The Federal Reserve has played an arguably important role in financial crises in the United States since its creation in 1913 through monetary policy tools. Thus, this paper aims to analyze the impact of monetary policy on the United States’ economic growth in the short and long run, measured by Gross Domestic Product (GDP). The Vector Autoregressive (VAR) method explores the relationship among the variables, and the Granger causality test assesses the predictability of the variables. Moreover, the Impulse Response Function (IRF) examines the behavior of one variable after a change in another, utilizing the time-series dataset from the first quarter of 1959 to the second quarter of 2022. This work demonstrates that expansionary monetary policy does have a positive impact on economic growth in the short term though it does not last long. However, in the long term, inflation, measured by the Consumer Price Index (CPI), is affected by expansionary monetary policy. Therefore, if the Federal Reserve wants to cease the expansionary monetary policy in the short run, this should be done appropriately, with the fiscal surplus, to preserve its credibility and trust in the US dollar as a global store of value asset. Also, the paper’s findings suggest that continuous expansion of the Money Supply will lead to a long-term inflationary problem. The purpose of this research is to bring the spotlight to the side effects of expansionary monetary policy on the US economy, but also allow other researchers to test this model in different economies with different dynamics.

This article studies the nonlocal inverse boundary value problem for a rectangular domain, a second-order, elliptic equation and a two-dimensional equation. The main objective of the article is to find the unidentified coefficient and provide a solution to the problem. The two-dimensional second-order, convection equation is solved directly using the finite difference method (FDM). However, the inverse problem was successfully solved the MATLAB subroutine lsqnonlin from the optimization toolbox after reformulating it as a nonlinear regularized least-square optimization problem with a simple bound on the unknown quantity. Considering that the problem under study is often ill-posed and that even a small error in the input data can have a large impact on the outcome, Tikhonov's regularization technique is used to obtain stable and regularized results.

The bivariate Poisson exponential-exponential distribution is an important lifetime distribution in medical data analysis. In this article, the conditionals, probability mass function (pmf), Poisson exponential and probability density function (pdf), and exponential distribution are used for creating bivariate distribution which is called bivariate Poisson exponential-exponential conditional (BPEEC) distribution. Some properties of the BPEEC model are obtained such as the normalized constant, conditional densities, regression functions, and product moment. Moreover, the maximum likelihood and pseudolikelihood methods are used to estimate the BPEEC parameters based on complete data. Finally, two data sets of real bivariate data are analyzed to compare the methods of estimation. In addition, a comparison between the BPEEC model with the bivariate exponential conditionals (BEC) and bivariate Poisson exponential conditionals (BPEC) is considered.

We analyze an inverse force problem that involves identifying a source term in a one‐dimensional fourth‐order beam equation depending on either space or time. Mixed boundary conditions and an overdetermination condition based on a single point in space or time address the problem. For both direct and inverse problems, we rely on the existence and uniqueness theorems from previous research. Likewise, we apply the Von Neumann method to determine stability. The finite difference method (FDM) with Tikhonov regularization effectively identifies displacement and source problems in numerical analysis. Consequently, a small amount of noise improves the accuracy and consistency of the final results, as demonstrated by tests conducted at various noise levels. Numerical experiments with both exact and noisy data show the accuracy, reliability, and efficiency of our approach.

This study introduces a mathematical model for predicting concrete compressive strength and employs data-driven inverse techniques. Six models are tested: Linear Regression, Pure Quadratic, Interaction, Full Quadratic, Artificial Neural Network (ANN), and Adaptive Neuro-Fuzzy Inference System (ANFIS). To evaluate inverse sensitivity, noise is introduced into the ANN models to assess how small errors in the data affect the results for concrete compressive strength. Tikhonov regularization is applied to mitigate these errors, ensuring reliable outcomes. The dependent variable, compressive strength (CS), is categorized into low-strength, normal-strength, and high-strength concrete, with values ranging from 7.98 to 92.93 MPa. Independent variables include coarse aggregate (CA), sand (S), cement (C), fly ash (FA), cement replacement (CR), water-to-binder ratio (w/b), calcium oxide ratio (CaO), silicon dioxide (SiO$_2$), and curing time (t). Model performance is evaluated using multiple metrics, including the correlation coefficient (R$^2$), objective function (OBJ), scatter index (SI), mean absolute error (MAE), and root mean squared error (RMSE). The results indicate that ANFIS outperforms the other models in both accuracy and efficiency, establishing it as the most reliable approach for predicting concrete compressive strength.