Abstract:
Binary Whiteman's cyclotomic sequences of orders 2 and 4 have a number of good randomness properties. In this paper, we compute the autocorrelation values and linear complexity of the first class two-prime Whiteman's generalized cyclotomic sequence (WGCS-I) of order $d=6$. Our results show that the autocorrelation values of this sequence is four-valued or five-valued if $(n_1-1)(n_2-1)/36$ is even or odd respectively, where $n_1$ and $n_2$ are two distinct odd primes and their linear complexity is quite good. We employ the two-prime WGCS-I of order 6 to construct several classes of cyclic codes over $\mathrm{GF}(q)$ with length $n_1n_2$. We also obtain the lower bounds on the minimum distance of these cyclic codes.

Abstract:
In this paper, we investigate cyclic codes over the ring $ \mathbb{F}_p[u,v,w]\langle u^2,$ $v^2, w^2$, $uv-vu, vw-wv, uw-wu \rangle$, where $p$ is a prime number. Which is a part of family of Frobenius rings. We find a unique set of generators for these codes and characterize the free cyclic codes. We also study the rank and the Hamming distance of these codes. We also constructs some good $p-ary$ codes as the Gray images of these cyclic codes.

Abstract:
Let $n_1$ and $n_2$ be two distinct primes with $\mathrm{gcd}(n_1-1,n_2-1)=4$. In this paper, we compute the autocorrelation values of generalized cyclotomic sequence of order $4$. Our results show that this sequence can have very good autocorrelation property. We determine the linear complexity and minimal polynomial of the generalized cyclotomic sequence over $\mathrm{GF}(q)$ where $q=p^m$ and $p$ is an odd prime. Our results show that this sequence possesses large linear complexity. So, the sequence can be used in many domains such as cryptography and coding theory. We employ this sequence of order $4$ to construct several classes of cyclic codes over $\mathrm{GF}(q)$ with length $n_1n_2$. We also obtain the lower bounds on the minimum distance of these cyclic codes.

Abstract:
Let $n_1=ef+1$ and $n_2=ef'+1$ be two distinct odd primes with positive integers $e,\ f,\ f'.$ In this paper, the two-prime Whiteman's generalized cyclotomic sequence of order $e=6$ is employed to construct several classes of cyclic codes over $\mathrm{GF}(q)$ with length $n_1n_2$. The lower bounds on the minimum distance of these cyclic codes are obtained.

Abstract:
Let $p$ be a prime number. In this paper, we discuss the structures of cyclic codes over the ring $ \mathbb{F}_p[u, v] / \langle u^k, v^2, uv-vu\rangle$. We find a unique set of generators for these codes. We also study the rank and the Hamming distance of these codes.

Abstract:
We show that the local exterior square L-functions of GL_n constructed via the theory of integral representations by Jacquet and Shalika coincide with those constructed by the Langlands-Shahidi method for square integrable representations (and for all irreducible representations when n is even). We also deduce several local and global consequences.

Abstract:
In this paper, we study cyclic codes over the ring $ \Z_p + u\Z_p +...+ u^{k-1}\Z_p $, where $u^k =0$. We find a set of generator for these codes. We also study the rank, the dual and the Hamming distance of these codes.

Abstract:
Let $p$ be a prime number. In this paper, we study cyclic codes over the ring $ \Z_p[u, v]/\langle u^2, v^2, uv-vu\rangle$. We find a unique set of generators for these codes. We also study the rank and the Hamming distance of these codes. We obtain all except one ternary optimal code of length 12 as the Gray image of the cyclic codes over the ring $ \Z_p[u, v]/\langle u^2, v^2, uv-vu\rangle$. We also characterize the $p$-ary image of these cyclic codes under the Gray map.

Abstract:
In post-colonial India the female foeticide, a practice evolved from customary female infanticide of
pre-colonial and colonial period, committed though in separate incidents, has made it almost a
unified wave of mass murder. It does not fulfil the widely accepted existing definition of genocide
but the high rate of abortion of legitimate girl-foetus by Indian parents makes their crime a kind of
group killing or genocide. The female foeticide in post-colonial India is not a modern phenomenon
but was also prevalent in pre-colonial India since antiquity as female infanticide and the custom
continued in the 19th century in many communities of colonial India, documentation of which are
widely available in various archives. In spite of the Act of 1870 passed by the Colonial Government
to suppress the practice, treating it a murder and punishing the perpetrators of the crime with
sentence of death or transportation for life, the crime of murdering their girl children did not stop.
During a period of five to ten years after the promulgation of the Act around 333 cases of female
infanticide were tried and 16 mothers were sentenced to death, 133 to transportation for life and
others for various terms of rigorous imprisonment in colonial India excluding British Burma and
Assam where no such crime was reported. The present paper, on the basis of unpublished proceedings
and files of Judicial and Criminal department of nineteenth century and published documents,
presents a critical discussion on consideration of such unified wave of customary criminality
as a sexually selective genocide, its concepts and location of female infanticide in selective
areas dominated by specific patriarchal ethos of Hinduism alone, the religious and economic
causes behind formation of a historically reliant peculiar Indian mind set, its nineteenth century
encounter with legislative measures of astounded colonial state still responsible for continuation
of such criminality in more sophisticated way with the help of modern technology, and historically
reliant patriarchal mind set of post-colonial Indian state.

Abstract:
Glucose-6-phosphate dehydrogenase has been purified from pigeon pea (Cajanus cajan) seeds and subjected to characterization. The enzyme was purified 123.69 fold with a yield of 21.37% by ammonium sulphate fractionation, PEG-4000 precipitation, CM cellulose column chromatography and DEAE cellulose column chromatography. The catalytically active enzyme is a dimer of 113 KDa with a subunit molecular weight of 55 KDa. Thermal inactivation of enzyme follows first order kinetics at 30°C and 40°C with half life of 6 and 1.5 min respectively. Km value for glucose-6-phosphate and NADP+ was found to be 2.68 mM and 0.75 mM respectively whereas Vmax value was found to be 0.11 U/mL and 0.13 U/mL respectively. The enzyme shows more affinity towards NADP+ than glucose-6-phosphate. The pKa value was found to be 10.41 indicating that the amino acid residue at active site might be lysine. The enzyme exhibited maximum catalytic activity at pH 8.2. The enzyme was found to be highly thermosensitive with gradual loss of activity above 30°C temperature.