We discuss the general theory of D-branes on Calabi-Yaus, recent results from the theory of boundary states, and new results on the spectrum of branes on the quintic CY. (Contribution to the proceedings of Strings ’99 in Potsdam, Germany.)

This is the part II of our series of two papers, “Clemens conjecture: part I”, “Clemens conjecture: part II”. Continuing from part I, in this paper we turn our attention to general quintic threefolds. In a universal quintic threefold X, we construct a family of quasi-regular deformations Bb such that the generic member in this family is non-deviated, but some special member is deviated. By the ...

In the field of mathematical physics, there exist many physically interesting nonlinear dispersive equations with peakon solutions, which are solitary waves discontinuous first-order derivative at wave peak. this paper, we apply multi-layer physics-informed neural networks (PINNs) deep learning to successfully study data-driven and periodic solutions some well-known dispersion initial-boundary ...

A method is proposed with which the locations of roots monic symbolic quintic polynomial $x^5 + a_4 x^4 a_3 x^3 a_2 x^2 a_1 x a_0$ can be determined using two resolvent quadratic polynomials: $q_1(x) = a_3$ and $q_2(x) a_0$, whose coefficients are exactly those polynomial. The different cases depend on $q_1(x)$ $q_2(x)$ some specific relationships between them. illustrated full analysis one pos...