A quantum particle constrained between two high potential barriers provides a paradigmatic example of a system sustaining quasi bound (or resonance) states. When the system is prepared in one of such quasi bound states, the wave function approximately maintains its shape but decays in time in a nearly exponential manner radiating into the surrounding space, the lifetime being of the order of the reciprocal of the width of the resonance peak in the transmission spectrum. Naively, one could think that adding more lateral barriers would preferentially slow down or prevent the quantum decay since tunneling is expected to become less probable and because of quantum backflow induced by multiple scattering processes. However, this is not always the case and in the early stage of the dynamics quantum decay can be accelerated (rather than decelerated) by additional lateral barriers, even when the barrier heights are arbitrarily large. The decay acceleration originates from resonant tunneling effects and is associated to large deviations from an exponential decay law. We discuss such a counterintuitive phenomenon by considering the hopping dynamics of a quantum particle on a tight-binding lattice with on-site potential barriers.

To improve the understanding of soil–pile interaction of laterally loaded piles, the quasi-static test of pile group foundation in silty clay with 5 foundation piles arranged in cross shape is carried out. The direct measurement-based p–y curves at different depths showed nonlinear behavior, in which the initial stiffness and ultimate soil reaction increased as the depth increased. The loading displacement amplitude corresponding to the failure of each foundation pile in the high axial compression reinforced concrete pile group foundation is given as follows: the front-end nappe foundation pile (#3 pile) is 6mm, the middle pile is 16mm, the front-end nappe foundation pile is 20mm, and the loading displacement amplitude of side pile is 24mm. In silty clay, due to the existence of pile group effect, the edge effect has little effect on the horizontal foundation bed coefficient of foundation pile in pile group, while the influence of masking effect on the horizontal foundation bed coefficient of each foundation pile in pile group is not related to the position of pile, but only to the existence of masking effect, and the influence of different columns of masking effect on the horizontal foundation bed coefficient is the same.

A system of simultaneous multi-variable nonlinear equations can be solved by the Newton’s method with local q-quadratic convergence if the Jacobian is analytically available. If this is not the case, then quasi-Newton methods with local q-superlinear convergence give solutions by approximating the Jacobian in some way. Unfortunately, the quasi-Newton condition (secant equation) doesn’t completely specify the Jacobian approximate in multi-dimensional case, so its full-rank update is not possible with classic variants of methods. The suggested new iteration strategy (“T-Secant”) allows full-rank update of the Jacobian approximate in each iteration by determining two independent approximates for the solution. They are used to generate a set of new independent trial approximates, then the Jacobian approximate can fully be updated. It is shown, that the T-Secant approximate is in the vicinity of the classic quasi-Newton approximate, providing that the solution is evenly surrounded by the new trial approximates. The suggested procedure increases the super-linear convergence of the secant method (φS = 1.618...) to super-quadratic (φT = φS + 1 = 2.618...) and the quadratic convergence of the Newton-method (φN = 2) to cubic (φT = φN + 1 = 3) in one dimensional case. The Broyden-type efficiency (mean convergence rate) of the suggested method in multi-dimensional case is an order higher than the efficiency of other classic low-rank update quasi-Newton methods as shown by numerical examples on a Rosenbrock-type test-function with up to 1000 variables. The geometrical representation (hyperbolic approximation) in single variable case helps explaining the basic operations and a vector-space description is also given in multi-variable case.

Although the empirical Kepler’s laws can be proven by applying Newton’s laws to the dynamics of two particles attracted due to the gravitational interaction, there is no explicit formula for the motion as a function of time. In this paper, a quasi-analytical solution for this problem is proposed. It approximates the real behavior of celestial bodies with an acceptable degree of accuracy. All calculations involved require a low computational cost. This problem is closely related to Kepler’s equation, since, the solution for the equations of motion as a function of time gives us the solution to Kepler’s equation as well. The results are presented for each planet of the solar system (including Pluto), and the solution is compared against the real orbits.

The main inhibitory neurotransmitter in the mammalian brain is 4-aminobutyric acid (GABA). Phthalimide acts as a sodium channel antagonist, one of the finest targets for treating epilepsy is the sodium channel and JNK kinase activity is inhibited to treat epilepsy. a novel compound with multiple targets of action for the treatment of epilepsy also anti-oxidant activity has been designed. The compounds are designed in two series aldehydes and aniline. Docking of all the designed compounds has been done with the suitable protein GABA-AT, sodium channel, JNK protein, and anti-oxidant from protein bank. QSAR was done for constructing many linear regression models. In combination with the developed Docking and QSAR outcomes, ADMET has been performed for the active compounds. The result shows that 11 of the compounds have excellent binding energy in docking with all the receptors and also have good QSAR results and follow the ADMET. The structural understanding of human GABA-AT inhibition was obtained from molecular dynamics simulation studies for compound no. 11 at 5 nanoseconds. Synthesis and pharmacological activity also suggest that the designed compound no.11 be considered the best Novel Compound.

Keywords: liquid alloys, microstratification, dispersed particles, spontaneous dispersion, criteria for true (entropic) spontaneous dispersion, mechanisms of quasi-spontaneous dispersion, methods and results for assessing size of dispersed particles.

This paper introduces an innovative Particle Swarm Optimization (PSO) Algorithm in-corporating Sobol and Halton Random number samplings. It evaluates the enhanced PSO's performance against conventional PSO employing Monte Carlo Random Number Samplings. The comparison involves assessing the algorithms across nine benchmark problems and the renowned Travelling Salesman Problem (TSP). The re-sults reveal consistent enhancements achieved by the enhanced PSO utilizing Sob-ol/Halton samplings across the benchmark problems. Particularly noteworthy are the substantial improvements demonstrated by the enhanced PSO in solving the Travel-ling Salesman Problem. These findings underscore the efficacy of employing Sobol and Halton random number generation methods in enhancing algorithm efficiency.

We prove a quasi-pseudometric version of the strong Ekeland principle proved by P. Georgiev and T. Suzuki.

In this paper, a class of coupled competitive neural networks, which subject to disturbance and discontinuous activation functions, is concerned. To realize the fixed-time quasi-bipartite synchronization, an aperiodic intermittent controller is initially designed. Subsequently, by combining the fixed-time stability theory and nonsmooth analysis, several criteria are established to ensure the bipartite synchronization in fixed time. Moreover, synchronization error bounds and settling time estimates are provided. Finally, numerical simulations are presented to verify the main results.

The paper examines common elements between Lévai’s and Milson’s potentials obtained by Liouville transformations of two rational canonical Sturm-Liouville equations (RCSLEs) with even density functions which are exactly solvable via Jacobi polynomials in a real or accordingly imaginary argument. We refer to the polynomial numerators of the given rational density function as ‘tangent polynomial’ (TP) and thereby term the aforementioned potentials as ‘e-TP’ A special attention is given to the overlap between the two potentials along symmetric curves which represent two different forms of the Ginocchio potential exactly quantized via Gegenbauer and Masjed-Jamei polynomials respectively. Our analysis reveals that the actual interconnection between Lévai’s parameters for these two rational realizations of the Ginocchio potential is much more complicated than one could expect based on the striking resemblance between two quartic equations derived by Lévai for ‘averaged’ Jacobi indexes.

In this paper we provide some important and significant observations on invo-regular rings appeared in Ann. Univ. Mariae Curie-Sklodowska Sect. A Mathematica (2018). In addition we exhibit that strongly invo-regular rings, invo-regular rings and quasi invo-regular rings all coincide with the well known and well characterized tripotent rings and all these rings further coincide with the well known unit regular rings.

Quasi-bound state in the continuum (QBIC) can effectively enhance the interaction of terahertz (THz) wave with matters due to the tunable high-Q property, which has a strong potential application in detection of low-concentration biological samples in the THz band. In this paper, a novel THz metamaterial sensor with a double-chain separated resonant cavity structure based on QBIC is designed and fabricated. The process of excitation of the QBIC mode is verified and the structural parameters are optimized after considering the ohmic loss by simulations. The simulated refractive index sensitivity of the sensor is up to 544 GHz/RIU, much higher than those of recently reported THz metamaterial sensors. Sensing sensitivity of the proposed metamaterial sensor is confirmed in experiment by detecting low-concentration lithium citrate (LC) and bovine serum albumin (BSA) solutions. The limits of detection (LoDs) are obtained to be 0.0025 mg/mL (12 μM) for LC and 0.03125 mg/mL (0.47 μM) for BSA, respectively, both of which excel over most of reported results in previous studies. These results indicate that the proposed THz metamaterial sensor has excellent sensing performances and can well be applied to the detection of low concentration biological samples.

The applicability of the distance aggregation problem has attracted the interest of many authors. Motivated by this fact, in this paper we face the modular quasi-(pseudo-)metric aggregation problem. We characterize those functions that allow merging a collection of modular quasi-(pseudo-)metrics into a single one. Specifically, a description of such functions in terms of triangle triplets is given and, in addition, the relationship between modular quasi-(pseudo-)metric aggregation functions and modular (pseudo-)metric aggregation functions is discussed. Such characterizations are illustrated with appropriate examples. A few methods to construct modular quasi-(pseudo-)metrics are yielded. Several properties of modular quasi-(pseudo-)metric aggregation functions are explored and used to develop quick tests for discarding candidate functions to aggregate modular quasi-(pseudo-)metrics. Moreover, a characterization of those modular quasi-(pseudo-)metric aggregation functions that preserve modular quasi-(pseudo-)metrics is also provided. Furthermore, the relationship between modular quasi-(pseudo-)metric aggregation functions and quasi-(pseudo-)metric aggregation functions is studied in such a way that significative differences are displayed.

This study presents a detailed computational investigation aimed at identifying and evaluating potential small organic molecular scaffolds as inhibitors targeting the Pks13 protein, a critical enzyme in tuberculosis (TB) drug discovery. Our approach integrates multiple computational techniques, including quantitative structure-activity relationship (QSAR) modelling, compound library generation, molecular docking, biological activity prediction, re-evaluation of screened compounds, molecular dynamics (MD) analysis, and binding free energy estimation using the MM-GBSA approach. We developed a robust QSAR model using multiple linear regression (MLR) techniques, specifically tailored to predict the minimum inhibitory concentration (MIC) values of potential anti-TB agents. This model demonstrated excellent predictive performance, validated through rigorous internal and external validation procedures. Through molecular docking simulations, we identified five promising inhibitors Ethyl (R,Z)-2-(2-((2-chlorobenzyl) oxy)benzylidene)-5-(4-chlorophenyl)-7-methyl-3-oxo-2,3-dihydro-5H-thiazolo [3,2-a] pyrimidine-6-carboxylate (PKD1), (7R,9aR)-7-(2-hydroxyphenyl)-4-(2-methoxyphenyl)-3-methyl-7,8,9,9a-tetrahydroisoxazolo[5,4-b]quinolin-5(6H)-one (PKD2), (7-(4-methoxy phenyl)-2-methyl-3-phenylpyrazolo[1,5-a]pyrimidin-5-yl)(4-(3-(trifluoromethyl)phenyl) piperazin-1-yl)methanone (PKD3), (8S,10S)-10-(((2R,4S,5S,6S)-4-amino-5-hydroxy-6-methyl tetrahydro-2H-pyran-2-yl)oxy)-6,8,11-trihydroxy-8-(2-hydroxyacetyl)-1-methoxy-7,8,9,10-tetra-hydrotetracene-5,12-dione (PKD4), 3-(3,4-dimethylphenyl)-5-((2-(4-fluorophenyl)-2-oxoethyl) thio)-6-phenyl-2-thioxo-2,3,5,7a-tetrahydrothiazolo[4,5-d]pyrimidin-7(6H)-one (PKD5)with high binding affinities, prioritizing them based on their binding energies. These selected compounds were further assessed for their biological activity predictions, guiding the selection of candidates for experimental validation. Subsequent re-evaluation using absolute binding free energy estimation and MD simulations provided insights into the stability and dynamics of the protein-ligand complexes over time. Our findings highlighted the potential of identified compounds as stable binders within the Pks13-TE domain binding pocket, underscoring their viability as drug candidates. Additionally, binding free energy analysis using MM-GBSA reaffirmed the strong affinity of the proposed compounds towards Pks13. Our integrated computational approach offers a systematic and detailed framework for the identification and characterization of potential Pks13 inhibitors with specific relevance to TB drug discovery.

For many disciplines of science, all conceivable collisional cross sections and reactions must be precisely known. Although the recent decades were a trial of large-scale research to give these data, many essential atomic and molecular cross section data still missing, and the reliability of the existing cross sections has to be validated. In this paper, we present electron stripping, electron capture, and system breakdown cross sections in carbon (C5+) ions and lithium (Li2+) ions collisions with atomic hydrogen based on the Monte Carlo models of classical and quasi-classical trajectories. According to our expectation, the QCTMC results show higher results in comparison to standard CTMC data, emphasizing the role of Heisenberg correction constraint, especially in the low energy regime. On the Other hand, at high energy, the Heisenberg correction term has less influence as a projectile momentum increase. We present the total cross sections of electron stripping, electron capture, and system breakdown in C5+ ions and Li2+ ions collisions with atomic hydrogen in the impact energy range from 10 keV to 160 keV, which is of interest in astrophysical plasmas, atmospheric sciences, plasma laboratories, and fusion research.

Quasi-interpolation is a powerful tool for approximating functions using radial basis functions (RBFs) such as Gaussian kernels. This avoids solving large systems of equations as in RBF interpolation. However, quasi-interpolation with Gaussian kernels on compact intervals can have significant errors near the boundaries. This paper proposes a quasi-interpolation method with Gaussian kernels using Chebyshev points and boundary corrections to improve the approximation near the boundaries. The boundary corrections use a linear approximation of the function beyond the interval to estimate the truncation error and add correction terms. Numerical studies on test functions show that the proposed method reduces errors significantly near boundaries compared to quasi-interpolation without corrections, for both equally spaced and Chebyshev points. The convergence and accuracy with the boundary corrections are generally better with Chebyshev points compared to equally spaced points. The proposed method provides an efficient way to perform quasi-interpolation on compact intervals while controlling the boundary errors.