Search Results (216)

This paper studies the effects of resource limitations, immunity decay, and delays on an Ebola epidemic model and an optimal control strategy. The model includes two types of delays: a delay in the incubation period of infected individuals and a delay in treatment. Conditions for a Hopf bifurcation at the endemic equilibrium are verified, with its direction and stability analyzed via normal form theory and the center manifold theorem. We also studied the optimal control problem for the SIRD delay model using educational campaigns and Ebola survivors’ immunity as control variables. Furthermore, we formulate an optimization problem based on Pontryagin’s maximum principle. This problem uses a modified Runge-Kutta approach with delays to discover the best control strategy to reduce infections and intervention costs. Finally, simulation results confirm analytical conclusions and show the practical implications of the optimum Ebola control plan using the dde23 MATLAB R2024a built-in solver and DDE-Biftool. Full article

Around 2–8% of children and adolescents in developed societies are young carers, who provide care for ill, disabled, or addicted family members. This paper investigates the vulnerability and multidimensional injustices faced by young carers, drawing on empirical studies—both qualitative and quantitative—and social theory to reveal how young carers navigate their roles within the broader context of social inequality, highlighting the social structures and mechanisms that contribute to their marginalization and the detrimental consequences for their social inclusion, well-being, and personal development. The methodology of this article is a narrative analysis of relevant empirical research on young carers, combined with an analysis of this literature through a normative framework of social justice, which examines four dimensions of justice in order to highlight the vulnerability of young carers. (1) Firstly, young carers are often pushed into their situation because of economic and social constraints, which do not allow the family to find a different solution. Economic inequalities lead to and enforce caring obligations and have a cumulative negative effect on the young carer. Limited resources can be problematic for social inclusion, and when combined with caring obligations, they are corrosive. (2) Secondly, young carers are often victims of moral blackmail, which is that they are trapped in a situation where it would be morally wrong for them to act otherwise. Such moral blackmail can be carried out by those who are cared for, by the family and relatives or even by society, which could, but does not provide alternatives to young carers. (3) Thirdly, young carers are often manipulated to accept their caring obligations through distorted social norms and practices. Other than in the case of moral blackmail, such young carers do not care because they want to do the morally right thing and do have no alternatives available, but because they internalized that it would be normal for them to do so. Two concepts are useful to capture this aspect: adaptive preferences and indoctrination. (4) Fourthly, young people caring is often a form of exploitation, in that it takes unfair advantage of the young carer by receiving something from them, without giving an equivalent in return (and harming them in the process). Full article

Selenium is an essential trace element for human health, but it mainly exists in an inorganic form that cannot be directly absorbed by the body. Brewer’s yeast efficiently converts inorganic selenium into bioavailable organic selenium, making selenium-enriched yeast highly significant for human health research. Selenomethionine (SeM) is an important indicator for evaluating the quality of selenium-enriched yeast. Brewer’s yeast was selected as the experimental subject, and the digestion of this yeast (Brewer’s yeast) was simulated using an in vitro biomimetic gastrointestinal reactor to evaluate the effects of selenium-enriched yeast with various SeM levels on the gut flora of a healthy population. The experimental design comprised normal yeast (control group, OR), yeast containing moderate SeM levels (selenium-enriched group, SE), yeast containing high SeM levels (high-selenium group, MU), and a commercially available group comprising selenium-enriched yeast tablets (MA). The MU group exhibited a significantly higher concentration of short-chain fatty acids than the OR and MA groups during 48 h of fermentation, with significant differences observed (p < 0.05). Sequencing results revealed that the MU group showed significantly increased relative abundances of Bacteroidetes and Actinobacteria, while exhibiting a decreased ratio of Firmicutes to Bacteroidetes, which may simultaneously affect multiple metabolic pathways in vivo. These findings support the theory that selenium-enriched yeast with a high SeM has a more positive effect on human health compared with traditional yeast and offer new ideas for the development and application of selenium-enriched yeast. Full article

Linking methods based on item response theory aim to place item parameters from different groups, test forms, or test administrations onto a common scale. Information-weighted Haebara linking has been proposed as an alternative to the widely used standard Haebara linking method. This study compares its performance against Haebara linking with weights based on the normal distribution. Simulations using the two-parameter logistic model indicate that while information-weighted Haebara linking outperforms the uniformly weighted variant, it does not surpass normal density-weighted Haebara linking in terms of bias and root mean square error. The results suggest that normal density weights should be preferred over both uniform and information-based approaches. Additionally, standard errors were derived for both methods, yielding satisfactory coverage rates. Full article

This study presents a procedure applied to design problems for lateral loaded piles. Calculations for a rigid concrete pile in non-cohesive soil are conducted with the aim of estimating the allowable horizontal force using the methods of Broms and Petrasovit. Random sets are applied to represent the uncertainties of soil parameters, including the internal friction angle and unit weight. Random variables are described using log-normal and beta distributions. Random set theory is utilised to represent variability in the form of probability boxes, possibility distributions, cumulative distribution functions, or intervals. Based on the assumed distributions of the subsoil, the lower and upper bounds for the precise probability of fulfilment of the limit state function of a laterally loaded pile are estimated. The reliability calculation procedure is implemented using the R package (R Studio v2024.12.1+563), and the limit forces and reliability indicators calculated using the two considered methods are compared. The presented procedure serves as an example of the use of a probabilistic approach for the assessment of the capacity of a laterally loaded pile, using a setup for the task involving set-based data and discrete probability distributions. Full article

Form grinding is a precision machining method for the modified ZI worms, and the grinding accuracy mainly depends on the dressing accuracy of the grinding wheel’s profile. A mathematical model of the modified involute helicoid of ZI worms is established based on the curve superposition method. Subsequently, the normal vector of the tooth surface is derived. After that, space meshing theory and matrix transformation methods are applied. Thus, the meshing equation between the grinding wheel and the tooth surface during the form grinding is constructed. Based on the equal error principle, an interpolation algorithm for the modified involute is proposed. The nonlinear meshing equations are solved using MATLAB R2019b software to obtain the discrete point coordinates of the worm end section profile and the grinding wheel axial section profile. The derivative of the discrete points is calculated by using the difference method, and the motion trajectory of the diamond wheel during the grinding wheel dressing process is solved based on the equidistant curve theory. The proposed methods holds certain reference value for calculating the profile of grinding wheels used in the form grinding of modified ZI worms. Full article

We investigated Im-3m H₃S at 200 GPa, a pressure regime where crystalline H₃S is widely considered to be a superconductor. Simulated circularly polarized 10 femtosecond (fs) laser pulses were applied and we quantified the effects on the electron dynamics both during the application of the ultra-fast laser pulse and 5.0 fs after the pulse was switched off. In addition, the carrier-envelope phase (CEP) angle ϕ, which quantifies the relationship between the time-varying direction of electric (E)-field and the amplitude envelope, is employed to control the time evolution of the wavefunction ψ(r). This is undertaken for the first application of Next Generation Quantum Theory of Atoms in Molecules (NG-QTAIM) to the solid state. Ultra-fast phenomena related to superconductivity are discovered in the form of a geometric Berry phase angle associated with the H--H bonding in addition to very high values of the chirality–helicity function that correspond to values normally found in chiral molecules. Future applications are discussed, including chiral spin selective phenomena in addition to high-temperature superconductivity and organic superconductors where phonons do not play a significant role. Full article

The standardized hydrological index (SHI) is the standardized but not normalized (normal probability variate) value of the streamflow used to characterize a hydrological drought, akin to the standardized precipitation index (SPI, which is both standardized and normalized) in the realm of the meteorological drought. The time series of the SHI can be used as a platform for deriving the longest duration, L_T, and the largest magnitude, M_T (in standardized form), of a hydrological drought over a desired return period of T time units (year, month, or week). These parameters are predicted based on the SHI series derived from the annual, monthly, and weekly flow sequences of Canadian rivers. An important point to be reckoned with is that the monthly and weekly sequences are non-stationary compared to the annual sequences, which fulfil the conditions of stochastic stationarity. The parameters, such as the mean, standard deviation (or coefficient of variation), lag 1 autocorrelation, and conditional probabilities from SHI sequences, when used in Markov chain-based relationships, are able to predict the longest duration, L_T, and the largest magnitude, M_T. The product moment and L-moment ratio analyses indicate that the monthly and weekly flows in the Canadian rivers fit the gamma probability distribution function (pdf) reasonably well, whereas annual flows can be regarded to follow the normal pdf. The threshold level chosen in the analysis is the long-term median of SHI sequences for the annual flows. For the monthly and weekly flows, the threshold level represents the median of the respective month or week and hence is time varying. The runs of deficit in the SHI sequences are treated as drought episodes and thus the theory of runs formed an essential tool for analysis. This paper indicates that the Markov chain-based methodology works well for predicting L_T on annual, monthly, and weekly SHI sequences. Markov chains of zero order (MC0), first order (MC1), and second order (MC2) turned out to be satisfactory on annual, monthly, and weekly scales, respectively. The drought magnitude, M_T, was predicted satisfactorily via the model M_T = I_d × L_c, where I_d stands for drought intensity and L_c is a characteristic drought length related to L_T through a scaling parameter, ɸ (= 0.5). The I_d can be deemed to follow a truncated normal pdf, whose mean and variance when combined implicitly with L_c proved prudent for predicting M_T at all time scales in the aforesaid relationship. Full article

This paper presents an extensive investigation into several interrelated topics in mathematical analysis and number theory. The author revisits and builds upon known results regarding the Maclaurin power series expansions for a variety of functions and their normalized remainders, explores connections among central factorial numbers, the Stirling numbers, and specific matrix inverses, and derives several closed-form formulas and inequalities. Additionally, this paper reveals new insights into the properties of these mathematical objects, including logarithmic convexity, explicit expressions for certain quantities, and identities involving the Bell polynomials of the second kind. Full article

The adsorption and reaction of nitric oxide (NO) molecules on the surface of the model-supported metal/oxide system, consisting of Ni nanoparticles deposited on α-Al₂O₃ (0001) in ultra-high vacuum, have been studied using in situ surface-sensitive techniques and density functional theory (DFT) calculations. As a combination of X-ray and Auger electron spectroscopy (XPS, AES), Fourier-transform infrared (FTIR) spectroscopy, and temperature-programmed desorption (TPD) techniques reveals, there is a threshold of Ni particle mean size (<d>) of c.a. 2 nm, differentiating the electron state of adsorbed NO molecules and their reaction. The main feature of Ni particles normally not exceeding 2 nm is that the NO adsorbs in the form of (NO)₂ dimers, whereas, for larger particles, the NO molecules adsorb in the form of monomers, usually characteristic for the bulk Ni substrate. This difference is demonstrated to be the main reason for the different reaction of NO molecules on the surface of Ni/alumina. The striking feature is that, in the case of ultra-small Ni particles (<d> ≤ 2 nm), the nitrous oxide (N₂O) molecules are formed upon heating as a result of the NO self-reduction mechanism, which are otherwise not formed in the case of larger Ni particles. According to DFT results, this is due to the significant synergistic impact of NO co-adsorption on the neighboring NO dissociation reaction over ultra-small Ni particles, mediated by the metal/oxide perimeter interface. The observed molecular conversion effects offer an opportunity to tune the catalytic selectivity of this and related metal/oxide systems via varying the supported metal particle size. Full article

This research demonstrates the possibility and expediency of forming local electric energy systems (LEESs) based on renewable sources of energy (RSE) as balancing groups in the electric power system (EPS), which can maintain efficiency and provide power supply to consumers in an autonomous mode. The LEES is a part of the EPS of thermal and nuclear power plants and is considered as a separate balancing group. LEESs are designed in such a way that they can operate autonomously in both normal and extreme conditions in the EPS. The sources of electricity in LEESs are small hydroelectric power plants (SHPPs), photovoltaic power plants (PVPPs), and wind power plants (WPPs), whose electricity generation is unstable due to dependence on natural conditions. Therefore, the structure of a LEES with RSE includes an energy storage system with reserves sufficient to compensate for the unstable generation and balancing of the mode. LEESs can differ significantly in terms of key technical and economic indicators (power supply reliability, power losses, and power quality), and therefore, it is necessary to choose the optimal one. It is not advisable to optimize the quality of power supply in a LEES by individual indicators, as improvement of one indicator may lead to deterioration of another. The functional readiness of a LEES should be assessed by the quality of operation, which depends on reliability, power losses, and power quality. To simplify the task of assessing the quality of operation, which is a vector optimization problem, a method for determining the integral indicator as a number that characterizes the LEES and reflects the compromise between the values of reliability, power losses, and power quality has been developed. The integral indicator of the functioning of complex systems is based on a combination of the theory of Markov processes and the criterion method of similarity theory. The value of the integral indicator of the quality of operation of the LEES allows for comparing different variants of power transmission and distribution systems without determining individual components of technical and economic indicators—reliability, power losses, and power quality. The offered integral indicator of the quality of functioning of a LEES with RSE corresponds to the general requirements for such indicators. It reflects the actual operating conditions; allows for assessing the efficiency, quality, and optimality of power supply systems; and can be easily decomposed into partial indicators. Full article

This article investigates an axisymmetric contact problem involving the interaction between a rigid cylindrical stamp and a poroelastic cylinder of finite dimensions, based on the Cowin–Nunziato theory of media with voids. The stamp is assumed to have a flat base and to be in frictionless contact with the cylinder. The cylinder, in turn, rests on a rigid base without friction, with no normal displacements or tangential stresses on its lateral surface. Under an applied vertical force, the stamp undergoes displacement, compressing the poroelastic cylinder. The mathematical formulation of this problem involves expressing the unknown displacements within the cylinder and the variation in pore volume fraction as a series of Bessel functions. This representation reduces the problem to an integral equation of the first kind, describing the distribution of contact stresses beneath the stamp. The kernel of the integral equation is explicitly provided in its transformed form. The collocation method is employed to solve the integral equation, enabling the determination of contact stresses and the relationship between the indenter’s displacement and the applied force. A comparative model parameter analysis is performed to examine the effects of different material porosity parameters and model geometrical characteristics on the results. Full article

A simple pore microstructure of parallel, identical, and inclined smooth-walled slits in a rigid solid, for which prediction of its geometrical and acoustic properties is straightforward, can yield useful sound absorption. This microstructure should be relatively amenable to 3D printing. Discrepancies between measurements and predictions of normal incidence sound absorption spectra of 3D printed vertical and slanted slit pore samples have been attributed to the rough surfaces of the slit walls and uneven slit cross-sections perpendicular to the printing direction. Theories of the influence of (a) sinusoidal walls and (b) periodically varying uniform slit widths on the normal incidence absorption spectra of a slit pore medium are outlined. Although the slit wall surface and geometrical imperfections due to 3D printing differ from these idealizations, predictions assuming the ideal forms of roughness confirm that pore-wall roughness could account for differences between predictions and data. Pore-wall roughness is predicted to increase both flow resistivity and tortuosity, thereby increasing the low-frequency sound absorption of thin hard-backed layers. The extent to which sinusoidal slit walls or periodically varying uniform slit widths could improve the sound absorption of a low flow resistivity hard-backed layer containing identical vertical slits is explored. Full article

In this paper, we present a “non-linear” factorization of a family of non-normal operators arising from Gribov’s theory of the following form: ${\displaystyle H_{{\lambda }^{\prime },\mu ,\lambda }={\lambda }^{\prime }{A}^{{*}^2}{A}^2+\mu A^{*}A+i\lambda A^{*}}$$(A+A^{*})A,$ where the quartic Pomeron coupling ${\lambda }^{\prime }$, the Pomeron intercept $\mu$ and the triple Pomeron coupling $\lambda$ are real parameters, and $i^2=-1$. $A^{*}$ and A are, respectively, the usual creation and annihilation operators of the one-dimensional harmonic oscillator obeying the canonical commutation relation $[A,A^{*}]=I$. In Bargmann representation, we have ${\displaystyle A⟷\frac{d}{dz}}$ and ${\displaystyle A^{*}⟷z}$, $z=x+iy$. It follows that ${\displaystyle H_{{\lambda }^{\prime },\mu ,\lambda }}$ can be written in the following form: ${\displaystyle H_{{\lambda }^{\prime },\mu ,\lambda }=p\left(z\right)\frac{d^2}{d{z}^2}+q\left(z\right)\frac{d}{dz},}$ where $p\left(z\right)={\lambda }^{\prime }{z}^2+i\lambda z$ and $q\left(z\right)=i\lambda z^2+\mu z.$ This operator is an operator of the Heun type where the Heun operator is defined by $H=p\left(z\right){\displaystyle \frac{d^2}{d{z}^2}}+q\left(z\right){\displaystyle \frac{d}{dz}}+v\left(z\right),$ where $p\left(z\right)$ is a cubic complex polynomial, $q\left(z\right)$ and $v\left(z\right)$ are polynomials of degree at most 2 and 1, respectively, which are given. For $z=-iy$, $H_{{\lambda }^{\prime },\mu ,\lambda }$ takes the following form: $H_{{\lambda }^{\prime },\mu ,\lambda }=-a\left(y\right){\displaystyle \frac{d^2}{d{y}^2}}+b\left(y\right){\displaystyle \frac{d}{dz}},$ with $a\left(y\right)=y(\lambda -{\lambda }^{\prime }y)$ and ${\displaystyle b\left(y\right)=y(\lambda y+\mu ).}$ We introduce the change of variable $y={\displaystyle \frac{\lambda }{2{\lambda }^{\prime }}}(1-cos\left(\theta \right))$, $\theta \in [0,\pi ]$ to obtain the main result of transforming ${\displaystyle H_{{\lambda }^{\prime },\mu ,\lambda }}$ into a product of two first-order operators: ${\displaystyle {\tilde{H}}_{{\lambda }^{\prime },\mu ,\lambda }={\lambda }^{\prime }(\frac{d}{d\theta }+\alpha \left(\theta \right))(-\frac{d}{d\theta }+\alpha \left(\theta \right)),}$ with $\alpha \left(\theta \right)$ being explicitly determined. Full article

This study examines the spinor representations of $\mathbf{TN}$ (tangent and normal), $\mathbf{NB}$ (normal and binormal), $\mathbf{TB}$ (tangent and binormal) and $\mathbf{TNB}$ (tangent, normal and binormal)–Smarandache curves in three-dimensional Euclidean space ${\mathbb{E}}^3$. Spinors are complex column vectors and move on Pauli spin matrices. Isotropic vectors in the ${\mathbb{C}}^3$ complex vector space form a two-dimensional surface in the ${\mathbb{C}}^2$ complex space. Additionally, each isotropic vector in ${\mathbb{C}}^3$ space corresponds to two vectors in ${\mathbb{C}}^2$ space, called spinors. Based on this information, our goal is to establish a relationship between curve theory in differential geometry and spinor space by matching a spinor with an isotropic vector and a real vector generated from the vectors of the Frenet–Serret frame of a curve in three-dimensional Euclidean space. Accordingly, we initially assume two spinors corresponding to the Frenet–Serret frames of the main curve and its ($\mathbf{TN}$, $\mathbf{NB}$, $\mathbf{TB}$ and $\mathbf{TNB}$)–Smarandache curves. Then, we utilize the relationships between the Frenet frames of these curves to examine the connections between the two spinors corresponding to these curves. Thus, we give the relationships between spinors corresponding to these Smarandache curves. For this reason, this study creates a bridge between mathematics and physics. This study can also serve as a reference for new studies in geometry and physics as a geometric interpretation of a physical expression. Full article