An efficient fourth order weighted-Newton method for systems of nonlinear equations

In this paper, we develop a fourth order method for solving the systems of nonlinear equations. The algorithm is composed of two weighted-Newton steps and requires the information of one function and two first Fréchet derivatives. Therefore, for a system of n equations, per iteration it uses n?+?2n ² evaluations. Computational efficiency is compared with Newton’s method and some other recently published methods. Numerical tests are performed, which confirm the theoretical results. From the comparison with known methods it is observed that present method shows good stability and robustness.     

Singular Lagrangian, Hamiltonization and Jacobi last multiplier for certain biological systems

We study the construction of singular Lagrangians using Jacobi’s last multiplier (JLM). We also demonstrate the significance of the last multiplier in Hamiltonian theory by explicitly constructing the Hamiltonian of the Host-Parasite model and a Lotka-Volterra mutualistic system, both of which are well known first-order systems of differential equations arising in biology.     

ESR study of the hydrogenated nanocrystalline silicon thin films

We studied the stability and light-induced paramagnetic centers in hydrogenated nanocrystalline silicon thin films (nc-Si:H) by electron-spin-resonance (ESR) and photothermal-deflection-spectroscopy (PDS). There is no measurable change in defect density upon illumination with white light with a light intensity of 300 mW cm^?2 for 300 h. At low temperatures, upon illumination with sub-bandgap light, a light-induced ESR signal appears. This signal is similar to that in hydrogenated micro-crystalline silicon (μc-Si:H).     

A Catalyst and Solvent Free Route for the Synthesis of N-Substituted Pyrrolidones from Levulinic Acid

An efficient, metal-free, catalyst-free and solvent-free methodology for the reductive amination of levulinic acid with different anilines has been developed using HBpin as the reducing reagent. This protocol offers an excellent method to avoid solvents and added catalysts on the synthesis of different kinds of N-substituted pyrrolidones under metal free conditions. It is also the first report for the synthesis of different pyrrolidones by solvent-free as well as catalyst-free methods. The proposed mechanism for the formation of pyrrolidone has been supported by DFT calculations and control experiments.     

Macroscopic Polarization Change of Mononuclear Valence Tautomeric Cobalt Complexes Through the Use of Enantiopure Ligand

The crystallization of a complex having electron transfer properties in a polar space group can induce the polarization switching of a crystal in a specific direction, which is attractive for the development of sensors, memory devices, and capacitors. Unfortunately, the probability of crystallization in a polar space group is usually low. Noticing that enantiopure compounds crystallize in Sohncke space groups, this paper reports a strategy for the molecular design of non-ferroelectric polarization switching crystals based on the use of intramolecular electron transfer and chirality. In addition, this paper describes the synthesis of a mononuclear valence tautomeric (VT) cobalt complex bearing an enantiopure ligand. The introduction of enantiomer enables the crystallization of the complex in the polar space group (P2₁). The polarization of the crystals along the b-axis direction is not canceled out and the VT transition is accompanied by a change in the macroscopic polarization of the polar crystal. Polarization switching via electron transfer is realized at around room temperature.     

Ionic Assembly,Anion–π, Magnetic,and Electronic Attributes of Ambient Stable Naphthalenediimide Radical Ions

Organic spin-based molecular materials are considered to be attractive for the generation of functional materials with emergent optoelectronic, magnetic, or magneto-conductive properties. However, the major limitations to the utilization of organic spin-based systems are their high reactivity, instability, and propensity for dimerization. Herein, we report the synthesis, characterization, and magnetic and electronic studies of three ambient stable radical ions ( 1 a^.+ , 1 b^.+ , and 1 c^.+ ). The radical ions 1 b^.+ and 1 c^.+ with BPh₄⁻ and BF₄⁻ counter anions, respectively, were synthesized in excellent yields by means of anion metathesis of 1 a^.+ with Br⁻ as its counter anion. Notably, synthesis of 1 a^.+ was achieved in an ecofriendly, solvent-free protocol. The radical ions were characterized by means of single-crystal X-ray diffraction studies, which revealed the discrete nature of the radical ions and extensive hydrogen-bonding interactions within the radical ions and with the counter anions. Thus, radical ions can be organized to form infinite supramolecular arrays using weak noncovalent interactions. In addition, the Br⁻, BF₄⁻, and BPh₄⁻ anions formed diverse types of anion–π interactions with the naphthalene and imide rings of the radical ions. The radical ions were characterized by means of X-band electron paramagnetic resonance (EPR) spectroscopy in solution and in the solid state. Magnetic studies revealed their paramagnetic nature in the range of 10 to 300 K. The radical ions exhibited high resistivity approaching the gigaohm (GΩ) scale. In addition, the radical ions exhibited panchromism.     

Reversible Ultra-Slow Crystal Growth of Mixed Lead Bismuth Perovskite Nanocrystals: The Presence of Dynamic Capping

An ultra-slow crystal growth over a period of 24 h of a newly synthesized CH₃NH₃Pb_1/2Bi_1/3I₃ perovskite (MPBI) nanocrystal in non-polar toluene medium is reported here. From several spectroscopic techniques as well as from TEM analysis we found that the size of nanocrystals changes continuously with time, in spite of being capped by the ligands. Using a single molecular spectroscopic technique, we also found that this size change is not due to the stacking of nanocrystals but due to crystal growth. The notable temperature dependence and reversible nature of the nanocrystals growth is explained by the dynamic nature of the capping. The observed temperature-dependent ultra-slow growth is believed to be a pragmatic step towards controlling the size of perovskite NC in a systematic manner.     

Structure--activity landscape index: identifying and quantifying activity cliffs

A new method for analyzing a structure-activity relationship is proposed. By use of a simple quantitative index, one can readily identify "structure-activity cliffs": pairs of molecules which are most similar but have the largest change in activity. We show how this provides a graphical representation of the entire SAR, in a way that allows the salient features of the SAR to be quickly grasped. In addition, the approach allows us view the SARs in a data set at different levels of detail. The method is tested on two data sets that highlight its ability to easily extract SAR information. Finally, we demonstrate that this method is robust using a variety of computational control experiments and discuss possible applications of this technique to QSAR model evaluation.     

A theoretical investigation of Zn?Zn and Be?Be one electron bond

Attachment of one electron to 1,2-diBeX-benzene and 1,2-diZnX-benzene derivatives leads to the formation of stronger Be Be and Zn Zn interaction compared to the neutral one. This is reflected in the dramatic shortening of the Be Be and Zn Zn distance. The formation of these 2-center-1-electron bonds have also been confirmed by topological survey of electron density using quantum theory of atoms in molecules and electron localization function. The formation of these bonds is expected to render stability to these radical anions. These radical anions are stable toward electron detachment and computed bond dissociation energy values are also significant.     

Interaction of chromium with resistant strain Aspergillus versicolor: investigation with atomic force microscopy and other physical studies

The interaction of chromium and a chromate resistant Aspergillus versicolor strain has been studied by atomic force (AFM) and transmission electron (TEM) microscopies. The nanomechanical properties such as cell wall rigidity and elasticity were measured by force spectroscopy and found to be 0.61 +/- 0.08 N/m, and 20.5 +/- 2.1 MPa, respectively. On chromium binding, ultrastuctural changes of the cell wall along with the formation of layered structures on the cell wall were observed. TEM and AFM micrographs demonstrate the accumulation of chromium on the cell wall, which were rough and irregular compared with the smooth pristine mycelia. The surface roughness, cell wall rigidity and elasticity increased to 35.5 +/- 3.5 nm, 0.88 +/- 0.05 N/m, and 62.5 +/- 3.5 MPa, respectively, from the corresponding values of 5.2 +/- 0.68 nm, 0.61 +/- 0.02 N/m, and 20.5 +/- 2.1 MPa for the pristine mycelia. X-ray photoelectron spectroscopy and Fourier transform infrared studies suggest that bound chromium was reduced to its trivalent state by the cell wall components. The reduced chromium species on the cell surface further electrostatically bind chromate ions forming layered structure on the cell wall.