On recursions for coefficients of mock theta functions

We use a generalized Lambert series identity due to the first author to present q-series proofs of recent results of Imamoglu, Raum and Richter concerning recursive formulas for the coefficients of two 3rd order mock theta functions. Additionally, we discuss an application of this identity to other mock theta functions.Comment: 21 pages, to appear in Research in Number Theor

Variations of Andrews-Beck type congruences

We prove three variations of recent results due to Andrews on congruences for $NT(m,k,n)$, the total number of parts in the partitions of $n$ with rank congruent to $m$ modulo $k$. We also conjecture new congruences and relations for $NT(m,k,n)$ and for a related crank-type function.Comment: 15 pages, typos corrected, to appear in the Journal of Mathematical Analysis and Application

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.

Noise expresses exponential growth under regime switching

Consider a given system under regime switching whose solution grows at most polynomially, and suppose that the system is subject to environmental noise in some regimes. Can the regime switching and the environmental noise work together to make the system change signicantly? The answer is yes. In this paper, we will show that the regime switching and the environmental noise will make the original system whose solution grows at most polynomially become a new system whose solution will grow exponentially. In other words, we reveal that the regime switching and the environmental noise will exppress the exponential growth

Cellulase immobilization on superparamagnetic nanoparticles for reuse in cellulosic biomass conversion

Current cellulosic biomass hydrolysis is based on the one-time use of cellulases. Cellulases immobilized on magnetic nanocarriers offer the advantages of magnetic separation and repeated use for continuous hydrolysis. Most immobilization methods focus on only one type of cellulase. Here, we report co-immobilization of two types of cellulases, β-glucosidase A (BglA) and cellobiohydrolase D (CelD), on sub-20 nm superparamagnetic nanoparticles. The nanoparticles demonstrated 100% immobilization efficiency for both BglA and CelD. The total enzyme activities of immobilized BglA and CelD were up to 67.1% and 41.5% of that of the free cellulases, respectively. The immobilized BglA and CelD each retained about 85% and 43% of the initial immobilized enzyme activities after being recycled 3 and 10 times, respectively. The effects of pH and temperature on the immobilized cellulases were also investigated. Co-immobilization of BglA and CelD on MNPs is a promising strategy to promote synergistic action of cellulases while lowering enzyme consumption