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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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Nowadays there is an ever increasing demand to obtain more accurate numericalsimulation results while at the same time using fewer computations. One area withsuch a demand is oil reservoir simulations, which builds upon Poisson's equation withvariable coefficients (PEWVC). This thesis focuses on applying and testing a high ordernumerical scheme to solve the PEWVC, namely Summation By Parts - SimultaneousApproximation Term (SBP-SAT). The thesis opens with proving that the method isconvergent at arbitrary high orders given sufficiently smooth coefficients. Theconvergence is furthermore verified in practice by test cases on the Poisson'sequation with smoothly variable permeability coefficients. To balance observed lowerboundary flux convergence, the SBP-SAT method was modified with additionalpenalty terms that were subsequently shown to work as expected. Finally theSBP-SAT method was tested on a semi-realistic model of an oil reservoir withdiscontinuous permeability. The correctness of the resulting pressure distributionvaried and it was shown that flux leakage was the probable cause. Hence theproposed SBP-SAT method performs, as expected, very well in continuous settingsbut typically allows undesirable leakage in discontinuous settings. There are possiblefixes, but these are outside the scope of this thesis.

This thesis asks the question: how can one describe the development of gated communities in Guatemala City? It collects and analyzes data on gated communities in Guatemala City in order to explore the nature of their development in a violent geographical region, which has also been neglected by the academic community. It argues that the development of gated communities in Guatemala City does not fit the mutually exclusive ‘security’ argument as scholars have made. Instead, a mixture of economic factors, social status, weak governance, and security concerns are involved as large private corporations draw upon security-related fears, unregulated development of real estate and weak governance, resulting in a disorganized model of spatial organization. This study adds to the growing body of literature on gated communities by laying the groundwork needed to fill the gap that currently exists in Central America.