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

Selective Breeding to Improve Productive and Reproductive Performances and Survivability of Indigenous Sakini Chicken

Indigenous chickens are quite popular in Family Poultry Production System (FPPS) in Nepal, but are constrained with their low productive performance. The present study evaluated the productive and reproductive performance of Sakini chicken in different filial generations and sexes. In addition, research also aimed at understanding the effect of generations on above performances. Initially, base populations (G-0) of Sakini were maintained by collecting eight weeks old birds from different agro-ecologial zones of Nepal. Performance of the birds of G-0 was evaluated based on weekly body weight (12-24 weeks), laying performance, fertility, hatchability, hatch weight and survivability. Selected birds of base population (G-0) were used to produce first (G-1), second (G-2) and third (G-3) generations through selective breeding in each generation. Similarly, body weights at hatching, 12 weeks, 16 weeks, 20 week and 24 weeks were significantly (p<0.001) improved from G0 to G3 and were also significantly (p<0.001) differ for sex (males were always heavier than females). Likewise, there was significant (p<0.05) improvement in egg production (per hen per year), age at first lay (days), body weight at sexual maturity, egg number and egg weight at 90 days of laying in progressive generations. Fertility, hatchability and survivability significantly (p<0.05) improved in selected generations in comparison to base population, whereas, no significant difference was obtained within the different selected population. Thus, indigenous Sakini chicken under this experiment performed better with respect to survivability, fertility and hatchability in later generations that provides ample scope of advancing selective breeding activities within the indigenous population in order to bring significant improvement in the overall productive performance of Sakini chicken in Nepal

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

Comment on: "Quantum dynamics of a general time-dependent coupled oscillator"

By using dynamical invariants theory, Hassoul et al. [1,2] investigate the quantum dynamics of two (2D) and three (3D) dimensional time-dependent coupled oscillators. They claim that, in the 2D case, introducing two pairs of annihilation and creation operators uncouples the original invariant operator so that it becomes the one that describes two independent subsystems. For the 3D case, the authors pretend that they have obtained a diagonalized invariant which is exactly the sum of three simple harmonic oscillators. We show that their investigations suffer from basic errors and therefore the found results are not valid .Comment: 11 page

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

Proximate composition and fatty acids profiles of Artemia cysts and nauplii from different geographical regions of Iran

Artemia has been widely used in aquaculture as a suitable live food. The presence of highly unsaturated fatty acids is a key factor that determines the nutritional value and marketing of Artemia for shrimp, marine larvae, sturgeon and ornamental fish industries. To determine the variation in nutritional content in cysts, decapsulated cysts and nauplii of Artemia from three different biotopes of Iran, were tested for their protein, lipid, energy, and fatty acid profiles, particularly essential fatty acids. The cysts collected from Urmia, Maharlou and Meighan lakes, were rinsed, processed, decapsulated, hatched and then analyzed for proximate and fatty acid composition using standard methods. Statistical comparisons of the results revealed significant differences not only in proximate composition but also in fatty acid contents (p<0.05). The highest mean (±SD) level of protein (60.5±3.3%), lipid (18.60±1.1%) and energy contents (5448.3±10.4 Kcal/kg) were observed in Instar I nauplii hatched from Urmia Lake cysts, Instar I nauplii hatched from Maharlou Lake cyst and Instar I nauplii hatched from Urmia Lake decapsulated cyst, respectively. The highest content of DHA (0.78 mg/g DW) was observed in nauplii of cysts from Urmia Lake whereas it was around zero in other samples. The highest level of EPA (24.24 mg/g DW) was measured in nauplii from Maharlou Lake decapsulated cysts and the lowest (0.24 mg/g DW) was observed in Urmia lake cysts. The results revealed that the nauplii from decapsulated cysts of Maharlou Lake Artemia contained significantly higher levels of EPA and n-3 HUFA compared to others. Therefore, it is recommended to use it in aquatic larviculture

In vitro search for synergy between flavonoids and epirubicin on multidrug-resistant cancer cells

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Exact Finite-Size-Scaling Corrections to the Critical Two-Dimensional Ising Model on a Torus

We analyze the finite-size corrections to the energy and specific heat of the critical two-dimensional spin-1/2 Ising model on a torus. We extend the analysis of Ferdinand and Fisher to compute the correction of order L^{-3} to the energy and the corrections of order L^{-2} and L^{-3} to the specific heat. We also obtain general results on the form of the finite-size corrections to these quantities: only integer powers of L^{-1} occur, unmodified by logarithms (except of course for the leading $\log L$ term in the specific heat); and the energy expansion contains only odd powers of L^{-1}. In the specific-heat expansion any power of L^{-1} can appear, but the coefficients of the odd powers are proportional to the corresponding coefficients of the energy expansion.Comment: 26 pages (LaTeX). Self-unpacking file containing the tex file and three macros (indent.sty, eqsection.sty, subeqnarray.sty). Added discussions on the results and new references. Version to be published in J. Phys.

Tecnologie Digitali e DSA

Il termine “strumento compensativo”, concetto essenziale nel percorso educativo degli studenti con DSA, è spesso fonte di dubbio per genitori, insegnanti e ragazzi: quali sono gli strumenti compensativi digitali presenti sul mercato? Uno strumento vale l’altro? Come si fa a scegliere quello giusto? Per contribuire a rispondere a queste domande è stata redatta una “rassegna ragionata” di 233 tecnologie digitali, raccogliendo informazioni sugli strumenti utilizzati da docenti, esperti, genitori e studenti con DSA. La rassegna offre un aiuto per orientarsi tra le varie opportunità e attuare una scelta consapevole delle tecnologie compensative a supporto dell’apprendimento e dello studio autonomo