Abstract. In this article we study the 2-Selmer groups of number fields F as well as some related groups, and present connections to the quadratic reciprocity law in F. Let F be a number field; elements in F × that are ideal squares were called singular numbers in the classical literature

fitting three-dimensional surfaces of stress components and potential strain energy. Examples of cracks named in the paper as PR-Z-16 and PR-P-22, with exactly the same geometry of crack and plate are analyzed. The same finite element lattice for calculation in both cases is selected. The first example

The authors investigate the behavior of buoyancy-driven coastal currents in a series of numerical experiments based on a two-layer frontal geostrophic model. The model focuses on baroclinic instability, allows for finite amplitude variations in the upper-layer thickness, and includes a topographic background vorticity gradient. Simulations of isolated fronts demonstrate meandering of the frontal outcropping, filamentation, and the de-velopment of both warm core and cold core eddies. Eddies can merge with each other, separate, or be reabsorbed into the current. Despite the assumption of only two layers, it is found that growth rates and length scales of the emergent features are in agreement with results of studies based on more sophisticated primitive equation models. It is determined that the cross-front topographic slope has a significant effect on the instability. In particular, a bottom that slopes in the same sense as the fluid interface hinders the growth of perturbations. Simulations with two outcroppings (i.e., coupled fronts) are also described. The authors found that such currents break up into distinct vortices that propagate very little but exhibit merging and splitting, behavior consistent with previous numerical studies involving similar models as well as laboratory experiments. Finally, an analytical nonlinear wave-packet stability theory for a marginally unstable flow with a simple linearly varying height profile is presented. The authors show that the unstable modes can saturate as solitons. 1.

Introduction and aim of the work Deployment of wave energy converters (WECs) in large arrays is envisaged as a fundamental market ac-celeration strategy towards the commmercialisation of wave energy systems. When working together in

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Abstract — Given some geometric elements such as points and lines in , subject to a set of pairwise distance constraints, the problem tackled in this paper is that of finding all possible configurations of these elements that satisfy the constraints. Many problems in Robotics (such

facilitated the task of understanding complex sys-tems at cellular and molecular levels in recent years. Segmentation, an important yet dif-ficult problem, is often the first processing step following acquisition. Our team previously demonstrated that a stochastic active contour based algorithm together

fundamental frequency (F 0 ), standard deviation of F 0 , and F 0 range, in semitones (st); mean intensity, standard deviation of intensity, and intensity range, in decibels (dB); and speech rate (syllables per second). The intonationdependent variable was the shape of the contour (linear, quadratic

ii iii CHRISTOPHER CHARLES WEIGLE: Displays for Exploration and Comparison of Nested

Algebraic algorithms deal with numbers, vectors, matrices, polynomials, for-mal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matri-ces and polynomials is fundamental for modern computations