r function

We consider two simple non-resonant boundary value problems for a nabla fractional difference equation. First, we construct associated Green's functions and obtain some of their properties. Under suitable constraints on the nonlinear part of the nabla fractional difference equation, we deduce sufficient conditions for the existence of solutions to the considered problems through an appropriate fixed point theorem. We also provide two examples to demonstrate the applicability of the established results.

Site quality evaluation is considered an important aspect of forest management whereby forest managers can assess potential forest stand timber production for a particular species or forest type. The dominant diameter growth models and site index curves were developed to assess site quality of certified Acacia forests in Thua Thien Hue province, Vietnam. In this study, the correlation between dominant diameter (Dgo) and diameter at breast height (DBH) was selected from four common correlation function forms: linear, power, exponential, and parabolic function. In addition, Schumacher and Korf growth functions were used to select and develop the most suitable site index curves. to evaluate the developed models, the coefficient of determination (R^2) and root mean square error (RMSE) were used as statistical criteria. The study investigated 50 sample plots of certified acacia forests from age 2 to age 10 in Thua Thien Hue to develop the models and other 20 sample plots were used to evaluate the developed models. The results showed that the dominant diameter had the best correlation with diameter at breast height in the form of logarithmic function(Dgo = 8.8446*ln(DBH) – 7.0985). Meanwhile, the Schumacher function with equation Dgo = 24.366 . e^(-4.193/A^1.2) is the best describes the relationship between dominant diameter and forest age. Certified Acacia plantations forest in Thua Thien Hue province can be divided into three soil classes based on the diameter of dominant trees at age 5. The site index (according to dominant diameter) for good soil class (I), average soil class (II), and poor soil class (III) at age 5 are 14 cm, 12 cm, and 10 cm, respectively.

The purpose of this study is to develop a mathematical model that incorporates a diffusion term in one dimension in the dynamics of coronavirus disease-19 (COVID-19) in Ghana. A reaction-diffusion model is derived by applying the law of conservation of matter and Fick's law, which are fundamental theorems in fluid dynamics. Since COVID-19 is declared to be a pandemic, most African countries are affected by the negative impacts of the disease. However, controlling the spread becomes a challenge for many developing countries like Ghana. A lot of studies about the dynamics of the infection do not consider the fact that since the disease is pandemic, its model should be spatially dependent, therefore failing to incorporate the diffusion aspect. In this study, the local and global stability analyses are carried out to determine the qualitative solutions to the SEIQRF model. Significant findings are made from these analyses as well as the numerical simulations and results. The basic reproduction number ($R_o$) calculated at the disease-free fixed point is obtained to be $R_o\approx2.5$, implying that, an infectious individual is likely to transmit the coronavirus to about three susceptible persons. A Lyapunov functional constructed at the endemic fixed point also explains that the system is globally asymptotically stable, meaning that COVID-19 will be under control in Ghana for a long period of time.

The Cs2AgBi0.75Sb0.25Br6 based perovskite solar cell (PSC) has demonstrated a high power conversion efficiency (PCE > 16%) and exceptional air stability. A comprehensive study of the interfaces in perovskite solar cells, coupled with the optimization of many parameters, is still necessary for further enhancement in PCE. This study quantitatively analyzes lead-free Cs2AgBi0.75Sb0.25Br6 utilizing a solar cell capacitance simulator (SCAPS–1D). The electron transport layer (ZnO) and the hole transport layer (Cu2O) were analyzed comparably. The work function, temperature, and thickness of the PSC layers have been meticulously examined. The results indicate that the efficiency of the device is significantly influenced by the thickness of the absorber layer. The simulation determined the maximum PCE of Cs2AgBi0.75Sb0.25Br6-based PSCs to be 16.23%, at thickness 0.1μm of absorber layer with an open circuit voltage (Voc) of 1.3666 V, a short-circuit current density (Jsc) of 23.825 mA/cm², and a fill factor (FF) of 49.84%. Our exceptional results unequivocally indicate that Cs2AgBi0.75Sb0.25Br6- based PSCs are poised to emerge as the most efficient single-junction solar cell technology in the near future.

The main objective of this work is to present a high-order numerical method to solve a class of nonlinear Fredholm integro-differential equations. By multiplying appropriate efficient factors and constructing an appropriate approximate function,  as well as employing a numerical integration method of order $\gamma$, the above-mentioned problem can be simplified to a nonlinear system of algebraic equations. Furthermore, we discuss the convergence analysis of the presented method in detail and demonstrate that it converges with an order $\mathcal{O}(h^{3.5})$ in the $L^2$-norm. Some test examples are provided to demonstrate that the claimed order of convergence is obtained.

In bang-bang optimal control problems, the control function is inherently piecewise constant. This feature creates substantial difficulties for the standard Legendre-Gauss-Radau pseudospectral method, which relies on polynomial approximation for the control function. This study introduces a simplified approach that seamlessly integrates sigmoid-based control parameterization with the traditional Legendre-Gauss-Radau pseudospectral method. This integration enables precise approximation of discontinuous control profiles while maintaining the polynomial approximation for state variables. The proposed method significantly minimizes the number of decision variables in the optimization problem while precisely determining both the number and locations of switching points. This leads to notable enhancements in computational efficiency and solution accuracy. Numerical experiments conducted on two benchmark problems, a bridge crane system and a robotic arm control problem, demonstrate the exceptional precision and efficiency of the proposed method. Despite its simplicity, the method delivers results that are on par with those produced by more advanced and intricate techniques.

In this paper, the superiority conditions for a general class of shrinkage estimators in the estimation problem of the normal mean are established under divergence loss. This approach is an extension of the work of Ghosh and Mergel (2009).

‎In this article‎, ‎first we review some basic definitions and‎ results about fuzzy sets and intuitionistic fuzzy sets; then we‎ state the definitions of intuitionistic fuzzy (m‎, ‎n)-sub near‎ ‎rings and intuitionistic fuzzy ideals of (m‎, ‎n)-near rings‎, ‎which are generalizations of intuitionistics subrings and‎ ‎intuitionistic fuzzy ideals of rings and near-rings‎, ‎respectively‎. ‎We provide several examples for the definitions and discuss and‎ investigate some results in this respect‎. ‎Finally‎, ‎we investigate‎ the direct product of intuitionistic fuzzy  (m‎, ‎n)-sub near‎ rings of two (m‎, ‎n)-near rings and state and prove some results‎ on these topics‎.

This paper introduces a nanotube heterojunctionless tunneling field-effect transistor (NT-HJLTFET) thatcombines core-shell gate technology with a Ga0.8In0.2As/Ga0.85In0.15Sb heterojunction to enhance deviceperformance. The NT-HJLTFET achieves anION/IOF Fratio of 9.84×1013, an average subthreshold slope(SS) of 9.4 mV/dec,IONof 6.4 mA, transconductance (gm) of 17.5 mS, and unit gain cutoff frequency (fT) of42.7 THz. These results represent a significant improvement in performance, including a nearly two orders ofmagnitude increase inION,gm, andfTcompared to silicon-based nanotube junctionless tunneling field-effecttransistor (NT-JLTFET). The NT-HJLTFET also exhibits a five orders of magnitude enhancement inION/IOF Fand a 76% improvement in SS. Additionally, the presence of defects is shown to decreasefT, impacting thedevice’s high-frequency response. These findings suggest that the NT-HJLTFET is a promising candidate foruse in both digital and analog applications in integrated circuits.

In this paper, we consider a general class of nonautonomous abstract delayed evolution equations with a nonlinear source term. Under appropriate assumptions on the time-independent operator and the initial data, we establish global existence using the method of steps and employing classical results from the theory of inhomogeneous evolution problems. Then, by assuming that the operator associated with the non-delayed part of the system generates an exponentially stable semigroup, we obtain an exponential decay estimate. This is achieved through a direct proof based on Duhamel's formula combined with Gronwall's inequality, under Lipschitz continuity conditions on the nonlinear source term. Finally, we conclude the paper by providing illustrative examples that validate the generalized setting of our system.

The skewed and weighted distributions may be considered as nice alternatives to fit a real data set in practical situations in which the well-known distributions are not suitable. The weighted distributions are first discussed and then two extensions of weighted models are proposed in this paper to analyze the skew data. The flexibility of the models is studied in view of the moment skewness coefficient for some cases. Finally, two real data sets are used to illustrate the results of the paper.

The aim of this paper is to solve a class of  auto-convolution Volterra integral equations by the well-known differential transform method. The analytic property of solution and convergence of the method under some assumptions are discussed and some illustrative examples are given to clarify the theoretical results, accuracy and performance of the proposed method.

In the present paper, we introduce and investigate a new result connected to subclasses of normalized and univalent functions in the open unit disk. Some majorization results and geometric properties such as radii of starlikeness, convexity, pre-Schwarzian norm and coefficient estimates are obtained.

he Lyman Alpha forest is one of the most powerful cosmological tools for studying large-scale structures of the universe. The flux autocorrelation function for Lyman alpha forest is used to study the clustering of structures. This paper, uses the Lyman alpha forest of 49 high-resolution, high signal-to-noise (S/N>20) QSO spectra observed with VLT/UVES. The studied quasars have emission redshifts in the range of ( 1.89< zem < 3.80). The flux autocorrelation function is calculated for each sample, and then, the effect of metal absorption lines in the Lyman alpha forest on the flux autocorrelation function is investigated. The results of the present study show that the effect of removing metal absorption lines is more visible in the transition to lower redshifts, where there are relatively fewer Lyman alpha absorption lines. Moreover, the change in the flux autocorrelation function at different redshifts is investigated. The results indicate that the flux autocorrelation function at higher redshifts has a larger average value than that at lower redshifts.

Multivariate regression is an approach for modeling the linear relationship between several variables. This paper proposed a ridge methodology with a kernel-based weighted absolute error target with exact predictors and fuzzy responses. Some standard goodness-of-fit criteria were also used to examine the performance of the proposed method. The effectiveness of the proposed method was then illustrated through two numerical examples including a simulation study. The effectiveness and advantages of the proposed fuzzy multiple linear regression model were also examined and compared with some well-established methods through some common goodness-of-fit criteria. The numerical results indicated that our prediction/estimation gives more accurate results in cases where multicollinearity and/or outliers occur in the data set.

Some Hilbert $C^*$-module versions of H$\ddot{o}$lder-McCarthy and H$\ddot{o}$lder type inequalities and their complementary on a Hilbert $C^*$-module are obtained by Seo \cite{seo-2014}. The purpose of this paper is to extend these results for some operator convex (resp. concave) functions on a Hilbert $C^*$-module via the operator perspective approach. By choosing some elementary functions, we reach some new types of inequalities in Hilbert $C^*$-modules.

In this study, beta-derived Sturm–Liouville problems are discussed. First, the existence and uniqueness problem for such equations is discussed. Then, self-adjointness is obtained with the help of boundary conditions. Eigenfunction expansion was obtained with the help of characteristic determinants and Green’s function. Finally, an example is given showing the theoretical results obtained.

In this paper, new generalized variants of Ostrowski’s type identities involving the Atangana-Baleanu-Katugampola fractional integral operator for differentiable convex and twice differentiable convex functions are presented. Using these equalities or lemmas along with several known identities, new inequalities for convex functions and the Atangana-Baleanu-Katugampola, fractional integral operators are proved. By making appropriate choices of parameters, some connections between our results and various other findings are also recognized in the paper. Finally, some applications to unique means for positive real numbers are offered.