Journal of Pure & Applied Sciences

A Study of a Basic Sufficient Condition for the Compactness of Linear Operators on Banach Spaces

2025-04-10T11:29:47+02:00

This work examines conditions for the compactness of linear operators in Banach spaces, a key question in functional analysis with broad applications. Compactness ensures that bounded sets are mapped to relatively compact sets, making it a fundamental tool in the study of operators on infinite-dimensional spaces. This paper provides a detailed investigation of three conditions ensuring compactness: total boundedness, finite dimensionality, and completeness. It addresses a significant gap in the literature and provides a sound theoretical framework.

This paper aims to (1) explain the connection between finite dimensionality and total boundedness as conditions for compactness, (2) present unified sufficient conditions for the compactness of linear operators with proofs, and (3) offer new insights into operator theory for broader mathematical applications. This study employs advanced functional analytic techniques to deduce and validate these well-founded conditions.

This work addresses gaps in compact operator theory, with implications for quantum physics, differential equations, and numerical analysis. By enhancing the understanding of Banach spaces and operator theory, this study may inspire further exploration of their properties.

Effects of Traditional and Chemical Ripening Methods on the Physicochemical Properties and Microbial Quality of Banana and Pawpaw Fruits

2025-04-11T11:30:10+02:00

This study was conducted to evaluate the effects of traditional and chemical ripening methods on the physicochemical properties and microbial quality of banana and pawpaw fruits. The physicochemical properties and microbial load of the fruits were analyzed using standard analytical and microbiological methods. Unripe banana and pawpaw fruits served as control samples. Naturally ripened bananas had the highest protein (4.63%), fat (1.54%), sugar (9.33%), pH (4.47), and vitamin C (6.16 mg/100 g) contents after 72 hours. In contrast, bananas ripened with calcium carbide exhibited the highest moisture (97.55%), ash (3.00%), fiber (1.67%), carbohydrate (55.16%), and titratable acidity (0.20%) at 72 hours. For pawpaw, the sample placed in an airtight bag had the highest moisture (97.21%) and ash (0.50%) content, whereas the blanched sample had the highest fat (0.13%), carbohydrate (13.33%), and pH (7.77) values. Pawpaw ripened with calcium carbide showed the highest protein (0.96%), titratable acidity (1.20%), and vitamin C (0.98 mg/100 g) contents at 72 hours. Microbial analysis revealed that after 72 hours of ripening, bacterial and fungal isolates were present on the fruit surfaces. The identified bacterial isolates included Pseudomonas spp., Citrobacter spp., Staphylococcus aureus, Enterobacter spp., Micrococcus spp., and Escherichia coli. Fungal isolates included Aspergillus flavus, Aspergillus niger, and Fusarium spp. The results indicate that natural ripening methods, such as open-shelf ripening and airtight bag storage, led to a significant increase in nutrient content compared to chemical ripening with calcium carbide.

Study of the Economic Factors Affecting the Outcomes of Agricultural Education in the Municipality of Sebha in South Libya

2024-07-10T02:12:14+02:00

This study aimed to identify the economic factors that affect agricultural education outcomes to meet the requirements of the labor market in the municipality of Sebha in south Libya during the period 2023. The study relied on field data of the study sample. A descriptive and quantitative analysis, means, standard deviation, and T-test were used to meet the objectives of the study. The results of the study showed that agricultural training courses, agricultural faculties, and institutes in southern Libya have a significant impact on improving the outcomes of agricultural education. The study also indicated that the level of income and agricultural investments have a significant impact on the effectiveness and efficiency of an agricultural education graduate. The study recommended holding agricultural training courses and providing agricultural loans to new farmers, improving the infrastructure of agricultural faculties and institutes, expanding the culture of agricultural education, and determining the requirements of the agricultural labor market.

The The Role of Applying Actuarial Accounting in Enhancing Banking Supervision by Application on a Sample of Libyan Commercial Banks

2024-11-01T17:42:31+02:00

The study aimed to identify the role of actuarial accounting in enhancing banking supervision in the Libyan banking sector from the perspective of banking sector employees. To achieve the objectives of the study, the descriptive and analytical approach was used, as the researchers used the questionnaire form as a tool in collecting the information necessary to analyze the research variables. The two researchers reached a set of conclusions. The most important of which is: the existence of a statistically significant relationship between the application of actuarial accounting and improving risk management, enhancing financial stability and increasing confidence in the most important of what the researchers recommended. Working to enhance the use of actuarial accounting in all Libyan institutions by directing attention and investment in developing actuarial accounting systems and providing appropriate training for working personnel.

Elevational Effect on Aleppo Pine Seed Production and Seed Germination in east north Libya

2024-11-06T06:00:17+02:00

Al Jabal Al Akhdar mountain south of the Mediterranean in Northern Libya is the only native habitat for Aleppo Pine (Pinus halepensis Mill.) in eastern North Africa. Located between the Mediterranean Sea and the Sahara Desert, climate change and human activities are threatening its existence. We studied three woodlands of P. halepensis at different elevations in this unusual and rare ecosystem. We found that P. halepensis is producing more cones per tree and more seeds per cone than trees in more northern populations, with a net result at higher altitude of more than 7 times the number of seeds per tree compared to the northern Mediterranean. Moreover, seeds from woodland at the highest altitude showed better germination, longer root length, higher root and shoot dry mass and better growth than the other two populations, so are most likely to grow better during intermittent precipitation and be big enough to survive subsequent dry periods. We conclude that P. halepensis is capable of self-maintenance in this southern outpost in the short-term, but is likely to rapidly deteriorate in the face of climate change and a lack of protection. Conservation action to protect and facilitate spread of natural stands is urgently needed.

The Role of Financial Analysis in Evaluating the Financial Performance of Private Commercial Banks in Libya: Case Study at the Aman Bank for Trade and Investment During the Period (2019-2023)

2025-01-25T14:25:24+02:00

The study aimed to show the role of financial analysis using financial indicators in evaluating the financial performance of private commercial banks in Libya, and to achieve this goal, Al-Aman Bank for Trade and Investment was chosen as a case study, by following the descriptive analytical approach based on the data of the financial statements by doing a partial financial analysis using profitability and indebtedness indicators during the study period from 2019 to 2023, and the study reached many results, including: It was found through the use of profitability indicators that they were positive, and that the bank's management achieved profits during the study period, and this indicates the performance and efficiency of the management in employing its assets and generating profits.

Government Financial Dominance and the Independence of the Central Bank of Libya: A Study of Asymmetric Effects

2025-01-26T14:24:59+02:00

is study aims to analyse and measure an impact the government financial dominance on an independence of the Central Bank of Libya by analysing the annual data for the period (1990-2022), where the non-linear autoregressive distributed lag (NARDL) technique was used, through which the effects of symmetric and asymmetric relationships of financial dominance variables (public spending - public debt) on the independence of the Central Bank of Libya can be verified. Results of the study showed that an increase/decrease in the impact (positive and negative) of public spending will lead to an increase/rise in the money supply, which means a decrease in the index of central bank independence. An increase/decrease in the impact (positive and negative) of public debt will result in an increase/rise in the money supply, which indicates a decrease in the index of central bank independence. As well as relationships between the indicators of government financial dominance and the independence of the Central Bank of Libya were asymmetric in the long run, and symmetric in the short run. The results of the study agreed with the Sargent and Wallace hypothesis and with King's interpretation, as the results showed that financial dominance limits the independence of the Central Bank of Libya, and both the increase in public spending and public debt had a negative impact on the role of monetary policy in achieving its goals in the long run. The study also recommended the necessity of coordination between fiscal and monetary policies and emphasizing on the independence of the Central Bank.

The Role of Governance Indicators in Achieving the Sustainable Development Goals: The Case of Libya

2024-11-22T20:40:10+02:00

All countries of the world are aware that governance is an essential element in the successful implementation of sustainable development policies and goals, but there are few studies that explore the relationship between governance and sustainability, especially in Arab countries that have passed and are still going through a state of political and security instability. This study attempts to identify and analyze the role of governance in promoting the transition towards sustainable growth in the country of Libya, where the global governance indicators (WGI) are presented, which appear in the World Bank databases, to assess the role of governance in the pursuit of achieving the Sustainable Development Goals and the extent of commitment to transition to a more stable society, which allows determining the direction of change for the better. This study seeks to review the governance indicators in Libya during the period (2011-2022), as it became clear that Libya is ranked among the Low Countries in terms of achieving the Global Governance Indicators set by the World Bank (WGI), which covers several dimensions of governance, and the study concluded after analyzing the level of global governance indicators, that the Libyan state will not be able to achieve the Sustainable Development Goals unless it paves the way to this, in reference to the weakness and low lag indicators that express good governance, in a call for urgent reform so as not to remain at the bottom of the list of the world is striving for Sustainable Development Growth).

Exposure to Abamectin affected early embryonic development and caused changes in erythrocytes in chicken embryos (Gallus gallus)

2025-03-23T14:42:52+02:00

Early embryonic development is tightly regulated, and environmental factors can disrupt vital processes, resulting in poor embryo development. Abamectin, a pesticide and insecticide, has been shown to cause infertility in farmers. Despite its benefits, little is known about its impact on embryonic development and pregnancy. Therefore, this study aimed to examine the effects of Abamectin at two different concentrations on the nuclear erythrocyte morphology and general embryonic development in domestic Gallus chick embryos. Eggs were injected with Abamectin (ABM) at doses of 0.01 mg/kg and 0.05 mg/kg body weight per egg at two stages of development: the zero and third days of incubation. The embryos were collected on the fifth and ninth days of incubation, and their morphology was examined under a dissecting microscope. Blood samples were collected on the twelfth day of incubation. Blood smears were prepared on slides and stained; the density of blood cells, as well as the shape and abnormalities of nuclei, were examined under a light microscope.

The results from this study demonstrate that exposure to ABM led to developmental defects in embryos at stages HH29 to HH38. These defects affected overall morphology, blood vessel formation, and erythrocyte shape, with higher concentrations producing more severe outcomes.

Effect of heat treatment on the physicochemical and functional properties of nutritional mixtures prepared for pregnant women

2025-03-26T14:43:04+02:00

The stages of pregnancy are divided into three phases; and in each phase, the fetus needs different nutritional components. Therefore, the aim of this study was to prepare three nutritional mixtures from plant and animal sources meet the nutritional needs during the different stages of pregnancy. Then, studying the effects of heat treatment on their physicochemical and functional properties. The mixtures were prepared using grains, legumes, oil seeds, dried fruits, legumes and whole milk powder with different proportions based on the fetus’s needs in the three stages of pregnancy. The first and second mixtures were cooked on a direct heat for 15 min after mixing them with water in a ratio of 1:10. Subsequently, the cooked samples were dried in an air oven at 40°C. The results indicated that the ability of the first mixture to bind water increased to almost double, and it was higher than the ability of the second mixture. It was noted that the swelling ability significantly increased (p≤0.05) for the first and second samples after cooking. The second mixture recorded the highest swelling ability, whether for the raw or cooked sample. The results showed that the solubility of the first and second mixtures significantly decreased after cooking from 14.98 to 9.32% and from 14.32 to 11.29%, respectively. The total ash content ranged b.1etween 2.07% and 2.60%. Whereas, the protein content in the studied samples ranged from 10.09% to 13.75%, which recorded by the third sample. Heat treatment led to an increase in the protein content in the first mixture, and decreased in the second mixture. It was found in this investigation that the third mixture had the highest level of total fiber (7.68%), while the first and second cooked samples documented the lowest value of dietary fiber (4.83 and 5.08%) respectively. The content of selenium, manganese, potassium and zinc significantly differed in the studied samples, whether raw or heat-treated once.

Generative Adversarial Networks in Brain Imaging: A Decade-Long Review of Progress and Future Directions

2025-04-11T11:30:02+02:00

Due to the increasing demand for effective and objective analysis to address complex challenges such as brain medical image reconstruction, segmentation, and classification, medical image analysis for brain tumor research has gained significant attention. The ability of Generative Adversarial Networks (GANs) to increase the probability density over data distributions by estimating density ratios, along with their capacity to uncover high-dimensional latent distributions, has led to substantial performance improvements in visual feature extraction. Furthermore, the adversarial loss incurred by the discriminator offers a subtle method of incorporating unlabeled samples into training, thereby improving accuracy at higher orders. These characteristics of GANs have proven valuable in various applications, including enhancing medical images and translating images across different modalities. Additionally, the ability of GANs to generate images with remarkable realism offers hope that, through these generative models, the ongoing challenge of limited labelled data in the medical field may be overcome. The aim of this review is to provide a comprehensive overview, starting with a concise summary of the range of available GAN architectures and datasets. This study then highlights the research conducted in processing and interpreting GAN-based brain images. Finally, the limitations of GAN-based methods for brain image analysis are discussed, identifying unresolved research issues and suggesting avenues for further exploration in this emerging field.