Line intensities of acetylene: New measurements in the 1.5-μm spectral region and global modelling in the ΔP=10 series

Using the Fourier transform spectra of the acetylene molecule recorded near 1.5-μm, the intensities of 111 lines belonging to seven hot bands of the main isotopologue ¹²C₂H₂ have been retrieved by means of a multispectrum fitting procedure. Considering the density of lines in the spectra, and the fact that the measured bands are the weakest observed, the accuracy of the measurements is around 10%. At first stage, an empirical treatment of these data has been performed, leading to the vibrational transition dipole moment squared and some Herman–Wallis coefficients. Then the measured line intensities of this work and collected ones from the literature have been treated simultaneously within the framework of the effective operator approach.     

The influence of structural changes of symmetrical dimers containing two phenyl groups on liquid crystalline behaviour

Some symmetrical dimeric compounds containing biphenyl, biphenylcarboxylic acid or benzoiloxyphenyl moieties and polymethylene spacers were synthesised. The mesogenic properties of the synthesised compounds were investigated by optical microscopy, calorimetric and X-ray methods. It was shown that the location and direction of the ester bonds has a crucial significance in mesophase formation.     

Asymptotic expansions of the moments of extremes from general error distribution

In this paper, we derive the asymptotic expansions of the moments of normalized partial maxima for general error distribution. A byproduct is to deduce the convergence rates of the moments of normalized maxima to the moments of the corresponding extreme value distribution.     

A Minty variational principle for set optimization

Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so-called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such problems, introduced by F. Heyde and A. Löhne, comprises the attainment of the infimum as well as a minimality property. The main result is a Minty type variational inequality for set optimization problems which provides a sufficient optimality condition under lower semicontinuity assumptions and a necessary condition under appropriate generalized convexity assumptions. The variational inequality is based on a new Dini directional derivative for set-valued functions which is defined in terms of a “lattice difference quotient.” A residual operation in a lattice of sets replaces the inverse addition in linear spaces. Relationships to families of scalar problems are pointed out and used for proofs. The appearance of improper scalarizations poses a major difficulty which is dealt with by extending known scalar results such as Diewert's theorem to improper functions.     

A new approach to pointwise heat kernel upper bounds on doubling metric measure spaces

On doubling metric measure spaces endowed with a strongly local regular Dirichlet form, we show some characterisations of pointwise upper bounds of the heat kernel in terms of global scale-invariant inequalities that correspond respectively to the Nash inequality and to a Gagliardo–Nirenberg type inequality when the volume growth is polynomial. This yields a new proof and a generalisation of the well-known equivalence between classical heat kernel upper bounds and relative Faber–Krahn inequalities or localised Sobolev or Nash inequalities. We are able to treat more general pointwise estimates, where the heat kernel rate of decay is not necessarily governed by the volume growth. A crucial role is played by the finite propagation speed property for the associated wave equation, and our main result holds for an abstract semigroup of operators satisfying the Davies–Gaffney estimates.     

Approximate controllability for a class of hemivariational inequalities

In this paper, we deal with the approximate controllability for control systems described by a class of hemivariational inequalities. Firstly, we introduce the concept of mild solutions for hemivariational inequalities. Then the approximate controllability is formulated and proved by utilizing a fixed-point theorem of multivalued maps and properties of generalized Clarke subdifferential.     

Metric inequalities for routings on direct connections with application to line planning

We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the well-known feasibility condition for arc capacities in ordinary multi-commodity flows. The condition can be expressed in terms of a class of metric inequalities for routings on direct connections. We illustrate the concept on the example of the line planning problem in public transport and present an application to large-scale real-world problems.     

Theoretical and photophysical investigation of biologically active fluorophore: 2-amino-6-chlorofluoren-9-one

The optimized geometric parameters of the 2-Amino-6-chlorofluoren-9-one (2A6CF9O) compound were estimated by employing density functional theory. The electronic characteristics of the molecule were explored using molecular frontier orbital energies and the MEP surface. Kamlet's and Catalan's multiple linear regression techniques along with different polarity functions were used to investigate the influence of pure solvents on spectral properties. In the system, both general solute-solvent and hydrogen bonding interactions are active. However, as compared to normal solute-solvent interactions, hydrogen bonding interactions have a smaller role. In addition, using computed ground state dipole moment, solvatochromic correlations were employed to infer excited state dipole moment.     

Basis Sets Dependency in Constructing Spectroscopy-Accuracy Ab Initio Global Electric Dipole Moment Functions

Recently, more attention have been paid on the construction of dipole moment functions (DMF) using theoretical methods. However, the computational methods to construct DMFs are not validated as much as those for potential energy surfaces do. In this letter, using Ar...He as an example, we tested how spectroscopyaccuracy DMFs can be constructed using ab initio methods. We especially focused on the basis set dependency in this scenario, i.e., the convergence of DMF with the sizes of basis sets, basis set superposition error, and mid-bond functions. We also tested the explicitly correlated method, which converges with smaller basis sets than the conventional methods do. This work can serve as a pictorial sample of all these computational technologies behaving in the context of constructing DMFs.