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Yuhua Sun

Publications and source records attributed to Yuhua Sun.

41 records · Page 3Linked to original sources
arXiv2011

The cross-correlation distribution of a $p$-ary $m$-sequence of period $p^{2m}-1$ and its decimation by $\frac{(p^{m}+1)^{2}}{2(p^{e}+1)}$

Let $n=2m$, $m$ odd, $e|m$, and $p$ odd prime with $p\equiv1\ \mathrm{mod}\ 4$. Let $d=\frac{(p^{m}+1)^{2}}{2(p^{e}+1)}$. In this paper, we study the cross-correlation between a $p$-ary $m$-sequence $\{s_{t}\}$ of period $p^{2m}-1$ and its decimation $\{s_{dt}\}$. Our result shows that the cross-correlation function is six-valued and that it takes the values in $\{-1,\ \pm p^{m}-1,\ \frac{1\pm p^{\frac{e}{2}}}{2}p^{m}-1,\ \frac{(1- p^{e})}{2}p^{m}-1\}$. Also, the distribution of the cross-correlation is completely determined.

cs.IT↗
arXiv2011

$p$-ary sequences with six-valued cross-correlation function: a new decimation of Niho type

For an odd prime $p$ and $n=2m$, a new decimation $d=\frac{(p^{m}-1)^{2}}{2}+1$ of Niho type of $m$-sequences is presented. Using generalized Niho's Theorem, we show that the cross-correlation function between a $p$-ary $m$-sequence of period $p^{n}-1$ and its decimated sequence by the above $d$ is at most six-valued and we can easily know that the magnitude of the cross correlation is upper bounded by $4\sqrt{p^{n}}-1$.

cs.IT↗
arXiv2011

Inhomogeneous parabolic equations on unbounded metric measure spaces

We study inhomogeneous semilinear parabolic equations with source term f independent of time u_{t}=Δu+u^{p}+f(x) on a metric measure space, subject to the conditions that f(x)\geq 0 and u(0,x)=ϕ(x)\geq 0. By establishing Harnack-type inequalities in time t and some powerful estimates, we give sufficient conditions for non-existence, local existence, and global existence of weak solutions. This paper generalizes previous results on Euclidean spaces to general metric measure spaces.

math-ph↗
arXiv2010

Heat flow method to Lichnerowicz type equation on closed manifolds

In this paper, we establish existence results for positive solutions to the Lichnerowicz equation of the following type in closed manifolds -Δu=A(x)u^{-p}-B(x)u^{q},\quad in\quad M, where $p>1, q>0$, and $A(x)>0$, $B(x)\geq0$ are given smooth functions. Our analysis is based on the global existence of positive solutions to the following heat equation {ll} u_t-Δu=A(x)u^{-p}-B(x)u^{q},\quad in\quad M\times\mathbb{R}^{+}, u(x,0)=u_0,\quad in\quad M with the positive smooth initial data $u_0$.

math.DG↗