Generalized variational inequalities and generalized quasi-variational inequalities

AbstractA very general minimax inequality is first established. Three generalized variational inequalities are then derived, which improve those obtained by Tan and Browder. By applying a fixed point theorem of Himmelberg, two generalized quasi-variational inequalities are also proved, one of which generalizes those of Shih-Tan to the non-compact case with much weaker hypotheses and in a more general setting

Generalized bi-quasi-variational inequalities

AbstractLet E, F be Hausdorff topological vector spaces over the field Φ (which is either the real field or the complex field), let 〈 , 〉: F × E → Φ be a bilinear functional, and let X be a non-empty subset of E. Given a multi-valued map S: X → 2x and two multi-valued maps M, T: X → 2F, the generalized bi-quasi-variational inequality (GBQVI) problem is to find a point ŷ ϵ X such that ŷ ϵ S(ŷ) and infw ϵ T(ȳ)Re〈ƒ − w, ŷ − x〉 ⩽ 0 for all x ϵ S(ŷ) and for all ƒ ϵ M(ŷ). In this paper two general existence theorems on solutions of GBQVIs are obtained which simultaneously unify, sharpen, and extend existence theorems for multi-valued versions of Hartman-Stampacchia variational inequalities proved by Browder and by Shih and Tan, variational inequalities due to Browder, existence theorems for generalized quasi-variational inequalities achieved by Shih and Tan, theorems for monotone operators obtained by Debrunner and Flor, Fan, and Browder, and the Fan-Glicksberg fixed-point theorem

Generalized Games and Non-compact Quasi-variational Inequalities

AbstractIn this paper, by developing an approximation approach which is originally due to Tuleca in 1986, we prove the existence of equilibria for generalized games in which constraint mappings (correspondences) are lower (resp., upper) semicontinuous instead of having lower (resp., upper) open sections or open graphs in infinite dimensional topological spaces. Then, existence theorems of solutions for quasi-variational inequalities and non-compact generalized quasi-variational inequalities are also established. Finally, existence theorems of constrained games with non-compact strategy sets are derived. Our results unify and generalize many well known results given in the existing literature. In particular, we answer the question raised by Yannelis and Prabhakar in 1983 in the affirmative under more weaker conditions

Protective coating for gabion wires against weathering elements and site conditions

Gabions are one of the most essential elements in the geotechnical field for their versatility and strength in slope stabilization. According to BS 8002:2015, gabions are rectangular large cages or baskets made of either steel wire or square welded mesh, and are usually filled with stones. Besides slope stabilization, gabions have been widely used for various purposes, including closing of river banks, road construction, landslide consolidation and hilly terrain reclamation [1]

Posterolateral spinal fusion with ostegenesis induced BMSC seeded TCP/HA in a sheep model

Autogenous bone graft is the gold standard for fusion procedure. However, pain at donor site and inconsistent outcome have left a surgeon to venture into some other technique for spinal fusion. The objective of this study was to determine whether osteogenesis induced bone marrow stem cells with the combination of ceramics granules (HA or TCP/HA), and fibrin could serve as an alternative to generate spinal fusion. The sheep's bone marrow mesenchymal stem cells (BMSCs) were aspirated form iliac crest and cultured for several passages until confluence. BMSCs were trypsinized and seeded on hydroxyapatite scaffold (HA) and tricalcium phosphate/hydroxyapatite (TCP/HA) for further osteogenic differentiation in the osteogenic medium one week before implantation. Six adult sheep underwent three-level, bilateral, posterolateral intertransverse process fusions at L1–L6. Three fusion sites in each animal were assigned to three treatments: (a) HA constructs group/L1–L2, (b) TCP/HA constructs group/L2–L3, and (c) autogenous bone graft group/L5–L6. The spinal fusion segments were evaluated using radiography, manual palpation, histological analysis and scanning electron microscopy (SEM) 12 weeks post implantation. The TCP/HA constructs achieved superior lumbar intertransverse fusion compared to HA construct but autogenous bone graft still produced the best fusion among all

Tricalcium phosphate/hydroxyapatite (TCP-HA) bone scaffold as potential candidate for the formation of tissue engineered bone

Background & objectives: Various materials have been used as scaffolds to suit different demands in tissue engineering. One of the most important criteria is that the scaffold must be biocompatible. This study was carried out to investigate the potential of HA or TCP/HA scaffold seeded with osteogenic induced sheep marrow cells (SMCs) for bone tissue engineering. Methods: HA-SMC and TCP/HA-SMC constructs were induced in the osteogenic medium for three weeks prior to implantation in nude mice. The HA-SMC and TCP/HA-SMC constructs were implanted subcutaneously on the dorsum of nude mice on each side of the midline. These constructs were harvested after 8 wk of implantation. Constructs before and after implantation were analyzed through histological staining, scanning electron microscope (SEM) and gene expression analysis. Results: The HA-SMC constructs demonstrated minimal bone formation. TCP/HA-SMC construct showed bone formation eight weeks after implantation. The bone formation started on the surface of the ceramic and proceeded to the centre of the pores. H&E and Alizarin Red staining demonstrated new bone tissue. Gene expression of collagen type 1 increased significantly for both constructs, but more superior for TCP/HA-SMC. SEM results showed the formation of thick collagen fibers encapsulating TCP/HA-SMC more than HA-SMC. Cells attached to both constructs surface proliferated and secreted collagen fibers. Interpretation & conclusions: The findings suggest that TCP/HA-SMC constructs with better osteogenic potential compared to HA-SMC constructs can be a potential candidate for the formation of tissue engineered bone

Equilibria of generalized games with L

In this paper, we shall prove three equilibrium existence theorems for generalized games in Hausdorff topological vector spaces

Potential recombinant vaccine against influenza A virus based on M2e displayed on nodaviral capsid nanoparticles

Influenza A virus poses a major threat to human health, causing outbreaks from time to time. Currently available vaccines employ inactivated viruses of different strains to provide protection against influenza virus infection. However, high mutation rates of influenza virus hemagglutinin (H) and neuraminidase (N) glycoproteins give rise to vaccine escape mutants. Thus, an effective vaccine providing protection against all strains of influenza virus would be a valuable asset. The ectodomain of matrix 2 protein (M2e) was found to be highly conserved despite mutations of the H and N glycoproteins. Hence, one to five copies of M2e were fused to the carboxyl-terminal end of the recombinant nodavirus capsid protein derived from Macrobrachium rosenbergii. The chimeric proteins harboring up to five copies of M2e formed nanosized virus-like particles approximately 30 nm in diameter, which could be purified easily by immobilized metal affinity chromatography. BALB/c mice immunized subcutaneously with these chimeric proteins developed antibodies specifically against M2e, and the titer was proportional to the copy numbers of M2e displayed on the nodavirus capsid nanoparticles. The fusion proteins also induced a type 1 T helper immune response. Collectively, M2e displayed on the nodavirus capsid nanoparticles could provide an alternative solution to a possible influenza pandemic in the future