Total Edge Irregularity Strength for Graphs

An edge irregular total $k$-labelling $f : V(G)\cup E(G)\rightarrow \{1,2,\dots,k\}$ of a graph $G$ is a labelling of the vertices and the edges of $G$ in such a way that any two different edges have distinct weights. The weight of an edge $e$, denoted by $wt(e)$, is defined as the sum of the label of $e$ and the labels of two vertices which incident with $e$, i.e. if $e=vw$, then $wt(e)=f(e)+f(v)+f(w)$. The minimum $k$ for which $G$ has an edge irregular total $k$-labelling is called the total edge irregularity strength of $G.$ In this paper, we determine total edge irregularity of connected and disconnected graphs

The Ideological Questions of Marriage in Thomas Hardy's Jude the Obscure

As one of the prominent ideologies of the nineteenth-century— in a complex interrelation with other contemporary ideological discourses particularly femininity and marriage—religion adopts a critical stance in Hardy's presentation of characters. Breaching the religio-conventional image of femininity as “Angel in the House” and “Cow Woman,” Hardy's Jude the Obscure (1895) is indeed deemed to be his milestone in presenting his anti-Christian attitudes towards the contemporary religion. This study aims to present Hardy's outright hostility towards the nineteenth-century Christianity through his creation of non-conformist characters, necessitating a parallel study with other contemporary discourses regarding marriage and femininity, and conflict with the religion of the time. Hardy's magnum opus, the work on which he was to stake his final reputation as a novelist, was clearly Jude the Obscure which as a noticeable socio-religious experimentation of the late nineteenth-century, reveals Hardy's perception of new ideas about femininity and marriage by presenting the hot contemporary issues of “New Woman” and “Free Union” through the development and presentation of Sue Bridehead and her free union with Jude, respectively. Hardy's presentation of Sue Bridehead as a “New Woman,” and employing the “Free Union” in marked contrast with the nineteenth-century convention of marriage as a “Bonded Pair” is Hardy's closing upshot of his final novelistic attempt. The non-conformist Jude and Sue are presented as figures touching the Victorian Christian standards of morality, while, the final tragic destiny of Jude and Sue's helplessness attest to the writer's substantial contribution as a Victorian male novelist to the ideologies circulating at the time

A Novel User Pairing Scheme for Functional Decode-and-Forward Multi-way Relay Network

In this paper, we consider a functional decode and forward (FDF) multi-way relay network (MWRN) where a common user facilitates each user in the network to obtain messages from all other users. We propose a novel user pairing scheme, which is based on the principle of selecting a common user with the best average channel gain. This allows the user with the best channel conditions to contribute to the overall system performance. Assuming lattice code based transmissions, we derive upper bounds on the average common rate and the average sum rate with the proposed pairing scheme. Considering M-ary quadrature amplitude modulation with square constellation as a special case of lattice code transmission, we derive asymptotic average symbol error rate (SER) of the MWRN. We show that in terms of the achievable rates, the proposed pairing scheme outperforms the existing pairing schemes under a wide range of channel scenarios. The proposed pairing scheme also has lower average SER compared to existing schemes. We show that overall, the MWRN performance with the proposed pairing scheme is more robust, compared to existing pairing schemes, especially under worst case channel conditions when majority of users have poor average channel gains.Comment: 30 pages, 6 figures, submitted for journal publicatio

Approximate Capacity of Gaussian Relay Networks

We present an achievable rate for general Gaussian relay networks. We show that the achievable rate is within a constant number of bits from the information-theoretic cut-set upper bound on the capacity of these networks. This constant depends on the topology of the network, but not the values of the channel gains. Therefore, we uniformly characterize the capacity of Gaussian relay networks within a constant number of bits, for all channel parameters.Comment: This paper is submited to 2008 IEEE International Symposium on Information Theory (ISIT 2008) -In the revised format the approximation gap (\kappa) is sharpene

The Ideological Questions of Marriage in Thomas Hardy’s Jude the Obscure

As one of the prominent ideologies of the nineteenth-century— in a complex interrelation with other contemporary ideological discourses particularly femininity and marriage—religion adopts a critical stance in Hardy’s presentation of characters. Breaching the religio-conventional image of femininity as “Angel in the House” and “Cow Woman,” Hardy’s Jude the Obscure (1895) is indeed deemed to be his milestone in presenting his anti-Christian attitudes towards the contemporary religion. This study aims to present Hardy’s outright hostility towards the nineteenth-century Christianity through his creation of non-conformist characters, necessitating a parallel study with other contemporary discourses regarding marriage and femininity, and conflict with the religion of the time. Hardy’s magnum opus, the work on which he was to stake his final reputation as a novelist, was clearly Jude the Obscure which as a noticeable socio-religious experimentation of the late nineteenth-century, reveals Hardy’s perception of new ideas about femininity and marriage by presenting the hot contemporary issues of “New Woman” and “Free Union” through the development and presentation of Sue Bridehead and her free union with Jude, respectively. Hardy’s presentation of Sue Bridehead as a “New Woman,” and employing the “Free Union” in marked contrast with the nineteenth-century convention of marriage as a “Bonded Pair” is Hardy’s closing upshot of his final novelistic attempt. The non-conformist Jude and Sue are presented as figures touching the Victorian Christian standards of morality, while, the final tragic destiny of Jude and Sue’s helplessness attest to the writer’s substantial contribution as a Victorian male novelist to the ideologies circulating at the time