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Abstract: The Gauß Sum and its Applications to Number Theory
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Abstract: The purpose of this article is to determine the monogenity of families of certain biquadratic fields K and cyclic bicubic fields L obtained by composition of the quadratic field of conductor 5 and the simplest cubic fields over the field Q of rational numbers applying cubic Gauß sums. The monogenic biquartic fields K are constructed without using the integral bases. It is found that all the bicubic fields L over the simplest cubic fields are non-monogenic except for the conductors 7 and 9. Each of the proof is obtained by the evaluation of the partial differents x-xr of the different ¶F/Q (x) with F=K or L of a candidate number x, which will or would generate a power integral basis of the fields F. Here r denotes a suitable Galois action of the abelian extensions F/Q and ¶F/Q (x) is defined by ÕreG\{i} (x-x)r, where G and i denote respectively the Galois group of F/Q and the identity embedding of F. Keywords: Monogenity, Biquadratic field, Simplest cubic field, Cyclic sextic field, Discriminant, Integral basis. Download Full Article |
Abstract: Review of Pharmacological Activities of Vetiveria zizanoide (Linn) Nash
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Abstract: Vetiveria zizanioides (Linn) Nash is a perennial magical grass of family poaceae commonly known as Khas which is highly valued grass due to its adventitious root system. It is widely distributed in the Pakistan. It is cultivated in all provinces of Pakistan due to its great economic importance. This grass grows plain ascending up to 1200m. Mostly roots stem and leaves were used for treatment of different diseases by ancestors. Adventitious roots contain essential oil which used for multipurpose such as perfumery and in pharmacological industry. Vetiver oil contains approximately 150 compounds, including sesquiterpenoide, hydrocarbons. Phytochemical analysis of leaves shows the presence of flavonoides, saponins, tannins and phenols. Various tribes of India used this tuft grass for commercial purposes. Khas serve as broom, for cooling, roof of huts and as medicine for different diseases such as sunstroke, ulcer, fever, epilepsy and in skin diseases. In this study we summaries the magical pharmacological activities of Vetiveria zizanioides such as anti inflammatory, antibacterial, antifungal, and anti malarial, anti tubercular, anti hyperglycemic, anti hepatoprotective and antioxidant activity. Keywords: Pharmacological activities, Khas, perfume, traditional medicine, biodiversity. Download Full Article |
Abstract: Edge Version of Harmonic Index and Harmonic Polynomial of Rooted Product Graphs
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Abstract: In this paper we computed explicit formulas for the edge version of harmonic index and harmonic polynomial of some classes of rooted product of graphs and i-th vertex rooted product of graphs. Keywords: Topological indices, line graph, harmonic index and harmonic Polynomial. Download Full Article |
Abstract: Investigation of Ethnic Diversity In Pakistan: A Case Study of Karachi
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Abstract: In developing countries increasing population and lack of good governance are the major issues and Pakistan is no exception. These issues are highlighted most in the context of urban centers. Karachi is the most populous city of Pakistan and currently ranked 6th among the mega cities of the world. After partition this city has grown up rapidly due to influx of both national and international immigrants. Urdu speaking persons are the largest ethnic group in Karachi and Pashtuns are second largest group who came to Karachi. It can’t be wrong to say that there are even more Pashtuns in Karachi than in Peshawar itself. Almost 50% of the total population is Urdu speaking whereas 25% of total population is Pashtun in Karachi, whereas, 14% are from Punjab and remaining 9% speaking other languages are settled here. Similarly there are areas in the city marked for Christians, Hindus, Parsis etc. Census Data for the years 1951, 1961, 1972, 1981 and 1998 are taken to analyze the variability of Religion, Population and Language (language data is not available for 1972 census). Spatial development of Slums / Katchi-Abadi 1988 and projection for 2000 has also been discussed. The change in population for the years 1981 and 1988 has been mapped using GIS. MP & ECD Analysis Zones have been used and according to the findings during the years 1986-2000 population increase percent is higher in Surjani Town and Taisar Town. It is also concluded that 96% population living in the city are Muslims and speak more than 9 different languages. Keywords: Karachi, Population, GIS, Language, Religion. Download Full Article |



