Consider the following question. Given a suitable linear series L on a smooth surface S, how many curves in L have a given analytic or topological type of singularity? By “suitable” linear series with respect to a type of singularity, we mean that there are finitely many curves with the singularity in the linear series and their codimension is maximal. Our approach to this question is to expres...

The notion of a generalized helix in R3, a curve making a constant angle with a fixed direction, can be generalized to higher dimensions in many ways. In [7] the same definition is proposed but in R. In [4] the definition is more restrictive: the fixed direction makes a constant angle with all the vectors of the Frenet frame. It is easy to check that this definition only works in the odd dimens...

creep phenomenon in rock engineering plays a key role in development of underground spaces as they must be stable enough for a long period of time. current research involved designing and manufacturing of a new creep testing machine. the equipment is capable to perform simultaneous light-duty creep tests on more than one cylindrical rock samples at a very low cost.to evaluate the equipment’s pe...

We generalize the Allais common consequence effect by describing three common consequence effect conditions and characterizing their implications for the probability weighting function in rank-dependent expected utility. The three conditions—horizontal, vertical, and diagonal shifts within the probability triangle—are necessary and sufficient for different curvature properties of the probabilit...

The velocity-response curves of the cat's superior colliculus neurons responding to moving stimuli mere studied quantitatively. They were fitted by logarithmic Gaussian curves described by three parameters: optimal stimulus velocity, amplitude and dispersion of the curve. Since reversal of the stimulus movement direction changed neither optimal stimulus velocity nor dispersion of the velocity t...

All rational parametric curves with prescribed polynomial tangent direction form a vector space. Via directions norm, this includes the important case of Pythagorean hodograph curves. We study subspaces defined by fixing denominator and describe construction canonical bases for them. also show (as an analogy to fraction decomposition functions) that any element space can be obtained as finite s...

The general equation from previous work is specialized to a linear potential V (r) = −a + F r acting in the space of spherically symmetric S wave functions. The fine and hyperfine interaction creates then a 1 r -dependence in the effective potential energy equation and a position dependent mass m̃(r) in the effective kinetic energy of the associated Schrödinger equation. The results are compared...

1. This study tested the hypothesis that muscle synergies underlie the invariance in the direction of corrective forces observed following stance perturbations in the horizontal plane. Electromyographic activity was recorded from selected forelimb and hindlimb muscles of cats subjected to horizontal translations of the supporting surface in 16 different directions. The responses of muscles were...

1997 2 Kevin Lee James On con gruences for the coefficients of modular forms and some applications (Under the direction of Andrew Granville) In this dissertation, we will study two different conjectures about elliptic curves and modular forms. First, we will exploit the theory developed by Shimura and Waldspurger to address Goldfeld's conjecture which states that the density of rank zero curves...