The volume and ehrhart polynomial of the alternating sign matrix polytope

Alternating sign matrices (ASMs), polytopes and partially-ordered sets are fascinating combinatorial objects which form the main themes of this thesis. In Chapter 1, the origins and various aspects of ASMs are discussed briefly. In particular, bijections between ASMs and other objects, including monotone triangles, corner sum matrices, configurations of the six-vertex model with domain-wall boundary conditions, configurations of simple flow grids and height function matrices, are presented. The ASM lattice and ASM partially ordered set are also introduced. In Chapter 2, the ASM polytope and related polytopes, including the Birkhoff polytope, Chan-Robbins-Yuen polytope, ASM order polytope and ASM Chan-Robbins-Yuen polytope, are defined and their properties are summarised. In Chapter 3, new results for the volume and Ehrhart polynomial of the ASM polytope are obtained. In particular, by constructing an explicit bijection between higher spin ASMs and a disjoint union of sets of certain (P, ω)-partitions (where P is a subposet of the ASM poset and ω is a labeling), a formula is derived for the number of higher spin ASMs, or equivalently for the Ehrhart polynomial of the ASM polytope. The relative volume of the ASM polytope is then given by the leading term of its Ehrhart polynomial. Evaluation of the formula involves computing numbers of linear extensions of certain subposets of the ASM poset, and numbers of descents in these linear extensions. Details of this computation are presented for the cases of the ASM polytope of order 4, 5, 6 and 7. In Chapter 4, some directions for further work are outlined. A joint paper with Roger Behrend, based on Chapter 3 of the thesis, is currently in preparation for submission

The annihilating-ideal graph of z(n) is weakly perfect

A graph is called weakly perfect if its vertex chromatic number equals its clique number. Let RR be a commutative ring with identity and A(R)A(R) be the set of ideals with non-zero annihilator. The annihilating-ideal graph of RR is defined as the graph AG(R)AG(R) with the vertex set A(R)∗=A(R)∖{0}A(R)∗=A(R)∖{0} and two distinct vertices II and JJ are adjacent if and only if IJ=0IJ=0. In this paper, we show that the graph AG(Zn)AG(Zn), for every positive integer nn, is weakly perfect. Moreover, the exact value of the clique number of AG(Zn)AG(Zn) is given and it is proved that AG(Zn)AG(Zn) is class 1 for every positive integer nn

Using Generation 3 Polyamidoamine Dendrimer as Adsorbent for the Removal of Pentavalent Arsenic from Aqueous Solutions

Introduction: Arsenic is known as a carcinogenic compound in drinking water. It can cause acute and chronic effects on human health. In this study, the effect of polyamidoamine dendrimer generation 3 (PAMAM G3) as adsorbents for removal of arsenic (V) from aqueous solutions was evaluated. Materials and Methods: Adsorption experiment was studied in batch system and the effect of different variables such as pH, contact time, concentrations of arsenic and adsorbent dosage on adsorption was studied. Therefore, absorption kinetics and equilibrium isotherms were determined. Results: The results showed that adsorption process is affected by some parameters such as initial concentration, adsorbent dose and contact time. The three models of isotherm including Langmuir, Freundlich and Dubinin- Radeshkuvich were studied while Freundlich and Langmuir isotherms were more compliant with results. Conclusion: According to the results, it can be concluded that adsorption with dendrimer is an appropriate method with high efficiency for arsenic removal from aqueous solutions

Phenol Photocatalytic Degradation by Advanced Oxidation Process under Ultraviolet Radiation Using Titanium Dioxide

Background. The main objective of this study was to examine the photocatalytic degradation of phenol from laboratory samples and petrochemical industries wastewater under UV radiation by using nanoparticles of titanium dioxide coated on the inner and outer quartz glass tubes. Method. The first stage of this study was conducted to stabilize the titanium dioxide nanoparticles in anatase crystal phase, using dip-coating sol-gel method on the inner and outer surfaces of quartz glass tubes. The effect of important parameters including initial phenol concentration, TiO2 catalyst dose, duration of UV radiation, pH of solution, and contact time was investigated. Results. In the dip-coat lining stage, the produced nanoparticles with anatase crystalline structure have the average particle size of 30 nm and are uniformly distributed over the tube surface. The removal efficiency of phenol was increased with the descending of the solution pH and initial phenol concentration and rising of the contact time. Conclusion. Results showed that the light easily passes through four layers of coating (about 105 nm). The highest removal efficiency of phenol with photocatalytic UV/TiO2 process was 50% at initial phenol concentration of 30 mg/L, solution pH of 3, and 300 min contact time. The comparison of synthetic solution and petrochemical wastewater showed that at same conditions the phenol removal efficiency was equal

Prevalence of using baking soda in different types of most commonly consumed breads by Iranian people

Background: Nowadays, in most bakeries in order to accelerate bread production process and reduce work pressure on bakers, harmful chemicals like baking soda are in use. Therefore, the aim of the present study was to investigate the prevalence of using baking soda in different types of most commonly consumed breads by Iranian people. Materials and Methods: This cross-sectional descriptive study was carried out on 234 bakeries in Qom, Iran, during 2017. The proportional stratified sampling method was used to select bakeries and bakers in different districts of Qom. Age, bakery experience, education of bakers and bread's pH were collected by a questionnaire and an electrical pH meter. Results: The results showed that seventy bakeries (29.9%) of Qom were using baking soda in bread. The highest frequent use of baking soda was observed in Taftoon (38.7%) and Lavash bread (31.5%). There was a significant difference between the use of baking soda and demographic variables such as age and literacy level. The attitude and knowledge of bakery employees about the complications of the baking soda were not appropriate. Conclusions: To reduce the use of baking soda and improve their knowledge and attitude, there is a need of strict supervision and monitoring by responsible organisations, especially the Ministry of Health

Antiviral Therapeutic Potential of Curcumin: An Update

The treatment of viral disease has become a medical challenge because of the increasing incidence and prevalence of human viral pathogens, as well as the lack of viable treatment alternatives, including plant-derived strategies. This review attempts to investigate the trends of research on in vitro antiviral effects of curcumin against different classes of human viral pathogens worldwide. Various electronic databases, including PubMed, Scopus, Web of Science, and Google Scholar were searched for published English articles evaluating the anti-viral activity of curcumin. Data were then extracted and analyzed. The forty-three studies (published from 1993 to 2020) that were identified contain data for 24 different viruses. The 50% cytotoxic concentration (CC50), 50% effective/inhibitory concentration (EC50/IC50), and stimulation index (SI) parameters showed that curcumin had antiviral activity against viruses causing diseases in humans. Data presented in this review highlight the potential antiviral applications of curcumin and open new avenues for further experiments on the clinical applications of curcumin and its derivatives