Abstract:
In the framework of a chiral constituent quark model, considering the contributions of $\pi$ annihilation and one-gluon annihilation, the proton-antiproton $S$-wave elastic scattering cross section experimental data can be reproduced by adjusting properly one-gluon annihilation coupling constant. Meanwhile, using the fixed model parameter, we do a dynamical calculation for all possible $S$-wave nucleon-antinucleon states, the results show that, there is no $S$-wave bound state as indicated by a strong enhancement at threshold of $p\bar{p}$ in $J/\psi$ and $B$ decays.

Abstract:
The Omega-Omega (SIJ=-6,0,0) dibaryon state is studied with the extended quark-delocalization color-screening model including a pi meson exchange tail, which reproduces the properties of the deuteron quantitatively. We find the mass of the di-Omega to be about 45 MeV lower than the Omega-Omega threshold. The effect of channel coupling due to the tensor force has been calculated and found to be small in this case. We have also studied the effect of other pseudoscalar meson exchanges and sensitivity to the short-range cutoff radius, r_0, for the meson exchanges.

Abstract:
The influence of gluon and Goldstone boson induced tensor interactions on the dibaryon masses and D-wave decay widths has been studied in the quark delocalization, color screening model. The effective S-D wave transition interactions induced by gluon and Goldstone boson exchanges decrease rapidly with increasing strangeness of the channel. The tensor contribution of K and $\eta$ mesons is negligible in this model. There is no six-quark state in the light flavor world studied so far that can become bound by means of these tensor interactions besides the deuteron. The partial D-wave decay widths of the $IJ^p={1/2}2^+$ N$\Omega$ state to spin 0 and 1 $\Lambda\Xi$ final states are 12.0 keV and 21.9 keV respectively. This is a very narrow dibaryon resonance that might be detectable in relativistic heavy ion reactions by existing RHIC detectors through the reconstruction of the vertex mass of the decay product $\Lambda\Xi$ and by the COMPAS detector at CERN or at JHF in Japan and the FAIR project in Germany in the future.

Abstract:
Through a quantitative comparative study of the properties of deuteron and nucleon-nucleon interaction with chiral quark model and quark delocalization color screening model. We show that the $\sigma$-meson exchange used in the chiral quark model can be replaced by quark delocalization and color screening mechanism.

Abstract:
Dibaryon candidates with strangeness S=-2,-3,-4,-5,-6 are studied in terms of the extended quark delocalization and color screening model. The results show that there are only a few promising low lying dibaryon states: The H and di-Omega may be marginally strong interaction stable but model uncertainties are too large to allow any definitive statement. The SIJ=-3,1/2,2 N-Omega state is 62 MeV lower than the N-Omega threshold and 24 MeV lower than the Lambda-Xi-pi threshold. It might appear as a narrow dibaryon resonance and be detectable in the RHIC detector through the reconstruction of the vertex mass of the Lambda-Xi two body decay. The effects of explicit K and eta meson exchange have been studied and found to be negligible in this model. The mechanisms of effective intermediate range attraction, sigma meson exchange and kinetic energy reduction due to quark delocalization are discussed.

Abstract:
In this paper, we consider the function field analogue of the Lehmer's totient problem. Let $p(x)\in\mathbb{F}_q[x]$ and $\varphi(q,p(x))$ be the Euler's totient function of $p(x)$ over $\mathbb{F}_q[x],$ where $\mathbb{F}_q$ is a finite field with $q$ elements. We prove that $\varphi(q,p(x))|(q^{{\rm deg}(p(x))}-1)$ if and only if (i) $p(x)$ is irreducible; or (ii) $q=3, \; p(x)$ is the product of any $2$ non-associate irreducibes of degree $1;$ or (iii) $q=2,\; p(x)$ is the product of all irreducibles of degree $1,$ all irreducibles of degree $1$ and $2,$ and the product of any $3$ irreducibles one each of degree $1, 2$ and $3$.

Abstract:
Let $X$ be a smooth projective curve over a finite field $\mathbb{F}$ with $q$ elements. For $m\geq 1,$ let $X_m$ be the curve $X$ over the finite field $\mathbb{F}_m$, the $m$-th extension of $\mathbb{F}.$ Let $K_n(m)$ be the $K$-group $K_n(X_m)$ of the smooth projective curve $X_m.$ In this paper, we study the structure of the groups $K_n(m).$ If $l$ is a prime, we establish an analogue of Iwasawa theorem in algebraic number theory for the orders of the $l$-primary part $K_n(l^m)\{l\}$ of $K_n(l^m)$. In particular, when $X$ is an elliptic curve $E$ defined over $\mathbb{F},$ our method determines the structure of $K_n(E).$ Our results can be applied to construct an efficient {\bf DL} system in elliptic cryptography.

Abstract:
Lehmer's conjecture for Ramanujan's tau function says that $\tau(n) \neq 0$ for all $n$. In this paper, we generalize D. H. Lehmer's result to give a sufficient condition for level one cusp forms $f$ such that the smallest $n$ for which the Fourier coefficients $a_n(f)=0$ must be a prime. For the unique cusp form $\Delta_{k}$ of level one and weight k with $k=16, 20, 22$, we achieve a large bound $B_k$ of $n$ such that $a_n(\Delta_k)\ne0$ for all $n

Abstract:
In this paper we mainly study the homological properties of dual modules over $k$-Gorenstein rings. For a right quasi $k$-Gorenstein ring $\Lambda$, we show that the right self-injective dimension of $\Lambda$ is at most $k$ if and only if each $M \in$mod $\Lambda$ satisfying the condition that Ext$_{\Lambda}^i(M, \Lambda)=0$ for any $1\leq i \leq k$ is reflexive. For an $\infty$-Gorenstein ring, we show that the big and small finitistic dimensions and the self-injective dimension of $\Lambda$ are identical. In addition, we show that if $\Lambda$ is a left quasi $\infty$-Gorenstein ring and $M\in$mod $\Lambda$ with grade$M$ finite, then Ext$_{\Lambda}^i($Ext$_{\Lambda ^{op}}^i($Ext$_{\Lambda}^{{\rm grade}M}(M, \Lambda), \Lambda), \Lambda)=0$ if and only if $i\neq$grade$M$. For a 2-Gorenstein ring $\Lambda$, we show that a non-zero proper left ideal $I$ of $\Lambda$ is reflexive if and only if $\Lambda /I$ has no non-zero pseudo-null submodule.

In this paper, a new
method for discovering the candidate car license plate locations is presented.
First, the image is decomposed using a Haar wavelet to get the HL band with
vertical edges. Then, the HL band image is binarized using an Otsu threshold. Next
a black top-hat algorithm is applied to reduce the effects of interfering large
continuous features other than the license plate. At this time, a moving window
based modified variance score calculation is made for areas with white pixels.
This work found that the top 3 detected rectangle windows correctly locate the
license plate regions with a success rate of about 98.2%. Moreover, the
proposed method is robust enough to locate the plates in cases where the rough
vehicle position has not been previously discovered and the cars are not
centered in the image.