Euclidean minimum spanning trees and bichromatic closest pairs

We present an algorithm to compute a Euclidean minimum spanning tree of a given setS ofN points inE ^d in timeO(F _d (N,N) log ^d N), whereF _d (n,m) is the time required to compute a bichromatic closest pair amongn red andm green points inE ^d . IfF _d (N,N)=Ω(N ^1+ε), for some fixed ɛ>0, then the running time improves toO(F _d (N,N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closest pair in expected timeO((nm logn logm)^2/3+m log² n+n log² m) inE ₃, which yields anO(N ^4/3 log^4/3 N) expected time, algorithm for computing a Euclidean minimum spanning tree ofN points inE ³. Ind≥4 dimensions we obtain expected timeO((nm)^{1−1/([d/2]+1)+ε}+m logn+n logm) for the bichromatic closest pair problem andO(N ^{2−2/([d/2]+1)ε}) for the Euclidean minimum spanning tree problem, for any positive ɛ. The first, second, and fourth authors acknowledge support from the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS), a National Science Foundation Science and Technology Center under NSF Grant STC 88-09648. The second author's work was supported by the National Science Foundation under Grant CCR-8714565. The third author's work was supported by the Deutsche Forschungsgemeinschaft under Grant A1 253/1-3, Schwerpunktprogramm “Datenstrukturen und effiziente Algorithmen”. The last two authors' work was also partially supported by the ESPRIT II Basic Research Action of the EC under Contract No. 3075 (project ALCOM).     

Existence of multiple positive solutions for second order nonlinear dynamic BVPs by variational methods

The aim of this paper is to employ variational techniques and critical point theory to prove some sufficient conditions for the existence of multiple positive solutions to a nonlinear second order dynamic equation with homogeneous Dirichlet boundary conditions.     

The generalized Thomas–Fermi singular boundary value problems for neutral atoms

This paper presents an upper and lower solution theory for singular boundary value problems modelling the Thomas–Fermi equation, subject to a boundary condition corresponding to the neutral atom with Bohr radius equal to its existence interval. Furthermore, we derive sufficient conditions for the existence–construction of the above‐mentioned upper–lower solutions. Copyright © 2005 John Wiley & Sons, Ltd.     

A novel programmed shrinkage dilatometer for optimized sintering of powder ceramics

A fast-firing shrinkage rate controlled dilatometer was developed as a tool for optimizing sintering of powder compacts. The instrument described in this work features an infrared imaging radiation furnace and a low thermal mass dilatometer assembly which allowed controlled heating and cooling rates of up to 500°C min^?1. Shrinkage control was accomplished using a computer interfaced PID control algorithm. Adjustments were made to hardware and software which reduced specimen creep under dilatometer pushrod load, eliminated non-uniform pushrod expansion, fostered reproducible specimen temperature determination, accounted for thermal expansion during sintering, and generated instantaneous termination of sintering at the specified end of RCS. Tests performed on ZnO samples demonstrated very rapid thermal response and excellent shrinkage control.     

n-Colour self-inverse compositions

MacMahon’s definition of self-inverse composition is extended ton-colour self-inverse composition. This introduces four new sequences which satisfy the same recurrence relation with different initial conditions like the famous Fibonacci and Lucas sequences. For these new sequences explicit formulas, recurrence relations, generating functions and a summation formula are obtained. Two new binomial identities with combinatorial meaning are also given.     

Quantum imaging with incoherent photons

We propose a technique to obtain subwavelength resolution in quantum imaging with potentially 100% contrast using incoherent light. Our method requires neither path-entangled number states nor multiphoton absorption. The scheme makes use of N photons spontaneously emitted by N atoms and registered by N detectors. It is shown that for coincident detection at particular detector positions a resolution of lambda/N can be achieved.     

Generation of symmetric Dicke states of remote qubits with linear optics

We propose a method for generating all symmetric Dicke states, either in the long-lived internal levels of N massive particles or in the polarization degrees of freedom of photonic qubits, using linear optical tools only. By means of a suitable multiphoton detection technique, erasing Welcher-Weg information, our proposed scheme allows the generation and measurement of an important class of entangled multiqubit states.     

Self‐Organization of Gold Nanoparticle Assemblies with 3D Spatial Order and Their External Stimuli Responsiveness

Gold nanoparticles (AuNP) with pyridyl end‐capped polystyrenes (PS‐4VP) as “quasi‐monodentate” ligands self‐assemble into ordered PS‐4VP/AuNP nanostructures with 3D hexagonal spatial order in the dried solid state. The key for the formation of these ordered structures is the modulation of the ratio AuNP versus ligands, which proves the importance of ligand design and quantity for the preparation of novel ordered polymer/metal nanoparticle conjugates. Although the assemblies of PS‐4VP/AuNP in dispersion lack in high dimensional order, strong plasmonic interactions are observed due to close contact of AuNP. Applying temperature as an external stimulus allows the reversible distortion of plasmonic interactions within the AuNP nanocomposite structures, which can be observed directly by naked eye. The modulation of the macroscopic optical properties accompanied by this structural distortion of plasmonic interaction opens up very interesting sensoric applications.

     

Discovery of novel inhibitors for <Emphasis Type="Italic">Leishmania</Emphasis> nucleoside diphosphatase kinase (NDK) based on its structural and functional characterization

Nucleoside diphosphate kinases (NDKs) are ubiquitous enzymes that catalyze the transfer of the γ-phosphate moiety from an NTP donor to an NDP acceptor, crucial for maintaining the cellular level of nucleoside triphosphates (NTPs). The inability of trypanosomatids to synthesize purines de novo and their dependence on the salvage pathway makes NDK an attractive target to develop drugs for the diseases they cause. Here we report the discovery of novel inhibitors for Leishmania NDK based on the structural and functional characterization of purified recombinant NDK from Leishmania amazonensis. Recombinant LaNDK possesses auto-phosphorylation, phosphotransferase and kinase activities with Histidine 117 playing an essential role. LaNDK crystals were grown by hanging drop vapour diffusion method in a solution containing 18% PEG-MME 500, 100 mM Bis-Tris propane pH 6.0 and 50 mM MgCl₂. It belongs to the hexagonal space group P6₃22 with unit cell parameters a?=?b?=?115.18, c?=?62.18 Å and α?=?β?=?90°, γ?=?120°. The structure solved by molecular replacement methods was refined to crystallographic R-factor and R_free values of 22.54 and 26.52%, respectively. Molecular docking and dynamics simulation-based virtual screening identified putative binding compounds. Protein inhibition studies of selected hits identified five inhibitors effective at micromolar concentrations. One of the compounds showed ~45% inhibition of Leishmania promastigotes proliferation. Analysis of inhibitor-NDK complexes reveals the mode of their binding, facilitating design of new compounds for optimization of activities as drugs against leishmaniasis.     

$$\mathcal {H}^+$$-multivalued contractions and their application to homotopy theory

Kikkawa and Suzuki (Nonlinear Anal 69:2942–2949, 2008) and Kikkawa and Suzuki (Fixed Point Theory Appl, 2008, Art. ID 649749) proved some fixed point results that are generalizations of Kannan’s, Nadler’s and Suzuki’s fixed point theorems. Here, we present fixed point results of this kind for multivalued mappings in the setting of \(\mathcal {H}^+\)-metric spaces. The theorems provided allow upgrading of some known results which is shown by examples. Moreover, we give a homotopy result as an application of our main theorem.