An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

Comparison between analytical and numerical methods for the assessment of masonry arch bridges: Case study of Clemente Bridge on Savio river

This research has focused on the study of the behavior and of the collapse of masonry arch bridges. The latest decades have seen an increasing interest in this structural type, that is still present and in use, despite the passage of time and the variation of the transport means. Several strategies have been developed during the time to simulate the response of this type of structures, although even today there is no generally accepted standard one for assessment of masonry arch bridges. The aim of this thesis is to compare the principal analytical and numerical methods existing in literature on case studies, trying to highlight values and weaknesses. The methods taken in exam are mainly three: i) the Thrust Line Analysis Method; ii) the Mechanism Method; iii) the Finite Element Methods. The Thrust Line Analysis Method and the Mechanism Method are analytical methods and derived from two of the fundamental theorems of the Plastic Analysis, while the Finite Element Method is a numerical method, that uses different strategies of discretization to analyze the structure. Every method is applied to the case study through computer-based representations, that allow a friendly-use application of the principles explained. A particular closed-form approach based on an elasto-plastic material model and developed by some Belgian researchers is also studied. To compare the three methods, two different case study have been analyzed: i) a generic masonry arch bridge with a single span; ii) a real masonry arch bridge, the Clemente Bridge, built on Savio River in Cesena. In the analyses performed, all the models are two-dimensional in order to have results comparable between the different methods taken in exam. The different methods have been compared with each other in terms of collapse load and of hinge positions.

On the incoming water waves against a vertical cliff

The problems of obliquely incident surface water waves against a vertical cliff have been handled in both the cases of water of infinite as well as finite depth by straightforward uses of appropriate Havelock-type expansion theorems. The logarithmic singularity along the shore-line has been incorporated in a direct manner, by suitably representing the Dirac's delta function.

The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships with fundamental theorems of convex analysis. The second part is about externality in sponsored search auctions. It shows that in these auctions, advertisers have externality effects on each other which influence their bidding behavior. It proposes Hal R.Varian model and shows how adding externality to this model will affect its properties. In order to have a better understanding of the interaction among advertisers in on-line auctions, it studies the structure of the Google advertisements networ.k and shows that it is a small-world scale-free network.

Análise funcional e aplicações

Pós-graduação em Matemática Universitária - IGCE

On the properness of an impulsive control extension of dynamic optimization problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On Properness of Impulsive Extension

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Structural optimization

The non-linear programming algorithms for the minimum weight design of structural frames are presented in this thesis. The first, which is applied to rigidly jointed and pin jointed plane frames subject to deflexion constraints, consists of a search in a feasible design space. Successive trial designs are developed so that the feasibility and the optimality of the designs are improved simultaneously. It is found that this method is restricted lo the design of structures with few unknown variables. The second non-linear programming algorithm is presented .in a general form. This consists of two types of search, one improving feasibility and the other optimality. The method speeds up the 'feasible direction' approach by obtaining a constant weight direction vector that is influenced by dominating constraints. For pin jointed plane and space frames this method is used to obtain a 'minimum weight' design which satisfies restrictions on stresses and deflexions. The matrix force method enables the design requirements to be expressed in a general form and the design problem is automatically formulated within the computer. Examples are given to explain the method and the design criteria are extended to include member buckling. Fundamental theorems are proposed and proved to confirm that structures are inter-related. These theorems are applicable to linear elastic structures and facilitate the prediction of the behaviour of one structure from the results of analysing another, more general, or related structure. It becomes possible to evaluate the significance of each member in the behaviour of a structure and the problem of minimum weight design is extended to include shape. A method is proposed to design structures of optimum shape with stress and deflexion limitations. Finally a detailed investigation is carried out into the design of structures to study the factors that influence their shape.

Fractional Korovkin Theory Based on Statistical Convergence

2000 Mathematics Subject Classification: 41A25, 41A36, 40G15.

Some theorems in asymptotic analysis

Basing ourselves on the analysis of magnitude of order, we strictly prove fundamental lemmas for asymptotic integral, including the cases of infinite region. Then a general formula for asymptotic expansion of integrals is given. Finally, we derive a sufficient condition for an ordinary differential equation to possess a solution of the Frobenius series type at finite irregular singularities or branching points.

Coincidence and common fixed point theorems for Suzuki type hybrid contractions and applications

Coincidence and common fixed point theorems for a class of Suzuki hybrid contractions involving two pairs of single-valued and multivalued maps in a metric space are obtained. In addition, the existence of a common solution for a certain class of functional equations arising in a dynamic programming is also discussed.

Whitney's type theorems for infinite dimensional spaces

It is proved that for any $f$ is an element of $C^k(L,R)$, where k is a natural number and L is a closed linear subspace of a nuclear Frechet space $X$, the function $f$ can be extended to a function of class $C^{k-1}$ defined on the entire space $X$. It is also proved that for any $f$ is an element of $C^k(L, R)$, where $k$ is a natural number of infinity and L is a closed linear subspace of a dual $X$ of a nuclear Frechet space, the function $f$ can be extended to a function of class $C^k$ defined on the entire space $X$. In addition, it is proved that under these conditions, the existence of a linear extension operator is equivalent to the complementability of the subspace.

On Szegö’s Type Theorems

This study is to look the effect of change in the ordering of the Fourier system on Szegö’s classical observations of asymptotic distribution of eigenvalues of finite Toeplitz forms.This is done by checking proofs and Szegö’s properties in the new set up.The Fourier system is unconditional [19], any arbitrary ordering of the Fourier system forms a basis for the Hilbert space L2 [-Π, Π].Here study about the classical Szegö’s theorem.Szegö’s type theorem for operators in L2(R+) and check its validity for certain multiplication operators.Since the trigonometric basis is not available in L2(R+) or in L2(R) .This study discussed about the classes of orderings of Haar System in L2 (R+) and in L2(R) in which Szegö’s Type TheoreT Am is valid for certain multiplication operators.It is divided into two sections. In the first section there is an ordering to Haar system in L2(R+) and prove that with respect to this ordering, Szegö’s Type theorem holds for general class of multiplication operators Tƒ with multiplier ƒ ε L2(R+), subject to some conditions on ƒ.Finally in second section more general classes of ordering of Haar system in L2(R+) and in L2(R) are identified in such a way that for certain classes of multiplication operators the asymptotic distribution of eigenvalues exists.