On Reduction of Some Differential Equations using Symmetry Methods

In this paper Lie group theory is used to reduce the order of ordinary differential equations. For an ordinary differential equation admitting one parameter Lie group symmetry, order of differential equation, in principle, can always be reduce by one. Ordinary differential equation admitting mutli parameter Solvable Lie symmetry,  the order can be reduced by cardinality of admitted symmetry group.Seperation of variables by canonical coordinates of admitted is also given. Keywords: Lie group, infinitesimal transformations, vector algebra, admitted symmetr

A Class of Constacyclic Codes Containing Formally Self-dual and Isodual Codes

In this paper, we investigate a class of constacyclic codes which contains isodual codes and formally self-dual codes. Further, we introduce a recursive approach to obtain the explicit factorization of $x^{2^m\ell^n}-\mu_k\in\mathbb{F}_q[x]$, where $n, m$ are positive integers and $\mu_k$ is an element of order $\ell^k$ in $\mathbb{F}_q$. Moreover, we give many examples of interesting isodual and formally self-dual constacyclic codes

A Study of the Social and Political Implication of Friedrich Schlegel’s ‘Comedy of Freude’

Generally speaking, scholarship in the field of Germanistik has taken an interest in Friedrich Schlegel’s early publication, “Vom aesthetischen Werte der griechischen Komoedie” (1794), either because of its perceived influence on German Romantic Comedy [(Catholy 1982), (Kluge 1980), (Holl 1923), (Japp 1999)], or else because of its relevance as an example of Schlegel\u27s still inchoate aesthetic philosophy [(Dierkes 1980), (Behrens 1984), (Schanze 1966), (Michel 1982), (Dannenberg 1993), (Mennemeier 1971)]. As a theory of comedy in its own right, Schlegel’s essay has garnered little attention, in part because of its supposed inapplicability to comedic praxis and at times utopian implications, in part because of its seemingly contradictory argument, and lastly in part because Schlegel himself abandoned the essay’s central premise soon after its publication. However, it is the central argument of the present study that Schlegel’s essay can be shown to be interesting and relevant precisely for the theory of comedy it contains. Through a close reading of Schlegel’s essay on Old Greek Comedy, as well as an examination of Schlegel’s early political and aesthetic beliefs, which will help render Schlegel’s theory more intelligible, it will be shown that Schlegel’s theory of comedy is novel in so far as it is one of the first aesthetic theories to claim that comedic practice is necessarily deprived of aesthetic validity unless it exists in a social atmosphere of freedom of expression, namely, such as that of the Athenians. The implication is that Schlegel here predicates an aesthetic theory upon one of society. Schlegel’s theory is also interesting for the peculiar type of comedy it advocates, namely a joyous comedy (Comedy of ‘Freude’), which stands in direct opposition to the ‘Satirische Verlachskomoedie’ of the Enlightenment and makes use of a comedic mechanism (joy) that is anathema to traditional negative comedic elements (satire, derision, mockery etc.). The conclusion discusses what the relevance and value of these implications might be for future research

Resilience, Reliability, and Recoverability (3Rs)

Recent natural and human-made disasters, mortgage derivatives crises, and the need for stable systems in different areas have renewed interest in the concept of resilience, especially as it relates to complex industrial systems with mechanical failures. This concept in the engineering systems (infrastructure) domain could be interpreted as the probability that system conditions exceed an irrevocable tipping point. But the probability in this subject covers the different areas that different approaches and indicators can evaluate. In this context, reliability engineering is used the reliability (uptime) and recoverability (downtime) indicators (or performance indicators) as the most useful probabilistic tools for performance measurement. Therefore, our research penalty area is the resilience concept in combination with reliability and recoverability. It must be said that the resilience evaluators must be considering a diversity of knowledge sources. In this thesis, the literature review points to several important implications for understanding and applying resilience in the engineering area and The Arctic condition. Indeed, we try to understand the application and interaction of different performance-based resilience concepts. In this way, a collection of the most popular performance-based resilience analysis methods with an engineering perspective is added as a state-of-the-art review. The performance indicators studies reveal that operational conditions significantly affect the components, industry activities, and infrastructures performance in various ways. These influential factors (or heterogeneity) can broadly be studied into two groups: observable and unobservable risk factors in probability analysis of system performance. The covariate-based models (regression), such as proportional hazard models (PHM), and their extent are the most popular methods for quantifying observable and unobservable risk factors. The report is organized as follows: After a brief introduction of resilience, chapters 2,3 priorly provide a comprehensive statistical overview of the reliability and recoverability domain research by using large scientific databases such as Scopus and Web of Science. As the first subsection, a detailed review of publications in the reliability and recoverability assessment of the engineering systems in recent years (since 2015) is provided. The second subsection of these chapters focuses on research done in the Arctic region. The last subsection presents covariate-based reliability and recoverability models. Finally, in chapter 4, the first part presents the concept and definitions of resilience. The literature reviews four main perspectives: resilience in engineering systems, resilience in the Arctic area, the integration of “Resilience, Reliability, and Recoverability (3Rs)”, and performance-based resilience models

An Improved Aluminium Conductor

The engineering requirements of a conductor material are that it should be (i) plentiful and not too expensive, (ii) an adequate conductor of electrical (iii) mechani-cally strong to withstand stresses an strains, (iv) duct-ile and strong enough to be satisfactorily with a copper conductor cable in performance, reliability, durability and cost. Aluminium meets most of these requirements and is extensively available in India