Interpreting the number of ramified covering of a Riemann surface by Riemann surfaces as the relative Gromov-Witten invariants and applying a gluing formula, we derive a recursive formula for the number of ramified covering of a Riemann surface by Riemann surface with elementary branch points and prescribed ramification type over a special point.
Defect prediction on projects with limited historical data has attracted great interest from both researchers and practitioners. Cross-project defect prediction has been the main area of progress by reusing classifiers from other projects. However, existing approaches require some degree of homogeneity (<i>e.g.</i>, a similar distribution of metric values)… (More)
The main purpose of this paper is to obtain the wellposed-ness of abstract parabolic systems in the sense of Petrovsij and Shilov under sharper conditions by using regularized semi-groups. We also consider these systems with time-dependent coeecients, and give the applications to the corresponding parabolic systems on many function spaces.
This paper proposes an adaptive photon tracing approach based on a novel importance function, which combines visual importance and photon path visibility. The generation of photon path is guided by sampling this function to trace more photons to visible and more contributive regions. As a first step, a hierarchy of visual importance maps is constructed.… (More)
This paper is concerned with Schrödinger equations whose principal operators are homogeneous elliptic. When the corresponding level hypersurface is convex, we show the L p-L q estimate of solution operator in free case. This estimate, combining with the results of fractionally integrated groups, allows us to further obtain the L p estimate of solutions for… (More)
Interpreting the number of ramified covering of the sphere by Riemann surface as the relative Gromov-Witten invariants and applying a gluing formula, we derive a recursive formula for the number of ramified covering of the sphere by Riemann surface with any genus, with elementary branch points and prescribed ramification type over infinity.
The position of a magnetic target can be obtained through magnetic anomaly which is measured by a magnetic sensor. Comparing with vector magnetic sensor, the measurement value of the scalar magnetic sensor is almost not influenced by its orientation in measurement coordinate axes. Therefore, scalar magnetic sensors can be easily assembled into an array.… (More)