Framing conflicting scientific views of John Robison on the Euler’s column buckling problem in the socio-political context of the late XVIII century

Meccanica - The analytical approach of Leonhard Euler to the solution of an elastic column under compression is seen today as a landmark in buckling studies. However, this work was not well...     

Simultaneous determination of nicotinamide,nicotinic acid,riboflavin, thiamin,and pyridoxine in enriched Brazilian foods by HPLC

The control of the enrichment levels in foods is difficult, due mainly to the lack of appropriate analytical methodologies. The amounts of the five B-group vitamins (nicotinamide, nicotinic acid, ribofla-vin, thiamin, and pyridoxine) have been determined in enriched Brazilian foods by a high-performance liquid chromatography (HPLC) method. Fifty products, such as biscuits, liquid and dry milks, flavored milk drinks, flour, macaroni, and cereals were analyzed. Some products showed the amounts declared on the package. Although some slight quantitative variations were shown in the biscuits, one showed levels of riboflavin 35% lower than the value declared. Of five different corn cereal brands, only one showed the declared vitamin content, the others showing levels 30 % lower than that declared. No B-group vitamins were detected in one brand of enriched macaroni, except for the nicotinic acid naturally present in the flour. On the other hand, one flavored milk drink exhibited vitamins levels 200% higher than the amounts declared and one milk drink mix presented thiamin, riboflavin, and nicotinamide levels 3 to 5 times greater than stated. These results suggest an absence of control of the amount of vitamins in enriched foods.     

Catalyzed chain growth of polyethylene on magnesium for the synthesis of macroalkoxyamines: Application to the production of block copolymers using controlled radical polymerization

A synthetic method for the production of polyethylene (PE) chains carrying alkoxyamine end‐group has been proposed first by successfully reacting the well‐known 2,2,6,6‐tetramethylpiperidine‐N‐oxyl (TEMPO) and N‐(2‐methyl‐2‐propyl)‐N‐(1‐diethylphosphono‐2,2‐dimethylpropyl)‐N‐oxyl (commonly called SG1) stable radicals with dipolyethylenylmagnesium compounds to give PE‐TEMPO and PE‐SG1. Since the homolytic cleavage of these two macroalkoxyamines for the production of block copolymers using controlled radical polymerization would require temperatures higher than 160 °C, two original new nitroxides (4‐[(2,2‐dimethyl‐4‐(N‐tert‐Butyl‐N‐(1‐diethoxyphosphoryl‐2,2‐dimethylpropyl)aminoxy)‐4‐n‐butoxycarbonyl)butanoyloxyl]‐2,2,6,6‐tetramethylpiperidinyl‐1‐oxy, DD1) and 4‐[(2,2‐dimethyl‐4‐(N‐tert‐Butyl‐N‐(1‐diethoxyphosphoryl‐2,2‐dimethylpropyl)aminoxy)‐4‐phenyl) butanoyloxyl]‐2,2,6,6‐tetramethylpiperidinyl‐1‐oxy, DD2) containing a TEMPO moiety and incorporating an SG1‐based alkoxyamine (cleavage temperature: 60 °C) were then synthesized. NMR analyses showed that the resulting PE‐DD1 and PE‐DD2 were obtained using this functionalization strategy though with low to moderate yields (from 17% to 40%). PE‐DD2 (40% functionalization) was used under controlled radical polymerization conditions of n‐butyl acrylate. SEC analyses together with ¹H NMR analysis showed that a poly(ethylene‐b‐n‐butyl acrylate) block copolymer was produced and that the polymerization proceeded under control. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2705–2718, 2007     

Dynamic buckling of discrete structural systems under combined step and static loads

The dynamic instability of discrete, elastic, multiple degree of freedom (d.o.f.) systems under a combination of static and step loads is studied. Conservative, autonomous and holonomic systems are considered, in which the associated static response is a bifurcation under one load parameter, and a limit point under the second parameter. A review of different criteria and algorithms obtained from them for the computation of dynamic buckling loads is first presented, followed by a procedure derived from previous investigations on one d.o.f. systems. The different procedures are applied to a two d.o.f. problem under axial and lateral load, with quadratic and cubic non-linearities. The response in time shows that the system oscillates about the static equilibrium position before dynamic buckling is reached, with the kinetic energy tending to zero as assumed in the static (energy) procedures of stability.     

Navier–Stokes Equations on Weighted Graphs

Navier–Stokes equations arise in the study of incompressible fluid mechanics, star movement inside a galaxy, dynamics of airplane wings, etc. In the case of Newtonian incompressible fluids, we propose an adaptation of such equations to finite connected weighted graphs such that it produces an ordinary differential equation with solutions contained in a linear subspace, this subspace corresponding to the Newtonian conservation law. We discuss the particular case when the graph is the complete graph K _m , with constant weight, and provide a necessary and sufficient condition for it to have solutions.     

On the asymptotic behavior of the principal eigenvalues of some elliptic problems

This paper is concerned with nonself-adjoint elliptic problems involving indefinite weights and boundary conditions of the Dirichlet, Neumann or Robin type. We study the asymptotic behavior of the principal eigenvalues, when the first order term (drift term) becomes larger and larger. The basic results of Berestycki et al. (Commun. Math. Phys., 253:451–480, 2005) are extended to the present context. Moreover, answers are provided to some open problems raised in Berestycki et al. (Commun. Math. Phys., 253:451–480, 2005).     

On Certain Integral Operators of Fractional Type

In this paper we study integral operators of the form $$T\,f\left( x \right) = \int {k_1 \left( {x - a_1 y} \right)k_2 \left( {x - a_2 y} \right)...k_m \left( {x - a_m y} \right)f\left( y \right)dy} ,$$ $$k_i \left( y \right) = \sum\limits_{j \in Z} {2^{\frac{{jn}}{{q_i }}} } \varphi _{i,j} \left( {2^j y} \right),\,1 \leqq q_i < \infty ,\frac{1}{{q_1 }} + \frac{1}{{q_2 }} + ... + \frac{1}{{q_m }} = 1 - r,$$ $0 \leqq r < 1$ , and $\varphi _{i,j}$ satisfying suitable regularity conditions. We obtain the boundedness of $T:L^p \left( {R^n } \right) \to T:L^q \left( {R^n } \right)$ for $1 < p < \frac{1}{r}$ and $\frac{1}{q} = \frac{1}{p} - r$ .