In this paper, we prove a conjecture of Alexandrov that the generalized Brézin-Gross-Witten tau-functions are hypergeometric tau functions BKP hierarchy after re-scaling. particular, shows original BGW tau-function, which has enumerative geometric interpretations, can be represented as linear combination Schur Q-polynomials with simple coefficients.

the gravity recovery and climate experiment (grace), twin satellites launched in march 2002, are making detailed measurements of the earth's gravity field. it will yield discoveries about gravity and the earth's natural systems. different sensors and instruments have been placed in the grace satellites to fulfill the primary scientific objective of the mission in mapping the earth’s g...

We consider the number of zeros of the integral $I(h) = oint_{Gamma_h} omega$ of real polynomial form $omega$ of degree not greater than $n$ over a family of vanishing cycles on curves $Gamma_h:$ $y^2+3x^2-x^6=h$, where the integral is considered as a function of the parameter $h$. We prove that the number of zeros of $I(h)$, for $0 < h < 2$, is bounded above by $2[frac{n-1}{2}]+1$.

A well-designed loss function can effectively improve the characterization ability of network features without increasing amount calculation in model inference stage, and has become focus attention recent research. Given that existing lightweight adds a to last layer, which severely attenuates gradient during backpropagation process, we propose hierarchical polynomial kernel prototype this stud...