A sequence fxng generates by the formula x_{n+1} =(1- £\\_n)x_n+ £\\_nT_nx_n is called the Krasnosel'skii-Mann algorithm, where {£\\_n} is a sequence in (0,1) and {T_n} is a sequence of nonexpansive mappings. We introduce KM algorithm and prove that the sequence fxng generated by KM algorithm converges weakly. This result is used to solve the split feasibility problem which is to find a point x with the property that x ∈ C and Ax ∈ Q, where C and Q are closed convex subsets form H1 to H2, respectively, and A is a bounded linear operator form H1 to H2. The purpose of this paper is to present some results which apply KM algorithm to solve the split feasibility problem, the multiple-set split feasibility problem and other applications.

In recent years, new approaches to the problem of Automated Target Recognition using techniques of shape theory and algebraic geometry have been explored. The power of this shape theoretic approach is that it allows one to develop tests for object/image matching that do not require knowledge of the object’s position in relation to the sensor nor the internal parameters of the sensor. Furthermore, these methods do not depend on the choice of coordinate systems in which the objects and images are represented. In this dissertation, we will expand on existing shape theoretic techniques and adapt these techniques to new sensor models. In each model, we develop an appropriate notion of shape for our objects and images and define the spaces of such shapes. The goal in each case is to develop tests for matching object and image shapes under an appropriate class of projections. The first tests we develop take the form of systems of polynomial equations (the so-called object/image relations) that check for exact matches of object/image pairs. Later, a more robust approach to matching is obtained by defining metrics on the shape spaces. This allows us in each model to develop a measure of “how close” an object is to being able to produce a given image. We conclude this dissertation by computing a number of examples using these tests for object/image matching.

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<p>Savant syndrome is a rare condition in which some people have extraordinary talents despite some serious mental or physical disability. It is a syndrome with remarkable features, standing in stark contrast to a person’s overall character. The term savant, or idiot savant, describes a person who, in spite of low intelligence, has a skill in some specific narrow area. Savants can have a specific talent in, for instance, music, art, calendar calculation or foreign language but whatever the specific talent is, it is always connected to extraordinary memory. Savant syndrome seems to be also connected to autism or autistic characteristics. In this paper I aim to give a clear description of the savant syndrome and explain its connection to autism. Further, I present how specific theories try to describe the causes of savant syndrome, and connect the theories to results of empirical research in order to give an overall view of the syndrome’s appearance. I will also compare the theories and evaluate their strengths and weaknesses with respect to the discoveries and progress that has been made within the area of savant syndrome research.</p>

The Reproducing Kernel Element Method is a numerical technique that combines finite element and meshless methods to construct shape functions of arbitrary order and continuity, yet retains the Kronecker-d property. Central to constructing these shape functions is the construction of global partition polynomials on an element. This dissertation shows that asymmetric interpolations may arise due to such things as changes in the local to global node numbering and that may adversely affect the interpolation capability of the method. This issue arises due to the use in previous formulations of incomplete polynomials that are subsequently non-affine invariant. This dissertation lays out the new framework for generating general, symmetric, truly minimal and complete affine invariant global partition polynomials for triangular and tetrahedral elements. It is shown that this new class of reproducing kernel element solves the asymmetry issue that affected previous developed elements. The interpolation capabilities of this new class of reproducing kernel elements is studied in problems of surface representations and in solving problems of bending of thin plates using a Galerkin approach. Optimal convergence rates were observed in the solution of Kirchhoff plate problems with rectangular domains. Furthermore, it is shown that the new proposed two-dimensional elements out perform the previous elements with the addition of only a few internal degrees of freedom.

Magistro darbe nagrinėjamas Oilerio sandaugų reikšmių pasiskirstymas analizinių funkcijų erdvėje. Taip pat gaunamas išreikštinis ribinio mato pavidalas. / In the Master work, we investigate the value-distribution of Euler products in the space of analytic functions. Also, we give an explicit form of the limit measure.

For degenerate elliptic partial differential equations, it is often desirable to show that a weak solution is smooth. The first and most difficult step in this process is establishing local Hölder continuity. Sufficient conditions for establishing continuity have already been documented in [FP], [SW1], and [MRW], and their necessity in [R]. However, the complexity of the equations discussed in those works makes it difficult to understand the core structure of the arguments employed. Here, we present a harmonic-analytic method for establishing Hölder continuity of weak solutions in context of a simple linear equation div(Q?u) = f in a homogeneous space structure in order to showcase the form of the argument. Ad- ditionally, we correct an oversight in the adaptation of the John-Nirenberg inequality presented in [SW1], restricting it to a much smaller class of balls.

Tegul s=σ+it yra kompleksinis kintamasis. Oilerio sandaugos yra apibrėžiamos pagal pirminius skaičius, taip pat yra reikalaujama, kad funkcija L(s) tenkintų papidomas sąlygas. Mes įrodome diskrečią ribinę teoremą tikimybinių matų silpno konvergavimo prasme kompleksinėje plokštumoje C Oilerio sandaugoms. / Let s=σ+it be a complex variable. The Euler products L(s) is defined by the prime number. If the function L(s) satisfies some additional hypotheses. In the Master work we prove the discrete limit theorem in the sense of weakly convergent probability measures for the Euler products on the complex plane.

Tegul s yra kompleksinis kintamasis. Oilerio sandaugos apibrėžiamos pagal pirminius p skaičius. Funkcija L(s) turi tenkinti hipotezes. Magistro darbe, įrodome diskrečią ribinę teoremą silpno tikimybinių matų konvergavimo prasme Oilerio sandaugoms kompleksinėje plokštumoje. Gauta mato išreikštinė forma. / Let s be a complex variable. The Euler products is defined by the prime number p. The Function L(s) satisfies some additional hypoteses. In Master work, we prove the discrete limit theorem in the sense of weakly convergent probability measures for the Euler products on the complex plane. Then the probability measure weakly converges to the distribution of one explicitly given complex-valued random element as N-> infinity.

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