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The Representaion of Algebraic Integers as Sum of Units over the Real Quadratic Fields: REPRESENTAION OF ALGEBRAIC INTEGERS AS SUM OF UNITS OVER THE REAL QUADRATIC FIELDS
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In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

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Publication Date
Sat Nov 01 2025
Journal Name
Journal Of Molecular Liquids
Chitosan salt as a dual-function agent for CO₂ sequestration and acidizing enhancement
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The utilization of carbon dioxide (CO₂) to enhance wellbore injectivity presents a cost-effective and sustainable strategy for mitigating greenhouse gas emissions while improving reservoir performance. This study introduces an environmentally friendly method employing a water-soluble chitosan salt (CS) that generates a carbonated-rich acid solution upon contact with dry CO₂ at 25 °C and 508 psi. CS solutions (100–2000 ppm) were prepared and evaluated for CO₂ uptake, acid generation, and rheological behavior. Results show that 1000 ppm achieves an optimal CO2 uptake (2612 mg/l), with moderate viscosity increase (from 1.52 to 3.37 cp), while higher concentrations exhibit a sharp rise due to polymer-like network formation. Core floodi

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Publication Date
Fri Aug 12 2022
Journal Name
Future Internet
Improved DDoS Detection Utilizing Deep Neural Networks and Feedforward Neural Networks as Autoencoder
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Software-defined networking (SDN) is an innovative network paradigm, offering substantial control of network operation through a network’s architecture. SDN is an ideal platform for implementing projects involving distributed applications, security solutions, and decentralized network administration in a multitenant data center environment due to its programmability. As its usage rapidly expands, network security threats are becoming more frequent, leading SDN security to be of significant concern. Machine-learning (ML) techniques for intrusion detection of DDoS attacks in SDN networks utilize standard datasets and fail to cover all classification aspects, resulting in under-coverage of attack diversity. This paper proposes a hybr

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Publication Date
Tue Jul 01 2025
Journal Name
South African Journal Of Chemical Engineering
Expired azithromycin and cephalexin as corrosion inhibitors for aluminum in saline-acidic solution
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Publication Date
Wed Feb 11 2026
Journal Name
Chemistryselect
Gelatin Nanoparticles as a Carrier for Acriflavine and Triethylenetetramine: Cytotoxicity and Antibacterial Activity
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ABSTRACT<p> Despite extensive investigation as biocompatible drug carriers, gelatin nanoparticles (GNPs) have not been thoroughly assessed for carrying chemically distinct cationic molecules such as acriflavine (ACF) and triethylenetetramine (TETA). In this study, we hypothesize that GNPs can effectively encapsulate ACF and TETA, forming stable delivery systems with distinct antibacterial and cytotoxic activities. ACF encapsulated in gelatin was prepared adapting desolvation technique. The procedure involved stirring of an aqueous solution of gelatin and ACF at room temperature, the pH was titrated to eight using NaOH followed by addition of ethanol. The resulting nanopart</p> ... Show More
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Publication Date
Sat Feb 02 2019
Journal Name
Journal Of The College Of Education For Women
The Role of the Arab oil to the achievement of Economic security in the Arab: The Role of the Arab oil to the achievement of Economic security in the Arab
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Abstract:
This research aims to the importance of oil in achieving economic
security in the Arab. Oil is not an ordinary subject and returns it significance to
the followings:
1. The importance of skipping a source of energy.
2. The importance of oil as raw material for petrochemical industry.
3. The importance of the oil sector as an area of foreign investment
4. The importance of oil in the marketing activities, transport, insurance
and various services
In addition to the importance of oil in general and the Arab oil has
additional strategic advantages such as geographic location, And the
magnitude of reserves and production of heavy investment costs are relatively
simple, And the ability to meet the

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Publication Date
Thu Feb 19 2026
Journal Name
Journal Of Studies And Researches Of Sport Education
The effect of using the educational bag on the level of learning some offensive skills with the epee weapon
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Publication Date
Sat Sep 30 2023
Journal Name
Journal Of The College Of Education For Women
The Degree of Availability of Design Thinking Indicators in the content of Arabic Language Curricula at the secondary stage in Syrian Arab Republic
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The study aimed to identify the degree of availability of design Thinking Indicators in The content of the Arabic Language Curricula at the secondary stage in the Syrian Arab Republic; to achieve the goal of the study. The researcher used the Descriptive Approach based on the analysis method according to the Cognitive Theory. The study tools consist of a list of Design Thinking Indicators and a Content Analysis Tool. The researcher completed the Validity and Reliability procedures for the tools. After applying them, the results of the study resulted in the following: Greater Interest than other sub-skills. The results also showed a Divergence of care for the sub-skills and the Difference in their recurrence rate, and the Omission of some

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Publication Date
Sun Sep 30 2012
Journal Name
College Of Islamic Sciences
The benefits of striking proverbs in the Holy Quran
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The researcher dealt with the importance of striking proverbs in the Holy Qur’an and their uses and benefits in Islamic education and ethics and between the types of proverbs, so it emerged through the study the following things that the proverbs are of three types: authorized, latent, and transmitted, and it has been shown through the current study that the proverb has conditions that the proverb is not valid except There are five: (realism, clarity, environmental, meaning injury, and good pronunciation). If the example violates these conditions, it is not an example. This study showed that proverbs have a prominent role in persuasion, argument, statement, education, clarity, approximation, education, refinement, correct belief, etc.

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Publication Date
Sun Jul 02 2017
Journal Name
Journal Of Educational And Psychological Researches
The rights of non-Muslims in the Islamic state
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The Islamic religion is a religion of tolerance and is pleased with worship and other legislation and the idea of peace is an authentic and profound idea related to the call for coexistence with all religions. The Prophet (PBUH) was keen to organize his relations with non-Muslims on the basis of cohabitation, On the basis of love and intolerance, God Almighty says: "If your Lord wants to make people one nation and they are still backward." Surah Hud: 118 Islam has taken care of the people and made them tolerant brothers who sympathize with their different beliefs. Which means that everyone has the right to live, believe and believe what he sees right and have the freedom to perform the acts of worship and beliefs he deems correct. The di

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Publication Date
Fri Jun 30 2023
Journal Name
College Of Islamic Sciences
The artistic image of flowers in the poetry of Abi Waki` al-Tanisi
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Man was closely associated with nature in its various forms, as it represented the incubator for him in all areas of his life, so writers often made it a material for their literature and a fertile ground for their productions, so it appeared in its various forms and man’s need for it, its good and its bad in literature throughout history, and the Arabs are like Other nations, since the pre-Islamic era, nature was an important outlet and a refuge for poets in the production and creativity of literature and to this day, and when we talk about a poet from the Fatimid state, we find that nature - especially spring and its flowers - in that period took its take from literature and represented a phenomenon for many Among the

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