Baku Engineering University

Financial forecasting on stock market returns has always posed challenges for investors, economists, and policymakers. Various forecasting modelling techniques are employed to obtain accurate data predictions, but most provide limited insights. This study systematically evaluates the Spline-GARCH model with the GARCH family, Neural Network (NN), and Machine Learning (ML) techniques. Specifically, Random Forest (RF), Support Vector Machine (SVM), Nonlinear Autoregressive Neural Networks (NARNN), and Long-Short Term Model (LSTM) models are employed to predict stock market returns. The recursive forecasting method is used to forecast daily returns of nine selected stock market indices of the Belt and Road Initiative linked with the China-Pakistan Economic Corridor (CPEC) from January 2015 to September 2024. The models’ forecasting performance is assessed using various forecast error measurement criteria. The empirical results revealed that the Spline-GARCH is the best-fitted model compared to other GARCH family models in all stock markets, with a high significance level in seven forecast evaluation criteria. The forecasting performance of the Spline-GARCH model outperforms that of all NN and ML models in the stock markets of Kazakhstan, Malaysia, Pakistan, Russia, and Saudi Arabia. This paper explicitly demonstrated that the Spline-GARCH model is a better ML model as a superior alternative for accomplishing accurate financial forecasts of stock market returns of BRI countries. To improve the accuracy of financial forecasts and guide sound investment decisions, particularly within Belt and Road Initiative (BRI) countries, economists are advised to incorporate spline-GARCH modelling into their analytical toolkit.

In this paper, we study a Dirichlet problem involving a nonlinear and nonhomogeneous differential operator. The driven operator in the problem is in fact the sum of a negative p(· ) -Laplace operator and a negative q(· ) -Laplace operator weighted by a positive parameter. In the reaction of the problem, we have a Carathéodory function, which depends on the solution and its gradient. Moreover, such function is composed with a continuous map defined on the variable exponent Sobolev space W_0^1, q(· )(D) , which we call intrinsic operator. Making use of tools from the theory of pseudomonotone operators, we here establish the existence of at least one solution for the problem under consideration. Further, we produce an upper bound for the solutions to the problem. Then, we prove the boundedness, closedness and compactness of the related solution set.

This paper investigates the inverse spectral properties of a quadratic operator pencil with steplike almost-periodic potentials in space L_2(R) . The operator, which is generally non-self-adjoint, is analyzed under the conditions of specific potential forms. Key theorems are established to construct special solutions, examine spectral singularities, and demonstrate the absence of real eigenvalues. Additionally, the continuous spectrum is characterized, and the inverse spectral problem is formulated, providing a procedure to uniquely reconstruct the potentials from given spectral data. The findings contribute to the broader understanding of spectral theory in non-self-adjoint operator settings.

This work analyzes a multi-server retrial queueing system regulated by a batch Markovian arrival process and phase-type service times, incorporating a control mechanism for retrial customers. Retrial attempts from the orbit succeed only when the number of busy servers is at or below specific thresholds, which vary depending on the state of the arrival process. Customers waiting to retry may abandon the system independently due to impatience. When all servers become idle, they first remain on standby for a limited time, serving any arriving primary or retrial customers immediately; if no arrival occurs before this period ends, the servers take a synchronous working vacation, providing service at a reduced rate. Upon batch arrival, if insufficient servers are free, the batch is rejected or served partially, with the rest going into the orbit–a policy applied in both normal and working vacation modes. While in normal service mode, a disaster may occur at any time, causing all main servers to fail and forcing all customers in service to leave the system, causing no impact on the orbit. Repair begins immediately, during which no service is provided, and arriving batches may leave the system or join the orbit. The system state evolves as a multidimensional Markov chain in the asymptotically quasi-Toeplitz class, which facilitates obtaining the ergodicity conditions, enabling the derivation of steady-state probabilities and system performance measures. A case study involving the resolution of an optimization challenge is shown. Results highlight the influence of batch arrivals and system parameters on performance measures.

This essay explores Pride and Prejudice through a linguistic lens, revealing how Jane Austen uses language not just to develop characters and relationships but to reflect and critique the social norms of her time. Rather than focusing solely on the novel’s romantic elements, this analysis highlights how Austen's characters communicate within—and sometimes push against—the constraints of gender, class, and politeness. Drawing on key concepts from pragmatics and sociolinguistics, including Brown and Levinson’s politeness theory, Grice’s theory of conversational implicature, and speech act theory developed by Austin and Searle, the essay examines how meaning is shaped by indirectness, power dynamics, and unspoken social rules. Specific scenes—such as Mr. Collins’s failed proposal, Lady Catherine’s confrontational speech, and Elizabeth Bennet’s witty and often subversive dialogue—demonstrate how language can be both a tool of social control and personal resistance. The analysis shows that Austen’s mastery lies not only in her narrative structure or irony, but in her deep understanding of how people use speech to negotiate status, express defiance, or maintain dignity. Even brief exchanges carry layers of implication and social meaning. Ultimately, this linguistic perspective reveals Austen as a subtle social critic who understood that in a society governed by rules and appearances, the way people speak often says more than what they say.