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.     

Erdős matching conjecture for almost perfect matchings

In 1965 Erd?s asked, what is the largest size of a family of k-element subsets of an n-element set that does not contain a matching of size $s+1$? In this note, we improve upon a recent result of Frankl and resolve this problem for $s>101k^3$ and $(s+1)k?n<(s+1)(k+\frac{1}{100k})$.     

Parameters Tied to Treewidth

Treewidth is a graph parameter of fundamental importance to algorithmic and structural graph theory. This article surveys several graph parameters tied to treewidth, including separation number, tangle number, well‐linked number, and Cartesian tree product number. We review many results in the literature showing these parameters are tied to treewidth. In a number of cases we also improve known bounds, provide simpler proofs, and show that the inequalities presented are tight.     

The polynomial reconstruction problem: The first 50 years

The problem of reconstructing the characteristic polynomial of a graph of order at least 3 from the collection of characteristic polynomials of its vertex-deleted subgraphs was posed by Cvetkovi? in 1973 as a spectral counter part to the well-known Ulam's reconstruction conjecture. Over the last 50 years, this problem has received notable attention, many positive results have been obtained, but in the general case the problem is still unresolved. In particular, no counter example is found in literature. In this expository paper we survey classical and some more recent results concerning the polynomial reconstruction problem, discuss some related problems, variations and generalizations.     

Classroom note: Using the binomial series to prove the arithmetic mean–geometric mean inequality

In 1968, Leon Gerber compared (1 + x) ^a to its kth partial sum as a binomial series. His result is stated and, as an application of this result, a proof of the arithmetic mean–geometric mean inequality is presented.     

运用CAFP教学提升学生化学意志素质的教学案例

鉴于当前学生化学意志素质缺乏的问题，探讨以认知、情绪唤醒、情感、意志为主控目标，在预习、尝试学习、交错搭配合作学习中，开展CAFP教学研究，以促成情意因素对认知的调动、动力、强化等功能。     

Peptide Property Modeling by Cluj Indices

Abstract

The novel Cluj property indices are used for modeling the biological properties of dipeptides: the ACE inhibition activity of a set of 58 dipeptides and the bitter tasting activity of a set of 48 dipeptides, taken from the literature. The results are compared to those reported in some previous works.