Journal of Mathematical Chemistry最新文献

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.

This work proposes a hybrid numerical strategy to effectively solve the singularly perturbed partial differential equations (SPPDEs) with integral boundary conditions and substantial spatial delays. For the time discretization, the Crank-Nicolson scheme was chosen because of its stability and second-order precision. In order to maximize accuracy in the vicinity of layers coming from the tiny perturbation parameter and delay parameter, the computational implementation will be carried out using a non-uniform Shishkin-type mesh for spatial discretization using cubic spline interpolation. The approach is tested numerically to verify its robustness and efficiency with respect to integral boundary conditions and delayed feedback. Applications to reaction-diffusion systems, catalytic reactions in porous media, and transport-reaction dynamics in tubular reactors are presented to illustrate the effectiveness of the proposed approach.

The Floating spherical Gaussian orbital model has existed for nearly half a century, yet it remains one of the lesser researched areas. Considering the potential of the model to address significant quantum-based or molecular problems, this article aims to bring renewed attention to this long neglected concept. This review presents, a brief overview of the background, literature and current status of the method, and concludes with suggestions for future research.

The qualitative relationship between the adsorption energy distribution of a microporous adsorbent and its total isotherms is modeled by the adsorption integral equation with Langmuir kernel. Due to the instability of the adsorption integral equation, a regularization is required. Recently, we have developed a general regularization using a transformation that will now be specialized for numerical application. In this paper, we perform the first step to this end, namely the construction of an approximation of the transformed total isotherm from finitely many measurement points. The method presented here is based on discrete convolution and is also suitable for the approximation of more general functions and their spectral functions. A full error analysis is given. In particular, the influences of the measurement error, the discretization error and the truncation error on the quality of the approximation of the transformed total isotherm are investigated.

We consider an electron confined in a quantum ring (QR) defined electrostatically within the phosphorene monolayer. A confinement potential with an elliptical shape is employed to account for the anisotropy of the effective masses. The Schrödinger equation is solved, leading to the determination of the energy levels. Subsequently, the Shannon formalism is applied to compute the probability distribution and partition function of the system. Finally, the magnetic and thermodynamic properties of the phosphorene QR are analyzed. The results reveal that the magnetic susceptibility exhibits a negative value, indicative of diamagnetic behavior. A maximum value of magnetic susceptibility is observed at low temperatures and high magnetic fields. At elevated magnetic temperatures, the specific heat remains constant, even in the absence of an external magnetic field.

The present study is on proton magnetic resonance spectroscopy (MRS), as it applies to tumor diagnostics in cancer precision medicine. The goal with the employed patients’ data, subjected to shape estimations alone with no fitting, is to reconstruct self-contained quantitative information of diagnostic relevance. This can be accomplished by proper evaluation of physical metabolites, especially cancer biomarkers (lactates, cholines, citrates,...). Such information is completely opaque in the encoded time signals, but can be transparent in the frequency domain. The optimized derivative fast Fourier transform (dFFT) can meet the challenge. The thorniest stumbling blocks in MRS are abundant overlapping resonances of low resolution and poor signal-to-noise ratio (SNR). Attempts to increase resolution are marred by decreased SNR. The long-sought strategy of MRS, simultaneous improvement of resolution and SNR, is achievable by the optimized dFFT. With the implied aid to decision-making, this is illustrated for ovarian MRS data encoded from benign and malignant human biofluid samples.