38 research outputs found
Nonsolvable Subalgebras of gl(4,R)
No full textAll the simple and then semisimple subalgebras of gl(4,R) are found. Each such semisimple subalgebra acts by commutator on gl(4,R). In each case the invariant subspaces are found and the results are used to determine all possible subalgebras of gl(4,R) that are not solvable
Minimal matrix representations of four-dimensional Lie algebras
No full textIt is known how to find minimal dimension matrix representations for fourdimensional complex Lie algebras. The method depends on constructing left symmetric structures. In this note it is explained how to obtain the representations directly and also how to extend the results to real Lie algebras. Two different bases for the four-dimensional Lie algebras are related to each other
Minimal Matrix Representations for Six-Dimensional Nilpotent Lie Algebras
No full textThis paper is concerned with finding minimal dimension linear representations for six-dimensional real, indecomposable nilpotent Lie algebras. It is known that all such Lie algebras can be represented in gl(6, R). After discussing the classification of the 24 such Lie algebras, it is shown that only one algebra can be represented in gl(4, R). A Theorem is then presented that shows that 13 of the algebras can be represented in gl(5, R). The special case of filiform Lie algebras is considered, of which there are five, and it is shown that each of them can be represented in gl(6, R) and not gl(5, R). Of the remaining five algebras, four of them can be represented minimally in gl(5, R). That leaves one difficult case that is treated in detail in an Appendix
Minimal matrix representations of five-dimensional Lie algebras
No full textWe obtain minimal dimension matrix representations for each indecomposable five- dimensional Lie algebra over ℝ and justify in each case that they are minimal. In each case a matrix Lie group is given whose matrix Lie algebra provides the required representation.peerReviewe
Normative and practical recommendations toward improved judicial independence in contemporary Iraq: The question of embedding judicial independence
No full textThis study stands on the fact that the judicial independence is a fundamental element to achieve the rule of law. When it comes to building the rule of law in war-torn nations such as Iraq, several steps has to be taken in order to achieve this end. In this regard, the civil peace is a key, however; the researcher believes that Iraq needs to reform the judiciary concurrently with defeating terrorism and building civil peace. This study stems from an axiom that a weak and corrupted judiciary will hamper the other steps of establishing a modern and democratic regime. In addition, rule of law will not work properly with a weak judiciary. Therefore, the author doesn’t claim that building a strong and independent judiciary in Iraq would resolve all problems! Instead, the author presents this study claiming that judicial independence is a key part of the reform, which depends on the security and political stabilization.
The researcher is aware that Iraq has not yet achieved the stage to be considered as a post conflict society; however, when Iraq defeat terrorism in the future this argument apply.
This thesis acquires primary research data about current challenges, and potential solutions towards embedding judicial independence as part of democratisation, and increasing protection of human rights. Various research methods have been used including theoretical, doctrinal and empirical analysis. The research provides an examination of formal legal structures, the recent development of the judicial system, including the role of the Iraqi Federal Supreme Court and judicial oversight mechanisms. Proposals to reform relevant laws are made.
The investigation develops a useful working definition of judicial independence and sets out practical principles in order to assess judicial independence in Iraq. These principles could be used to test other systems when considering judicial independence.
It is argued that Iraq has insufficient institutions and processes to build and uphold the rule of law, to safeguard human rights, and to prevent recurring violence. Weakness of judiciary has created a poor reputation in respect of its capacity to investigate and prosecute human rights violations. Current operational deficiencies can be traced to decades of conflict, the country’s geographical and religious background, and a culture reluctant to accept judicial independence. Further, it is concluded that the weakness of the Iraqi judiciary is a function of the lack of a culture of independence alongside political and religious pressures upon
iii
judges. Recommendations which follow include; reforms to judicial appointments, training, ethics, discipline, security, tenure and removal from office; reforms to judicial leadership and the broader oversight of the judiciary; increased transparency in judicial processes, and increased engagement and communication with citizens; abolishing quasi-judicial bodies compromised by political interference; tackling corruption in society; defining spheres of civil and Islamic law at legislative level alongside a conclusion that embedded Islamic laws need not necessarily reduce judicial independence
<b>Some Biological Aspects of</b> (Scolopsis Ghanam <b>(Forskal) Perciformes: Scolopsidae) in Zanzibar Channel</b>
No full textOn computing joint invariants of vector fields
No full textA constructive version of the Frobenius integrability theorem-that can be programmed effectively-is given. This is used in computing invariants of groups of low ranks and recover examples from a recent paper of Boyko etal. (2009).Scopu
Caves and Karsts of Northeast Africa.
No full textAt least potentially karstifiable rocks cover much of the surface of Egypt and northern Libya. Study of caves and other karstic features of this region has been hampered by lack of roads, rapid disintegration of the surface of friable, poorly consolidated limestone, wind-blown sand and other factors. Interbedding with marly aquicludes hampers speleogenesis locally. Calcareous and evaporite karsts are present, however, and their waters are important albeit generally limited resources. Large quantities of fresh water are lost through submarine springs downslope from Libya’s Gebel al Akhdar range; the caves and karst of that range may be among the world’s greatest. A recent attempted compendium of caves and karsts of Egypt and Libya contains several important errors; the supposed 5+ km Ain Zayanah Cave does not exist and the Zayanah System includes several smaller caves. The Bir al Ghanam gypsum karst of northwest Libya, however, has caves up to 3.5 km long. In Egypt, the Mokattam, South Galala, Ma’aza, Siwa and Western Desert karsts and the “White Desert” chalk karst of Farafra Depression are especially important. Qattara and nearby depressions may be karstic rather than structural in origin. Unique Wadi Sannur Cave is the world’s largest gour and a potential World Heritage site. Little knownsandstone karsts or pseudokarsts in southwestern Egypt may contain analogues of features recently identified on Mars. The well-publicised Uweinat caves of northwestern Sudan are talus caves
Embedding algorithms and applications to differential equations
No full textAlgorithms for embedding certain types of nilpotent subalgebras in maximal subalgebras of the same type are developed, using methods of real algebraic groups. These algorithms are applied to determine non-conjugate subalgebras of the symmetry algebra of the wave equation, which in turn are used to determine a large class of invariant solutions of the wave equation. The algorithms are also illustrated for the symmetry algebra of a classical system of differential equations considered by Cartan in the context of contact geometry. - 2017 Elsevier LtdScopu
