Journal of Mathematical Chemistry最新文献

The realm of the current study is ovarian magnetic resonance spectroscopy (MRS). Presented are the selected recent advances in the Padé-based signal processing by shape estimations alone. The goal is to substantially improve extraction of quantitative information by sole reliance upon non-parametric estimations of total shape spectra (envelopes) from encoded time signals. The task is to resolve the given envelope into its true partial spectra (components) without solving the quantification problem (i.e. no polynomial rooting, etc.). The rescue is in derivative quantitative shape estimations void of fitting. Splitting apart an envelope into the genuine components amounts to quantification. With any quadrature rule, integrations of the reconstructed well-isolated unstructured derivative lineshapes and their power spectra determine the peak areas and peak widths, respectively. Metabolite concentrations ensue thereby as a key diagnostic information for recognized and potential cancer biomarkers alike. Special attention is drawn to abundant non-derivative singlet-appearing resonances that can contain sub-peaks in derivative lineshapes. Failure to detect such occurrences compromises the critical decision-making (normal vs. diseased tissues or biofluids) in the clinic. The salient illustrations are reported for benign and malignant tumors from human ovarian cyst fluid samples.

The topic of aromaticity of polycyclic assembly of hexagons has been of considerable interest over the decades. Polyhex carbon nanotubes in different topologies are especially intriguing from the standpoint of aromaticity, Kekulé structures, Dewar structure counts and various polynomials pertinent to these structures. In this study we juxtapose the various novel aromatic measures of zigzag versus armchair polyhex single-walled carbon nanotubes as a function of their tube lengths and circumference. We have computed the matching, spectral and delta polynomials of the two topologies of these tubes as a function of their lengths and circumferences. Our computations reveal that for a single-walled tube, the armchair is more aromatic than zigzag by all measures, and as the tube length increases aromaticity increases for both configurations. In contrast, as the tube circumference increases the aromaticity increases for the zigzag while a less pronounced opposite trend is exhibited by the armchair. There is a dramatic odd-even alternation in zigzag tubes with even parameter exhibiting zero gap, and for both tubes odd parameters exhibit perfect square constant coefficients in the spectral polynomials correlating with the square of the Kekulé structure counts. The armchair tube exhibits a much greater number of Dewar and Kekulé structures for any given set of parameters of the tube compared to the zigzag tubes confirming a greater aromaticity of the armchair tube. For example, the armchair [5,7] tube exhibits K = 65,445 and DS = 12,001,780 compared to the zigzag[5,7] with K = 128 and DS = 1,071,345. On the other hand, the zigzag nanotubes exhibit greater entropies compared to the armchair nanotubes. Applications of the combinatorial and computational techniques to various parameters related to the aromaticity and stability of different topologies of carbon nanotubes are considered.

This work belongs to the field of chemical kinetics and is devoted to the frequency factor of particle collisions occurring in an inert gaseous or liquid medium. The objective of the research is to account for the influence of the inert medium on the rate of a chemical reaction. This was achieved using methods of traditional chemical kinetics and advanced mathematics (probability theory and mathematical analysis). By employing a special mathematical object – the Wiener sausage – an estimate of the probability of collision between two particles over time was obtained. In the case of multiple particles, the frequency factor was interpreted as a quantity proportional the collision probability. The new form of the Arrhenius equation derived in this study includes three terms on the pre-exponential factor, which adds novelty and significance to the research. Additionally, the paper provides a physical interpretation of each term in the newly obtained frequency factor formula and successfully validates the correctness of the new Arrhenius equation using a specific example for comparison with experimental results.

In this paper, a novel high-order, mass and energy-conserving scheme is proposed for the regularized logarithmic Schrödinger equation. Based on the idea of the supplementary variable method (SVM), we firstly reformulate the original system into an equivalent form by introducing two supplementary variables, and the resulting SVM reformulation is then discretized by applying a high-order prediction-correction method in time and a Fourier pseudo-spectral method in space, respectively. The newly developed scheme can produce numerical solutions along which the mass and original energy are precisely conserved, as is the case with the analytical solution. Additionally, it is extremely efficient in the sense that only requires solving a constant-coefficient linear systems plus two algebraic equations, which can be efficiently solved by the Newton iteration at every time step. Numerical experiments are presented to confirm the accuracy and structure-preserving properties of the new scheme.

We propose a new mathematical model of the Briggs–Rauscher reaction. This is an oscillatory phenomenon which is characterised by fluctuations in the concentrations of the various chemicals involved. A well-regarded existing model involves a complex reaction mechanism described by 15 differential equations. We derive a novel approximate mathematical model that consists only of three equations, for the concentrations of iodous acid, iodide, and molecular iodine. We demonstrate that this three-variable approximation is nevertheless in good agreement with the predictions of far more elaborate models, and it offers the possibility of yielding to detailed mathematical analysis not available with more complex models. We show that our novel three-variable description is in excellent accord with previously-reported experimental work. It is able to reproduce key details of the observed periodic oscillations, including their period and amplitude and precise features of their behaviour with time.

Starting from the probability theory of continuous random variables and the central limit theorem, a rigorous mathematical proof is presented to show that the one-dimensional velocity components of particles in gas phase at thermal equilibrium can only be normally distributed if the physical properties are independent of direction. As such direction-independence is true for all gases, no matter whether they are ideal or not, a general distribution can be introduced. It is also shown that the particle speeds, which are the Euclidean norms of the velocity vectors, are always described by a chi distribution with three degrees of freedom, which converts into the Maxwell-Boltzmann speed distribution if the ideal gas law is valid. Furthermore, many of the formulas derived for ideal gases have analogs for real gases, which can be constructed by replacing RT (gas constant multiplied by temperature) terms by pV_m (pressure multiplied by molar volume).

In the present work, we introduce several definitions of Rényi’s entropy, based on different definitions of probability. All the expressions presented were applied to the chemical reaction (textrm{CH}_{3} + textrm{NH}_{3} rightarrow textrm{CH}_{4} + textrm{NH}_{3}). The trends obtained exhibit a more complex structure than the trends of the electron energy or electron correlation energy. Also, our results show that Rényi’s entropies can indicate the zone where the bond-breaking and bond-forming process is carried out.

In this paper, the Michaelis–Menten dynamics are studied by reducing the original system to a new set of two nonlinear ordinary differential equations obtained via conservation relations and variable transformations. A stability analysis of the reduced system reveals the existence of a stable equilibrium point. The properties of boundedness, positivity, existence, and uniqueness of the solutions are established by constructing two sequences, which are subsequently proven to be Cauchy sequences. Finally, numerical simulations are performed to validate the theoretical results and illustrate the expected behavior of the model.

This study investigates the expectation values and Shannon entropy of selected diatomic molecules—HCl, CO, and LiH—within the framework of the Kratzer plus Generalized Morse Potential. The energy eigenvalues and wave functions are determined using the parametric Nikiforov–Uvarov approach, enabling a detailed analysis of key quantum mechanical properties, including kinetic energy, squared momentum, and inverse square distance expectation values. Furthermore, Shannon entropy is applied to examine wave function localization in both position and momentum spaces, emphasizing the impact of screening parameters on molecular behavior. The findings indicate that an increase in the rotational quantum number results in higher energy spectra and expectation values. The Shannon entropy analysis reinforces the uncertainty principle by demonstrating an inverse relationship between position and momentum entropy. These insights contribute to quantum information measures in molecular systems, with potential applications in spectroscopy, molecular modeling, and quantum chemistry.

This approach captures the different patterns of coupled nonlinear reaction–diffusion (RD) models which arises in chemical systems of biology and chemistry. To accomplish this task, a new algorithm based on modified trigonometric cubic B-spline functions is developed. Also, the computational complexity of the algorithm is discussed. From numerical experiments point of view, a test problem for accuracy, 1D and 2D Brusselator models and Grey-Scott model are considered.