On 3-Regular Tripartitions

Abstract In this article,we investigate the arithmetic behavior of the function D_3(n)which counts the number of 3-regular tripartitions of n.For example,we show that forα≥1 and n≥0,■and ■     

Supramolecular Assemblies of Sulfur- and Selenium- Containing Expanded Porphyrins Mediated Through Noncovalent Interactions

Abstract

Various supramolecular assemblies based on expanded porphyrins building blocks containing sulfur and/or selenium in the core, formed through multiple non-covalent hydrogen bonding interactions are highlighted. Specifically, modified expanded porphyrins such as 22 π sapphyrins, 26 π rubyrins, and 34 π octaphyrins self assemble in solid state through C–H…O, C–H…N, C–H…S, C–H…Se, C–H…π, and C–H…Cl interactions to form dimeric, oligomeric, and three dimensional networks. Furthermore, the supramolecular networks promoted by trapped solvent molecules such as nitrobenzene and bound anions such as chloride or trifluoroacetate through noncovalent interactions will be discussed.     

[40]π Fused and Nonfused Core‐Modified Nonaphyrins: Syntheses and Structural Diversity

The synthesis of fused and nonfused core‐modified 40π nonaphyrins are reported. Spectroscopic and X‐ray structural studies reveal a twisted figure‐eight conformation in the freebase form that is nonaromatic. Structural changes occur, from figure‐eight to open extended conformation, upon protonation, thereby adopting 4nπ Hückel antiaromatic character, which is reflected in spectroscopic and theoretical studies. Such a structural change also induces ring inversions of specific heterocyclic rings by 180°.     

Pd/CaCO3 in liquid poly(ethylene glycol) (PEG): an easy and efficient recycle system for partial reduction of alkynes to cis-olefins under a hydrogen atmosphere

Lindlar’s catalyst (Pd/CaCO₃) in PEG (400) has been found to be the most reusable reaction medium for selective reduction of alkynes to cis-olefins. The catalyst and PEG were recycled five times without loss of activity.     

Oxasmaragdyrin-ferrocene and oxacorrole-ferrocene conjugates: synthesis, structure, and nonlinear optical properties

Ferrocenyl macrocyclic conjugates involving 22 pi oxasmaragdyrins and 18 pi oxacorroles have been synthesized and characterized. The direct covalent linkage of the ferrocenyl moiety to the meso position of the macrocycle is achieved by simple oxidative coupling of appropriate precursors with trifluoroacetic acid as catalyst. The electronic coupling between the ferrocenyl moiety and the macrocyclic pi system is apparent from: a) the red shifts (293-718 cm(-1)) of the Soret and Q-bands in the electronic absorption spectra of ferrocenyl conjugates; b) the shift of oxidation potentials (50-130 mV) of both the ferrocene and the corrole rings to the positive potentials; and c) considerable shortening of the C-C bond which connects the ferrocene and the meso-carbon atom of the macrocycle. The single-crystal X-ray structure of oxasmaragdyrin-ferrocene conjugate 9 reveals the planarity of the 22 pi skeleton with very small deviations of the meso-carbon atoms. The meso-ferrocenyl substituent has a small dihedral angle of 38 degrees, making way for mixing of the molecular orbitals of the ferrocene and the macrocycle. However, the other two meso substituents are almost perpendicular to the mean plane, defined by the three meso carbon atoms. Classical C-H...O and nonclassical C-H...pi interactions lead to a two-dimensional supramolecular network. Ferrocene-smaragdyrin conjugate 9 bonds to a chloride ion in the protonated form and a rhodium(i) ion in the free base form. Nonlinear optical measurements reveal a larger nonlinear refractive index (-5.83 x 10(-8)cm(2)W(-1)) and figure of merit (2.28 x 10(-8)cm(3)W(-1)) for the rhodium smaragdyrin-ferrocene conjugate 19 than for the others, suggesting its possible application in optical devices.     

Core-modified expanded porphyrins with large third-order nonlinear optical response

The third-order nonlinear optical response through measurement of two-photon absorption cross-sections (TPACS) for aromatic core-modified expanded porphyrin analogues by a femtosecond open aperture Z-scan method is reported. The values reported here are among the largest known so far in the literature for any organic molecules.     

Assessment of Acrylamide Degradation Potential of Pseudomonas aeruginosa BAC-6 Isolated from Industrial Effluent

Acrylamide finds diverse industrial applications but is considered an environmental threat because of its neurotoxic, carcinogenic, and teratogenic effects. Certain bacteria enzymatically degrade acrylamide to acrylic acid and ammonia. The present investigation was carried out to isolate and identify an acrylamide-degrading bacterium from industrial effluent. Bacterial growth and extent of acrylamide degradation in the presence of different acrylamide concentrations, nutrients, varied range of pH, and temperature were analyzed. Among the eight acrylamide-degrading isolates, isolate BAC-6 demonstrated the highest degradation, and based upon the partial 16S rDNA sequencing, it was identified as Pseudomonas aeruginosa. P. aeruginosa BAC-6 grew over a wide range of acrylamide concentrations, but the highest degradation was recorded at 500 mg/L concentration with concomitant cell growth. Among the carbon supplements, mannitol supported the highest growth and degradation. Maximum degradation was reported at neutral pH. A mesophilic temperature range (25–40 °C) facilitated conducive bacterial growth followed by degradation. The highest degradation and bacterial growth were observed at 30 and 35 °C, respectively. Thus, it could be inferred from the present investigation that cultural conditions strongly affected the degradation potential of P. aeruginosa BAC-6 and advocated the utilization of the isolate in bioremediation of sites polluted with acrylamide.     

The relation between a microscopic threshold-force model and macroscopic models of adhesion

This paper continues our recent work on the relationship between discrete contact interactions at the microscopic scale and continuum contact interactions at the macroscopic scale(Hulikal et al., J. Mech. Phys. Solids 76,144–161, 2015). The focus of this work is on adhesion. We show that a collection of a large number of discrete elements governed by a threshold-force based model at the microscopic scale collectively gives rise to continuum fracture mechanics at the macroscopic scale. A key step is the introduction of an efficient numerical method that enables the computation of a large number of discrete contacts. Finally,while this work focuses on scaling laws, the methodology introduced in this paper can also be used to study roughsurface adhesion.     

Parrondo?s game using a discrete-time quantum walk

We present a new form of a Parrondo game using discrete-time quantum walk on a line. The two players A and B with different quantum coins operators, individually losing the game can develop a strategy to emerge as joint winners by using their coins alternatively, or in combination for each step of the quantum walk evolution. We also present a strategy for a player A (B) to have a winning probability more than player B (A). Significance of the game strategy in information theory and physical applications are also discussed.