Hoffman polynomials of nonnegative irreducible matrices and strongly connected digraphs

AbstractFor a nonnegative n×n matrix A, we find that there is a polynomial f(x)∈R[x] such that f(A) is a positive matrix of rank one if and only if A is irreducible. Furthermore, we show that the lowest degree such polynomial f(x) with tr f(A)=n is unique. Thus, generalizing the well-known definition of the Hoffman polynomial of a strongly connected regular digraph, for any irreducible nonnegative n×n matrix A, we are led to define its Hoffman polynomial to be the polynomial f(x) of minimum degree satisfying that f(A) is positive and has rank 1 and trace n. The Hoffman polynomial of a strongly connected digraph is defined to be the Hoffman polynomial of its adjacency matrix. We collect in this paper some basic results and open problems related to the concept of Hoffman polynomials

Homomorphisms, representations and characteristic polynomials of digraphs

AbstractThe existence of a homomorphism between two digraphs often implies many structural properties. We collect in this paper some characterizations of various digraph homomorphisms using matrix equations and fiber partitions. We also survey the relationship among the characteristic polynomials of a digraph and its divisors. This includes an introduction of the concept of branched coverings of digraphs, their voltage assignment representations, and a decomposition formula for the characteristic polynomial of a branched cover with branch index 1. Some open problems are included

Controlled Oxidation Studies of Coal/Refuse Fuel Blends

A study of the controlled combustion of blends of biomass materials and coals was conducted. Crushed limestone was added to the blends as an absorbent for sulfur oxides. The samples were combusted in quartz-fiber crucibles in a forced air furnace. Combustion at different times and temperatures were studied. The amount of carbon, hydrogen, and sulfur in the residues, as well as the amount of ash formed, were used as measures of combustion efficiency. The optimum temperature for combustion of most blends was found to be in the 700 - 800°C range. A study of methods for determining the amounts of inorganic and organic carbon in combustion residues was performed. The American Society for Testing and Materials (ASTM) Method D 1756 for inorganic carbon yielded accurate results but is tedious and requires a great deal of skill. An alternative method for determining inorganic carbon in combustion residues was developed

Correlation of Influenza Virus Excess Mortality with Antigenic Variation: Application to Rapid Estimation of Influenza Mortality Burden

The variants of human influenza virus have caused, and continue to cause, substantial morbidity and mortality. Timely and accurate assessment of their impact on human death is invaluable for influenza planning but presents a substantial challenge, as current approaches rely mostly on intensive and unbiased influenza surveillance. In this study, by proposing a novel host-virus interaction model, we have established a positive correlation between the excess mortalities caused by viral strains of distinct antigenicity and their antigenic distances to their previous strains for each (sub)type of seasonal influenza viruses. Based on this relationship, we further develop a method to rapidly assess the mortality burden of influenza A(H1N1) virus by accurately predicting the antigenic distance between A(H1N1) strains. Rapid estimation of influenza mortality burden for new seasonal strains should help formulate a cost-effective response for influenza control and prevention

Combined effect of celecoxib and glucosamine sulfate on inflammatory factors and oxidative stress indicators in patients with knee osteoarthritis

Purpose: To investigate the combined effect of celecoxib and glucosamine sulfate on inflammatory factors and oxidative stress indicators in patients with knee osteoarthritis (KOA).Methods: Patients were randomly assigned to two groups of 60 patients each: control group and study group. The control group received celecoxib at a dose of 200 mg/kg/day, while the study group received glucosamine sulfate (500 mg/kg) in addition to celecoxib, thrice a day. Treatment in both groups lasted 8 weeks. The serum levels of tumor necrosis factor α (TNF-α), interleukin-1 (IL-1), prostaglandin-2 (PGE2), malondialdehyde (MDA), and activity of superoxide dismutase (SOD) were assayed before and after treatment. Visual analogue scale (VAS), osteoarthritis index, Lysholm knee score scale (LKSS), and adverse reactions were also evaluated.Results: After treatment, total effectiveness was significantly higher in the study group (91.33 %) than in control group (71.67 %, p < 0.05). Serum TNF-α, IL-1 and PGE2 were significantly lesser in the glucosamine sulfate-treated patients than in control group (p < 0.05). The activity of SOD was significantly higher in glucosamine sulfate-exposed patients than control patients (p < 0.05). On the other hand, VAS and WOMAC scores were markedly lower in patients given glucosamine sulfate than in control patients (p < 0.05).Conclusion: The combination of celecoxib with glucosamine sulfate effectively reduces immune inflammatory response, oxidative stress damage, and joint pain associated with KOA.Keywords: Celecoxib, Glucosamine sulfate, Osteoarthritis, Inflammatory factors, Oxidative stres

Antiperovskite Li3OCl Superionic Conductor Films for Solid-State Li-Ion Batteries.

Antiperovskite Li3OCl superionic conductor films are prepared via pulsed laser deposition using a composite target. A significantly enhanced ionic conductivity of 2.0 × 10-4 S cm-1 at room temperature is achieved, and this value is more than two orders of magnitude higher than that of its bulk counterpart. The applicability of Li3OCl as a solid electrolyte for Li-ion batteries is demonstrated