On quasimodular eigenforms

We derive a multiplicity one result for quasimodular eigenforms on SL2(Z) by completing the description of all quasimodular eigenforms. As applications of our results, we complete the answer to the question of finding all quasimodular eigenforms arising as a product of two eigenforms and also give an estimate for the size of the maximum gap in the sequence of the Fourier coefficients of a quasimodular form.

Separation index of graphs and stacked 2-spheres

In 1987, Kalai proved that stacked spheres of dimension d >= 3 are characterised by the fact that they attain equality in Barnette's celebrated Lower Bound Theorem. This result does not extend to dimension d = 2. In this article, we give a characterisation of stacked 2-spheres using what we call the separation index. Namely, we show that the separation index of a triangulated 2-sphere is maximal if and only if it is stacked. In addition, we prove that, amongst all n-vertex triangulated 2-spheres, the separation index is minimised by some n-vertex flag sphere for n >= 6. Furthermore, we apply this characterisation of stacked 2-spheres to settle the outstanding 3-dimensional case of the Lutz-Sulanke-Swartz conjecture that ``tight-neighbourly triangulated manifolds are tight''. For dimension d >= 4, the conjecture has already been proved by Effenberger following a result of Novik and Swartz. (C) 2015 Elsevier Inc. All rights reserved.

Zinc acetylacetonate hydrate adducted with nitrogen donor ligands: Synthesis, spectroscopic characterization, and thermal analysis

We report synthesis, spectroscopic characterization, and thermal analysis of zinc acetylacetonate complex adducted by nitrogen donor ligands, such as pyridine, bipyridine, and phenanthroline. The pyridine adducted complex crystallizes to monoclinic crystal structure, whereas other two adducted complexes have orthorhombic structure. Addition of nitrogen donor ligands enhances the thermal property of these complexes as that with parent metal-organic complex. Zinc acetylacetonate adducted with pyridine shows much higher volatility (106 degrees C), decomposition temperature (202 degrees C) as that with zinc acetylacetonate (136 degrees C, 220 degrees C), and other adducted complexes. All the adducted complexes are thermally stable, highly volatile and are considered to be suitable precursors for metal organic chemical vapor deposition. The formation of these complexes is confirmed by powder X-ray diffraction, Fourier transform infrared spectroscopy, mass spectroscopy, and elemental analysis. The complexes are widely used as starting precursor materials for the synthesis of ZnO nanostructures by microwave irradiation assisted coating process. (c) 2015 Elsevier B.V. All rights reserved.

Tailoring energy absorption capacity of CNT forests through application of electric field

This study examines the effect of electric field on energy absorption capacity of carbon nanotube forests (CNTFs), comprising of vertically aligned multiwalled carbon nanotubes, under both quasistatic (strain rate, (epsilon) over dot = 10(-3) s(-1)) and dynamic ((epsilon) over dot = similar to 10(3) s(-1)) loading conditions. Under quasistatic condition, the CNTFs were cyclically loaded and unloaded while electric field was applied along the length of carbon nanotube (CNT) either throughout the loading cycle or explicitly during either the loading or the unloading segment. The energy absorbed per cycle by CNTF increased monotonically with electric field when the field was applied only during the loading segment: A 7 fold increase in the energy absorption capacity was registered at an electric field of 1 kV/m whereas no significant change in it was noted for other schemes of electro-mechanical loading. The energy absorption capacity of CNTF under dynamic loading condition also increased monotonically with electric field; however, relative to the quasistatic condition, less pronounced effect was observed. This intriguing strain rate dependent effect of electric field on energy absorption capacity of CNTF is explained in terms of electric field induced strengthening of CNTF, originating from the time dependent electric field induced polarization of CNT. (C) 2015 Elsevier Ltd. All rights reserved.

CheepSync: A Time Synchronization Service for Resource Constrained Bluetooth LE Advertisers

Clock synchronization is highly desirable in distributed systems, including many applications in the Internet of Things and Humans. It improves the efficiency, modularity, and scalability of the system, and optimizes use of event triggers. For IoTH, BLE - a subset of the recent Bluetooth v4.0 stack - provides a low-power and loosely coupled mechanism for sensor data collection with ubiquitous units (e.g., smartphones and tablets) carried by humans. This fundamental design paradigm of BLE is enabled by a range of broadcast advertising modes. While its operational benefits are numerous, the lack of a common time reference in the broadcast mode of BLE has been a fundamental limitation. This article presents and describes CheepSync, a time synchronization service for BLE advertisers, especially tailored for applications requiring high time precision on resource constrained BLE platforms. Designed on top of the existing Bluetooth v4.0 standard, the CheepSync framework utilizes low-level time-stamping and comprehensive error compensation mechanisms for overcoming uncertainties in message transmission, clock drift, and other system-specific constraints. CheepSync was implemented on custom designed nRF24Cheep beacon platforms (as broadcasters) and commercial off-the-shelf Android ported smartphones (as passive listeners). We demonstrate the efficacy of CheepSync by numerous empirical evaluations in a variety of experimental setups, and show that its average (single-hop) time synchronization accuracy is in the 10 mu s range.

Covalent Postassembly Modification and Water Adsorption of Pd3 Self-Assembled Trinuclear Barrels

Three new ditopic imidazole ligands (2-4) were synthesized in high yields and characterized by various spectroscopic techniques. These ligands resulted in the formation of 3 + 6] self-assembled trinuclear barrels (5-7) in quantitative yields by stoichiometric combination of individual ligands and Pd(NO3)(2) in DMSO. All the three assemblies (5-7) were characterized by `H NMR and ESI-MS analysis, and subsequently, structures of the complexes 5 and 6 were confirmed by single-crystal X-ray diffraction studies. Structure analysis reveals the presence of NO3- counter anions in the intermolecular channels/pockets, which could potentially act as H-bonding sites between adsorbed water molecules within the channels. In fact, both the assemblies (5 and 6) showed water uptake (136.58, and 123.78 cm(3) g(-1), respectively) at ambient temperature under maximum allowable humidity. In addition, free aldehyde group present in the bridging ligand in complex 7 provides reactive site for postassembly modification. Herein, Knoevenagel condensation with Meldrum's acid was utilized under mild conditions by targeting aldehyde group appended in prefabricated complex 7 and transformed into a different complex (8) with altered functional group. Such postassembly functionalization enables incorporation of a new functional group without disrupting the integrity of the trifacial structure.

Organization dependent collective magnetic properties of secondary nanostructures with differential spatial ordering and magnetic easy axis orientation

Achieving control on the formation of different organization states of magnetic nanoparticles is crucial to harness their organization dependent physical properties in desired ways. In this study, three organization states of iron oxide nanoparticles (gamma-Fe2O3), defining as (i) assembly (ii) network aggregate and (iii) cluster, have been developed by simply changing the solvent evaporation conditions. All three systems have retained the same phase and polydispersity of primary particles. Magnetic measurements show that the partial alignment of the easy axes of the particles in the network system due to the stacking aggregation morphology can result in significant enhancement of the coercivity and remanence values, while the opposite is obtained for the cluster system due to the random orientation of easy axes. Partial alignment in the aggregate system also results in noticeable non -monotonic field dependence of ZFC peak temperature (TpeaB). The lowest value of the blocking temperature (TB) for the cluster system is related to the lowering of the effective anisotropy due to the strongest demagnetizing effect. FC (Field cooled) memory effect was observed to be decreasing with the increasing strength of dipolar interaction of organization states. Therefore, the stacking aggregation and the cluster formation are two interesting ways of magnetic nanoparticles organization for modulating collective magnetic properties significantly, which can have renewed application potentials from recording devices to biomedicine. (C) 2016 Elsevier B.V. All rights reserved.