On the Roman domination number of a graph

A Roman dominating function of a graph G is a labeling f:V(G)?{0,1,2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number γ_R(G) of G is the minimum of ∑_v∈V(G)f(v) over such functions. A Roman dominating function of G of weight γ_R(G) is called a γ_R(G)-function. A Roman dominating function f:V?{0,1,2} can be represented by the ordered partition (V₀,V₁,V₂) of V, where V_i={v∈V∣f(v)=i}. Cockayne et al. [E.J. Cockayne, P.A. Dreyer, S.M. Hedetniemi, S.T. Hedetniemi, On Roman domination in graphs, Discrete Math. 278 (2004) 11-22] posed the following question: What can we say about the minimum and maximum values of |V₀|,|V₁|,|V₂| for a γ_R-function f=(V₀,V₁,V₂) of a graph G? In this paper we first show that for any connected graph G of order n≥3, , where γ(G) is the domination number of G. Also we prove that for any γ_R-function f=(V₀,V₁,V₂) of a connected graph G of order n≥3, , and .     

On the asymptotics of the on-diagonal Szegö kernel of certain Reinhardt domains

We compute the leading and subleading terms in the asymptotic expansion of the Szegö kernel on the diagonal of a class of pseudoconvex Reinhardt domains whose boundaries are endowed with a general class of smooth measures. We do so by relating it to a Bergman kernel over projective space.     

Application of MOS Gas Sensors Coupled with Chemometrics Methods to Predict the Amount of Sugar and Carbohydrates in Potatoes

Five potato varieties were studied using an electronic nose with nine MOS sensors. Parameters measured included carbohydrate content, sugar level, and the toughness of the potatoes. Routine tests were carried out while the signals for each potato were measured, simultaneously, using an electronic nose. The signals obtained indicated the concentration of various chemical components. In addition to support vector machines (SVMs that were used for the classification of the samples, chemometric methods, such as the partial least squares regression (PLSR) method, the principal component regression (PCR) method, and the multiple linear regression (MLR) method, were used to create separate regression models for sugar and carbohydrates. The predictive power of the regression models was characterized by a coefficient of determination (R²), a root-mean-square error of prediction (RMSEP), and offsets. PLSR was able to accurately model the relationship between the smells of different types of potatoes, sugar, and carbohydrates. The highest and lowest accuracy of models for predicting sugar and carbohydrates was related to Marfona potatoes and Sprite cultivar potatoes. In general, in all cultivars, the accuracy in predicting the amount of carbohydrates was somewhat better than the accuracy in predicting the amount of sugar. Moreover, the linear function had 100% accuracy for training and validation in the C-SVM method for classification of five potato groups. The electronic nose could be used as a fast and non-destructive method for detecting different potato varieties. Researchers in the food industry will find this method extremely useful in selecting the desired product and samples.     

How to Identify Roast Defects in Coffee Beans Based on the Volatile Compound Profile

The aim of this study was to detect and identify the volatile compounds in coffee that was obtained in defect roast processes versus standard roasting and to determine the type and strength of the correlations between the roast defects and the volatile compound profile in roasted coffee beans. In order to achieve this goal, the process of coffee bean roasting was set to produce an underdeveloped coffee defect, an overdeveloped coffee defect, and defectless coffee. The “Typica” variety of Arabica coffee beans was used in this study. The study material originated from a plantation that is located at an altitude of 1400–2000 m a.s.l. in Huehuetenango Department, Guatemala. The analyses were carried out with the use of gas chromatography/mass spectrometry (GC–MS) and an electronic nose. This study revealed a correlation between the identified groups of volatile compounds and the following coffee roasting parameters: the time to the first crack, the drying time, and the mean temperatures of the coffee beans and the heating air. The electronic nose helped to identify the roast defects.     

Curing Kinetics Modeling of Epoxy Modified by Fully Vulcanized Elastomer Nanoparticles Using Rheometry Method

In this study, the curing kinetics of epoxy nanocomposites containing ultra-fine full-vulcanized acrylonitrile butadiene rubber nanoparticles (UFNBRP) at different concentrations of 0, 0.5, 1 and 1.5 wt.% was investigated. In addition, the effect of curing temperatures was studied based on the rheological method under isothermal conditions. The epoxy resin/UFNBRP nanocomposites were characterized via Fourier transform infrared spectroscopy (FTIR). FTIR analysis exhibited the successful preparation of epoxy resin/UFNBRP, due to the existence of the UFNBRP characteristic peaks in the final product spectrum. The morphological structure of the epoxy resin/UFNBRP nanocomposites was investigated by both field emission scanning electron microscopy (FESEM) and transmission electron microscopy (TEM) studies. The FESEM and TEM studies showed UFNBRP had a spherical structure and was well dispersed in epoxy resin. The chemorheological analysis showed that due to the interactions between UFNBRP and epoxy resin, by increasing UFNBRP concentration at a constant temperature (65, 70 and 75 °C), the curing rate decreases at the gel point. Furthermore, both the curing kinetics modeling and chemorheological analysis demonstrated that the incorporation of 0.5% UFNBRP in epoxy resin matrix reduces the activation energy. The curing kinetic of epoxy resin/UFNBRP nanocomposite was best fitted with the Sestak–Berggren autocatalytic model.     

Nanoformulation of Polyphenol Curcumin Enhances Cisplatin-Induced Apoptosis in Drug-Resistant MDA-MB-231 Breast Cancer Cells

Triple Negative Breast Cancer (TNBC) is the aggressive and lethal type of breast malignancy that develops resistance to current therapies. Combination therapy has proven to be an effective strategy on TNBC. We aimed to study whether the nano-formulation of polyphenolic curcumin (Gemini-Cur) would affect the cisplatin-induced toxicity in MDA-MB-231 breast cancer cells. MDA-MB-231 cells were treated with Gemini-Cur, cisplatin and combination of Gemini-Cur/Cisplatin in a time- and dose-dependent manner. Cell viability was studied by using MTT, fluorescence microscopy and cell cycle assays. The mode of death was also determined by Hoechst staining and annexin V-FITC. Real-time PCR and western blotting were employed to detect the expression of BAX and BCL-2 genes. Our data demonstrated that Gemini-Cur significantly sensitizes cancer cells to cisplatin (combination index ≤ 1) and decreases IC50 values in comparison with Gemini-cur or cisplatin. Further studies confirmed that Gemini-Cur/Cisplatin suppresses cancer cell growth through induction of apoptosis (p < 0.001). In conclusion, the data confirm the synergistic effect of polyphenolic curcumin on cisplatin toxicity and provide attractive strategy to attain its apoptotic effect on TNBC.     

Nano‐Fe3O4@SiO2‐SO3H: A magnetic,reusable solid‐acid catalyst for solvent‐free reduction of oximes to amines with the NaBH3CN/ZrCl4 system

In this study, the immobilization of sulfonic acid on silica‐layered magnetite was carried out by the reaction of ClSO₃H with silica‐layered magnetite. The prepared magnetic nanoparticles of Fe₃O₄@SiO₂‐SO₃H were then characterized using scanning electron microscopy, energy dispersive X‐ray spectroscopy, X‐ray diffraction, Fourier transform infrared spectroscopy, vibrating sample magnetometry, and transmission electron microscopy. The sulfonated nanocomposite exhibited excellent catalytic activity and reusability in the reduction of various aldoximes and ketoximes with NaBH₃CN in the presence of ZrCl₄. All reactions were carried out under solvent‐free conditions (r.t. or 75–80°C) within 3–70 min to afford amines in high to excellent yields.     

An Effective and New Method for the Synthesis of Polysubstituted Imidazoles by the Use of CrCl3.6H2O as a Green and Reusable Catalyst: Synthasis of Some Novel Imidazole Derivatives

New, efficient and environmentally adapted synthesis of polysubstituted imidazoles in one‐pot is found. The multicomponent reaction of various aldehydes, benzil, aliphatic and aromatic primary amines and ammonium acetate under solvent‐free condition is explained. The highly efficient role of CrCl₃.6H₂O as catalyst in this synthesis was shown. By this advantage, several polysubstituted imidazoles as pharmaceutical important molecules can be prepared in high yield and high purity. This method is a very easy and a rapid reaction for the synthesis of imidazole derivatives. The crude products recrystallized to afford the crystalline pure products. Furthermore, catalyst exhibited remarkable reusable activity.     

Oxygen- versus carbon-coordination of the alpha-stabilized phosphorus ylide Ph<Subscript>3</Subscript>P=C(H)R in palladacycles bearing secondary amines

The ortho-metalated complex [Pd(x){κ ² (C,N)-[C₆H₄CH₂NRR′ (Y)}] (2a–4a and 2b–3b) was prepared by refluxing in benzene equimolecular amounts of Pd(OAc)₂ and secondary benzylamine [a, EtNHCH₂Ph; b, t-BuNHCH₂Ph followed by addition of excess NaCl. The reaction of the complexes [Pd(x){κ ² (C,N)-[C₆H₄CH₂NRR′ (Y)}] (2a–4a and 2b–3b) with a stoichiometric amount of Ph₃P=C(H)COC₆H₄-4-Z (Z = Br, Ph) (ZBPPY) (1:1 molar ratio), in THF at low temperature, gives the cationic derivatives [Pd(OC(Z-4-C₆H₄C=CHPPh₃){κ ² (C,N)-[C₆H₄CH₂NRR′(Y)}] (5a–9a, 4b–6b, and 4b′–6b′), in which the ylide ligand is O-coordinated to the Pd(II) center and trans to the ortho-metalated C(6)H(4) group, in an “end-on carbonyl”. Ortho-metallation, ylide O-coordination, and C-coordination in complexes (5a–9a, 4b–6b, and 4b′–6b′) were characterized by elemental analysis as well as various spectroscopic techniques.     

On polynomial EkP matrices

In this paper the relation betweenEP--matrices andE ^k P--matrices over an arbitrary filedF is studied. Further, conditions for the product ofE ^k P--matrices to be anE ^k P--matrix and for the reverse order law to hold for the polynomial Moore-Penrose inverse of the product ofE ^k P--matrices are determined