer synthesis, with a focus on methods that have employed “click chemistry” and controlled polymerization methodology. A variety of carbohydrates with clickable groups such as azide, alkyne, and thiol moieties provide new routes to glycopolymers. Several studies use copper catalyzed azide-alkyne cycloaddition (CuAAC) reactions to synthesize glycomonomers or to incorporate carbohydrates into a clickable polymeric backbone. Alternatively, there are many thiol based click reactions which provide metal-free synthesis, which are discussed in details.