Heterochromatic paths in edge colored graphs without small cycles and heterochromatic-triangle-free graphs

Conditions for the existence of heterochromatic Hamiltonian paths and cycles in edge colored graphs are well investigated in literature. A related problem in this domain is to obtain good lower bounds for the length of a maximum heterochromatic path in an edge colored graph G. This problem is also well explored by now and the lower bounds are often specified as functions of the minimum color degree of G - the minimum number of distinct colors occurring at edges incident to any vertex of G - denoted by v(G). Initially, it was conjectured that the lower bound for the length of a maximum heterochromatic path for an edge colored graph G would be 2v(G)/3]. Chen and Li (2005) showed that the length of a maximum heterochromatic path in an edge colored graph G is at least v(G) - 1, if 1 <= v(G) <= 7, and at least 3v(G)/5] + 1 if v(G) >= 8. They conjectured that the tight lower bound would be v(G) - 1 and demonstrated some examples which achieve this bound. An unpublished manuscript from the same authors (Chen, Li) reported to show that if v(G) >= 8, then G contains a heterochromatic path of length at least 120 + 1. In this paper, we give lower bounds for the length of a maximum heterochromatic path in edge colored graphs without small cycles. We show that if G has no four cycles, then it contains a heterochromatic path of length at least v(G) - o(v(G)) and if the girth of G is at least 4 log(2)(v(G)) + 2, then it contains a heterochromatic path of length at least v(G) - 2, which is only one less than the bound conjectured by Chen and Li (2005). Other special cases considered include lower bounds for the length of a maximum heterochromatic path in edge colored bipartite graphs and triangle-free graphs: for triangle-free graphs we obtain a lower bound of 5v(G)/6] and for bipartite graphs we obtain a lower bound of 6v(G)-3/7]. In this paper, it is also shown that if the coloring is such that G has no heterochromatic triangles, then G contains a heterochromatic path of length at least 13v(G)/17)]. This improves the previously known 3v(G)/4] bound obtained by Chen and Li (2011). We also give a relatively shorter and simpler proof showing that any edge colored graph G contains a heterochromatic path of length at least (C) 2015 Elsevier Ltd. All rights reserved.

Controlled material transport and multidimensional patterning at small length scales using electromigration

Electromigration, mostly known for its damaging effects in microelectronic devices, is basically a material transport phenomenon driven by the electric field and kinetically controlled by diffusion. In this work, we show how controlled electromigration can be used to create scientifically interesting and technologically useful micro-/nano-scale patterns, which are otherwise extremely difficult to fabricate using conventional cleanroom practices, and present a few examples of such patterns. In a solid thin-film structure, electromigration is used to generate pores at preset locations for enhancing the sensitivity of a MEMS sensor. In addition to electromigration in solids, the flow instability associated with the electromigration-induced long-range flow of liquid metals is shown to form numerous structures with high surface area to volume ratio. In very thin solid films on non-conductive substrates, solidification of flow-affected region results in the formation of several features, such as nano-/micro-sized discrete metallic beads, 3D structures consisting of nano-stepped stairs, etc.

Factors affecting distribution of fish within a tidally drained mangrove forest in the Andaman and Nicobar Islands, India

Mangrove forests in meso-tidal areas are completely drained during low tides, forming only temporary habitats for fish. We hypothesised that in such temporary habitats, where stranding risks are high, distance from tidal creeks that provided access to inundated areas during receding tides would be the primary determinant of fish distribution. Factors such as depth, root density and shade were hypothesised to have secondary effects. We tested these hypotheses in a tidally drained mangrove patch in the Andaman Islands, India. Using stake nets, we measured fish abundance and species richness relative to distance from creeks, root density/m(2), shade, water depth and size (total length) of fish. We also predicted that larger fish (including potential predators) would be closer to creeks, as they faced a greater chance of mortality if stranded. Thus we conducted tethering trials to examine if predation would be greater close to the creeks. Generalised linear mixed effects models showed that fish abundance was negatively influenced by increasing creek distance interacting with fish size and positively influenced by depth. Quantile regression analysis showed that species richness was limited by increasing creek distance. Proportion of predation was greatest close to the creeks (0-25 m) and declined with increasing distance. Abundance was also low very close to the creeks, suggesting that close to the creeks predation pressure may be an important determinant of fish abundance. The overall pattern however indicates that access to permanently inundated areas, may be an important determinant of fish distribution in tidally drained mangrove forests.

Ultra-small sulphur nanoparticles configured inside a flexible organic mixed conducting network as a cathode for lithium-sulphur batteries

The major challenges in Li-S batteries are the formation of soluble polysulphides during the reversible conversion of S-8 <-> Li2S, large changes in sulphur particle volume during lithiation and extremely poor charge transport in sulphur. We demonstrate here a novel and simple strategy to overcome these challenges towards practical realization of a stable high performance Li-S battery. For the first time, a strategy is developed which does away with the necessity of pre-fabricated high surface area hollow-structured adsorbates and also multiple nontrivial synthesis steps related to sulphur loading inside such adsorbates. A lithiated polyethylene glycol (PEG) based surfactant tethered on ultra-small sulphur nanoparticles and wrapped up with polyaniline (PAni) (abbreviated as S-MIEC) is demonstrated here as an exceptional cathode for Li-S batteries. The PEG and PAni network around the sulphur nanoparticles serves as an efficient flexible trap for sulphur and polysulphides and also provides distinct pathways for electrons (through PAni) and ions (through PEG) during battery operation. Contrary to the cathodes demonstrated based on various carbon-sulphur composites, the mixed conducting S-MIEC showed an extremely high loading of 75%. The S-MIEC exhibited a stable capacity of nearly 900 mA h g(-1) at the end of 100 cycles at a 1C current rate.

pi-Electron rich small molecule sensors for the recognition of nitroaromatics

Selective and discriminative detection of -NO2 containing high energy organic compounds such as picric acid (PA), 2,4,6-trinitrotoluene (TNT) and dinitrotoluene (DNT) has become a challenging task due to concerns over national security, criminal investigations and environment protections. Among various known detection methods, fluorescence techniques have gained special attention in recent time. A wide variety of fluorescent chemosensors have been developed for nitroaromatic explosive detection. In this review article, we provide an overview of the recent developments made in small molecule-based turn-off fluorescent sensors for nitroaromatic explosives with special focus on organic and H-bonded supramolecular sensors. The fluorescent sensors discussed in this review are classified and organized according to their functionality and their recognition of nitroaromatics by fluorescence quenching.

Fracture Testing at Small-Length Scales: From Plasticity in Si to Brittleness in Pt

The field of micro-/nano-mechanics of materials has been driven, on the one hand by the development of ever smaller structures in devices, and, on the other, by the need to map property variations in large systems that are microstructurally graded. Observations of `smaller is stronger' have also brought in questions of accompanying fracture property changes in the materials. In the wake of scattered articles on micro-scale fracture testing of various material classes, this review attempts to provide a holistic picture of the current state of the art. In the process, various reliable micro-scale geometries are shown, challenges with respect to instrumentation to probe ever smaller length scales are discussed and examples from recent literature are put together to exhibit the expanse of unusual fracture response of materials, from ductility in Si to brittleness in Pt. Outstanding issues related to fracture mechanics of small structures are critically examined for plausible solutions.

Small-Signal Stability Analysis of an Open-Loop Induction Motor Drive Including the Effect of Inverter Deadtime

This paper demonstrates light-load instability in a 100-kW open-loop induction motor drive on account of inverter deadtime. An improved small-signal model of an inverter-fed induction motor is proposed. This improved model is derived by linearizing the nonlinear dynamic equations of the motor, which include the inverter deadtime effect. Stability analysis is carried out on the 100-kW415-V three-phase induction motor considering no load. The analysis brings out the region of instability of this motor drive on the voltage versus frequency (V-f) plane. This region of light-load instability is found to expand with increase in inverter deadtime. Subharmonic oscillations of significant amplitude are observed in the steady-state simulated and measured current waveforms, at numerous operating points in the unstable region predicted, confirming the validity of the stability analysis. Furthermore, simulation and experimental results demonstrate that the proposed model is more accurate than an existing small-signal model in predicting the region of instability.

Population Recovery of Nicobar Long-Tailed Macaque Macaca fascicularis umbrosus following a Tsunami in the Nicobar Islands, India

Natural disasters pose a threat to isolated populations of species with restricted distributions, especially those inhabiting islands. The Nicobar long tailed macaque. Macaca fascicularis umbrosus, is one such species found in the three southernmost islands (viz. Great Nicobar, Little Nicobar and Katchal) of the Andaman and Nicobar archipelago, India. These islands were hit by a massive tsunami (Indian Ocean tsunami, 26 December 2004) after a 9.2 magnitude earthquake. Earlier studies Umapathy et al. 2003; Sivakumar, 2004] reported a sharp decline in the population of M. f. umbrosus after thetsunami. We studied the distribution and population status of M. f. umbrosus on thethree Nicobar Islands and compared our results with those of the previous studies. We carried out trail surveys on existing paths and trails on three islands to get encounter rate as measure of abundance. We also checked the degree of inundation due to tsunami by using Normalized Difference Water Index (NDWI) on landsat imageries of the study area before and after tsunami. Theencounter rate of groups per kilometre of M. f. umbrosus in Great Nicobar, Little Nicobar and Katchal was 0.30, 0.35 and 0.48 respectively with the mean group size of 39 in Great Nicobar and 43 in Katchal following the tsunami. This was higher than that reported in the two earlier studies conducted before and after the tsunami. Post tsunami, there was a significant change in the proportion of adult males, adult females and immatures, but mean group size did not differ as compared to pre tsunami. The results show that population has recovered from a drastic decline caused by tsunami, but it cannot be ascertained whether it has reached stability because of the altered group structure. This study demonstrates the effect of natural disasters on island occurring species.

A NOTE ON SMALL GAPS BETWEEN NONZERO FOURIER COEFFICIENTS OF CUSP FORMS

It is shown that there are infinitely many primitive cusp forms f of weight 2 with the property that for all X large enough, every interval (X, X + cX(1/4)), where c > 0 depends only on the form, contains an integer n such that the n-th Fourier coefficient of f is nonzero.

Multiple oligomeric structures of a bacterial small heat shock protein

Small heat shock proteins are ubiquitous molecular chaperones that form the first line of defence against the detrimental effects of cellular stress. Under conditions of stress they undergo drastic conformational rearrangements in order to bind to misfolded substrate proteins and prevent cellular protein aggregation. Owing to the dynamic nature of small heat shock protein oligomers, elucidating the structural basis of chaperone action and oligomerization still remains a challenge. In order to understand the organization of sHSP oligomers, we have determined crystal structures of a small heat shock protein from Salmonella typhimurium in a dimeric form and two higher oligomeric forms: an 18-mer and a 24-mer. Though the core dimer structure is conserved in all the forms, structural heterogeneity arises due to variation in the terminal regions.