One of the primary challenges in the application of metallic nanoparticles is achieving colloidal stability during the functionalization and conjugation processes. In this study we propose a protocol of stabilization, functionalization and conjugation for three types of metallic morphologies: Gold nanospheres, gold nanostars and gold nanorods; as well as for fluoride nanoparticles. This research serves as a foundation for future studies involving FRET-based sensing using Ytterbium and erbium-codoped sodium yttrium fluoride (NaYF 4 : Yb, Er) and gold nanoparticles. The procedure involves the removal of a cytotoxic surfactant, Hexadecyltrimethylammonium bromide (CTAB), as well as a ligand exchange of sodium citrate with 3-Mercaptopropionic acid (3-MPA) for better colloidal stability. In this study it is shown that the most important parameter for colloidal stabilization is pH control of the solution, and that is needed to optimize the time of interaction, and reagent concentration in ligand exchange for better results. With the proper adjustments in functionalization and conjugation, this procedure could be generalized to any type of nanoparticle, but further experiments are needed.

Arsenene, a two-dimensional pnictogen, has attracted interest due to its potential for next-generation nanoelectronics. In this work, we investigate the structural, electronic, and magnetic responses of germanium (Ge) doped arsenene over a concentration range from 2.0% to 12.5%. First-principles density functional theory calculations, incorporating spin polarization and fully relativistic spin-orbit coupling (SOC), reveal a tunability of the ground state driven by defect concentration. At high doping levels, inter-defect interactions induce a non-magnetic, semimetallic state. Conversely, diluting the Ge concentration spatially isolates the impurities, restoring a semiconducting behavior with a tunable bandgap up to 0.301 eV. The inclusion of SOC demonstrates that spatial confinement alters carrier dynamics, bifurcating the valence band into high-mobility light-hole and localized heavy-hole flat bands, creating a distinct dual-channel transport mechanism. Furthermore, in the diluted regime, the uncompensated spin of the Ge substitution induces a localized magnetic moment of $1.0 \, \mu_B$. These findings demonstrate the effectiveness of controlled Ge doping to tailor the intrinsic properties of arsenene, providing fundamental theoretical insights for the design of 2D field-effect transistors and spintronic devices.

We present the analysis of small-scale structure in Fuzzy Dark Matter (FDM) halos, separating the problem into two complementary parts. First, we characterize density fluctuations by decomposing the field into a smooth, spherically averaged core–halo model and a residual that isolates the interference pattern seen in these halos. The power spectrum of this residual shows a well-defined peak, clearly separated from that of the total and model densities, allowing us to identify the characteristic scale of the granules that dominate the halo. Second, we compute a local de Broglie wavelength directly from the velocity field obtained from the wavefunction. By constructing radial profiles, we show that λdB depends strongly on position and displays a non-monotonic behavior, reaching a minimum at the transition between the solitonic core and the outer halo. Taken together, these results establish a direct and quantitative connection between the spectral properties of density fluctuations and the velocity field within the structure. In particular, we find that the smallest effective wavelength, and therefore the highest characteristic velocities, is located at the core-halo transition sphere. Our analysis provides a picture of the granular structure in FDM halos and its relation to the core-halo morphology.

Los efluentes industriales que contienen colorantes sintéticos representan una de las fuentes más persistentes de contaminación de aguas superficiales, principalmente porque los procesos de tratamiento convencionales no logran su eliminación completa. En este trabajo, evaluamos la eficiencia de degradación de un sistema de plasma a presión atmosférica no térmico (NTAPP) para el colorante Azul Ácido 9 (AB9), utilizando FeSO₄ como aditivo catalítico en concentraciones que van de 0,2 a 1,0 mM. La degradación se monitorizó mediante absorbancia UV-Vis a 630 nm, y se registraron los parámetros fisicoquímicos de la solución: pH, conductividad eléctrica, salinidad, sólidos disueltos totales (TDS) y temperatura de la solución a lo largo del tratamiento. Después de 30 minutos de exposición al plasma, se logró una decoloración casi completa, observándose un rendimiento catalítico óptimo a 0,6 mM de FeSO₄ . La degradación mejorada a esta concentración es consistente con un mecanismo tipo Fenton, en el que los iones Fe²⁺ reaccionan con el H₂O₂ generado por el plasma para producir radicales OH adicionales. El análisis de COT confirmó una eficiencia de mineralización del colorante superior al 90 %. Estos resultados demuestran el potencial del NTAPP intensificado catalíticamente como una estrategia eficaz para el tratamiento de aguas contaminadas con colorantes.

This work presents a comprehensive ab initio investigation of the structural, electronic, elastic, and optical properties of aluminum doped zinc oxide (Zn 1-x Al x O) using the DFT+ U framework. A realistic 2×2×2 supercell model is employed to simulate substitutional doping at various Al concentrations (up to 25%). The results reveal a systematic reduction in band gap energy, reaching 2.216 eV at the highest doping level, which reflects enhanced electrical conductivity. Density of states analysis highlights the emergence of Al-3p states near the conduction band, contributing to donor-like behavior and supporting n-type conductivity. The elastic properties show a progressive decrease in stiffness and an increase in anisotropy with Al content, indicating mechanical softening of the ZnO matrix. Optically, the doped systems exhibit improved transparency, a blue shift in the absorption edge, and modulation of the dielectric response, consistent with the Burstein Moss effect. These findings suggest that Al doping significantly tailors the multifunctional behavior of ZnO, making it a promising candidate for transparent conducting electrodes, optoelectronic components, and sensor technologies. The theoretical insights presented herein provide useful guidelines for experimental optimization of Al doped ZnO-based materials.

Brain--Computer Interfaces (BCIs) establish communication pathways between brain activity and external devices through the analysis of electroencephalographic (EEG) signals. In this work, we present a methodology for classifying cognitive states associated with left- and right-hand motor imagery using recordings from Dataset IIa of the BCI Competition IV. EEG signals were band-pass filtered in the 8--30 Hz frequency range, processed using Common Spatial Patterns (CSP), and classified with a linear Support Vector Machine (SVM). The proposed model achieved an accuracy of 0.717, a Cohen's κ coefficient of 0.432, and an F1-score of 0.748. These results demonstrate the effectiveness of the CSP--SVM framework for motor imagery classification and support its application in BCI systems aimed at neurorehabilitation, neurofeedback, and assistive technologies

Beam monitoring detectors play a crucial role in experimental control and radiological protection by enabling real-time characterization and stabilization of particle or photon beams. They provide essential information on beam intensity, position, and scattering, helping to ensure measurement accuracy and prevent damage to sensitive detectors, while also contributing to radiation safety by quantifying stray radiation.
  In this work, a Geant4 simulation of an X-ray beam monitoring detector (BMD) composed of six hexagonal BC404 plastic scintillators was developed to improve granularity. The intrinsic time resolution was measured to be 203.2$\pm$4.0 ps, and simulations estimated that only about 10% of the beam photons interact with the BMD. The X-ray multiplicity was found to follow an inverse-square dependence on distance.   Additionally, a backscatter study using a water cube showed that approximately 6% of the beam was detected as backscattered radiation. These results potential suitability for X-ray beam characterization with minimal beam perturbation and highlight its potential role in scatter radiation protection.

This study investigates the optical behavior of photon rays and scalar waves in a three-dimensional static Black String Charged Wormhole (BSCWH) spacetime featuring topological disclinations. By analyzing null geodesics and the scalar Helmholtz equation, we present a unified treatment of light and wave propagation in curved spacetime with geometric defects. The disclination parameter accounts for angular deficits due to topological defects, the wormhole parameter governs throat geometry, and the Neveu-Schwarz (NS) charge introduces a string-inspired field contribution. These factors jointly influence light bending, photon orbits, and scalar wave modes. Scalar wave propagation reduces to a Schrödinger-like equation with an effective potential, from which we derive a spatially and frequency-dependent effective refractive index.  We obtain a closed-form weak-field deflection angle in terms of the geometric parameters and the disclination, and demonstrate that the trivial redshift function inherent to the BSCWH geometry precludes the formation of a photon sphere, yielding instead a critical impact parameter set by the throat radius. In the wave-optics sector, we show that the effective potential diverges at the throat, enforcing total reflection of scalar waves and producing frequency-dependent phase shifts characteristic of a dispersive analogue-gravity medium. Our findings reveal how curvature, charge, and topological features modify optical signatures, with implications for gravitational lensing, analogue gravity experiments, and optical media design. This work highlights the role of string-inspired effects and spacetime defects in shaping wave dynamics near wormholes.

Se muestra que los desarrollos y resultados del artículo [Rev. Mex. Fís. 62 (2016) 330], donde se estudia el cambio del índice de refracción y el coeficiente de absorción de un sistema formado por puntos cuánticos cilíndricos de GaAs/GaAlAs en presencia de un campo magnético externo, tienen errores, omisiones e incoherencias. La principal incoherencia es que algunas de sus gráficas no se pueden obtener de sus resultados analíticos.

In the present work we are reporting the preparation conditions of GaAs thin films and the technique which was employed to produce films deposited on Ge wafers substrate at constant substrate temperature by thermal evaporation method are described. Also it includes photovoltaic measurements which are presented by current – voltage characteristics, photocurrent, short – circuit, open – circuit voltage of GaAs/Ge heterojunction, at room temperature and different annealing temperatures have been measured. All the samples were prepared under constant conditions (pressure, substrate temperature and rate of deposition); the main parameters that control the nature of the film properties are thickness (0.4, 0.7, 1.0 and 1.5) μm and annealing temperature (473 and 523) K. The dark current decreases with increasing of thickness; whereas increases slightly with increasing of annealing temperatures. Under illumination, the photocurrent increases with increasing of annealing temperatures and decreases with increasing of thickness except at thickness equal to 1.5m. There is a linear increasing in the first part of the relation between Isc and Voc with incident power intensity and then the saturation region appeared. The Isc and Voc decrease with increasing of thickness, while increase with increase of annealing temperatures.

Los sensores ópticos interferométricos tienen múltiples ventajas entres las cuales destaca la inmunidad a la interferencia electromagnética, altas sensibilidades, sensibles a múltiples parámetros, fácil fabricación, entre otras. Para este tipo de sensores su principal limitación es la ambigüedad 2π la cual limita sus rangos de operación. En este trabajo se propone el uso de regresión multilineal simple basada en componentes principales del kernel como datos de entrada para estimar el valor del parámetro físico en un amplio rango de medición de un sensor óptico interferométrico. Con este método primero se obtienen las componentes principales de los atributos transformados y luego se aplica regresión multilineal. La transformación de los datos es por medio de funciones kernel (polinomial y Gaussiano) y se aplica con la finalidad de encontrar relaciones lineales entre los datos de entrada y la variable de salida. Las características fueron amplitudes de los picos y posiciones en longitud de onda de los picos del espectro de interferencia del sensor interferométrico. El método fue probado con señales experimentales de un sensor óptico interferométrico sensible a la temperatura basado en tres capas de distintos materiales. La raíz del error cuadrático medio alcanzado con la función de núcleo Gaussiano y 50 componentes principales fue de 0.001◦C para el rango de medición de 0−58◦C.
Interferometric optical sensors have multiple advantages, among which the following stand out, immunity to electromagnetic interference, high sensitivities, sensitivity to multiple parameters, easy manufacturing, among others. The main limitation of this type of sensor is the ambiguity of 2π, which limits its operating ranges. In this work, the use of multilinear regression based on kernel principal components as input features to estimate the value of a physical parameter over a wide measurement range of an interferometric optical sensor is proposed. With this method, the principal components of the transformed features are first obtained, and then simple multilinear regression is applied. Data transformation is performed using kernel functions (polynomial and Gaussian) and is applied to find linear relationships between the input data (features) and the output variable. The features were peak amplitudes and wavelength positions of the peaks of the interference spectrum of the interferometric sensor. The method was tested with experimental spectra from a temperature-sensitive interferometric optical sensor based on three layers of different materials. The root mean square error achieved with the Gaussian kernel function and 50 principal components was 0.001 o C for the measurement range from 0−58 o C.

We present a reproducible benchmark study on inverse parameter estimation in two Newtonian systems from trajectory data: a damped oscillator and projectile motion with drag. Beyond the standard exact-model setting, the manuscript introduces four stress scenarios that are decisive for publication-level assessment: partial observability, unknown initial conditions, sparse sampling, and model mismatch. Recoverability is quantified by median relative parameter error, while local identifiability is examined through cost surfaces and parameter-correlation structure. In the exact-model benchmark, Levenberg–Marquardt, Nelder–Mead and differential evolution reach similarly small errors, but their computational costs differ by more than one order of magnitude. The central contribution of the article is not merely to show that parameters can be recovered under favorable synthetic conditions, but to delimit where recovery remains reliable and where it deteriorates. The results show a recoverability frontier controlled jointly by noise level, sampling step, observability and model adequacy. Model mismatch produces systematic bias even when visual trajectory fitting remains acceptable, highlighting the difference between good reconstruction and trustworthy inference. These findings strengthen the use of synthetic Newtonian benchmarks as rigorous testbeds for computational physics, inverse problems and future experimental identification studies.

La geometría fractal ofrece un marco alternativo para describir la complejidad de las estructuras irregulares del cuerpo humano y, en paralelo, ha motivado el desarrollo de antenas que explotan la auto-semejanza para mejorar su desempeño. En particular, las antenas prefractales derivadas de configuraciones como el triángulo de Sierpinski permiten la miniaturización del radiador, la operación multibanda y un control más preciso de la directividad de radiación, lo cual resulta especialmente atractivo en aplicaciones médicas donde el espacio es limitado y las frecuencias de operación son críticas. Esta revisión examina los fundamentos de la dimensión fractal y su relación con la respuesta en frecuencia de las antenas, y posteriormente recorre el estado del arte de aplicaciones médicas recientes, incluyendo la detección de cáncer de piel y mama, sistemas de telemetría implantable, electrónica flexible tipo “tatuaje” y bobinas fractales para técnicas avanzadas de imagen. Se discuten ventajas prácticas reportadas, tales como miniaturización, comportamiento multibanda, mejora de la ganancia y la eficiencia, capacidad de relleno de espacio y reducción del acoplamiento no deseado, junto con desafíos asociados a la fabricación a microescala, las pérdidas en tejido, las restricciones de tasa de absorción específica (SAR) y la biocompatibilidad de los materiales. Finalmente, la revisión resume los criterios de diseño y simulación electromagnética más utilizados, basados en las ecuaciones de Maxwell, las funciones de Green y el análisis de directividad. Además, plantea líneas de investigación abiertas orientadas a traducir las antenas prefractales de prototipos de laboratorio a dispositivos médicos robustos y clínicamente viables.
Fractal geometry provides an alternative framework for describing the complexity of irregular human body structures and, in parallel, has motivated the development of antennas that exploit self-similarity to enhance their performance. In particular, prefractal antennas derived from configurations such as the Sierpinski triangle enable radiator miniaturization, multiband operation, and more precise control of radiation directivity, which is especially attractive in medical applications where space is limited and operating frequencies are critical. This review examines the fundamentals of fractal dimension and its relationship with antenna frequency response, and subsequently surveys the state-of-the-art in recent medical applications, including skin and breast cancer detection, implantable telemetry systems, flexible "tattoo-like" electronics, and fractal coils for advanced imaging techniques. It discusses reported practical advantages, such as miniaturization, multiband behavior, improved gain and efficiency, space-filling capacity, and reduced unwanted coupling, along with challenges associated with microscale fabrication, tissue losses, specific absorption rate (SAR) restrictions, and material biocompatibility. Finally, the review summarizes the most commonly used electromagnetic design and simulation criteria, based on Maxwell’s equations, Green’s functions, and directivity analysis. Additionally, it outlines open research lines aimed at translating prefractal antennas from laboratory prototypes to robust, clinically viable medical devices.

Scattering phase shifts for quantum mechanical potential scattering can be derived directly from the scattering amplitude, bypassing the need to solve the Schrödinger equation explicitly. This can be achieved by numerically integrating the phase equation from the origin to the asymptotic limit. The Phase Function Method (PFM) is considered an effective approach for computing scattering phase shifts in quantum mechanics. The Phase Function Method (PFM) is applied to analyze the Pöschl–Teller potential along with spin-orbit interactions. The strategy includes employing a five-parameter potential model to fit the calculated scattering phase shift curves to the established data for elastic scattering phase shifts. Numerical scattering phase shifts for nucleon-nucleon systems align well with prior research results.

It is known that, under the presence of a static external magnetic field, an electromagnetic wave rotates its polarization axes when transmitted across a single graphene layer. This phenomenon is a direct consequence of the anisotropic optical conductivity arising from the tight-charger carrier interaction in graphene due to the magnetic field.
Here, we report a study of Faraday rotation and ellipticity of the transmitted electromagnetic field across a graphene monolayer under uniform applied strain. Assuming the graphene layer is surrounded by two different semi-infinite dielectric media, the transmitted coefficient is derived as a function of the anisotropic optical conductivity. The strain not only changes the electronic band structure but also can be employed to tune the electronic collective excitations (magnetoplasmons) and thus the optical properties of graphene monolayers. Because both strain and magnetic field induce highly anisotropy in graphene optical conductivity, the strain-dependent amplitude and orientation play an important role in manipulating the variation of Faraday rotation angles and ellipticity in magneto-optical devices.

Positron emission tomography (PET) scans can be used to investigate the pathogenesis of
neurological disorders and diseases such as Alzheimer’s and Parkinson’s. PET scans use positron
to resolve an image of the internal biochemical process occurring inside the body,i.e, ionization cross
sections. Knowledge of ionization cross sections for atoms is evidently crucial in PET technology.
We will discuss some recent developments of the scaled Born positron (SBP) method for ionization
of atoms. The SBP method was originally proposed for electronic excitations of atoms (J.L.S.
Lino, Chin.J.Phys. 54 (2016) 504). First Born approximation (FBA) and the atomic orbital
wavefunctions have been approximated by Roothaan-Hartree-Fock, and the scattered positron
and ejected electron have been approximated by a plane wave and Coulomb wave as proposed by
Barlett et al (Atomic Data Tables 86 (2004) 235). It is shown that the FBA combined with an
analytical and elaborate factor results in a efficiency method when compared with the sophisticate
and traditional binary-encounter-dipole (BED) model. Results of ionization cross sections of H,
He, Ne, and C atom using the new representation are presented to illustrate the applicability of
the improved SBP method.
 

The Caputo-Fabrizio (CF) and Atangana-Baleanu (AB) derivatives, were proposed as alternatives to the usual Caputo and Riemann-Liouville fractional derivatives. The advantage of CF and AB derivatives is that they are defined in terms of non-singular kernels, such as the exponential function and the Mittag-Leffler function, respectively. However, the use and application of fractional derivatives with non-singular kernels has resulted in many models in terms of fractional differential equations that do not comply with the principle of dimensional homogeneity and therefore their solutions are not entirely satisfactory. In this work, we propose New Derivatives of the Caputo-Fabrizio (NDCF) and Atangana-Baleanu (NDAB) types, derive their Laplace transforms, and apply them to the solution of an RC circuit as an illustrative example. Furthermore, we confirm that the price to pay for attempting to avoid the singularity of the Caputo derivative is that the initial condition is not satisfied for kernels without singularities. The initial condition depends on the order of the fractional derivative γ and only reduces to the initial condition when γ = 1. To provide a more realistic response, a shift in the dynamic variable was introduced, yielding physical solutions consistent with the dimensionality, the initial condition, and the steady state.

We introduce a simple gauge-invariant spectral diagnostic for Euclidean Yang--Mills backgrounds based on covariant diffusion. Using the gauge-covariant Laplacian $\Delta_A$ , we consider heat-kernel trace observables built from the semigroup $e^{-t\Delta_A}$ and address the infinite-volume divergence through two complementary normalizations: a trace per unit volume in a finite domain followed by the thermodynamic limit, and a relative trace with respect to the trivial background $A=0$ that cancels the leading volume contribution. From these trace observables we define an effective spectral scale via a logarithmic derivative in diffusion time, yielding a mass-like parameter that characterizes the large- $t$ decay of covariant diffusion when the limit exists. In parallel, we outline a diffusion-based spectral-dimension diagnostic and discuss basic invariance and positivity properties of the construction. The framework is formulated in general dimension $d$ and is intended as a clean, continuum starting point for connecting gauge-invariant long-time diffusion behaviour with spectral information of the covariant operator, without discretization or lattice input.

 
Copper degradation in sulfuric acid remains a critical obstacle in many industrial processes due to the aggressive nature of acidic environments. In this study, the corrosion inhibition performance of 5-(5-(4-nitrophenyl)thiophen-2-yl)-1,3,4-oxadiazole-2(3H)-thione (NPT-OxT) was systematically investigated in 0.5 M H₂SO₄ using a combined experimental and theoretical framework. Weight-loss assays analyzed with Response Surface Methodology (RSM) demonstrated excellent statistical accuracy (R² = 0.999) and identified optimal conditions under which NPT-OxT achieved an inhibition efficiency of 97%. Adsorption thermodynamics indicated a mixed physisorption–chemisorption mechanism, with ΔG ads values ranging from −39.64 to −40.48 kJ·mol⁻¹, confirming spontaneous and strong surface binding. Kinetic assessments further revealed that the apparent activation energy increased markedly from 7.36 kJ·mol⁻¹ in the blank system to 40.38 kJ·mol⁻¹ with inhibitor addition, highlighting the establishment of a durable protective film. SEM analysis corroborated these findings by revealing a transition from a severely damaged surface in uninhibited acid to a smooth, compact morphology in the presence of NPT-OxT, confirming the formation of an adherent inhibitor film on copper. EDX analysis quantitatively confirmed this protective effect, showing a dominant copper peak and suppressed oxygen and sulfur signals in the presence of the inhibitor. Complementary density functional theory (DFT) analyses supported these observations, showing a moderate HOMO–LUMO gap (3.25 eV), a negative ΔN value ( – 0.139 ev), and an electrophilicity index of 3.97 eV, all consistent with efficient charge transfer interactions and strong affinity for copper surfaces. Together, these results demonstrate that NPT-OxT is a potent corrosion inhibitor, providing both mechanistic insights and promising applicability for industrial protection of copper in harsh acidic conditions.

We introduce an optimized protocol of fracture pattern classification using an artificial neural network to identify the solvent involved in the desiccation cracking process of starch-liquid slurries, even after it has been completely evaporated. For this purpose, image analysis techniques were used to characterize patterns obtained from drying suspensions using single solvents (water, ethanol, acetone) and two-component solvents (water-ethanol mixtures at different concentrations). Frequency histograms were generated based on nine morphological features, taking into account their size, shape, geometry and orientational ordering. Subsequently, we used these histograms as input data into artificial neural network variants to determine the set of features that lead to the higher accuracy in solvent identification. We obtained an average accuracy of $96(\pm 1)\%$ considering all solvents in the analysis. The highest accuracy was obtained with sets of features that include the crack area distribution, a parameter typically ignored in the literature. The proposed protocol can help to determine the combination of features that optimize pattern recognition in other fields of science and engineering.

In a bid to establish the impact of the temperature of the calcification on the structural, microstructural or the functional maturation of the nanoparticles, magnesium oxide (MgO) nanoparticles were prepared using a methodology that involves controlled coprecipitation technique. The presence of some single phase cubic percales MgO and refinement of the diffraction peaks have been performed through X-ray diffraction (XRD) and Lorentzian-Gaussian profile analysis of the lines respectively. TheWilliamsonHall (W-H) method gave a valid estimate of changes caused by thermo-contributing to the broadening of the peak by quantitative decoupling of crystallite-size and lattice strain contributions. The above increase in temperature to systematic crystallite growth 5.911 nm, lattice relaxation and strain elimination were observed as well as a decrease in the density of dislocations and an increase in structural coherence. The optimal crystal structure of MgO, as well as concentration of defects and internal stress, was achieved between, as the crystal structure of the MgO improved, the surface activity did not reduce significantly. Further heating above this regime increased grains coalescence and compressive stresses and reduced sites of active surface. The findings are a direct correlation between processingstructure property that explicitly shows that the dynamic of defects and mechanical stability of MgO nanocrystals depends on the precise control of the calcification temperature. The findings give a forecast analysis of designing MgO-based materials to enable catalysis, optical coating, dielectrical apparatus as well as biomedical applications.

This paper studies a Caputo time-fractional version of the modified Kawahara equation, ${}^{C}D_t^\rho u + a u^2 u_x + b u_{xxx} + c u_{xxxxx}=0$, $0<\rho\les 1$, which combines cubic nonlinearity, third- and fifth-order dispersion, and temporal memory. We begin with the corresponding classical equation and derive an exact traveling-wave family in Jacobi elliptic form, $ u(x,t)=A+B\,\cn^2\!\bigl(\kappa(x-\lambda t-\xi_0);m\bigr)$. The solitary-wave profile is then recovered as the limiting case $m\to1$, which yields a $\sech^2$-type wave. Next, these exact classical profiles are transferred to the fractional setting through the memory-adapted time law $g_\rho(t)=\frac{t^\rho}{\Gamma(\rho+1)}$. Because the Caputo derivative does not satisfy the ordinary local chain rule, the resulting fractional traveling profile is interpreted as an explicit approximation rather than an unproved exact solution. A residual identity is derived, and a simple L1 finite-difference scheme is presented to assess the quality of the approximation numerically. The analysis provides a structured bridge between exact classical wave theory and residual-validated fractional-wave modeling.

Poly(3,4-ethylenedioxythiophene)-polystyrenesulfonate (PEDOT: PSS) with secondary doping has been widely researched as a hole transport layer in solar cells because secondary doping can provide conformational change and improve the properties of PEDOT: PSS. PEDOT: PSS is doped with graphene oxide (GO) to form PEDOT: GO solution, then, sodium hydroxide is added into the acidic PEDOT: GO solution to study the pH effect. The HRTEM result indicates the formation of PEDOT: GO. Besides, the two-point probe results show that both acidic and basic PEDOT: GO is more conductive than PEDOT: PSS and GO alone. This was due to the transformation of benzoid structure to quinoid structure which has been supported by the lower d-spacings of acidic PEDOT: GO (3.48 Å) and basic PEDOT: GO (3.44Å) compared to PEDOT: PSS (3.56Å) in the XRD result. Other than that, the UV-Vis absorbance result shows that the PSS chain absorbance peak in basic PEDOT: GO is around 13% lower than that in acidic PEDOT: GO, indicating better replacement of insulating PSS chain and more successful formation of PEDOT: GO. In the EDX results, the basic PEDOT: GO shows higher oxygen content (93.34%) than acidic PEDOT: GO (44.58%) due to the increase of hydroxyl groups of GO in basic conditions caused by NaOH. Besides, the average resistance values of the basic PEDOT: GO and acidic PEDOT: GO layers are 3.72E+10 Ω and 1.30E+10 Ω, respectively. The Na+ ion in NaOH resulted in the damages of unreacted PEDOT: PSS, making the basic PEDOT: GO sample more electrically resistant than the acidic PEDOT: GO sample. Despite some of the adverse effects of basic PEDOT: GO, it shows the lowest surface roughness (Rq: 2.52 nm) among all potential HTLs investigated, indicating the best deposition on glass and wettability.

In this work, we investigated the fundamental electronic, optical, and thermoelectric properties of NaCl$_7$, an uncommon sodium chloride stoichiometry, using density functional theory (DFT) with the LSDA+mBJ approach in the Wien2k package. Our research represents a pioneering exploration of NaCl$_7$'s semiconducting nature in the Pm-3 phase, achieved without the application of external stress. Meanwhile, previous studies have predominantly focused on the high-pressure behavior of various Na$_m$Cl$_n$ configurations, particularly their metallization under extreme pressures. Here, electronic-structure calculations reveal that NaCl$_7$ behaves as a p-type semiconductor with a band gap of 1.198 eV. We also analyzed various optical properties, including the absorption coefficient, electron energy-loss function, refractive index, extinction coefficient, and the real and imaginary parts of the dielectric tensor and the optical conductivity. NaCl$_7$ exhibits promising absorption characteristics within the UV-visible spectrum. Furthermore, we investigated the Seebeck coefficient, electrical conductivity, electronic thermal conductivity, figure of merit, electronic specific heat, and Pauli magnetic susceptibility.

To analyze the temporal behavior of a fission nuclear reactor, the system of differential equations known as modified point kinetics has been widely used. It is well-known that the stability of the system depends on reactivity. Therefore, it is of interest to model different situations that may occur in a nuclear reactor. From the modified point kinetics equations, which is a set of two ordinary differential equations, a set of three first-order coupled linear equations can be constructed by taking an appropriate variable change. Taking reactivity ρ = ρ(x) as a variable parameter, we perform a stability analysis using the theory of dynamical systems. Furthermore, considering a more general case by taking the reactivity ρ = ρ(x, t) depending on time, the set of differential equations become nonlinear and nonautonomous, To determine the asymptotic stability of solutions for the system, a Lyapunov function V (x, t) is constructed, and also particular cases of reactivity ρ(x, t) are analyzed using the Kosambi Cartan Chern theory.

Using functional density theory within the framework of the FP-LAPW method within the generalized gradient approximation, based on Perdew 2008 functional GGA-PBEsol, spin-polarized density functional theory calculations were used to study the structural, electronic, and magnetic properties of the quaternary chalcogenide CuMnInSe3 crystal. The available experimental data and the computed equilibrium structural parameters agree well. Based on the examination of the spin-polarized band structures and density of states, we predict be half-metallic character of the examined compound, with a total magnetic moment of 6μB per unit-cell and a gap of 0.644eV. We noticed that the electronic structure is better described when the electronic exchange-correlation is included using the Tran-Blaha modified Becke-Johnson (TB-mBJ) potential and adopted to compute accurately the band gap of the compound, where an indirect band gap (X - Γ) of 1.546eV is obtained.
 The optical properties were predicted and the spectra of the real and imaginary parts of the permittivity, the reflectivity function, and the absorption coefficient, were analyzed. These calculations indicate that   this material could be a good ultraviolet sensor.

The purpose of this article is to address the issues of dimensional consistency that arise in the process of replacing the ordinary time derivative operator by a fractional derivative operator in order to write a fractional differential equation. We show that by performing a simple change of variables fulfilling certain conditions ensures the consistency in physical dimensions for fractional differential equations with non singular kernels. An example of the proposed method is given.

In a quantum system initially in the n-th eigenstate, an adiabatic evolution of the Hamiltonian ensures that the system remains in the corresponding instantaneous eigenstate while acquiring a phase factor. This phase has two components: one resulting from standard time evolution and another associated with the dependence of the eigenstate on the varying Hamiltonian, known as the Berry phase. In this work, we explore the concept of geometric amplitudes in the context of a Hermitian Hamiltonian. We introduce the notion of geometric amplitude and provide a novel derivation of this concept. Our study reveals that a system undergoing cyclic evolution under adiabatic conditions acquires an additional amplitude factor of purely geometric origin. To illustrate this idea, we apply it to a concrete case: a generalized inverted harmonic oscillator. Although a pseudo-inner product can be introduced to make resonance states formally normalizable, this procedure relies on a non-unitary metric operator and defines a modified Hilbert space; it does not restore normalizability nor self-adjointness in the standard L²(R) framework.

In this work, we investigate the energy levels and optimization of intrinsic parameters (such as number and width of wells, potential barrier width, refractive index, etc.) and extrinsic parameters (including temperature and pressure) in a laser diode based on the GaInP/AlGaInP structure. The computational techniques employed include the pseudo-empirical potential method to determine the electronic band structures and a graphical method for optimization. Our results are consistent with experimental and theoretical results.

The economic and environmental problems regarding of wastes encourage the researchers to reuse the wastes and produce new materials. Waste glass is a kind of industrial waste and attracts attention among the wastes. The goal for performing the study is to evaluate waste glasses obtained by our daily routines and to determine radiation shielding abilities of the materials based on other industrial wastes. With this purpose, three samples including both waste glass and industrial wastes (Bayburt stone dust and Oltu stone dust) were produced by mixing in different ratios. Also, tungsten was added to the samples in order to improve the protection ability. The Phy-X/PSD code was used to determine the radiation protection parameters. In addition to the shielding investigation, structural properties were provided based on EPR, XRD, and SEM-EDS spectroscopic techniques. It is obtained that the shielding performance of the sample including Bayburt stone dust and marble waste with tungsten addition is the highest. The least one is achieved for the sample including Oltu stone dust and marble dust with tungsten addition. Neutron shielding capabilities are also found same as photon shielding. It can be concluded that the newly prepared samples consisting of waste glass in order to support reusing and recycling have good protective features and the usage of the samples can be recommended.

The Clapp oscillator consists of one voltage amplifier, one inductor, three capacitors, and three resistors. The proposed work analyses the Clapp oscillator when two resistors are replaced by a commercially available physical memristor, e.g. the Knowm memristor, and a third case when the polarity of the memristor is inverted. In this manner, three cases are analyzed and compared with the responses of the Clapp oscillator without a memristive element. The responses of the experiments show how the position and polarity of the Knowm memristor influence the steady-state behavior of the LC resonant oscillator. The results show that the three cases, using the Knowm memristor, produce measurable changes in frequency of oscillation, amplitude, and temporal symmetry of the output waveform, whereas reversing the memristor polarity, reverses both frequency and temporal asymmetry trends. As a conclusion, the observed behaviors indicate that the memristor acts as a dynamic and history-dependent element, i.e. it modifies the oscillation conditions of the Clapp oscillator beyond the effects of a static resistive component. These findings establish that the Clapp oscillator topology, is a suitable experimental platform for studying memristive effects in LC resonant systems. The results provide insights into the role of memristive devices position and polarity in shaping oscillatory dynamics.

The fractional scale transform is introduced and studied to develop a new pattern recognition system invariant to scale, translation, and rotation. This system was also implemented with the fractional Mellin transform, and the results were compared with those obtained with the fractional scale transform. The analysis was performed to classify 30 phytoplankton species. For both transformations, optimal orders were found for each species. This study implemented nonlinear correlation and adaptive nonlinear correlation for the classification stage. The system achieved a mean accuracy of 0.998 with nonlinear correlation and 0.999 with adaptive nonlinear correlation.

Optimizing the thickness of the active layer is essential to improve the performance of organic solar cells. In this study, we examined how the thickness of the active layer, made of a P3HT:PC 61 BM blend, influences the key electrical parameters of inverted organic solar cells. Four prepared photovoltaic cells were prepared using a typical device structure of  ITO /ZnO /P3HT:PC 61 BM /MoO 3 /Ag . The active layer of  P3HT : PC 61 BM was deposited by spin coating with different thicknesses of 80, 150, 200, and 300 nm.  We used the different J-V characteristics to extract parameters such as the open-circuit voltage, short-circuit current density, series resistance, and shunt resistance. Based on these measurements, the results indicate that V oc remains nearly stable between 80 nm and 200 nm, before dropping sharply at 300 nm due to recombination losses. Furthermore, J sc increases with thickness and reaches its maximum at 300 nm, thanks to improved light absorption. The fill factor peaks (~50%) at a thickness of 150 nm, then decreases, reflecting an imbalance between charge collection and internal losses. To provide a deep understanding of this behavior, we also analyzed the resistive parameters. The series resistance R s increases from 27.11 Ω·m² to 27.52 Ω·m² when the thickness increases from 80 to 150 nm due by the increased defect density in the layer structure with additional layer stacking, then rises to 28.87 –34.55 Ω·m² for 200–300 nm respectively because of the longer charge transport path and increased recombination. Finally, the shunt resistance R sh increases up to 150 nm suggests improved film uniformity and better surface coverage, thus minimizing shunt defects, before decreasing at 200 and 300 nm. This suggests that increasing the material volume statistically leads to a higher density of volumetric defects.

Soil microbial fuel cells (SMFCs) are bioelectrochemical systems capable of generating electrical signals from microbially mediated oxidation processes occurring within the soil matrix. This study evaluates the electrical response of a soil microbial fuel cell (SMFC) subjected to controlled chemical perturbations induced by cobalt chloride (CoCl2). SMFC microcosms were established under four treatments: control, low (50 mg), medium (100 mg), and high (200 mg) CoCl2, with four replicates per treatment. Soil physicochemical parameters, including pH, conductivity, moisture, and nutrient content, were monitored together with voltage and current outputs. CoCl2 addition produced transient soil acidification and increased ionic strength. Current exhibited strong sensitivity to these changes, whereas voltage remained comparatively stable. Spearman correlation analysis revealed a consistent negative relationship between current and soil pH, identifying pH as the dominant controlling variable. A theoretical electrochemical framework confirmed that CoCl2 acts as a chemical modulator rather than an electron source. These results highlight the potential of SMFCs as responsive bioelectrochemical indicators of soil chemical dynamics.

In this work, the time evolution of the contact-angle dynamics of distilled water droplets and 0.9% sodium chloride solution droplets placed on a solid glass surface was investigated experimentally during evaporation. The contact angle was determined using a simple geometric approach based on spherical-cap geometry from the droplet height and base diameter, without employing complex optical goniometric systems. The experiments were conducted under controlled environmental conditions, and the time-dependent variation of the contact angle was analyzed in detail. The results show that, for the 0.9% sodium chloride solution droplet, the contact angle decreases faster and in an almost monotonic manner compared with the distilled water droplet. In contrast, the water droplet exhibits stick-slip behavior associated with contact-line pinning and depinning processes. The obtained results indicate that electrolyte ions influence wetting properties and contact-line dynamics. The proposed geometric method is a simple and practical approach for real-time investigation of droplet evaporation and wetting processes under controlled laboratory conditions.

This paper examines the reliability of SiC DMOS power transistors in a DC-DC Boost Converter circuit. This reliability analysis focuses on the impact of bias temperature instabilities (BTI) on the electrical performance of the transistor, taking into account the variation of one of the most critical parameters of a SiC power MOSFET: the on-resistance (Ron). The study presented in this work also provides an insight into the importance of using an accurate physical reliability model to estimate the transistor’s real threshold voltage drift for a long operating time. We demonstrate that SiC DMOS technology exhibits higher threshold voltage (Vth) and Ron stability when operated in a bipolar mode. As a result, data derived from measure-stress-measure (MSM) sequences are used to calibrate the defect parameters of a two-state non-radiative multi-phonon model (NMP) that captures the charge trapping kinetics of oxide and interface defects in a reliability simulation framework: Comphy. From the analysis it was obtained that an extrapolation of device deterioration at operating settings reduces bias temperature instabilities (BTI), leading to a small danger to on-state loss growth.

Physiological studies often involve recording multiple observations (e.g., repeated muscle contractions or cardiac cycles) from the same subject. To compare groups of subjects, observations from one subject are then sometimes pooled with observations from other subjects in the same group, and analyses are performed on these pooled data. This approach presents a number of potential problems, including over- or under-representing certain subjects in the sample and non-independence of measurements. There are statistical methods available to deal with repeated measures, but many make assumptions about the distribution and completeness of data. Instead, we developed a method to deal with multiple observations from physiological data that ensures that each subject is represented only once in the analysis (i.e. it avoids pseudoreplication), and makes no assumptions about the distribution of the data. We demonstrate this method using two different physiological datasets: (1) muscle recordings taken from Drosophila melanogaster larvae during fictive crawling, and (2) electrocardiogram recordings taken from human volunteers before, during, and after exercise. Our results show the broad applicability and validity of this method.

Shear wave propagation in a layered medium made of Voigt viscoelastic layers is studied. It is argued that is it possible to obtain closed-form analytical approximate expressions for the effective dynamical parameters of the layered medium in the high-frequency regime. The multiple scales method is applied to obtain the frequency-dependent effective dynamical parameters. Lower order analytical solution approximations for harmonic steady-state was obtained. Numerical comparison against precise numerical solutions via the tranfer matrix method were carried out. This could contribute to the model design of tissue-like phantom materials for ultrasound devices calibration as well as in the processing of signals from shear wave elastography.

In a model-independent context, we perform a systematic and detailed study of the fermion flavor masses and mixings. In this analysis, we present a most general parameterization form of the $3 \times 3$ mass matrix, as well as the Pontecorvo–Maki–Nakagawa–Sakata flavor mixing matrix, in terms of the fermionic masses and some free parameters. A likelihood test using the $\chi^{2}$ statistic is implemented to evaluate whether the theoretical expressions for the leptonic flavor mixing angles also reproduce the experimental data. The results of the $\chi^{2}$ fit show that the theoretical expressions obtained for the Pontecorvo–Maki–Nakagawa–Sakata mixing matrix correctly reproduce the actual experimental data on neutrino oscillations.

We analyze the problem of a free 1D Klein-Fock-Gordon-Majorana (KFGM) particle in an interval. By free, we mean that there is no potential within the interval and that its walls are penetrable; hence, the energy current density does not vanish at the walls. Certainly, quantization in an interval is not trivial because certain restrictions imposed by the domains of the operators involved arise. Here, our objective is to obtain the Hamiltonian for these particles. In practice, the Feshbach-Villars (FV)--free Hamiltonian is the proper operator for characterizing them and is a function of the momentum operator. Additionally, a Majorana condition must also be imposed on the wavefunctions on which these two operators can act. Thus, we start by calculating the pseudo self-adjoint momentum operator. A three-parameter set of boundary conditions (BCs) constitutes its domain. Up to this point, the domain of the Hamiltonian is induced by the domain of the momentum operator; however, we ensure that only the BCs for which the energy current density has the same value at each end of the interval are in its domain. All these BCs essentially belong to a one-parameter set of BCs. Moreover, because the FV equation is invariant under the operation of parity, the parity-transformed wavefunction is also a solution of this equation, which further restricts the domain of the free FV Hamiltonian. Finally, knowing the most general three-parameter set of BCs for the pseudo self-adjoint FV Hamiltonian for a 1D KFGM particle in an interval, we find that only two BCs can remain within the domain of the FV--free Hamiltonian: the periodic BC and the antiperiodic BC. These BCs are satisfied by both the two-component FV wavefunction, with these components being related, and the one-component KFG wavefunction, which can be real or imaginary.

A composite of a Zn22Al22Cu matrix and NaCl particles was developed to establish whether this material could be hot-rolled and, if feasible, to determine the structural changes according to the initial matrix microstructure and percent section reduction achieved with this process. The composite was made by melting the alloy, adding the particles, molding, compressing the mixture of metal and particles, and air cooling, with an approximate (mass of particles) / (mass of alloy) ratio equal to 0.6. Plates of the composite with the initial cast-metal matrix microstructure and with a heat-treated initial fine-grained matrix microstructure were hot-rolled in two stages to approximately 80% section reduction at 230 °C. Specimens of the plates that were not rolled, plates hot-rolled to approximately 50% section reduction and plates hot-rolled to the maximum percent reduction were mirror-polished, and the matrix and NaCl-particle interfaces were analyzed and imaged with a scanning electron microscope. Vickers microhardness was measured in the matrix and in the NaCl particles, and the Rockwell hardness F of the nonrolled and hot-rolled composites was determined. The cast-metal matrix microstructure acquired shape texture without recrystallization, while the fine-grained matrix microstructure recrystallized with increasing rolling %. The NaCl particles deformed together with the matrix and hardened, with the hardening speed being greater when the matrix was fine-grained. The composite could be hot-rolled with either microstructure, with the cast-metal matrix microstructure being more favorable. The hot-rolling of this material allows thin cellular sheets to be obtained.

In this research, we employed an ab initio calculation approach based on the full-potential linearized augmented plane wave (FP-LAPW) method within the framework of density functional theory (DFT), integrated into the WIEN2k code. By examining in detail the structural, elastic, electronic, magnetic, optical, and thermodynamic characteristics of the double perovskite compound Ba$_2$DySbO$_6$. Firstly, our study focused primarily on magnetic stability. The results presented in this work are in good agreement with the available experimental and theoretical data. Subsequently, we studied the electronic properties in which we calculated the band structure and the density of states. Regarding the magnetic properties of the compound Ba$_2$DySbO$_6$, it was found that the total magnetic moment is mainly due to the magnetic moment of the lanthanide atom. The optical properties, such as the real and imaginary parts of the dielectric function, the refractive index, the extinction coefficient, the reflectivity, the optical conductivity, and the absorption coefficient of the Ba$_2$DySbO$_6$ compound, were calculated for all photon energies. The thermodynamic study of our compound has shown that it is stable at high temperatures. The predictive calculations of the thermal properties of our compound show that it follows the same behavior with temperature variation.

The Marwick-Sigmund model has been widely used to calculate the lateral spread of ions transmitted through matter. However, this model neglects the effect of ion energy loss within the target material. In this study, the model is employed to calculate the lateral spread distributions of MeV helium ions transmitted through carbon, aluminum, and copper targets. Ion energy loss is incorporated into the calculations using an approach analogous to that used for determining the angular distributions of transmitted ions. A comparison of our results with experimental data indicates that incorporating energy loss substantially enhances the overall agreement.

A wide variety of two-dimensional (2D) materials provide an optional route for manipulating heat fluxes at the nanoscale. Nowadays, 2D carbon-based materials have received important attention due to their adjustable transport properties by a controlled tuning of composition, junction, geometry, etc. In the present paper, we address the thermal transport properties of the B-C-N (Boron-Carbon-Nitride) monolayers and graphene/X (X=hBN, hSiC, and graphane) nanoribbon heterojunctions by performing non-equilibrium molecular dynamics simulations. Our results show that the carbon concentration modifies the thermal conductivity of B-C-N monolayers at a mean temperature of 300 K, producing values of 29.47, 28.94, and 16.58 W/m−K for concentrations of 90, 10, and 50%, respectively. Nevertheless, no major effect of carbon concentration on the temperature profile of B-C-N monolayers is observed. On the other hand, the mean temperature influences the interface thermal resistance and thermal conductivity of coplanar graphene/X nanoribbon heterojunctions, these variations are observed for the forward direction of the heat flux, modulating the temperature drop at the interface. Besides, graphene/hBN and graphene/graphane heterojunctions show a pronounced thermal rectification at a mean temperature below 300 K, compared to graphene/hSiC heterojunction. In which the heat fluxes present an asymmetry in the j−∆ curve, highlighting that the heat flux in the backward direction preferentially flows from X (hBN and graphane) to graphene nanoribbons.

Graphene oxide (GO) is a highly versatile nanomaterial with remarkable structural, electrical, and surface properties, making it useful for energy storage, catalysis, and biomedical applications [1]. In this study, durian peel waste was used as a carbon-rich precursor for the synthesis of GO, offering a sustainable and cost-effective route to nanomaterials. The raw material was first subjected to pyrolysis at 400 °C in a rocket stove reactor to produce biochar. The resulting carbon was processed using liquid-phase acid sonication (LAS) and ultrasonication to synthesize GO. The samples were characterized by X-ray diffraction (XRD), Raman spectroscopy, and scanning electron microscopy (SEM). The XRD patterns confirmed the presence of oxidized graphitic structures, Raman spectra revealed the characteristic D and G bands with an increased ID/IG ratio indicating the formation of structural defects, and SEM images showed wrinkled, layered morphologies typical of GO sheets. These results demonstrate that tropical fruit waste can be valorized into advanced nanomaterials through environmentally friendly processing, highlighting the dual benefits of waste reduction and material innovation.

We propose a novel diagnostic framework to probe emergent structural behavior in finite quantum systems by applying the Kolmogorov–Smirnov (KS) distance to Fisher information profiles. Using an exactly solvable fermionic SU(2) model with a spin-flip interaction, we study the competition between symmetric Dicke-like states and low-spin configurations, modulated by interaction strength V , particle number N, and inverse temperature β. We compute the Fisher information FN(V, β) for varying N, and evaluate its KS distance from the N = 2 reference case. This nonparametric distance captures the global dissimilarity of sensitivity curves. It reveals a sharp decline for V ≳ 1, signaling a crossover from finite-size dominated behavior to collective thermal coherence. At weak coupling, the KS distance remains large, indicating persistent structural sensitivity to finite-size fluctuations. Our results establish the KS distance as a sensitive and interpretable tool for tracking the onset of macroscopic stability and information redundancy in quantum thermodynamic systems. The observed suppression of Hilbert space dimensionality provides a clear thermodynamic signature of emergent collectivity. I

Numerous everyday goods, including fabrics, electrical appliances, vehicles, and airplanes, are currently undergoing extensive testing and inspection for their flammability features. By lowering the total fire risk associated with the use of highly flammable raw materials in goods such as textiles, apparel, composites, and plastics, flame retardants perform a critical protective role in preserving lives and property. In this study, kaolin and epoxy were used to prepare a nanocomposite flame retardant. The used kaolin was tested by X-ray diffraction and (AFM) tests. The results showed that the powders possess multi-phases and also have a mean grain size of (38 nm) and root mean square (RMS) of (12.25). Also, the energy dispersive (XRD) spectroscopy analysis (EDX) showed that the presence of the essential elements of these powders was accurate and clear. The nanocomposites were prepared by mixing the kaolin nanopowder with the epoxy resin by weight percentages of (2, 4, 6, 8 and 10%). To determine the efficiency of these additives in flame retardant and to increase the combustion resistance of epoxy resin, different methods of measurement were used according to ASTM; average time of burning, average extent of burning, rate of burning, limiting oxygen index, maximum flame height and residue percentage succeeding combustion. Based flame retardant is commercially successful and they are more environmentally friendly as compared to halogenated and non-halogenated inorganic or organic types and they are being applied suitably with a cross-inker and/or binder copolymer that makes the FRs more resistant to common weathering conditions and exposures. They also produce less or no obnoxious gases while burning.

This study explores the pressure-dependent structural, elastic, electronic, magnetic, and optical properties of the half-Heusler alloy CrZrAs through first-principles calculations based on DFT within the PBE-GGA using the WIEN2k code. Five possible atomic configurations were analyzed, with Type II identified as the most energetically favorable in the ferromagnetic state, underscoring the stabilizing influence of spin polarization on the ground-state structure. Energy–volume trends reveal small energetic separations among competing configurations, suggesting that external stimuli such as pressure or doping could trigger structural rearrangements. Electronic structure analysis confirms the half-metallic nature of CrZrAs, characterized by an indirect bandgap in the majority spin channel, metallic conduction in the minority channel, and a total magnetic moment of 3.00 μ B per formula unit in line with the Slater–Pauling rule. Elastic constants validate its mechanical stability, ductility, and anisotropic response, supported by Pugh’s ratio, Poisson’s coefficient, and positive Cauchy pressure values. Optical investigations across 0–20 eV reveal moderate absorption coefficients, distinctive dielectric peaks from interband transitions, and favorable refractive and energy-loss behavior, indicating potential for optoelectronic integration. Increasing hydrostatic pressure contracts, the lattice, strengthens Cr–Zr orbital hybridization, narrows the electronic bandgap, shifts the Fermi level, and progressively diminishes the magnetic moment, eventually suppressing half-metallicity under extreme compression. These findings establish CrZrAs as a structurally robust, elastically adaptable, half-metallic material with promising spintronic and optoelectronic potential, while demonstrating pressure as an effective means to tailor its electronic and magnetic functionalities for advanced device applications.

Fractional calculus is a crucial mathematical tool for understanding complex systems across various fields, such as physics, engineering, and biology. This work delves into the intricate task of computing fractional order derivatives, which typically necessitates numerical methods due to their inherent complexity. We present a comprehensive comparative study of three significant numerical techniques: the Riemann-Liouville, Grunwald-Letnikov, and Caputo derivatives. The study begins with a thorough examination of fractional order derivatives, highlighting their fundamental importance in modern scientific research. We investigate basic transcendental functions—sine, cosine, and exponential—due to their vital role in modeling real-world systems. Our research reveals the complex relationship between sensitivity and precision by consistently computing fractional derivatives across various orders. Principal Component Analysis (PCA) is employed for statistical validation to enhance the credibility of our findings, demonstrating that fractional derivatives can reliably represent underlying data patterns. Consequently, this study significantly advances our understanding of fractional order derivatives and underscores the importance of carefully handling fractional orders in diverse applications. These findings support the reliability of data analytics and deepen our comprehension of the behavior of complex systems. An important application of this work lies in the modeling and control of viscoelastic materials, where fractional calculus provides a powerful framework for accurately capturing memory-dependent behaviors and complex stress-strain relationships.