Ab initio studies of the protonation of CO,N2 and NO+: Calculation of the minimum energy reaction paths

Ab initio molecular orbital calculations employing a 4-31G basis set have been used to study the minimum energy paths for the formation of HCO⁺, COH⁺, and HCOH²⁺ from CO by protonation. The protonation of N₂ to give NNH⁺ and HNNH²⁺ and of NO⁺ to form HNO²⁺ and NOH²⁺ have also been investigated. All species formed have linear equilibrium geometries and the minimum energy path for approach of the proton is along the line-of-centers of the heavy atoms. Energy barriers to the formation of the various species are given, where appropriate, and changes in geometry, ordering of molecular orbitals and orbital occupancy are discussed.     

Effect of bovine serum albumin on the surface properties of ionic liquid-type Gemini surfactant

The effect of bovine serum albumin on the surface properties of IL-type gemini surfactant ([C₁₀-4-C₁₀im]Br₂), have been investigated by surface tension method. The critical micelle concentration (CMC) as a function of BSA concentrations at various temperatures was investigated. The CMC of [C₁₀-4-C₁₀im]Br₂ increases with increasing the concentration of BSA as well as the temperature of the system. The interfacial parameters viz; maximum surface excess concentration (Γ_max), the minimum area per molecule (A_min), and surface pressure at CMC (Π_cmc) were calculated. In addition, thermodynamic parameters of adsorption and micellization were evaluated by using surface tension data. The results indicated that the binding of [C₁₀-4-C₁₀im]Br₂ to BSA is spontaneous and exothermic in nature. The process is entropy driven and hydrophobic interactions are the major driving forces.     

Three‐unit semicircles curve: A compact 3D graphical representation of DNA sequences based on classifications of nucleotides

A new three‐dimensional graphical representation of DNA sequences, three‐unit semicircles (TUS)‐curve, which maps a given sequence into a dot sequences embedded in three‐unit semicircles, is proposed based on three biclassifications of nucleotides. TUS‐curve has the merit of compactness and could avoid the degeneracy and loss of information. The geometrical center of the curve, which indicates the distribution of base frequencies of the corresponding DNA sequence, is extracted and applied to analyze the similarity of various species. Phylogenetic tree of 11 species based on their first exons of β‐globin genes showed that the TUS‐curve is a powerful tool to get valuable biological information. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

On the normalized Laplacian of Möbius phenylene chain and its applications

Let denote a molecular graph of linear [n] phenylene with n hexagons and n squares, and let the Möbius phenylene chain be the graph obtained from the by identifying the opposite lateral edges in reversed way. Utilizing the decomposition theorem of the normalized Laplacian characteristic polynomial, we study the normalized Laplacian spectrum of , which consists of the eigenvalues of two symmetric matrices ℒ _R and ℒ _Q of order 3n. By investigating the relationship between the roots and coefficients of the characteristic polynomials of the two matrices above, we obtain an explicit closed-form formula of the multiplicative degree-Kirchhoff index as well as the number of spanning trees of . Furthermore, we determine the limited value for the quotient of the multiplicative degree-Kirchhoff index and the Gutman index of .     

Maximizing the mean subtree order

This article focuses on properties and structures of trees with maximum mean subtree order in a given family; such trees are called optimal in the family. Our main goal is to describe the structure of optimal trees in and , the families of all trees and caterpillars, respectively, of order . We begin by establishing a powerful tool called the Gluing Lemma, which is used to prove several of our main results. In particular, we show that if is an optimal tree in or for , then every leaf of is adjacent to a vertex of degree at least . We also use the Gluing Lemma to answer an open question of Jamison and to provide a conceptually simple proof of Jamison's result that the path has minimum mean subtree order among all trees of order . We prove that if is optimal in , then the number of leaves in is and that if is optimal in , then the number of leaves in is . Along the way, we describe the asymptotic structure of optimal trees in several narrower families of trees.     

A safe minimum standard,the elasticity of substitution,and the cleanup of the Ganges in Varanasi

Despite repeated calls for a thorough cleanup of water pollution in the Ganges river, there are only two papers in the social sciences by Batabyal and Beladi (2017, 2019) that have shed theoretical light on this cleanup problem and its connection to the sustainability of tourism in Varanasi. Hence, we extend the above‐mentioned analyses and focus on two specific questions. First, we introduce the notion of a safe minimum standard (SMS) into the study and show how to analyze a probabilistic model of the Ganges cleanup problem when the SMS is accounted for. Second, for a representative citizen of Varanasi, we study how the magnitude of the elasticity of substitution between a composite consumption good and water quality in the Ganges—modeled by the SMS—affects the tradeoff between consumption and water quality maintenance.     

A Tree-valued Markov Process Associated with an Admissible Family of Branching Mechanisms

Let E?R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning Lévy trees accordingly such that for each t ∈E, Tt is a ψt-Lévy tree. We also obtain an analogous process {Tt*,t ∈E} by pruning a critical Levy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, we show that the law of {Tt,t ∈E} at the ascension time A := inf{t ∈E;Tt is finite} can be represented by{Tt*,t∈E}.The results generalize those studied in Abraham and Delmas [Ann. Probab., 40, 1167-1211(2012)].     

Embedding hypertrees into steiner triple systems

In this paper, we are interested in the following question: given an arbitrary Steiner triple system on vertices and any 3‐uniform hypertree on vertices, is it necessary that contains as a subgraph provided ? We show the answer is positive for a class of hypertrees and conjecture that the answer is always positive.