s-$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.

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).

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.

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 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.

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.

In this paper, we extend the $q$-derivative operator, which plays an essential role in quantum calculus. Indeed, by using the Hadamard product and generalized Koebe function we define the following $(\alpha,\beta,\gamma)$-derivative operator\begin{equation*}    {\rm d}_{\alpha,\beta,\gamma} f(z)=\frac{1}{z}\left\{f(z)*\mathfrak{L}_{\alpha,\beta,\gamma}(z)\right\},\end{equation*}where\begin{equation*}    \mathfrak{L}_{\alpha,\beta,\gamma}(z)=\frac{2(1-\gamma)z}{(1-\alpha z)(1-\beta z)},\end{equation*}and $\alpha\in[-1,1]$, $\beta\in[-1,1]$, $\alpha\beta\neq \pm1$ and $\gamma\in[0,1)$. Then by subordination relation, the operator ${\rm d}_{\alpha,\beta,\gamma} f(z)$, and a special function $\phi_\delta(z)=1+\delta z/\exp(\delta z)$ ($0<\delta\leq1$), we define a new particular Ma-Minda class. We investigate some properties of this class, such as, radius problem and coefficient estimate.

The receiver operating characteristic curve is a simple graphical tool used to assess the accuracy of diagnostics tests‎. ‎Pulit (2016) proposed an innovative approach for estimating the receiver operating characteristic curves based on kernel smoothing‎. ‎Although his proposed estimator is highly appealing in several aspects‎, ‎it suffers from the well-known boundary bias effect‎. ‎In this paper‎, ‎we highlight this drawback and propose a new modified estimator that uses an appropriate boundary kernel‎. ‎The asymptotic convergence of the proposed estimator at boundary points is demonstrated‎. ‎Using both simulated and real data sets‎, ‎we illustrate the performance of the proposed estimator‎. ‎The results show that the proposed estimator outperforms not only the Pulit’s estimator but also other commonly used estimators‎.

In this paper‎, ‎we study a nonparametric Bayesian inference on the family of nonincreasing density functions on real positive data‎. ‎One interesting problem is the goodness of fit test in such a context‎. ‎In other words‎, ‎we consider nonparametric Bayesian testing on the family of nonincreasing density in this domain‎. ‎So‎, ‎we define nonparametric hypothesis testing and compare two different testing approaches‎. ‎The first approach is given based on the Bayes factor‎. ‎This approach is the well-known Bayesian approach for testing‎, ‎although its computation is complicated‎. ‎Decision-theoretic considerations with the loss function drive the second approach for a given distance‎. ‎This second approach has the advantage of considering the distance to the null hypothesis but needs the definition of a threshold‎. ‎When no threshold is known as a priori‎, ‎a possibility exists to calculate a p-value‎, ‎and the method becomes more complicated to compute‎. ‎We propose a hybrid algorithm to accelerate the computation of the p-value‎. ‎The comparison of both approaches is performed based on a simulation study.

The Passive Image Interferometry (PII) approach, which incorporates a cross-correlation process to reconstruct the green function between two stations, is emerging as an effective tool for studying seismic velocity changes. These changes provide significant information about the earth's structural and mechanical properties between the stations. Despite its numerous benefits, monitoring fault zones with PII can be challenging due to various processes that can cause velocity changes in the crust. In this study, we investigated the usefulness of this method on the noise recorded in two seismic stations near the fault zone that caused the Sefid-Sang earthquake with a magnitude of Mw = 6.1. Our study covers a period of 15 months, including 12 months before and three months after the earthquake. We investigated velocity changes across different frequency ranges and examined the effect of stacking on the results. Our analysis revealed a 0.3% increase in seismic velocity two months before the earthquake.