This paper presents a simple and robust method for computing the bisector of two planar rational curves. We represent the correspondence between the foot points on two planar rational curves C1(t) and C2(r) as an implicit curve F(t; r) = 0, where F(t; r) is a bivariate polynomial B-spline function. Given two rational curves of degree m in the xy-plane, the curve F(t; r) = 0 has degree 4m 2, whi...

The DeWitt expansion of the matrix element M xy = x| exp −[ 1 2 (p − A) 2 + V ]t |y, (p = −i∂) in powers of t can be made in a number of ways. For x = y (the case of interest when doing one-loop calculations) numerous approaches have been employed to determine this expansion to very high order; when x = y (relevant for doing calculations beyond one-loop) there appear to be but two examples of p...

We consider the Duhamel equation ? f = g in subspace C? xy {f ([0, 1] [0, 1]) : (x, y) F (xy) for some of space and prove that if pxy=0, 0, then this is uniquely solvable x y. The commutant restricted double integration operator Wxy := ?x 0 ?y (t?) d?dt on y also described. Some other related questions are discussed.

Shastri proved[3] that every knot can be expressed as the image of a parametric function t 7→ (x(t), y(t), z(t)), where x, y, and z are polynomials in t. However, it is difficult based on his proof to actually find a polynomial knot of a given knot type. We present an algorithm for converting a piecewise linear parameterization of a knot into a polynomial parameterization of a knot of the same ...

The current report presents a case of de novo acute myeloid leukemia (AML) in a 32-year-old male. Cytogenetic analysis showed that the karyotype of the bone marrow cells was as follows: 46,XY,t(11;22)(q23;q11.2)[13]/46,X,-Y,+10,t(11;22)(q23;q11.2)[7]/47,XY,+10,t(11;22)(q23;q11.2)[1]/46,XY[1]. Fluorescence in situ hybridization analysis using a mixed lineage leukemia (MLL)-specific probe showed ...

We discuss a gauged XY model $\ensuremath{\theta}$-term on an arbitrary lattice in $1+1$ dimensions and show that the theory reduces exactly to 2d Ising dual limit of strong gauge coupling, provided topological term is defined via Villain action. phase diagram by comparing weak coupling limits perform Monte Carlo simulations at intermediate couplings. generalize duality higher-dimensional model...

We report the existence of two new topologically ordered glass phases of smectics in strained aerogel. In contrast to the case of unstrained aerogel, we find compelling theoretical arguments that a smectic in uniaxially stretched aerogel exhibits, for homeotropic nematic–aerogel alignment, a ‘smectic Bragg glass’ in the universality class of the ‘XY Bragg glass’. On the other hand, a uniaxial c...

We performed thermoelectric Hall conductivity ${\ensuremath{\alpha}}_{xy}$ measurements on single-crystal graphite in the quantum limit up to 13 T. Both electrical and transport were same crystal extract pure ${\ensuremath{\alpha}}_{xy}$, avoiding any sample quality dependence. The converges a plateau with linear dependence temperature. This behavior is analogous quantized effect (QTHE) observe...