The large-time development of the solution to an initial-boundary value problem for the Korteweg-de Vries equation on the negative quarter-plane

In this paper, we consider an initial-boundary value problem for the Korteweg-de Vries equation on the negative quarter-plane. The normalized Korteweg-de Vries equation considered is given by

     

Some properties of Lagrangian sequences

Here we discuss a sequence of Lagrangians and corresponding Euler–Lagrange equations and point out some interesting properties that this particular sequence holds. This is an extension on recent results obtained on sequences of differential equations to Lagrangians as it leads to differential equations on the application of the Variational Principle.     

Influence of molecular weight on nanoscale modification of poly(methyl methacrylate) due to simultaneous mechanical and chemical stimulation

We report observations of poly(methyl methacrylate) films modified by the synergistic effect of solvent exposure and mechanical stress applied by the tip of an atomic force microscope (AFM). We show that these modifications are sensitive to polymer molecular weight as well as solvent strength and the force applied by the tip. Small-area scanning often produces localized patches of raised material as well as depressed areas. The volume change associated with the depressed areas generally increases with increasing solvent strength, increasing applied normal force, and decreasing polymer molecular weight. In contrast, the volume change associated with the raised patches is greatest for 25-145K Mw films in 60 and 100% ethanol solutions. In each case, the normal force applied by the AFM tip must exceed a threshold to significantly modify the surface; this threshold is associated with an increase in lateral force applied by the AFM tip during small-area scanning. We attribute the raised patches to mechanically enhanced swelling due to diffusion of solvent into near-surface material. Permanent net volume loss, when observed, is attributed to localized polymer dissolution.     

TITAN: an ion trap for accurate mass measurements of ms-half-life nuclides

The introduction of Paul traps, in particular linear radio-frequency quadrupoles in the early 2000s, has revolutionized the use of ion traps for probing the properties of radioactive nuclides. It opened the path to trapping all available nuclides, independent of their chemical properties. We present an overview of direct mass measurements of short-lived nuclides using TITAN, a Penning trap mass spectrometer facility particularly suitable for precision measurements of ms-half-life nuclides.     

Mechanistic studies on a sulfoxide transfer reaction mediated by diphenyl sulfoxide/triflic anhydride

Sulfoxides are frequently used in organic synthesis as chiral auxiliaries and reagents to mediate a wide variety of chemical transformations. For example, diphenyl sulfoxide and triflic anhydride can be used to activate a wide range of glycosyl donors including hemiacetals, glycals and thioglycosides. In this way, an alcohol, enol or sulfide is converted into a good leaving group for subsequent reaction with an acceptor alcohol. However, reaction of diphenyl sulfoxide and triflic anhydride with oxathiane-based thioglycosides, and other oxathianes, leads to a different process in which the thioglycoside is oxidised to a sulfoxide. This unexpected oxidation reaction is very stereoselective and proceeds under anhydrous conditions in which the diphenyl sulfoxide acts both as oxidant and as the source of the oxygen atom. Isotopic labelling experiments support a reaction mechanism that involves the formation of oxodisulfonium (S-O-S) dication intermediates. These intermediates undergo oxygen-exchange reactions with other sulfoxides and also allow interconversion of axial and equatorial sulfoxides in oxathiane rings. The reversibility of the oxygen-exchange reaction suggests that the stereochemical outcome of the oxidation reaction may be under thermodynamic control, which potentially presents a novel strategy for the stereoselective synthesis of sulfoxides.     

Furanyl cyclic amines: a diastereoselective synthesis of 2,6-syn-disubstituted piperidines under thermodynamic control

Utilising the propensity of the 2-furanyl group to facilitate equilibration of an adjacent tosylamide chiral centre, a diastereoselective route to 2,6-syn-piperidines was developed that proceeds with high levels of thermodynamic stereocontrol. X-ray crystallography structures suggest that, as seen in similar systems, pseudo-allylic strain between the N-tosyl group and the substituents at the 2 and 6 positions dominates stereochemical preference, overriding 1,3 diaxial interactions.     

Linking supply chain processes’ performance to a company’s financial strategic objectives

The main aim of this paper is to develop a performance measurement method which links supply chain (SC) processes’ performance to a company’s financial strategy through demonstrating and utilising the relationship between SC processes’ performance and a company’s financial performance.     

Structure and Reactivity of Al−O(H)−Al Moieties in Siloxide Frameworks: Solution and Gas‐Phase Model Studies

Even though aluminas and aluminosilicates have found widespread application, a consistent molecular understanding of their surface heterogeneity and the behavior of defects resulting from hydroxylation/dehydroxylation remains unclear. Here, we study the well‐defined molecular model compound, [Al₃(μ₂‐OH)₃(THF)₃(PhSi(OSiPh₂O)₃)₂], 1 , to gain insight into the acid–base reactivity of cyclic trinuclear Al₃(μ₂‐OH)₃ moieties at the atomic level. We find that, like zeolites, they are sufficiently acidic to catalyze the isomerization of olefins. DFT and gas phase vibrational spectroscopy on solvent‐free and deprotonated 1 show that the six‐membered ring structure of its Al₃(μ₂‐OH)₃ core is unstable with respect to deprotonation of one of its hydroxy groups and rearranges into two edge‐sharing four‐membered rings. This renders Al_IV?O(H)?Al_IV units strong acid sites, and all results together suggest that their acidity is similar to that of zeolitic Si_IV?O(H)?Al_IV groups.     

Electronic spectra and transitions of the fullerene C60

Absorption spectra of C₆₀ have been measured in the ranges (a) 190–700 nm in n-hexane solutions at 300 K, (b) 390–700 nm in n-hexane and in 3-methylpentane solutions at 77 K. 40 vibronic bands were observed. They exhibit a large range of bandwidths and intensities, whose significance is discussed. Assignment of electronic transitions has been carried out using the results of theoretical calculations. Vibronic structures have been analyzed within the framework of theories of electronic transitions of polyatomic molecules applied to the I_h symmetry group. Nine allowed ¹T_1u−¹A_g transitions have been assigned in the 190–410 nm region. Observed and calculated allowed transition energies and oscillator strengths are compared. Detailed vibronic analyses of the 1 ¹T_1u−1 ¹A_g and 2 ¹T_1u−1 ¹A_g transitions illustrate the role of Jahn-Teller couplings. Orbitally forbidden singlet-singlet transitions are observed between 410 and 620 nm. Their vibronic structures were analyzed in terms of concurrent Herzberg-Teller and Jahn-Teller vibronic interactions. The 77 K spectra provided useful information on hot bands and on other aspects of the analyses. Vibronic bands belonging to triplet←singlet transitions were detected between 620 and 700 nm.