Nowadays, hydropower plants are being used to compensate for the variable power produced by the new fluctuating renewable energy sources, such as wind and solar power, and to stabilise the grid. Consequently, hydraulic turbines are forced to work mor...
Pollution of water sources with heavy metals is a pressing environmental issue. To this end, various procedures are being used to remediate water, including sorption. The aim of this study was to investigate the effectiveness of humic acids (HAs) and...
In this study, we present a convergence analysis of a Newton-like midpoint method for solving nonlinear equations in a Banach space setting. The semilocal convergence is analyzed in two different ways. The first one is shown by replacing the existing...
The discussion of what matter and mass are has been going on for more than 2500 years. Much has been discovered about mass in various areas, such as relativity theory and modern quantum mechanics. Still, quantum mechanics has not been unified with gr...
In this paper, we study a coupled system of nonlinear proportional fractional differential equations of the Hilfer-type with a new kind of multi-point and integro-multi-strip boundary conditions. Results on the existence and uniqueness of the solutio...
This work reviews a range of fundamental theoretical considerations in pore structural characterisation. The pore concept is essential for providing a better understanding of physical processes arising within porous media than purely phenomenological...
The rising demand for both water and energy has intensified the urgency of addressing the water–energy nexus. Energy is required for water treatment and distribution, and energy production processes require water. The increasing demand for ener...
In this survey, we have included the recent results on Lyapunov-type inequalities for differential equations of fractional order associated with Dirichlet, nonlocal, multi-point, anti-periodic, and discrete boundary conditions. Our results involve a...
In glass physics, order parameters have long been used in the thermodynamic description of glasses, but their nature is not yet clear. The difficulty is how to find order in disordered systems. This study provides a coherent understanding of the natu...
Theories on life’s origin generally acknowledge the advantage of a semi-permeable vesicle (protocell) for enhancing the chemical reaction–diffusion processes involved in abiogenesis. However, more and more evidence indicates that the orig...
High-convergence order iterative methods play a major role in scientific, computational and engineering mathematics, as they produce sequences that converge and thereby provide solutions to nonlinear equations. The convergence order is calculated usi...
Iterative methods which have high convergence order are crucial in computational mathematics since the iterates produce sequences converging to the root of a non-linear equation. A plethora of applications in chemistry and physics require the solutio...
One of the key applications of the Caputo fractional derivative is that the fractional order of the derivative can be utilized as a parameter to improve the mathematical model by comparing it to real data. To do so, we must first establish that the s...
This article establishes a comparison principle for the nabla fractional difference operator
There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-ar...
This paper addresses the modelling of material behaviour in terms of differential (or rate) equations. To comply with the objectivity principle, recourse is made to invariant fields in the Lagrangian description or to objective time derivatives in th...
Using the results of numerical simulations and astrophysical observations (mainly in the WMAP and Planck frequency bands), it is shown that Galactic foreground emission becomes more sensitive to the mean magnetic field with the frequency, resulting i...
The review provides a pedagogical but comprehensive introduction to the foundations of a recently proposed statistical mechanics (
A review of results on Hermite–Hadamard (H-H) type inequalities in quantum calculus, associated with a variety of classes of convexities, is presented. In the various classes of convexities this includes classical convex functions, quasi-convex...
Diagnostic classification models (DCMs) are statistical models with discrete latent variables (so-called skills) to analyze multiple binary variables (i.e., items). The one-parameter logistic diagnostic classification model (1PLDCM) is a DCM with one...
In this article, we present some results on the existence and uniqueness of random solutions to a non-linear implicit fractional differential equation involving the generalized Caputo fractional derivative operator and supplemented with non-local and...
The present paper includes the local and semilocal convergence analysis of a fourth-order method based on the quadrature formula in Banach spaces. The weaker hypotheses used are based only on the first Fréchet derivative. The new approach provides th...
The dynamic equilibrium between death and regeneration is well established at the cell level. Conversely, no study has investigated the homeostatic control of shape at the whole organism level through processes involving apoptosis. To address this fu...
We aim to derive a super-radiance solution of coherent light and sound waves involving water degrees of freedom in the environment of a microtubule. We introduce a Lagrangian density functional of quantum electrodynamics with non-relativistic charged...
In spite of its unbroken PT symmetry, the popular imaginary cubic oscillator Hamiltonian
In this work, we present a new theoretical approach to interpreting and reproducing quantum mechanics using trajectory-guided wavelets. Inspired by the 1925 work of Louis de Broglie, we demonstrate that pulses composed of a difference between a delay...
In this paper, we study the fault-tolerant metric dimension in graph theory, an important measure against failures in unique vertex identification. The metric dimension of a graph is the smallest number of vertices required to uniquely identify every...
Hyperfine splittings play an important role in quantum information and spintronics applications. They allow for the readout of the spin qubits, while at the same time providing the dominant mechanism for the detrimental spin decoherence. Their exact...
Alkaline–surfactant–polymer (ASP) flooding by means of which alkali additives, surfactant and polymer are inserted as the same slug is one of the most favourable worldwide focuses of Chemical Enhanced Oil Recovery (cEOR) research and fiel...
In axisymmetric fusion devices like tokamaks, the winding of the magnetic field is characterized by its safety profile
We introduce the concept of the magnetic metapole—a theoretical extension of classical multipole theory involving a fractional j pole count (related to the harmonic degree n as j = 2n). Defined by a scalar potential with colatitudinal dependenc...
Vectors are almost always introduced as objects having magnitude and direction. Following that idea, textbooks and courses introduce the concept of a vector norm and the angle between two vectors. While this is correct and useful for vectors in two-...
Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on the repres...
The empirical wavelet transform is a fully adaptive time-scale representation that has been widely used in the last decade. Inspired by the empirical mode decomposition, it consists of filter banks based on harmonic mode supports. Recently, it has be...
We investigate the application of the Galerkin finite element method to approximate a stochastic semilinear space–time fractional wave equation. The equation is driven by integrated additive noise, and the time fractional order
Any two points are close together in a θ-contraction by a factor of θ. The function Δ is implied to be a contraction under this condition, but with a tighter bound on the contraction factor. In this paper, we introduce the notions of orthogonal θ-con...
The nonlocality (superdiffusion) of turbulence is expressed in the empiric Richardson t3 scaling law for the mean square of the mutual separation of a pair of particles in a fluid or gaseous medium. The development of the theory of nonlocality of var...
This paper examines the controllability of a class of heterogeneous networked systems where the nodes are linear time-invariant systems (LTI), and the network topology is triangularizable. The literature contains necessary and sufficient conditions f...
Inrecent years, there has been a notable increase in utilising multiple criteria decision-making (MCDM) methods in practical problem solving. The advancement of enhanced decision models with greater capabilities, coupled with technologies like geogra...
Building on previous work that considered gravity to emerge from the collective behaviour of discrete, pre-geometric spacetime constituents, this work identifies these constituents with gravitons and rewrites their effective gravity-inducing interact...
Mathematical analysis is conducted on cyclical systems with goodwill in capitalization. Proportional goodwill vanishes with vanishing tangible value. Correspondingly, periodic boundary condition does not enable commercial utilization of the goodwill....
This article considers the Dirac field in polar formulation and shows that when torsion is taken in effective approximation the theory has the thermodynamic properties of a van der Waals gas. It is then shown that in the limit of zero chiral angle th...
We study the multiviews of algebraic space curves X from n pin-hole cameras of a real or complex projective space. We assume the pin-hole centers to be known, i.e., we do not reconstruct them. Our tools are algebro-geometric. We give some general the...
In the present work, we classify sets of type (4,n) in PG(3,q). We prove that PG(3,q), apart from the planes of PG(3,3), contains only sets of type (4,n) with standard parameters. Thus, somewhat surprisingly, we conclude that there are no sets of typ...
We analyze time-of-arrival probability distributions for relativistic particles in the context of quantum field theory (QFT). We show that QFT leads to a unique prediction, modulo post-selection that incorporates properties of the apparatus into the...
In this study, we undertake a systematic study of historic market volatility spanning roughly five preceding decades. We focus specifically on the time series of the realized volatility (RV) of the S&P500 index and its distribution function. As e...
I. The arena of quantum mechanics and quantum field theory is the abstract, unobserved and unobservable, M-dimensional formal Hilbert space ≠ spacetime. II. The arena of observations—and, more generally, of all events (i.e., everything) in the real p...
As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of the numerical results becomes increasingly important. This presentation concerns the development of another benchmark for t...
In part I of this work to appear in Foudations-MDPI 2024, some existence and uniqueness results for the solutions of some equations were reviewed, such as the Korteweg–de Vries equation (KdV), the Kuramoto–Sivashinsky equation (KS), the g...
This paper presents a comprehensive analytical–numerical algorithm constructed for proprotor performance evaluation, focusing on accommodating large inflow angles. The algorithm’s design, range, and analytical features are clarified, indi...
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