Estimating Mass of Sigma-Meson and Study on Application of the Linear Sigma-Model

Whether the $\sigma-meson$ ($f_0(600)$) exists as a real particle is a long-standing problem in both particle physics and nuclear physics. In this work, we analyze the deuteron binding energy in the linear $\sigma$ model and by fitting the data, we are able to determine the range of $m_{\sigma}$ and also investigate applicability of the linear $\sigma$ model for the interaction between hadrons in the energy region of MeV's. Our result shows that the best fit to the data of the deuteron binding energy and other experimental data about deuteron advocates a narrow range for the $\sigma-$meson mass as $520\leq m_{\sigma}\leq 580$ MeV and the concrete values depend on the input parameters such as the couplings. Inversely fitting the experimental data, our results set constraints on the couplings. The other relevant phenomenological parameters in the model are simultaneously obtained.Comment: 12 page

Bivariate functions with low c-differential uniformity

Starting with the multiplication of elements in F2 q which is consistent with that over Fq2 , where q is a prime power, via some identification of the two environ- ments, we investigate the c-differential uniformity for bivariate functions F (x, y) = (G(x, y), H(x, y)). By carefully choosing the functions G(x, y) and H(x, y), we present several constructions of bivariate functions with low c-differential unifor- mity, in particular, many PcN and APcN functions can be produced from our con- structions.acceptedVersio

Bivariate functions with low cc-differential uniformity

Starting with the multiplication of elements in $\mathbb{F}_{q}^2$ which is consistent with that over $\mathbb{F}_{q^2}$, where $q$ is a prime power, via some identification of the two environments, we investigate the $c$-differential uniformity for bivariate functions $F(x,y)=(G(x,y),H(x,y))$. By carefully choosing the functions $G(x,y)$ and $H(x,y)$, we present several constructions of bivariate functions with low $c$-differential uniformity. Many P$c$N and AP$c$N functions can be produced from our constructions.Comment: Low $c$-differential uniformity, perfect and almost perfect $c$-nonlinearity, the bivariate functio

Infinite families of optimal and minimal codes over rings using simplicial complexes

In this paper, several infinite families of codes over the extension of non-unital non-commutative rings are constructed utilizing general simplicial complexes. Thanks to the special structure of the defining sets, the principal parameters of these codes are characterized. Specially, when the employed simplicial complexes are generated by a single maximal element, we determine their Lee weight distributions completely. Furthermore, by considering the Gray image codes and the corresponding subfield-like codes, numerous of linear codes over $\mathbb{F}_q$ are also obtained, where $q$ is a prime power. Certain conditions are given to ensure the above linear codes are (Hermitian) self-orthogonal in the case of $q=2,3,4$. It is noteworthy that most of the derived codes over $\mathbb{F}_q$ satisfy the Ashikhmin-Barg's condition for minimality. Besides, we obtain two infinite families of distance-optimal codes over $\mathbb{F}_q$ with respect to the Griesmer bound.Comment: 26 page

LGmap: Local-to-Global Mapping Network for Online Long-Range Vectorized HD Map Construction

This report introduces the first-place winning solution for the Autonomous Grand Challenge 2024 - Mapless Driving. In this report, we introduce a novel online mapping pipeline LGmap, which adept at long-range temporal model. Firstly, we propose symmetric view transformation(SVT), a hybrid view transformation module. Our approach overcomes the limitations of forward sparse feature representation and utilizing depth perception and SD prior information. Secondly, we propose hierarchical temporal fusion(HTF) module. It employs temporal information from local to global, which empowers the construction of long-range HD map with high stability. Lastly, we propose a novel ped-crossing resampling. The simplified ped crossing representation accelerates the instance attention based decoder convergence performance. Our method achieves 0.66 UniScore in the Mapless Driving OpenLaneV2 test set