A Chebyshev collocation scheme formulated in trigonometric coordinates — the Chebyshev Trigonometric Collocation (CTC) method — is presented for computing eigenvalues of Sturm–Liouville boundary value problems. The method uses the identity T_k (cosθ)=cos(kθ) to express the Chebyshev basis in trigonometric form, enabling all collocation matrix entries to be assembled from closed-form analytic expressions rather than numerically approximated differentiation weights. This yields a generalized algebraic eigenvalue problem at Chebyshev–Gauss–Lobatto (CGL) nodes. A conditional convergence result is established: for regular problems with analytic coefficient data, the k-th eigenvalue error is expected to satisfy |λ_k-λ_k^((N) ) |≤C_k ρ^(-2N) for a Bernstein-ellipse parameter ρ>1 determined by the domain of analyticity of the coefficients, subject to two technical hypotheses (collective compactness and operator consistency) that are stated explicitly but whose verification for the CTC scheme is deferred to future work. The method is benchmarked against the Hermite-interpolation method and the sinc-collocation/ differential quadrature methods. For problems where independent exact eigenvalues are available, the CTC method at larger basis sizes achieves substantially smaller errors than competing methods.

In the current investigation, we formulate and analyze the Square–Logistic distribution (SLD), which is developed by integrating the half–logistic and odd Fréchet–G families. The SLD exhibits highly versatile probability functions: it encompasses hazard rate functions that are decreasing, increasing, exhibit a bathtub shape, and an inverted U shape, thereby demonstrating the model’s inherent flexibility. A thorough examination of the mathematical and statistical characteristics of the proposed model is provided. From an estimation perspective, different methodologies are employed to estimate the unknown parameter(s) of the SLD. In addition, an extensive Monte Carlo simulation study is conducted to assess the effectiveness of these estimators. Lastly, real data applications are employed to illustrate the adaptability of the proposed method, with comparisons drawn against the half–logistic and some of its prominent extensions.

The analytical inversion of Laplace and Fourier transforms often presents significant challenges for functions commonly encountered in engineering and scientific fields. Although numerous numerical inversion methods are available, these techniques tend to be highly specialized, algorithmically complex, and sensitive to parameter variations. This paper introduces an innovative, unified methodological framework for the numerical computation of these inverse transforms. By leveraging the intrinsic relationship between the two transforms through analytic continuation and implementing a robust regularization strategy within a Fourier inversion framework, we derive a generalized inversion formula. This method effectively converts the problem of inverting a Laplace transform into a specially designed Fourier inversion, which is then solved using a computationally efficient and stable algorithm based on the Fast Fourier Transform (FFT) with a smoothing kernel. We validate the effectiveness and precision of this universal method through several standard examples, comparing its performance with traditional techniques such as the Bromwich integral and Stehfest's algorithm for Laplace inversion. The proposed approach offers a streamlined, powerful, and versatile computational tool for researchers and practitioners.

Indian graphic novels are now fully formed and unique, joining visual art, literature, and criticism of society. Over the years, comics have mirrored how India's culture and ideology have changed, starting with the familiar stories of Amar Chitra Katha and going on to modern tales about city feelings, caste, gender, and politics. The paper looks back at how Indian graphic novels have developed, starting with early influences and the work of Orijit Sen in The River of Stories, and then considers important themes, new styles, and fresh ways of storytelling in these works. It examines how the medium is being adopted on the internet in webcomics, visual journalism, and educational stories. Moreover, the paper describes the trouble of reaching more viewers brought by limited broadcasting, online censorship, and the lack of speaking ideas in vernacular languages. Because of this, the text points out that graphic novels in India act as a communicative medium through which people talk about their culture, tradition, and modern times, fiction and reality, while connecting. By following these trajectories, the paper gives a clear picture of the medium’s growth, how significant it is today, and what it may become in the future of Indian visual culture.

In an era where computational demands continually escalate, the quest for more efficient and powerful processors persists. Computer engineering and VLSI design industries are facing challenges with the trade-offs between the cost and performance of components in the implementation domain. Reduced Instruction Set Computer (RISC) architecture relies its focus mainly on scaling down the complexity and the number of instructions in the microprocessor. RISC-V is an Open-source Instruction set architecture (ISA) designed to be simple, modular, and customizable. The most important feature of RISC is that it supports load-store architecture. With this feature, an optimized 32-bit microprocessor has been designed with Verilog, simulated and synthesized in Xilinx Vivado. Verilog enables us to describe the behavior and structure of our processor at a register-transfer level. Overall, RISC-V's combination of simplicity, openness, and flexibility positions it as a promising ISA for a wide range of applications, from low-power IoT devices to high-performance computing systems.

Modem digital security based on classical cryptographic methods is likely to become obsolete because quantum algorithms such as Shor's and Grover's algorithms will become available. The paper uses research data and experimental findings and methodological analysis to understand new trends in the field. The manuscript examines the path toward post-quantum cryptography together with the necessary tactics to defend future security systems facing quantum-computing technological advancement.

The enterprise resource planning (ERP) systems with SAP S/4HANA were defined as the the primary financial processes for Bank General Ledger (Bank GL) management. Our review discusses the new framework of Bank GL consolidation through House Bank-focused design on SAP S/4HANA environment. The conventional SAP ECC systems maintained several GL accounts for each bank account and company code, resulting in complex reconciliation, and poor visibility into cash. S/4HANA can solve these inefficiencies by using single reconciliation GL account for the entire banking which offers an integrated model of data that supports real-time financial reporting and integration of modules. In a critical analysis, the paper examines the architectural change to an object-oriented House Bank with centralized architecture with a discussion of its configuration, posting logic, reconciliation mechanism, and integration to embedded treasury functions, including Bank Account Management (BAM), Cash Management, and Bank Communication Management (BCM). The literature review and SAP documentation indicate such benefits as the decrease of GL volumes, better audit trails, and higher liquidity insights. There are, however, still difficulties in terms of complexity of transition, configuration risks, resistance within the organization and capability gaps amongst end-users. The review examines other toolsets, including SAP Activate, Readiness Check, and Transformation Navigator, and outlines future research directions in AI-driven reconciliation, API-based bank integration, and ESG-related financial reporting. The paper will add into the current discussion of the financial digital transformation by offering an in-depth analysis of the House Bank-oriented GL consolidation model that may be used by researchers and practitioners undertaking SAP S/4HANA finance implementations.

Poisson regression serves as a crucial method for modeling count data; however, it encounters challenges when the data display overdispersion, frequently due to outliers, which can lead to biased inferences and underestimated standard errors. This research introduces an Outlier-Weighted Poisson Model (OWPM) that utilizes robust weights derived from Cook’s distance to reduce the impact of outliers. By employing enhanced simulation designs that account for heteroscedasticity, zero inflation, and correlated predictors, we assess the performance of OWPM in comparison to standard Poisson and Negative Binomial models through various metrics and tests. The findings indicate that OWPM effectively addresses overdispersion, resulting in lower prediction errors and more dependable inferences, akin to those obtained from Negative Binomial regression. Statistical evaluations reveal significant enhancements over the conventional Poisson model, particularly in scenarios with moderate to high levels of outliers. This study offers a practical and computationally efficient method for robust regression of count data, demonstrating wide-ranging applicability.

With the expansion of online recruitment platforms, the hiring process has become more efficient; however, this advancement has also led to a rise in fraudulent job postings, causing significant financial harm to job seekers. To address this growing concern, the study introduces a deep learning-based framework for detecting Online Recruitment Fraud (ORF). A novel, comprehensive dataset is constructed by integrating data from Fake Job Postings, Pakistan Job Postings, and US Job Postings. The proposed method leverages state-of-the-art Natural Language Processing (NLP) models—Bidirectional Encoder Representations from Transformers (BERT) and its optimized variant, RoBERTa—to encode job descriptions into meaningful vector representations. To resolve the challenge of class imbalance in the dataset, the Synthetic Minority Over-sampling Technique with Borderline Detection (SMOBD) is employed. These processed features are then input into a two-dimensional Convolutional Neural Network (CNN2D) for classification. Experimental results demonstrate that this integrated approach achieves an impressive classification accuracy of 98.68%. The proposed model not only surpasses existing techniques but also provides a robust and scalable solution for identifying fraudulent job listings, thereby contributing significantly to the prevention of online recruitment scams.

Sentiment analysis is a crucial part of natural language processing (NLP) that categorizes text into positive, negative, or neutral sentiments. This technology helps businesses automatically interpret customer emotions, enabling informed decisions in marketing, product development, and customer support. Traditional machine learning models like Random Forest, Naive Bayes, and Support Vector Machine (SVM) have been commonly used for sentiment classification, especially effective for short and concise texts such as brief customer comments. SVM, in particular, performs well in classifying sentiments in short texts. However, the emergence of advanced large language models (LLMs) like GPT-4 has revolutionized sentiment analysis by capturing more nuanced emotional expressions. GPT-4 excels in understanding complex context, sarcasm, and subtle emotional tones within longer texts, offering multi-dimensional sentiment insights such as satisfaction, frustration, and uncertainty. This makes it more capable than traditional models when analyzing detailed customer reviews or conversations. Comparative studies reveal that while traditional models handle short texts efficiently, GPT-4 surpasses them in analyzing in-depth content with greater precision, recall, and F1 scores. GPT-4 also uniquely identifies mixed sentiments that simpler models often miss. In conclusion, although traditional machine learning approaches remain useful for straightforward sentiment analysis tasks, GPT-4 provides a more sophisticated and comprehensive understanding of customer emotions in complex texts. Integrating GPT-4 into sentiment analysis workflows can significantly enhance the accuracy and richness of insights derived from customer feedback, supporting better business decisions.