A Creative Review on Integer Additive Set-Valued Graphs

For a non-empty ground set $X$, finite or infinite, the {\em set-valuation} or {\em set-labeling} of a given graph $G$ is an injective function $f:V(G) \to \mathcal{P}(X)$, where $\mathcal{P}(X)$ is the power set of the set $X$. A set-indexer of a graph $G$ is an injective set-valued function $f:V(G) \to \mathcal{P}(X)$ such that the function $f^{\ast}:E(G)\to \mathcal{P}(X)-\{\emptyset\}$ defined by $f^{\ast}(uv) = f(u){\ast} f(v)$ for every $uv{\in} E(G)$ is also injective, where $\ast$ is a binary operation on sets. An integer additive set-indexer is defined as an injective function $f:V(G)\to \mathcal{P}({\mathbb{N}_0})$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $\mathbb{N}_0$ is the set of all non-negative integers. In this paper, we critically and creatively review the concepts and properties of integer additive set-valued graphs.Comment: 14 pages, submitted. arXiv admin note: text overlap with arXiv:1312.7672, arXiv:1312.767

Strong Integer Additive Set-valued Graphs: A Creative Review

For a non-empty ground set $X$, finite or infinite, the {\em set-valuation} or {\em set-labeling} of a given graph $G$ is an injective function $f:V(G) \to \mathcal{P}(X)$, where $\mathcal{P}(X)$ is the power set of the set $X$. A set-indexer of a graph $G$ is an injective set-valued function $f:V(G) \to \mathcal{P}(X)$ such that the function $f^{\ast}:E(G)\to \mathcal{P}(X)-\{\emptyset\}$ defined by $f^{\ast}(uv) = f(u){\ast} f(v)$ for every $uv{\in} E(G)$ is also injective., where $\ast$ is a binary operation on sets. An integer additive set-indexer is defined as an injective function $f:V(G)\to \mathcal{P}({\mathbb{N}_0})$ such that the induced function $g_f:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective, where $\mathbb{N}_0$ is the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ is its power set. An IASI $f$ is said to be a strong IASI if $|f^+(uv)|=|f(u)|\,|f(v)|$ for every pair of adjacent vertices $u,v$ in $G$. In this paper, we critically and creatively review the concepts and properties of strong integer additive set-valued graphs.Comment: 13 pages, Published. arXiv admin note: text overlap with arXiv:1407.4677, arXiv:1405.4788, arXiv:1310.626

A Study on Set-Graphs

A \textit{primitive hole} of a graph $G$ is a cycle of length $3$ in $G$. The number of primitive holes in a given graph $G$ is called the primitive hole number of that graph $G$. The primitive degree of a vertex $v$ of a given graph $G$ is the number of primitive holes incident on the vertex $v$. In this paper, we introduce the notion of set-graphs and study the properties and characteristics of set-graphs. We also check the primitive hole number and primitive degree of set-graphs. Interesting introductory results on the nature of order of set-graphs, degree of the vertices corresponding to subsets of equal cardinality, the number of largest complete subgraphs in a set-graph etc. are discussed in this study. A recursive formula to determine the primitive hole number of a set-graph is also derived in this paper.Comment: 11 pages, 1 figure, submitte

Avogadro constant measurements using enriched 28Si monocrystals

Since 2011, the International Avogadro Coordination has been measuring the Avogadro constant by counting the atoms in enriched Si-28 monocrystals. This communication provides guidance on how the recently published results should be used to update the values of the Avogadro constant measured so far

Withaferin a alone and in combination with Cisplatin suppresses growth and metastasis of ovarian cancer by targeting putative cancer stem cells.

Currently, the treatment for ovarian cancer entails cytoreductive surgery followed by chemotherapy, mainly, carboplatin combined with paclitaxel. Although this regimen is initially effective in a high percentage of cases, unfortunately within few months of initial treatment, tumor relapse occurs because of platinum-resistance. This is attributed to chemo-resistance of cancer stem cells (CSCs). Herein we show for the first time that withaferin A (WFA), a bioactive compound isolated from the plant Withania somnifera, when used alone or in combination with cisplatin (CIS) targets putative CSCs. Treatment of nude mice bearing orthotopic ovarian tumors generated by injecting human ovarian epithelial cancer cell line (A2780) with WFA and cisplatin (WFA) alone or in combination resulted in a 70 to 80% reduction in tumor growth and complete inhibition of metastasis to other organs compared to untreated controls. Histochemical and Western blot analysis of the tumors revealed that inclusion of WFA (2 mg/kg) resulted in a highly significant elimination of cells expressing CSC markers - CD44, CD24, CD34, CD117 and Oct4 and downregulation of Notch1, Hes1 and Hey1 genes. In contrast treatment of mice with CIS alone (6 mg/kg) had opposite effect on those cells. Increase in cells expressing CSC markers and Notch1 signaling pathway in tumors exposed to CIS may explain recurrence of cancer in patients treated with carboplatin and paclitaxel. Since, WFA alone or in combination with CIS eliminates putative CSCs, we conclude that WFA in combination with CIS may present more efficacious therapy for ovarian cancer

Tribological characteristics of Pongamia oil methyl ester

The tribological characteristics of biodiesel PME (Pongamia oil methyl ester) is analysed in this work. Three blends B20, B50 and B80 of pongamia methyl ester with diesel were prepared. Tribological studies were performed with these blends using fourball tribotester and reciprocating wear tester to analyse the friction and wear behavior at various operating parameters. It was observed that wear and frictional torque reduced with increase in biodiesel content. The frictional torque was found to decrease with time. Thus, higher blends have a lower coefficient of friction than lower blends. Wear in the steel ball for the B50 blend is 25% less than that for the B20 blend and the wear appears to stabilize for concentrations greater than B50. Reciprocating wear test on cylinder liner-piston ring suggested that PME could offer better lubricity between the sliding surfaces than that of pure diesel. SEM anlaysis of the worn surfaces suggested that the surface lubricated with PME blends were less affected during the wear process when compared to those with pure diesel

Information and The Brukner-Zeilinger Interpretation of Quantum Mechanics: A Critical Investigation

In Brukner and Zeilinger's interpretation of quantum mechanics, information is introduced as the most fundamental notion and the finiteness of information is considered as an essential feature of quantum systems. They also define a new measure of information which is inherently different from the Shannon information and try to show that the latter is not useful in defining the information content in a quantum object. Here, we show that there are serious problems in their approach which make their efforts unsatisfactory. The finiteness of information does not explain how objective results appear in experiments and what an instantaneous change in the so-called information vector (or catalog of knowledge) really means during the measurement. On the other hand, Brukner and Zeilinger's definition of a new measure of information may lose its significance, when the spin measurement of an elementary system is treated realistically. Hence, the sum of the individual measures of information may not be a conserved value in real experiments.Comment: 20 pages, two figures, last version. Section 4 is replaced by a new argument. Other sections are improved. An appendix and new references are adde

A New Approach for Analytic Amplitude Calculations

We present a method for symbolic calculation of Feynman amplitudes for processes involving both massless and massive fermions. With this approach fermion strings in a specific amplitude can be easily evaluated and expressed as basic Lorentz scalars. The new approach renders the symbolic calculation of some complicated physical processes more feasible and easier, especially with the assistance of algebra manipulating codes for computer.Comment: LaTex, no figure, to appear in PR

Quasi-probability representations of quantum theory with applications to quantum information science

This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasi-probability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness.Comment: v3: typos fixed, references adde