Small strong epsilon nets

Let P be a set of n points in R-d. A point x is said to be a centerpoint of P if x is contained in every convex object that contains more than dn/d+1 points of P. We call a point x a strong centerpoint for a family of objects C if x is an element of P is contained in every object C is an element of C that contains more than a constant fraction of points of P. A strong centerpoint does not exist even for halfspaces in R-2. We prove that a strong centerpoint exists for axis-parallel boxes in Rd and give exact bounds. We then extend this to small strong epsilon-nets in the plane. Let epsilon(S)(i) represent the smallest real number in 0, 1] such that there exists an epsilon(S)(i)-net of size i with respect to S. We prove upper and lower bounds for epsilon(S)(i) where S is the family of axis-parallel rectangles, halfspaces and disks. (C) 2014 Elsevier B.V. All rights reserved.

Digestive ripening and green synthesis of ultra-small (r < 2 nm) stable ZnO quantum dots

Given the recent reports pertaining to novel optical properties of ultra-small quantum dots (QDs) (r <2 nm), this nanomaterial is of relevance to both technology and science. However it is well known that in these size regimes most chalocogenide QD dispersions are unstable. Since applications often require use of QD dispersions (e.g. for deployment on a substrate), stabilizing these ultra-small particles is of practical relevance. In this work we demonstrate a facile, green, solution approach for synthesis of stable, ultra-small ZnO QDs having radius less than 2 nm. The particle size is calculated using Brits' equation and confirmed by transmission electron micrographs. ZnO QDs reported remain stable for > 120 days in ethanol (at similar to 298-303 K). We report digestive ripening (DR) in TEA capped ZnO QDs; this occurs rapidly over a short duration of 5 min. To explain this observation we propose a suitable mechanism based on the Lee's theory, which correlates the tendency of DR with the observed zeta potentials of the dispersed medium. To the best of our knowledge this is the (i) first report on DR in oxide QDs, as well as the first direct experimental verification of Lee's theory, and (ii) most rapid DR reported so far. The facile nature of the method presented here makes ultra-small ZnO readily accessible for fundamental exploration and technologically relevant applications. (C) 2014 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

MolBridge: a program for identifying nonbonded interactions in small molecules and biomolecular structures

Identification and analysis of nonbonded interactions within a molecule and with the surrounding molecules are an essential part of structural studies, given the importance of these interactions in defining the structure and function of any supramolecular entity. MolBridge is an easy to use algorithm based purely on geometric criteria that can identify all possible nonbonded interactions, such as hydrogen bond, halogen bond, cation-pi, pi-pi and van der Waals, in small molecules as well as biomolecules. The user can either upload three-dimensional coordinate files or enter the molecular ID corresponding to the relevant database. The program is available in a standalone form and as an interactive web server with Jmol and JME incorporated into it. The program is freely downloadable and the web server version is also available at http://nucleix.mbu.iisc.ernet.in/molbridge/index.php.

Structural and magnetic properties of ultra-small scale eutectic CoFeZr alloys

Aiming to develop high mechanical strength and toughness by tuning ultrafine lamellar spacing of magnetic eutectic alloys, we report the mechanical and magnetic properties of the binary eutectic alloys Co90.5Zr9.5 and Fe90.2Zr9.8, as well as the pseudo-binary eutectic alloys Co82.4Fe8Zr9.6, Co78Fe12.4Zr9.6 and Co49.2Fe49.2Zr9.6 developed by suction-casting. The lower lamellar spacing around 100 nm of the eutectics Co49.2Fe49.2Zr9.6 yields a high hardness of 713(+/- 20) VHN. Magnetic measurements reveal high magnetic moment of 1.92 mu B (at 5 K) and 1.82 mu B (at 300 K) per formula unit for this composition. The magnetization vs. applied field data at 5 K show a directional preference to some extent and therefore smaller non-collinear magnetization behavior compared to Co11Zr2 reported in the literature due to exchange frustration and transverse spin freezing owing to the presence of smaller Zr content. The decay of magnetization as a function of temperature along the easy axis of magnetization of all the eutectic compositions can be described fairly well by the spin wave excitation equation Delta M/M(0) = BT3/2 + CT5/2. (C) 2014 Elsevier B.V. All rights reserved.

Evaluating shock absorption behavior of small-sized systems under programmable electric field

A simple ball-drop impact tester is developed for studying the dynamic response of hierarchical, complex, small-sized systems and materials. The developed algorithm and set-up have provisions for applying programmable potential difference along the height of a test specimen during an impact loading; this enables us to conduct experiments on various materials and smart structures whose mechanical behavior is sensitive to electric field. The software-hardware system allows not only acquisition of dynamic force-time data at very fast sampling rate (up to 2 x 10(6) samples/s), but also application of a pre-set potential difference (up to +/- 10 V) across a test specimen for a duration determined by feedback from the force-time data. We illustrate the functioning of the set-up by studying the effect of electric field on the energy absorption capability of carbon nanotube foams of 5 x 5 x 1.2 mm(3) size under impact conditions. (C) 2014 AIP Publishing LLC.

Small-Signal Stability Analysis of an Open-loop Induction Motor Drive Including the Effect of Inverter Dead-Time

This paper demonstrates light-load instability in open-loop induction motor drives on account of inverter dead-time. The dynamic equations of an inverter fed induction motor, incorporating the effect of dead-time, are considered. A procedure to derive the small-signal model of the motor, including the effect of inverter dead-time, is presented. Further, stability analysis is carried out on a 100-kW, 415V, 3-phase induction motor considering no-load. For voltage to frequency (i.e. V/f) ratios between 0.5 and 1 pu, the analysis brings out regions of instability on the V-f plane, in the frequency range between 5Hz and 20Hz. Simulation and experimental results show sub-harmonic oscillations in the motor current in this region, confirming instability as predicted by the analysis.

Performance Assessment of a Small Biogas-fuelled Power Generator Prototype

This study reports the development and performance evaluation of prototypes of biogas-fuelled stationary power generators in the range of 1 kW. Strategies to achieve high engine efficiency namely pulsed manifold injection, electronic throttle control and dual spark plugs, have been incorporated in the prototype. A complete closed-loop control of the engine operation to maintain a steady engine speed of 3000 rpm (+/- 5%) across the entire load range while maintaining an optimum fuel-air equivalence ratio is made possible by an electronic control unit (ECU) controlling the injection duration, ignition timing and throttle position. This study specifically focuses on the response of the generator to transient loads, and the overall efficiency obtained. The results obtained from testing the prototype have been found to be satisfactory and show that biogas power generators for low power applications can be made efficient (overall efficiency of 19% at electrical load of 640 W) using the strategies of biogas fuel injection.

Solution processable diketopyrrolopyrrole (DPP) cored small molecules with BODIPY end groups as novel donors for organic solar cells

Two novel triads based on a diketopyrrolopyrrole (DPP) central core and two 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY) units attached by thiophene rings have been synthesised having high molar extinction coefficients. These triads were characterised and used as donor materials in small molecule, solution processable organic solar cells. Both triads were blended with PC71BM as an acceptor in different ratios by wt% and their photovoltaic properties were studied. For both the triads a modest photovoltaic performance was observed, having an efficiency of 0.65%. Moreover, in order to understand the ground and excited state properties and vertical absorption profile of DPP and BODIPY units within the triads, theoretical DFT and TDDFT calculations were performed.

Small signal Nonquasi-Static Model for Common Double-Gate MOSFETs Adapted to Gate Oxide Thickness Asymmetry

We present a physics-based closed form small signal Nonquasi-static (NQS) model for a long channel Common Double Gate MOSFET (CDG) by taking into account the asymmetry that may prevail between the gate oxide thickness. We use the unique quasi-linear relationship between the surface potentials along the channel to solve the governing continuity equation (CE) in order to develop the analytical expressions for the Y parameters. The Bessel function based solution of the CE is simplified in form of polynomials so that it could be easily implemented in any circuit simulator. The model shows good agreement with the TCAD simulation at-least till 4 times of the cut-off frequency for different device geometries and bias conditions.

Equilibrium and equivariant triangulations of some small covers with minimum number of vertices

Small covers were introduced by Davis and Januszkiewicz in 1991. We introduce the notion of equilibrium triangulations for small covers. We study equilibrium and vertex minimal 4-equivariant triangulations of 2-dimensional small covers. We discuss vertex minimal equilibrium triangulations of RP3#RP3, S-1 x RP2 and a nontrivial S-1 bundle over RP2. We construct some nice equilibrium triangulations of the real projective space RPn with 2(n) + n 1 vertices. The main tool is the theory of small covers.

Targeting Mycobacterium tuberculosis Topoisomerase I by Small-Molecule Inhibitors

We describe inhibition of Mycobacterium tuberculosis topoisomerase I (MttopoI), an essential mycobacterial enzyme, by two related compounds, imipramine and norclomipramine, of which imipramine is clinically used as an antidepressant. These molecules showed growth inhibition of both Mycobacterium smegmatis and Mycobacterium tuberculosis cells. The mechanism of action of these two molecules was investigated by analyzing the individual steps of the topoisomerase I (topoI) reaction cycle. The compounds stimulated cleavage, thereby perturbing the cleavage-religation equilibrium. Consequently, these molecules inhibited the growth of the cells overexpressing topoI at a low MIC. Docking of the molecules on the MttopoI model suggested that they bind near the metal binding site of the enzyme. The DNA relaxation activity of the metal binding mutants harboring mutations in the DxDxE motif was differentially affected by the molecules, suggesting that the metal coordinating residues contribute to the interaction of the enzyme with the drug. Taken together, the results highlight the potential of these small molecules, which poison the Mycobacterium tuberculosis and Mycobacterium smegmatis topoisomerase I, as leads for the development of improved molecules to combat mycobacterial infections. Moreover, targeting metal coordination in topoisomerases might be a general strategy to develop new lead molecules.

THREE-LAYER FLUID FLOW OVER A SMALL OBSTRUCTION ON THE BOTTOM OF A CHANNEL

Many boundary value problems occur in a natural way while studying fluid flow problems in a channel. The solutions of two such boundary value problems are obtained and analysed in the context of flow problems involving three layers of fluids of different constant densities in a channel, associated with an impermeable bottom that has a small undulation. The top surface of the channel is either bounded by a rigid lid or free to the atmosphere. The fluid in each layer is assumed to be inviscid and incompressible, and the flow is irrotational and two-dimensional. Only waves that are stationary with respect to the bottom profile are considered in this paper. The effect of surface tension is neglected. In the process of obtaining solutions for both the problems, regular perturbation analysis along with a Fourier transform technique is employed to derive the first-order corrections of some important physical quantities. Two types of bottom topography, such as concave and convex, are considered to derive the profiles of the interfaces. We observe that the profiles are oscillatory in nature, representing waves of variable amplitude with distinct wave numbers propagating downstream and with no wave upstream. The observations are presented in tabular and graphical forms.

Characterization of rice small heat shock proteins targeted to different cellular organelles

Small heat shock proteins (sHSPs) are a family of ATP-independent molecular chaperones which prevent cellular protein aggregation by binding to misfolded proteins. sHSPs form large oligomers that undergo drastic rearrangement/dissociation in order to execute their chaperone activity in protecting substrates from stress. Substrate-binding sites on sHSPs have been predominantly mapped on their intrinsically disordered N-terminal arms. This region is highly variable in sequence and length across species, and has been implicated in both oligomer formation and in mediating chaperone activity. Here, we present our results on the functional and structural characterization of five sHSPs in rice, each differing in their subcellular localisation, viz., cytoplasm, nucleus, chloroplast, mitochondria and peroxisome. We performed activity assays and dynamic light scattering studies to highlight differences in the chaperone activity and quaternary assembly of sHSPs targeted to various organelles. By cloning constructs that differ in the length and sequence of the tag in the N-terminal region, we have probed the sensitivity of sHSP oligomer assembly and chaperone activity to the length and amino acid composition of the N-terminus. In particular, we have shown that the incorporation of an N-terminal tag has significant consequences on sHSP quaternary structure.

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.