Search Results (43)

In this paper, we address the lack of general Janowski-type subclasses for analytic functions involving higher-order q-derivatives, unifying cases with both positive and negative coefficients. Using a combination of higher-order q-derivative techniques and Janowski subordination, we introduce two new q-analytic classes and derive sharp coefficient inequalities that fully characterize them. Our main theorems provide explicit coefficient bounds, distortion and neighborhood inclusion results, extending the classical Goodman–Ruscheweyh theory to the q-calculus setting. Applications are given to fractional q-integral operators, in particular to the q-Jung–Kim–Srivastava operator, and the results reduce to several known cases as $q\to 1^{-}$. Full article

In this paper, we derive novel formulas and identities connecting Cauchy numbers and polynomials with both ordinary and generalized Stirling numbers, binomial coefficients, central factorial numbers, Euler polynomials, r-Whitney numbers, and hyperharmonic polynomials, as well as Bernoulli numbers and polynomials. We also provide formulas for the higher-order derivatives of Cauchy polynomials and obtain corresponding formulas and identities for poly-Cauchy polynomials. Furthermore, we introduce a multiparameter framework for poly-Cauchy polynomials, unifying earlier generalizations like shifted poly-Cauchy numbers and polynomials with a q parameter. Full article

This study introduces a novel numerical approach to analyze the axisymmetric bending behavior of functionally graded (FG) graphene platelet (GPL)-reinforced annular sandwich nanoplates featuring a porous core. The nanostructures are exposed to coupled magnetic and hygrothermal environments. The porosity distribution and GPL weight fraction are modeled as nonlinear functions through the thickness, capturing realistic gradation effects. The governing equations are derived using the virtual displacement principle, taking into account the Lorentz force and the interaction with an elastic foundation. To address the size-dependent behavior and thickness-stretching effects, the model employs the nonlocal strain gradient theory (NSGT) integrated with a modified version of Shimpi’s quasi-3D higher-order shear deformation theory (Q3HSDT). The differential quadrature method (DQM) is applied to obtain numerical solutions for the displacement and stress fields. A detailed parametric study is conducted to investigate the influence of various physical and geometric parameters, including the nonlocal parameter, strain gradient length scale, magnetic field strength, thermal effects, foundation stiffness, core thickness, and radius-to-thickness ratio. The findings support the development of smart, lightweight, and thermally adaptive nano-electromechanical systems (NEMS) and provide valuable insights into the mechanical performance of FG-GPL sandwich nanoplates. These findings have potential applications in transducers, nanosensors, and stealth technologies designed for ultrasound and radar detection. Full article

Potentially toxic elements such as cadmium (Cd) in agricultural soils represent a global concern due to their toxicity and potential accumulation in the food chain. However, our understanding of cadmium’s complex sources and the mechanisms controlling its spatial distribution across diverse edaphic and geological contexts remains limited, particularly in underexplored agricultural regions. Our study aimed to assess the total accumulated Cd content in soils under avocado cultivation and its association with edaphic, geochemical, and geomorphological variables. To this end, we considered the total concentrations of other metals and explored their associations to gain a better understanding of Cd’s spatial distribution. We analyzed 26 physicochemical properties, the total concentrations of 22 elements (including heavy and trace metals such as As, Ba, Cr, Cu, Hg, Ni, Pb, Sb, Se, Sr, Tl, V, and Zn and major elements such as Al, Ca, Fe, K, Mg, and Na), and six geospatial variables in 410 soil samples collected from various avocado-growing regions in Peru in order to identity potential associations that could help explain the spatial patterns of Cd. For data analysis, we applied (1) univariate statistics (skewness, kurtosis); (2) multivariate methods such as Spearman correlations and principal component analysis (PCA); (3) spatial modeling using the Geodetector tool; and (4) non-parametric testing (Kruskal–Wallis test with Dunn’s post hoc test). Our results indicated (1) the presence of hotspots with Cd concentrations exceeding 3 mg·kg⁻¹, displaying a leptokurtic distribution (skewness = 7.3); (2) dominant accumulation mechanisms involving co-adsorption and cation competition (Na⁺, Ca²⁺), as well as geogenic co-accumulation with Zn and Pb; and (3) significantly higher Cd concentrations in Leptosols derived from Cretaceous intermediate igneous rocks (diorites/tonalites), averaging 1.33 mg kg⁻¹ compared to 0.20 mg·kg⁻¹ in alluvial soils (p < 0.0001). The factors with the greatest explanatory power (q > 15%, Geodetector) were the Zn content, parent material, geological age, and soil taxonomic classification. These findings provide edaphogenetic insights that can inform soil cadmium (Cd) management strategies, including recommendations to avoid establishing new plantations in areas with a high risk of Cd accumulation. Such approaches can enhance the efficiency of mitigation programs and reduce the risks to export markets. Full article

Rice tillering is an important trait that is genetically and environmentally co-regulated. Nitorgen is one of the key nutrients affecting tillering, and straw return further affects tiller development by altering soil heterogeneity. In order to analyze the genetic regulation mechanism of rice tillering and its interactions with the environment, 124 recombinant inbred line (RIL) populations derived from two superior Peijiu lines, 9311 and PA64s, were used as materials in this study, and the dynamic tillering phenotypes were measured under three treatments (no nitrogen application, nitrogen application, and nitrogen + straw return) for two consecutive years. Using an existing genetic map, we conducted single-environment, multi-environment, and meta-QTL analyses to systematically identify tiller-related genetic loci and their environmental interactions. The main findings were as follows: (1) A total of 57 QTLs were identified in the single-environment QTL analysis, of which 44 were unreported new QTLs. Four QTLs showed temporal pleiotropy, ten QTLs contributed more than 10% to the phenotypes under the no-N treatment, and five QTLs contributed more than 10% under the straw return treatment. Among them, the phenotypic contribution of mks1-355 (qD1tn1-3) and mks1-352 (qD2TN1-2) both exceeded 40%. (2) Multi-environmental QTL analysis detected 15 QTLs. Of these, qmD1TN1 (mks1-356) showed no environmental interaction effect, while qmD1TN12 (mks12-267), qmD2TN1 (mks1-334), qmD2TN3-1 (mks3-105), and qmD5TN6 (mks6-71) exhibited antagonistic pleiotropy, suggesting that these QTL need to be considered for environmental specificity in breeding. (3) Meta-QTL analysis localized 52 MQTLs, of which MQTL3.1 and MQTL6.8 contained 82 and 59 candidate genes, respectively, and no reported tiller-related genes were found. (4) mks1-355 (qD1tn1-3), mks1-352 (qD2TN1-2), and mks1-356 (qmD1TN1) may be located in the same genetic locus, and their phenotypic contributions were more than 40%. These QTLs were detected stably for two consecutive years, and they may be the main effector QTLs in tillering that are less affected by the environment. Further analysis revealed that these QTLs corresponded to MQTL1.6, which contains 56 candidate genes. Of these, the expression level of OsSPL2 gene in the parental line 9311 was significantly higher than that of PA64s, and there were polymorphic differences in the coding region. It was hypothesized that OsSPL2 was the main effector gene of this QTL. This study provides important genetic resources for mining candidate genes related to tillering and nitrogen efficiency in rice and lays a theoretical foundation for directional breeding and molecular marker development in specific environments. Full article

Background: There is currently no study examining the mental health consequences of deployed German service members in Iraq. The aim is, therefore, to determine the cumulative incidence and latency period until the first diagnosis of deployment-related mental disorders. We hypothesized a lower rate than for Afghanistan with 2.4%. Methods: All registered N = 1635 German military personnel who were deployed to the mission “Training support contingent Northern Iraq” between 2015 and 2018 were included. Individuals with mental disorders attributed to this deployment were identified in a central database. Differences in latency between diagnoses were calculated by t-tests for independent samples. Results: By January 2024, n = 55 (3.4%) individuals had been recorded who developed a mental disorder as a result of this deployment. Most of them (54.5%) had a post-traumatic stress disorder (PTSD) as the main or comorbid diagnosis. There were no gender differences in the cumulative incidence (male 3.6%; female 2.9). The latency period between the onset of disease and initial diagnosis was, on average, 1.0 years (standard deviation 1.1 years; Q₂₅ < 1 year, Q₅₀ = 1 year and Q₇₅ = 2 years). With 1.3 vs. 0.6 years, the latency was significantly longer for individuals with PTSD. Conclusions: The cumulative incidence appears to be higher after the Iraq deployment than after most other Bundeswehr deployments. This is attributed to particular threats. The latency period is higher for those affected with PTSD than with other disorders. This could be due to a higher degree of stigmatization. It is, therefore, worthwhile to compare the different deployments in order to be able to derive better preventive and aftercare measures as well as destigmatization programs to prevent chronification. Full article

Many properties of special numbers, such as sum formulas, symmetric properties, and their relationships with each other, have been studied in the literature with the help of the Binet formula and generating function. In this paper, higher-order generalized Fibonacci hybrid numbers with q-integer components are defined through the utilization of q-integers and higher-order generalized Fibonacci numbers. Several special cases of these newly established hybrid numbers are presented. The article explores the integration of q-calculus and hybrid numbers, resulting in the derivation of a Binet-like formula, novel identities, a generating function, a recurrence relation, an exponential generating function, and sum properties of hybrid numbers with quantum integer coefficients. Furthermore, new identities for these types of hybrids are obtained using two novel special matrices. To substantiate the findings, numerical examples are provided, generated with the assistance of Maple. Full article

In this paper, we investigate the global attractivity of a higher-order rational difference equation in the form $x_{n+1}={\displaystyle \frac{p+q{x}_n}{1+r{x}_n+s{x}_{n-k}}}$, where $p,q,r,s\ge 0$, k is a positive integer, and the initial conditions are nonnegative. This equation generalizes several well-known rational difference equations studied in the literature. By employing a combination of advanced mathematical techniques, including the use of key lemmas and intricate computations, we establish that the unique nonnegative equilibrium point of the equation is globally attractive under specific parameter conditions. Our results not only extend and improve upon existing findings but also resolve several conjectures posed by previous researchers, including those by G. Ladas and colleagues. The methods involve transforming the higher-order equation into a first-order difference equation and analyzing the properties of the resulting function, particularly its Schwarzian derivative. The findings demonstrate that the equilibrium point is globally attractive when certain inequalities involving the parameters are satisfied. This work contributes to the broader understanding of the dynamics of rational difference equations and has potential applications in various fields such as biology, physics, and cybernetics. Full article

We explore nonlocal symmetries in a class of Hamiltonian dynamical systems governed by second-order differential equations. Specifically, we establish an algorithm for deriving nonlocal symmetries by utilizing the Jacobi metric and the Eisenhart–Duval lift to geometrize the dynamical systems. The geometrized systems often exhibit additional local symmetries compared to the original systems, some of which correspond to nonlocal symmetries for the original formulation. This novel approach allows us to determine nonlocal symmetries in a systematic way. Within this geometric framework, we demonstrate that the second-order differential equation $\ddot{q}-F\left(q\right)=0$ admits an infinite number of nonlocal symmetries generated by the infinite-dimensional conformal algebra of a two-dimensional Riemannian manifold. Applications to higher-dimensional systems are also discussed. Full article

This research focuses on the dynamic analysis of an oscillating conveyor mechanism using numerical methods to solve nonlinear differential equations that govern its motion. The system under study is modeled by a second-order differential equation of the form $R\left(t\right){\displaystyle \frac{d{\omega }_1}{dt}}+Q\left(t\right){\omega }_1^2\left(t\right)=W\left(t\right)$, where R(t), Q(t), and W(t) are time-dependent functions representing system parameters such as resistance, damping, and external driving forces. To solve these equations, we employed a numerical approach based on Euler’s method, which discretizes the time domain into small steps h and approximates the derivatives of angular velocity and angular displacement. The angular velocity ${\omega }_{k+1}$ and angular displacement ${\phi }_{k+1}$ are updated iteratively using the formulas ${\omega }_{k+1}={\omega }_k+h\left({\displaystyle \frac{W_k}{R_k}}-{\displaystyle \frac{Q_k}{R_k}}{\omega }_k^2\right)$ and ${\phi }_{k+1}={\phi }_k+h{\omega }_k$, respectively. Initial conditions, with ${\omega }_0=0$ and ${\phi }_0=0$, were specified, and the system was simulated over a specified time range divided into N time steps. In the simulation, key parameters such as $A\left(t\right)$, B(t), D(t), E(t), F(t), $H\left(t\right)$, N(t), M(t), $Q\left(t\right)$, $R\left(t\right)$, and $W\left(t\right)$ were evaluated at each time step based on the system’s geometry and the angular displacements. Due to the complexity of the system, analytical solutions were impractical, so the Runge–Kutta method was employed for higher accuracy in the integration process. The results from the numerical simulations were validated by comparing them with theoretical expectations, and the system’s dynamic behavior was visualized using time-series and 3D plots. The simulation demonstrated that the system’s stability and accuracy were highly dependent on the time step h, with smaller values providing more precise results at the cost of increased computational time. The research confirms the applicability of numerical methods in solving complex nonlinear differential equations for dynamic systems and provides insights into the system’s behavior under various operating conditions. Full article

Goal: Current methodologies for assessing cerebral compliance using pressure sensor technologies are prone to errors and issues with inter- and intra-observer consistency. RAP, a metric for measuring intracranial compensatory reserve (and therefore compliance), holds promise. It is derived using the moving correlation between intracranial pressure (ICP) and the pulse amplitude of ICP (AMP). RAP remains largely unexplored in cases of moderate to severe acute traumatic neural injury (also known as traumatic brain injury (TBI)). The goal of this work is to explore the general description of (a) RAP signal patterns and behaviors derived from ICP pressure transducers, (b) temporal statistical relationships, and (c) the characterization of the artifact profile. Methods: Different summary and statistical measurements were used to describe RAP’s pattern and behaviors, along with performing sub-group analyses. The autoregressive integrated moving average (ARIMA) model was employed to outline the time-series structure of RAP across different temporal resolutions using the autoregressive (p-order) and moving average orders (q-order). After leveraging the time-series structure of RAP, similar methods were applied to ICP and AMP for comparison with RAP. Finally, key features were identified to distinguish artifacts in RAP. This might involve leveraging ICP/AMP signals and statistical structures. Results: The mean and time spent within the RAP threshold ranges ([0.4, 1], (0, 0.4), and [−1, 0]) indicate that RAP exhibited high positive values, suggesting an impaired compensatory reserve in TBI patients. The median optimal ARIMA model for each resolution and each signal was determined. Autocorrelative function (ACF) and partial ACF (PACF) plots of residuals verified the adequacy of these median optimal ARIMA models. The median of residuals indicates that ARIMA performed better with the higher-resolution data. To identify artifacts, (a) ICP q-order, AMP p-order, and RAP p-order and q-order, (b) residuals of ICP, AMP, and RAP, and (c) cross-correlation between residuals of RAP and AMP proved to be useful at the minute-by-minute resolution, whereas, for the 10-min-by-10-min data resolution, only the q-order of the optimal ARIMA model of ICP and AMP served as a distinguishing factor. Conclusions: RAP signals derived from ICP pressure sensor technology displayed reproducible behaviors across this population of TBI patients. ARIMA modeling at the higher resolution provided comparatively strong accuracy, and key features were identified leveraging these models that could identify RAP artifacts. Further research is needed to enhance artifact management and broaden applicability across varied datasets. Full article

The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which simplifies and generalizes the study of tensor derivatives, making it a powerful tool in Differential Geometry and related fields. To perform this, the generic derivative is introduced, which is defined in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. Subsequently, the transformation law of these quantities is determined by the requirement that the generic derivative of a tensor is a tensor. The quantities $Q_k^{\left(i\right)}\left(X\right)$ and their transformation law define a specific geometric object on M, and consequently, a geometric structure on M. Using the generic derivative, one defines the tensor fields of torsion and curvature and computes them for all linear derivatives in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. The general model is applied to the cases of Lie derivative, covariant derivative, and Fermi derivative. It is shown that the Lie derivative has non-zero torsion and zero curvature due to the Jacobi identity. For the covariant derivative, the standard results follow without any further calculations. Concerning the Fermi derivative, this is defined in a new way, i.e., as a higher-order derivative defined in terms of two derivatives: a given derivative and the Lie derivative. Being linear derivative, it has torsion and curvature tensor. These fields are computed in a general affine space from the corresponding general expressions of the generic derivative. Applications of the above considerations are discussed in a number of cases. Concerning the Lie derivative, it is been shown that the Poisson bracket is in fact a Lie derivative. Concerning the Fermi derivative, two applications are considered: (a) the explicit computation of the Fermi derivative in a general affine space and (b) the consideration of Freedman–Robertson–Walker spacetime endowed with a scalar torsion field, which satisfies the Cosmological Principle and the computation of Fermi derivative of the spatial directions defining a spatial frame along the cosmological fluid of comoving observers. It is found that torsion, even in this highly symmetric case, induces a kinematic rotation of the space axes, questioning the interpretation of torsion as a spin. Finally it is shown that the Lie derivative of the dynamical equations of an autonomous conservative dynamical system is equivalent to the standard Lie symmetry method. Full article

The mineralogical composition of the parent material, together with plant species and soil microorganisms, constitutes the foundational components of an ecosystem’s energy cycle. Afforestation in arid-semi arid regions plays a crucial role in preventing erosion and enhancing soil quality, offering significant economic and ecological benefits. This study evaluated the effects of afforestation and different parent materials on the physicochemical and microbiological properties of soils, including microbial basal respiration (MR), as well as how these changes in soil properties after 15 years influence plant growth. For this purpose, various soil physicochemical parameters, MR, soil microbial biomass carbon (C_mic), stoichiometry (microbial quotient = C_mic/C_org = qMic and metabolic quotient = MR/C_mic = qCO₂), and tree growth metrics such as height and diameter were measured. The results indicated that when the physicochemical and microbiological properties of soils from different bedrock types, along with the average values of tree growth parameters, were analyzed, afforestation areas with limestone bedrock performed better than those with andesite bedrock. Notably, sensitive microbial properties, such as C_mic, MR, and qMic, were positively influenced by afforestation. The highest values of C_mic (323 μg C g⁻¹) and MR (1.3 CO₂–C g⁻¹ h⁻¹) were recorded in soils derived from limestone. In contrast, the highest qCO₂ was observed in the control plots of soils with andesite parent material (7.14). Considering all the measured soil properties, the samples can be ranked in the following order: limestone sample (LS) > andesite sample (AS) > limestone control (LC) > andesite control (AC). Similarly, considering measured plant growth parameters were ranked as LS > AS. As a result, the higher plant growth capacity and carbon retention of limestone soil indicate that it has high microbial biomass and microbial activity. This study emphasizes the importance of selecting suitable parent material and understanding soil properties to optimize future afforestation efforts on bare lands. Full article

Cancer is a serious threat to human life and social development and the use of scientific methods for cancer prevention and control is necessary. In this study, HQSAR, CoMFA, CoMSIA and TopomerCoMFA methods are used to establish models of 65 imidazo[4,5-b]pyridine derivatives to explore the quantitative structure-activity relationship between their anticancer activities and molecular conformations. The results show that the cross-validation coefficients q² of HQSAR, CoMFA, CoMSIA and TopomerCoMFA are 0.892, 0.866, 0.877 and 0.905, respectively. The non-cross-validation coefficients r² are 0.948, 0.983, 0.995 and 0.971, respectively. The externally validated complex correlation coefficients r²_pred of external validation are 0.814, 0.829, 0.758 and 0.855, respectively. The PLS analysis verifies that the QSAR models have the highest prediction ability and stability. Based on these statistics, virtual screening based on R group is performed using the ZINC database by the Topomer search technology. Finally, 10 new compounds with higher activity are designed with the screened new fragments. In order to explore the binding modes and targets between ligands and protein receptors, these newly designed compounds are conjugated with macromolecular protein (PDB ID: 1MQ4) by molecular docking technology. Furthermore, to study the nature of the newly designed compound in dynamic states and the stability of the protein-ligand complex, molecular dynamics simulation is carried out for N3, N4, N5 and N7 docked with 1MQ4 protease structure for 50 ns. A free energy landscape is computed to search for the most stable conformation. These results prove the efficient and stability of the newly designed compounds. Finally, ADMET is used to predict the pharmacology and toxicity of the 10 designed drug molecules. Full article

The saturation properties of symmetric and asymmetric nuclear matter have been computed using the finite range simple effective interaction with Yukawa form factor. The results of higher-order derivatives of the energy per particle and the symmetry energy computed at saturation, namely, $Q_0$, $K_{sym}$, $K_{\tau }$, $Q_{sym}$, are compared with the corresponding values extracted from studies involving theory, experiment and astrophysical observations. The overall uncertainty in the values of these quantities, which results from a wide spectrum of studies described in earlier literature, lies in the ranges $-1200\lesssim Q_0\lesssim 400$ MeV, $-400\lesssim K_{sym}\lesssim 100$ MeV, $-840\lesssim K_{\tau }\lesssim -126$ MeV and $-200\lesssim Q_{sym}\lesssim 800$ MeV, respectively. The ability of the equations of state computed with this simple effective interaction in predicting the threshold mass for prompt collapse in binary neutron star merger and gravitational redshift has been examined in terms of the compactness of the neutron star and the incompressibility at the central density of the maximum mass star. The correlations existing between neutron star properties and the nuclear matter saturation properties have been analyzed and compared with the predictions of other model calculations. Full article