A Revisit to Quadratic Programming with One Inequality Quadratic Constraint via Matrix Pencil

The quadratic programming over one inequality quadratic constraint (QP1QC) is a very special case of quadratically constrained quadratic programming (QCQP) and attracted much attention since early 1990's. It is now understood that, under the primal Slater condition, (QP1QC) has a tight SDP relaxation (PSDP). The optimal solution to (QP1QC), if exists, can be obtained by a matrix rank one decomposition of the optimal matrix X? to (PSDP). In this paper, we pay a revisit to (QP1QC) by analyzing the associated matrix pencil of two symmetric real matrices A and B, the former matrix of which defines the quadratic term of the objective function whereas the latter for the constraint. We focus on the \undesired" (QP1QC) problems which are often ignored in typical literature: either there exists no Slater point, or (QP1QC) is unbounded below, or (QP1QC) is bounded below but unattainable. Our analysis is conducted with the help of the matrix pencil, not only for checking whether the undesired cases do happen, but also for an alternative way to compute the optimal solution in comparison with the usual SDP/rank-one-decomposition procedure.Comment: 22 pages, 0 figure

Deflationary Expansion : an Overshooting Perspective to the Recent Business Cycle in China

Deflationary expansion has puzzled economists both in and outside China. We study this business cycles phenomenon within a model of discrete time dynamics. We find that deflationary expansion could be possible if driven by an overshooting in investing and if the state of the economy maintains high rate of growth. This expression is consistent with the recent variables. The high steady state of growth could be explained by the current institutional environment of China.Deflationary Expansion, China, Existence and Stability Conditions of Equilibrium, Business Fluctuations, monetary policy, Central Banking, Supply of Money and Credit

Ds+ -- Ds- Asymmetry in Photoproduction

Considering of the possible difference in strange and antistrange quark distributions inside nucleon, we investigate the Ds+ -- Ds- asymmetry in photoproduction in the framework of heavy-quark recombination mechanism. We adopt two distribution models of strange sea, those are the light-cone meson-baryon fluctuation model and the effective chiral quark model. Our results show that the asymmetry induced by the strange quark distributions is distinct, which is measurable in experiments. And, there are evident differences between the predictions of our calculation and previous estimation. Therefore, the experimental measurements on the Ds+ -- Ds- asymmetry may impose a unique restriction on the strange-antistrange distribution asymmetry models.Comment: 11 page, 5 figure

Possible Deuteron-like Molecular States Composed of Heavy Baryons

We perform a systematic study of the possible loosely bound states composed of two charmed baryons or a charmed baryon and an anti-charmed baryon within the framework of the one boson exchange (OBE) model. We consider not only the $\pi$ exchange but also the $\eta$, $\rho$, $\omega$, $\phi$ and $\sigma$ exchanges. The $S-D$ mixing effects for the spin-triplets are also taken into account. With the derived effective potentials, we calculate the binding energies and root-mean-square (RMS) radii for the systems $\Lambda_c\Lambda_c(\bar{\Lambda}_c)$, $\Xi_c\Xi_c(\bar{\Xi}_c)$, $\Sigma_c\Sigma_c(\bar{\Sigma}_c)$, $\Xi_c^\prime\Xi_c^\prime(\bar{\Xi}_c^\prime)$ and $\Omega_c\Omega_c(\bar{\Omega}_c)$. Our numerical results indicate that: (1) the H-dibaryon-like state $\Lambda_c\Lambda_c$ does not exist; (2) there may exist four loosely bound deuteron-like states $\Xi_c\Xi_c$ and $\Xi_c^\prime\Xi_c^\prime$ with small binding energies and large RMS radii.Comment: 17 pages, 32 figure

Prompt heavy quarkonium production in association with a massive (anti)bottom quark at the LHC

In this work, we investigate the associated production of prompt heavy quarkonium with a massive (anti)bottom quark to leading order in the NRQCD factorization formalism at the LHC. We present numerical results for the processes involving $J/\psi,\chi_{cJ},\Upsilon$ and $\chi_{bJ}$. From our work, we find that the production rates of these processes are quite large, and these processes have the potential to be detected at the LHC. When $p_T$ is smaller than about 10 GeV, the $c\bar{c} [ ^1S_0^{(8)} ]$ state give the main contribution to the $p_T$ distribution of prompt $J/\psi$ with a (anti)bottom quark production. For the process of $pp \to \Upsilon+b(\bar{b})$, the contribution of the CSM is larger than that in the COM at low $p_T$ region. We also investigate the processes of $pp\to \chi_{cJ}+b(\bar{b})$ and $pp \to \chi_{bJ}+b(\bar{b})$, in these processes, the $p_T$ distribution are dominated by the CO Fock state contribution at the large $p_T$ region. These processes provide an interesting signature that could be studied at the LHC, and the measurement of these processes is useful to test the CSM and COM.Comment: 14 pages, 11 figures, accepted by Phys.Rev.

B_{s1}(5830) and B_{s2}^*(5840)

In this paper we investigate the strong decays of the two newly observed bottom-strange mesons $B_{s1}(5830)$ and $B_{s2}^*(5840)$ in the framework of the quark pair creation model. The two-body strong decay widths of $B_{s1}(5830)^0\to B^{*+}K^-$ and $B_{s2}^*(5840)^0\to B^+K^-, B^{*+}K^-$ are calculated by considering $B_{s1}(5830)$ to be a mixture between $|^1P_1>$ and $|^3P_1>$ states, and $B_{s2}^*(5840)$ to be a $|^3P_2>$ state. The double pion decay of $B_{s1}(5830)$ and $B_{s2}^*(5840)$ is supposed to occur via the intermediate state $\sigma$ and $f_0(980)$. Although the double pion decay widths of $B_{s1}(5830)$ and $B_{s2}^*(5840)$ are smaller than the two-body strong decay widths of $B_{s1}(5830)$ and $B_{s2}^*(5840)$, one suggests future experiments to search the double pion decays of $B_{s1}(5830)$ and $B_{s2}^*(5840)$ due to their sizable decay widths.Comment: 9 pages, 8 figures and 6 tables. More references and discussions added, typos corrected, some descriptions changed. Publication version in PR