Vol. 11, No. 11 [November 2025]

In this new article, the Adomian Decomposition Method is presented, along with the application of the ZJ transform together for the solution of second-order nonlinear Mixed PDEs and a generalization of this type of equation through illustrative examples, the effectiveness and potential of this hybrid approach to obtain approximate analytical solutions of nonlinear problems will be analyzed.
Keywords: ZJ Transform, Adomian Decomposition Method, Adomian Polynomials, Nonlinear Differential Equations, Series, Mixed Nonlinear Partial Differential Equations.

In an era where both accountability and transparency hold great importance, it is crucial for public sectors to demonstrate economic efficacy alongside social responsibility. While private enterprises are already familiar with ESG reporting, its importance is growing within public organizations. A review of current studies concerning ESG in public institutions reveals that these entities have begun to adopt such practices, though they face significant challenges. This research concentrates on the application of ESG reporting among public institutions in Romania, aiming to assess its implementation and impact on financial viability. The investigation identifies key elements influencing the decision to embrace ESG practices, particularly highlighting the institution's size and its location (central, regional, or local). It examines the hypothesis that the presence of ESG reporting is positively associated with financial performance, with organizational characteristics and contextual factors playing a major role in the decision-making process. An empirical analysis was conducted using data collected from a varied array of Romanian public entities. The results demonstrate a significant connection between ESG reporting and financial outcomes, revealing both the progress made and the obstacles encountered by the Romanian public sector in promoting sustainability.
Keywords: ESG reporting, financial sustainability, public sector, adoption, social responsibility.

Counseling services are beneficial interventions meant to enable an offender take responsibility for their actions by changing thoughts, feelings and actions so as to lead a crime free life. Committing crimes is one of the major social concerns in Malindi Sub- County. A situational analysis conducted to identify gaps in offender management in the Department of Probation and Aftercare Service. The results revealed that the department had adopted utilization of systematic evidence-based treatment programs which include corrective therapeutic approaches. The study however did not indicate whether these treatment programs have made any impact in the rehabilitation of community-based offenders. The objectives of the study were; to establish the effectiveness of counseling services on rehabilitation of criminal behavior in Malindi Sub-County; to establish the types of offences that are being committed in Malindi Sub-County and to find out the criminogenic factors responsible for criminal behaviors in Malindi Sub-County. A descriptive design was used for this study. A population of 25 counselling service providers from Malindi administered the questionnaires. The data collected was coded, arranged, classified and analyzed using tabulation and frequency calculations and percentage distribution. The data was presented in frequency tables. The response rate was 83.33%, the findings establish that a majority 56% of the respondents were male. 32% indicated that counselling results to Improved interpersonal skills, 36% indicated that assault crimes rates are very high. 68% indicated that drug and substance abuse factor is responsible for criminal behavior phenomenon.

This paper involved the synthesis and characterisation of Zinc Oxide (ZnO) nanoparticles and the analysis of their structure and optical characteristics, and one of their potential applications in Photodetectors.ZnO nanoparticles were prepared by a simple chemical procedure (chemical precipitation) which included the use of aqueous zinc nitrate and sodium hydroxide and then drying at 200 Celsius. Structural and Morphological Characterization X-ray Diffraction (XRD). The structural characterization confirmed the proper formation of Zinc Oxide crystals in the hexagonal crystalline phase (Wurtzite). The crystallite size was estimated between 5.65 nm and 12.52 nm which proves the nano-scale nature of the material. Atomic Force Microscopy (AFM) and Field Emission Scanning Electron Microscopy (FESEM). The obtained results indicated a rough and granular surface morphology, and size of the large nanorods or nanowires fell between 2-5 μm long and the width measured in the nanometer range. FTIR verified the existence of the characteristic Zn-O bond, further confirming the nanocrystalline nature of the material. Optical Investigations and Quantum Confinement Effect Optical analysis (UV-Vis) revealed that the optical band gap of the prepared material is 3.43 ev electron volts (eV). This is a bulk Zinc Oxide value band gap that is about 3.37 eV. This high band gap is being regarded as a decisive confirmation of the Quantum Confinement Effect, and it proved the achievement of the formation of nanostructures with quantum-confined dimensions. The material had spectral characteristics of the wide-bandgap semiconductors, which are highly sensitive in the Ultraviolet (UV) region and have high transparency in the visible spectrum. These properties render the material a viable solution in the next generation of applications on Ultraviolet Photodetectors (UV Photodetectors) and transparent electronics.
Keywords: zinc oxide (ZnO), Wide energy gap, Optical properties, Spectral response, XRD, FTIR.