Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

In this paper, we have computed the dimensions of the vector space of relative symmetric polynomials with respect to all irreducible characters of the projective special linear group P SL2(F7). © 2021, International Journal on Emerging Technolgies. All rights reserved.

World University root node

Mathematics

School of Advanced Sciences

Chennai Campus

Physics

Advances in Mathematics: Scientific Journal

Formula for the dimensions of the relative invariants of projective special linear group p sl2(F7)

In this paper, we have computed the dimensions of the relative symmetric polynomials associated with all the irreducible characters of Pre Mathieu groups M9, M10 and Small Mathieu groups M11, M12. © 2020, Research Publication. All rights reserved.

Dimesional formulÆ for the relative invariants of pre-mathieu and mathieu groups

For positive integers d and n, the vector space Hd(x1, x2, … , xn) of homogeneous polynomials of degree d is a representation of the symmetric group Sn acting by permutation of variables. Regarding this as a representation for the dihedral subgroup Dn, we prove a formula for the dimension of all the isotypical subrepresentations. Our formula is simpler than the existing one found by Zamani and Babaei (Bull. Iranian Math. Soc.40(4) (2014) 863–874). By varying the degrees d we compute the generating functions for these dimensions. Further, our formula leads us naturally to a specific supercharacter theory of Dn. It turns out to be a ∗ -product of a specific supercharacter theory studied in depth by Fowler et al. (The Ramanujan Journal (2014)), with the unique supercharacter theory of a group of order 2. © 2020, Indian Academy of Sciences.

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Dimension formula for the space of relative symmetric polynomials of Dn with respect to any irreducible representation

Permutation representations arise from the action of groups on sets. Every conjugacy class C of a finite group G has a transitive action on G:g.x=gxg-1 for xɛC and gɛG. In this paper we consider the group S6, group of all permutations on 6 symbols and completely describe the inter relationship among permutation representations arising from all its conjugacy classes. We have achieved a complete specification of these permutation representations: how they are mutually disposed to each other. For this purpose, we define subordination relationship between two conjugacy classes.Given two conjugacy classes C1 and C2, we say that C1 is subordinate to C2 if the permutation representation corresponding to C1 is a subrepresentation included in that of C2. As in whole of Mathematics relationship that are expressed in the form of functions will have special significance when these functions turn out to be injective. Our subordinate relationship naturally captures these significant cases. This relation is reflexive and transitive. Though not antisymmetric it has many desirable properties. The Hasse diagram has a very nice visual symmetry. In this paper we determine which conjugacy classes are subordinate to which for the case of the group G=S6. Our method involves averaging process as used in Reynold’s operator. Another important feature employed in our methodology is using duality which converts the problem of constructing an injective homomorphism to constructing a surjective homomorphism in the opposite direction. © BEIESP.

International Journal of Recent Technology and Engineering

Inclusion relation among permutation representations of S6

Here, we discuss the influence of higher-order nonlinear effects like third-order dispersion, intra-pulse Raman scattering, and self-steepening effects on 1-ps soliton pulse shift or displacement from its initial position. The temporal shifts of soliton due to these higher-order nonlinear effects were studied numerically by “Method of Moments” to realize the contribution of these HOE on shifts. Further, we note the influence of positive and negative TOD on the shift produced by the combined HOE. The soliton shift is then analyzed in 160-Gbps telecommunication system implemented with conventional single-mode fiber (C-SMF) for the length 10 and 20 km. The disturbances between the adjacent soliton pulses in noted with different 16-bit data sequences, and the deterioration of system is characterized in terms of quality factor. It could be seen for an unchirped soliton of pulsewidth To∼ 1 ps , the shift is highly influenced due to intra-pulse Raman scattering, while the shifting due to third-order dispersion can be treated negligibly small. Moreover, negative TOD was expected to inhibit the soliton temporal shift such that it would reduce collision with adjacent pulses; it results in more resonant radiation resulting in pulse decaying. Although negative TOD helps in good reception of pulses for 10 km, it fails to perform in system with 20 km C-SMF, where the dispersive components break more and more while traveling along the length of fiber. © 2015, Springer Science+Business Media New York.

Electronics

School of Electronics Engineering

Photonic Network Communications

Combined influence of third-order dispersion, intra-pulse Raman scattering, and self-steepening effect on soliton temporal shifts in telecommunications

Rare cases of 9 complete androgen insensitivity syndromes, 9 cases of partial androgen insensitivity syndromes and equal number of male control samples were selected for this study. Few strong variations in clinical features were noticed; Giemsa banded metaphase revealed a 46,XY karyotype and the frequency of chromosome aberrations were significantly higher when compared with control samples. DNA sequence analysis of the androgen receptor gene of androgen insensitivity syndromes revealed three missense mutations - c.C1713. >. G resulting in the replacement of a highly conserved histidine residue with glutamine p.(His571Glu) in DNA-binding domain, c.A1715. >. G resulting in the replacement of a highly conserved tyrosine residue with cysteine p.(Tyr572Cys) in DNA-binding domain and c.G2599. >. A resulting in the replacement of a highly conserved valine residue with methionine p.(Val867Met) in ligand-binding domain of androgen receptor gene respectively. The heterozygous type of mutations c.C1713. >. G and c.G2599. >. A observed in mothers of the patients for familial cases concluding that the mutation was inherited from the mother. The novel mutation c.C1713. >. G is reported first time in androgen insensitivity syndrome. In-silico analysis of mutations observed in androgen receptor gene of androgen insensitivity syndrome predicted that the substitution at Y572C and V867M could probably disrupt the protein structure and function. © 2015 Elsevier B.V..

Department of Bio-Medical Sciences

School of Bio Sciences and Technology

Vellore Campus

Department of Biotechnology

Department of Structural and Geotechical Engineering

School of Civil Engineering

Clinica Chimica Acta

Clinical, cytogenetic and molecular analysis of androgen insensitivity syndromes from south Indian cohort and detection and in-silico characterization of androgen receptor gene mutations