Irregularity strength of trees

The main result of this paper establishes that the irregularity strength of any tree with no vertices of degree two is its number of pendant vertices.     

Computing the maximum transient energy growth

The calculation of maximum transient energy growth is a problem of interest in several areas of science and engineering. An algorithm that guarantees the calculation of this measure to an arbitrary accuracy in a finite number of steps is proposed for finite-dimensional linear-time-invariant dynamical systems. The algorithm is illustrated with a numerical example.     

Predicting Bitcoin (BTC) Price in the Context of Economic Theories: A Machine Learning Approach

Bitcoin (BTC)—the first cryptocurrency—is a decentralized network used to make private, anonymous, peer-to-peer transactions worldwide, yet there are numerous issues in its pricing due to its arbitrary nature, thus limiting its use due to skepticism among businesses and households. However, there is a vast scope of machine learning approaches to predict future prices precisely. One of the major problems with previous research on BTC price predictions is that they are primarily empirical research lacking sufficient analytical support to back up the claims. Therefore, this study aims to solve the BTC price prediction problem in the context of both macroeconomic and microeconomic theories by applying new machine learning methods. Previous work, however, shows mixed evidence of the superiority of machine learning over statistical analysis and vice versa, so more research is needed. This paper applies comparative approaches, including ordinary least squares (OLS), Ensemble learning, support vector regression (SVR), and multilayer perceptron (MLP), to investigate whether the macroeconomic, microeconomic, technical, and blockchain indicators based on economic theories predict the BTC price or not. The findings point out that some technical indicators are significant short-run BTC price predictors, thus confirming the validity of technical analysis. Moreover, macroeconomic and blockchain indicators are found to be significant long-term predictors, implying that supply, demand, and cost-based pricing theories are the underlying theories of BTC price prediction. Likewise, SVR is found to be superior to other machine learning and traditional models. This research’s innovation is looking at BTC price prediction through theoretical aspects. The overall findings show that SVR is superior to other machine learning models and traditional models. This paper has several contributions. It can contribute to international finance to be used as a reference for setting asset pricing and improved investment decision-making. It also contributes to the economics of BTC price prediction by introducing its theoretical background. Moreover, as the authors still doubt whether machine learning can beat the traditional methods in BTC price prediction, this research contributes to machine learning configuration and helping developers use it as a benchmark.     

Role of solvent in the compatibility of a vinylchloride–vinylacetate–maleic acid terpolymer and nitrocellulose blends

The compatibility of cast films of a vinylchloride–vinylacetate–maleic acid terpolymer (VMCH) and nitrocellulose (NC) blends is influenced by solvents. Transparent films of VMCH/NC blends are obtained when cast from solvents such as tetrahydrofuran or cyclohexanone, whereas hazy films are obtained when cast from solvents such as acetone or ethylacetate. Visible spectroscopy and phase morphology were used to analyse the compatibility–incompatibility of the blend. Differential scanning calorimetry (DSC) studies demonstrate that the transparent film is compatible, but the hazy film is incompatible. Fourier transform infra-red (FTIR) studies establish that a greater interaction is observed between the polymer pair in case of the compatible blend than in the case of the incompatible blend. A solvent dependency of blend compatibility is reflected in this study. The conformational state of the polymers in solution, which is responsible for the compatibility phenomena, may depend on the donor number and/or Taft-β value of the solvent. The greater the donor number and/or the Taft-β value, the higher may be the level of interaction between the solvent and the polymer molecules, which in turn may give a compatible blend after removal of the solvent.     

Plasmonic Pollen Grain Nanostructures: A Three-Dimensional Surface-Enhanced Raman Scattering (SERS)-Active Substrate

A new route has been developed to design plasmonic pollen grain-like nanostructures (PGNSs) as surface-enhanced Raman scattering (SERS)-active substrate. The nanostructures consisting of silver (Ag) and gold (Au) nanoparticles along with zinc oxide (ZnO) nanoclusters as spacers were found highly SERS-active. The morphology of PGNSs and those obtained in the intermediate stage along with each elemental evolution has been investigated by a high-resolution field emission scanning electron microscopy. The optical band gaps and crystal structure have been identified by UV-vis absorption and X-ray powder diffraction (XRD) measurements, respectively. For PGNSs specimen, three distinct absorption bands related to constituent elements Ag, Au, and ZnO were observed, whereas XRD peaks confirmed the existence of Ag, Au, and ZnO within the composition of PGNSs. SERS-activity of PGNSs was confirmed using Rhodamine 6G (R6G) as Raman-active dyes. Air-cooled solid-state laser kits of 532 nm were used as excitation sources in SERS measurements. SERS enhancement factor was estimated for PGNSs specimen and was found as high as 3.5×10⁶. Finite difference time domain analysis was carried out to correlate the electromagnetic (EM) near-field distributions with the experiment results achieved under this investigation. EM near-field distributions at different planes were extracted for s-, p- and 45° of incident polarizations. EM near-field distributions for such nanostructures as well as current density distributions under different circumstances were demonstrated and plausible scenarios were elucidated given SERS enhancements. Such generic fabrication route as well as correlated investigation is not only indispensable to realize the potential of SERS applications but also unveil the underneath plasmonic characteristics of complex SERS-active nanostructures.     

On interpolation of interpolating sequences

Let A be a uniform algebra on the compact space X and σ a probability measure on X. We define the Hardy spaces H^P(σ) and the H^P(σ) interpolating sequences S in the p-spectrum M_p of σ. Under some structural hypotheses on (A, σ), we prove that if a sequence S ⊂ M_p is H^P(σ) interpolating, then it is H^s(σ) interpolating for s < p. In the special case of the unit ball B of ?ⁿ this answers a natural question asked in [8].     

Non division dansA ∞(Ω)

Sans résumé     

Dielectric studies in dilute solutions

Dielectric studies in dilute solutions of cyclohexane and benzene have been carried out in the temperature range 294–318°K. The observed data have been utilized to evaluate the relaxation times and thermodynamic parameters of these molecules. The high values ofα for 2-acetyl pyridine indicate the occurrence of more than one relaxation time. In the remaining systems, the observed lowα values indicate their rigid behaviour. The variation in the dielectric relaxation time is mostly correlated with the change in the heterocyclic configuration of the system.     

Über die Verformung der Röntgenabsorptionskanten in Metallen und Legierungen durch Gitterleerstellen

In order to account for the distortion in the shape of x-ray absorption edges in some metals and alloys, a mechanism involving lattice vacancies is proposed. It is shown that an atom near a lattice vacancy will be under the influence of an electrical field resulting from the asymmetric surroundings. The magnitude of this field is found to be large enough to produce a Stark-splitting in the exciton orbit of the absorbing atom. The distortion appearing as a kink on the slope of the absorption curve is shown to be a consequence of this splitting.     

Evaluation of the thermodynamic parameters for association process of hydrogen bond complexes from the dielectric relaxation measurements.

A relation between the free energy for dipole relaxation process and that for the association process has been proposed. Using this relation, an equation has been defined for evaluating the association equilibrium constant from the dielectric relaxation measurements. These equations have been applied to study the association of dimethyl sulphoxide and p-tolyl sulphoxide with proton donors (phenol and O-cresol) in an inert solvent carbon-tetra-chloride in the temperature range 298–322K. The calculation of the association equilibrium constant and hence the thermodynamic parameters have shown the wide scope, the proposed relations can be put to in the study of the association process of hydrogen bond complexes.