Powers of edge ideals with linear resolutions

We show that if G is a gap-free and diamond-free graph, then I(G)^s has a linear minimal free resolution for every s≥2.     

The uranium recovery from aqueous solutions using amidoxime modified cellulose derivatives. IV. Recovery of uranium by amidoximated hydroxypropyl methylcellulose

Amidoxime modified hydroxypropyl methylcellulose (HPMC) films (HPMC-g-AO) were used for the recovery of uranium from aqueous solutions by a complexation process. The adsorption experiments were carried out by immersion of a certain amount of films in UO₂ ²⁺ solutions (resultant pH 4.1) ranging in concentration from 100 to 1,000 ppm. The effect of temperature (25–50 °C) on the adsorption capacity of HPMC-g-AO was investigated at the optimized time. The adsorption kinetics and the thermodynamics as well as the adsorption capacity of HPMC-g-AO films were investigated. The adsorption capacity was found as 765 mg UO₂ ²⁺/g dry film. The kinetic and the thermodynamic parameters (i.e. activation energy, enthalpy, entropy and Gibbs free energy) for the interaction of UO₂ ²⁺ with HPMC-g-AO were calculated based on known basic relations. The results showed that adsorption occurred through strong electrostatic interactions with an enthalpy of ?36.5 kJ/mol. The desorption of UO₂ ²⁺ were investigated using different desorption agents such as EDTA, HCl, NaHCO₃, and NaOH. After the 2 weeks treatment period, the highest desorption yield were found as 23 % with NaHCO₃.     

Radiation synthesis of n-vinyl 2-pyrrolidone/acrylonitrile interpenetrating polymer networks and their use in uranium recovery from aqueous systems

Interpenetrating Polymer Networks (IPNs) based on Poly n-vinyl 2-pyrrolidone (PVP) and Acrylonitrile (AN) were prepared by irradiating PVP solutions prepared in AN. PVP/AN mixtures were irradiated by ⁶⁰Co-γ rays at room temperature at a dose rate of 0.5 kGy/hour. IPNs were characterized by using FT-IR and Thermal Analysis techniques. The chelating adsorbents containing amidoxime groups were prepared by the reaction of these IPNs with hydroxylamine in aqueous NaOH solution at 50°C. These amidoxime containing adsorbents were used in adsorption studies for the recovery of uranium from aqueous systems. The adsorption capacity of an IPN with equivolume fraction of PVP and amidoximated PAN was found to be 750mg UO₂²⁺/g dry amidoximated IPN.     

Powers of ideals associated to (C4,2K2)-free graphs

Let G be a $(C_4,2K_2)$-free graph with edge ideal $I(G)?\mathbb{k}[x_1,\dots ,x_n]$. We show that $I{(G)}^s$ has linear resolution for every $s\ge 2$. Also, we show that every power of the vertex cover ideal of G has linear quotients. As a result, we describe the Castelnuovo–Mumford regularity of powers of $I{(G)}^{\vee }$ in terms of the maximum degree of G.     

Thermal degradation of [poly(N-vinylimidazole)-polyacrylic acid] interpolymer complexes

Interpolymer complexes of a slightly basic polymer, poly(N-vinylimidazole) (PVIm) with a strongly acidic polymer, poly(acrylic acid) (PAA) have been prepared by mixing aqueous solutions of the respective components. Spectroscopy and thermal methods were used to reveal interaction between VIm and AA moieties. FT-IR analysis showed that the nitrogen atoms at 3rd position of imidazole ring are involved in strong H-bonding with acid groups of PAA leading to a uniform and fully miscible complex structure. As the quantity of PAA increases the thermal stability of complex increases based on TG results. In the DSC analyses, the single T_g for all IPC samples showed that IPCs have good or definite miscibility over the whole range of composition as a result of H-bond formation between acrylic acid and imidazole units.     

The synthesis,characterization and effect of molar mass distribution on solid-state degradation kinetics of oligo(orcinol)

Journal of Thermal Analysis and Calorimetry - In this study, the oxidative polymerization of orcinol monohydrate using different oxidants such as NaOCl, H2O2, and air was investigated....     

A new generalization of complex Stancu operators

In this paper, we investigate approximation properties of the complex form of an extension of the Bernstein polynomials, defined by Stancu by means of a probabilistic method. We obtain quantitative upper estimates for simultaneous approximation and the exact order of approximation by these operators attached to analytic functions in closed disks. Also, we prove that the new generalized complex Stancu operators preserve the univalence, starlikeness, convexity, and spirallikeness in the unit disk.     

Multigraded Betti numbers of simplicial forests

We prove that multigraded Betti numbers of a simplicial forest are always either 0 or 1. Moreover a nonzero multidegree appears exactly in one homological degree in the resolution. Our work generalizes work of Bouchat [2] on edge ideals of graph trees.     

Preparation of poly(vinyl alcohol) hydrogels with radiation grafted citric and succinic acid groups

Ternary mixtures of PVA/Citric acid (CA)/water and PVA/Succinic acid (SA)/water were gamma irradiated to various doses in air at ambient temperature. Gelation % vs dose curves were constructed and swelling behavior of gels with maximum conversions was studied. In maximum gelled systems 80% of CA used in the feed composition was retained in the gel structure whereas this was only 20% for SA. The volume of swelling of ionic PVA gels increased from 230% to 530% for PVA/CA systems when pH was increased from 2.6 to 7.5. Less significant increase in swelling was observed for PVA/SA gels, from 250% to 330% in the same pH interval. The incorporation of SA and CA groups onto PVA networks improved remarkably the affinity of these structures for Co²⁺ and Ni²⁺ ion uptake.     

On the Real Roots of $$\sigma $$-Polynomials

The \(\sigma \)-polynomial is given by \(\sigma (G,x) = \sum _{i=\chi (G)}^{n} a_{i}(G)\, x^{i}\), where \(a_{i}(G)\) is the number of partitions of the vertices of G into i nonempty independent sets. These polynomials are closely related to chromatic polynomials, as the chromatic polynomial of G is given by \(\sum _{i=\chi (G)}^{n} a_{i}(G)\, x(x-1) \ldots (x-(i-1))\). It is known that the closure of the real roots of chromatic polynomials is precisely \(\{0,~1\} \bigcup [32/27,\infty )\), with \((-\infty ,0)\), (0, 1) and (1, 32 / 27) being maximal zero-free intervals for roots of chromatic polynomials. We ask here whether such maximal zero-free intervals exist for \(\sigma \)-polynomials, and show that the only such interval is \([0,\infty )\)—that is, the closure of the real roots of \(\sigma \)-polynomials is \((-\infty ,0]\).