The aim of this paper is to establish the prime state ideal theorem in state residuated lattices (SRLs). We study the state ideals lattice SI(L) of a state residuated lattice (L, φ, ) and prove that it is a complete Brouwerian lattice in which the meet and the join of any two compact elements are compact (coherent frame). We characterize the notion of prime state ideals in SRLs. In addition, we establish the condition for which the lattice SI(L) is a Boolean algebra.

Plato, in his famous political opus, "Republic", has formalized an Ideal state according to epistemological and ontological bases, which can be mentioned as the first comprehensive and coherent thought about politics. This Ideal state, from years ago, has been construed in different interpretations. The present article seeks to examine the distinctions of Plato's Ideal state from others by reading this Ideal state on the sociopolitical context of classical Greece on the one hand and Plato's intellectual and philosophical basics on the other hand. According to this reading, it seems that the sociopolitical characteristics of classical Greece and Plato’s intellectual and philosophical basics have caused that the Ideal (actual) state on Plato’s view be distinguished from any abstract Idealism, on the one hand, and Utopianism and Millenarianism on the other hand.

In this paper, the notions of prime state ideals and state semi-maximal ideals of state MV -algebras are introduced. We prove prime state ideal theorem and we show that a state MV -algebra A is semi-simple if and only if A has no state infinitesimals. We introduce the concept of state radical of state ideals in a state MV -algebra, we present a characterization of a state radical ideal. We show that the set of state radicals of state ideals in (A, σ) is a Heyting algebra.

One of the proposed models for the realization of good governance is the "local governance" model, which is based on administrative decentralization and emphasizes the direct role of people in managing their local and regional affairs. The current research, with a descriptive-analytical approach and relying on library and documentary sources, has tried to research and investigate the desirable state of managerial decentralization in the political-administrative system of Iran from the perspective of Shahid Beheshti (RA). The main question is that in Shahid Beheshti's thought, what is the ideal state of local governance and what is the model of decentralization he wants. The findings of the research show that avoiding centralism and paying attention to local self-governance is one of the important principles of popular governance from Shahid Beheshti's point of view. From his point of view, among the various models that have been proposed for decentralization, the ideal model for the Islamic Republic system is the "local self-government" model, which will gradually change towards a kind of federalism, while maintaining the principle of centrality and hierarchy. delegates broad powers to local institutions and organizations. The limits of the powers of the local elected bodies are as long as they do not lead to separatism and autonomy.

A new empirical correlation is developed for the accurate prediction of isobaric heat capacity, enthalpy, and entropy of pure hydrocarbons and petroleum fractions in the ideal gas state, with a particular emphasis on the low-temperature region (200–300 K). Unlike traditional models such as Kesler-Lee, Huang, and Kuznetsov, which are often limited in accuracy or applicability at low temperatures or for heavy hydrocarbons, the proposed correlation integrates a fourth-degree polynomial approach and molecular weight dependence to extend predictive capabilities across a broad range of components—from butane to heavy fractions exceeding 570 g/mol. Validation against 340 experimental data points for heat capacity and 112 data points for enthalpy and entropy reveals a significant reduction in AARE and MARE values, achieving errors of 0. 90% and 2. 10%, respectively. While the correlation provides excellent results for normal alkanes, its applicability to cycloalkanes and aromatic hydrocarbons is limited and may require further refinement. The proposed model holds strong potential for implementation in thermodynamic simulators for oil, gas, and condensate production and processing, especially under surface conditions where precise thermophysical data at subambient temperatures are critical.

Many thinkers have designed a form of an ideal state in their thought. Plato, the Greek thinker, and Iqbal, the Islamic thinker, are among these thinkers who have designed a form of the ideal state in their thought. What these two thinkers have the fundamental differences in the ideal state are their way of looking at the relation between poetry and philosophy in ideal state. This article with hermeneutic method attempts to explain the position of poetry and its relation with philosophy in Plato and Iqbal's views and on this basis, it deals with different view of the two thinkers on the poetry and philosophy. Generally, Plato has a negative attitude toward poetry in ideal state, and considers Poetry and poets against Philosophy and philosophers while Iqbal thoroughly believes in the positive role of poetry in ideal state and with emphasizing the relation between poetry and philosophy, he considers the same the poet and philosopher based on purpose. The main reason for this difference is the method of viewpoint of these two thinkers towards poetry from the epistemic aspect. Plato does not consider poetry to be any knowledge and reality and therefore, in the ideal state that philosophers are ruling he orders the rejection of poetry and the banishment of poets from ideal state. But in Iqbal's thought, poetry has knowledge and reflects reality and even due to its profound influence, any further knowledge comes to the work of reforming the city and society. Therefore, with a deep link between the philosophic knowledge and poetry, the philosopher and poet are one in Iqbal's view and both of them have rational knowledge and their presence is essential for the ideal state.

This study seeks to explicate a model of the political system and the ideal state based on the Holy Qur’an, adopting a systems approach within the framework of political philosophy. While Qur’anic studies are commonly situated within jurisprudential, mystical, or theological frameworks, this article moves beyond these conventional approaches to discover and infer the components of a divine system of governance distinct from secular models. The ultimate objective of this political system is the realization of the divine command to establish the religion (iqamat al-din), as emphasized in the verse: “He has ordained for you of religion what He enjoined upon Noah … [saying], ‘Establish the religion’” (Qur’an, al-Shura 42: 13). Accordingly, one dimension of establishing the religion—addressed to all monotheistic worshippers—is fulfilled through recognizing and instituting Islamic systems. The innovation of this research operates on two levels. First, a systemic innovation that, by offering a structured framework, enables deep and comprehensive comparison with other political systems. Second, an innovation in content and concepts, which introduces fundamental and distinctive components—such as taqwa (piety), tazkiya (purification), the linkage of leadership to tawhid (monotheism), and the precedence of the ummah and leadership over the state—as integral elements of the Qur’anic political theory. Methodologically, the study combines inferential analysis with the theory of signification—employing the three levels of denotative, implicative, and necessary meanings—alongside the method of istintaq al-Qur’an (interrogating the Qur’an). Through this approach, the article proposes a novel divine model of governance whose ultimate end is establishing the religion, and contends that a return to its foundations delineates the path to human felicity and salvation. The central question addressed is: What structure and functions characterize the Qur’anic model of the political system? To answer this overarching question, eight subsidiary questions are examined based on a systems-analytical framework. First, regarding the necessity of establishment, the findings indicate that the Qur’an—by emphasizing the command to establish the religion and the need to ensure comprehensive security encompassing both worldly life and the Hereafter—deems the formation of a divine state necessary. This necessity is also reflected in Qur’anic narratives, such as the story of Talut. Second, concerning constituent elements, in addition to the four elements common to all states (territory, population, government, and sovereignty), the Qur’an highlights three exclusive pillars: tawhid as the foundation, divine leadership as the axis, and Islam as the comprehensive roadmap. Third, in analyzing the boundaries of the Islamic political system, a structural distinction is observed. At the operational level of the state, geographical and contractual borders are recognized,however, at the identity level of the ummah and leadership, Islam is universal and transboundary. This distinction offers a solution for reconciling the universality of religious teachings with the practical realities of governance. Fourth, with respect to the power network, the criteria for selecting officials include merit, expertise, trustworthiness, and justice. The use of non-Muslims in non-sovereign and service-oriented positions—subject to specific regulations—is considered permissible. Moreover, the participation of women in the sphere of social management is affirmed, based on Qur’anic verses and precedent. Fifth, the decision-making center resides in divine leadership, whose legitimacy is intrinsic and derives from God. This leadership exercises final authority within the framework of Sharia, utilizing consultation (shura) as a method and allegiance (bay‘a) as public confirmation and commitment. In times of crisis, this central authority is strengthened to preserve the system. Sixth, the scope of authority and duties of the Islamic state is extensive, encompassing both fixed matters (such as the promotion of monotheism, provision of multidimensional security, implementation of justice, and enjoining good and forbidding evil) and contingent matters (responding to the changing needs of society). The state is obligated to provide a good life (hayat tayyiba) for all citizens, while respecting privacy, unless an overriding public interest necessitates otherwise. Seventh, in analyzing the process of power, the Qur’an outlines three overarching models: the ideal model of love and affection, which establishes relationships grounded in faith and beneficence,the model of religious democracy, which, within the framework of Islamic rulings, is based on participation and consultation,and the condemned tyrannical (taghuti) model, founded on despotism and transgression. Eighth, regarding feedback, the Qur’an establishes a robust and active oversight system through the key principle of enjoining good and forbidding evil. Accordingly, constructive criticism and protest by the people against governmental decisions—within criteria such as justice and anti-corruption—not only are permitted but are necessary to ensure the health and dynamism of the system. In sum, by moving beyond prevailing approaches in Qur’anic studies and relying on the methods of istintaq (a thematic–analytical reading of the Qur’an), systems analysis, and signification, this research succeeds in extracting a coherent and innovative model of the ideal political system from the Holy Qur’an.

Introduction: This study evaluated the degree of micro leakage of Ideal Makoo and Tetric Flow composites using two dentin adhesives of Scotch Bond Multipurpose (SBMP) and Excite.Materials &Methods: 60 premolar teeth were divided in to four groups of 15. and class V cavity preparations were done in CEJ. Group 1 was rest orated with SBMP and Ideal Makoo, Group II with SBMP and Tetric Flow, Group III with Excite and Ideal Makoo, and Group IV with Excite and Tetric Flow. Stereomicroscope (X40) was used to evaluate and dye penetration in occlusal and gingival margins. Chi Square test, Pearson’s correlation test and Fishers exact test were used for data analysis (α= 0.05).Results: 1- The degree of leakage was not in correspondence to the type of composite.2- The degree of leakage was not in correspondence to the type of dentin adhesive.3- In four groups, the degree of leakage in gingival wall was significantly more than occlusal wall.Conclusion: Type of composite and dentin adhesive have no effect on degree of leakage. The important factor is the type of wall. It means that in class V restorations, gingival wall is always observed to have more micro leakage than occlusal wall.