• Journal of Microbiology and Biotechnology
• /
• v.3 no.4
• /
• pp.292-297
• /
• 1993

Aspergillus niger No. PFST-38 was grown on complex media in 30L agitated fermentors at various aeration rates and stirrer speeds. We could correlate the mixing time as a function of the Reynolds number and the apparent viscosity, as follows. ${\theta}_M=2.95\;\NRe^{-0.52},\;{\theta}_M=1.88\;{\eta_a}^{0.57}$ Also, the effects of the apparent viscosity (${\theta}_a$), the impeller rotational speed (N), the air flow rate ($V_s$), and the mixing time (${\theta}_M$) on the oxygen transfer coefficient, $K_L a$ were determined experimentally, and equated as follows. $K_La=12.04N^{0.88}Vs^{0.71}{n_a}^{-0.83},\;K_La=30.2N^{0.88}Vs^{0.71}{\theta_M}^{-1.45}$ $K_La$ increased as the agitation speed and the air flow rate increased. The rate of $K_La$ increase was dependent more on the rotational speed of impeller than on the air flow rate. The glucoamylase production increased with the increase of the agitation speed upto at 500 rpm and increased with the increase of air flow rate upto at 1.0 vvm. The values calculated from the above equation confirmed that the experimental maximum production of glucoamylase was achieved when the $K_La$ and the apparent viscosity of the broth were $260\;hr^{-1}$ and 1800 cps, respectively.

• Journal of the Chungcheong Mathematical Society
• /
• v.16 no.1
• /
• pp.37-48
• /
• 2003

In this paper, we show that for a pure hyponormal operator the analytic spectral subspace and the algebraic spectral subspace are coincide. Using this result, we have the following result: Let T be a decomposable operator on a Banach space X and let S be a pure hyponormal operator on a Hilbert space H. Then every linear operator ${\theta}:X{\rightarrow}H$ with $S{\theta}={\theta}T$ is automatically continuous.

• Honam Mathematical Journal
• /
• v.39 no.3
• /
• pp.379-399
• /
• 2017

The objective of this research article is to establish two relationships between q-product identities, theta function identities and combinatorial partition identities, using elementary results.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.3
• /
• pp.431-441
• /
• 2015

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. Our purpose of this study is to give new topologies on the family ${\tau}(X)$ of all topologies induced by old one and its ${\theta}$ topology and to compare them.

• Communications of the Korean Mathematical Society
• /
• v.30 no.1
• /
• pp.35-43
• /
• 2015

We study two types of 1-lightlike submanifolds, so-called lightlike hypersurface and half lightlike submanifold, of an indefinite trans-Sasakian manifold $\bar{M}$ admitting non-metric ${\theta}$-connection. We prove that there exist no such two types of 1-lightlike submanifolds of an indefinite trans-Sasakian manifold $\bar{M}$ admitting non-metric ${\theta}$-connections.

• Proceedings of the IEEK Conference
• /
• 1998.10a
• /
• pp.179-182
• /
• 1998

Carrier recovery, the process of recoverying the carrier in receiver, removes the phase difference between VCO and the received signal. However, the conventional structure of carrier recovery cannot be applied to multi-level QAM demodulator because of the increasing decision interval and the complexity of control as the number of symbol increases. In this paper, we suggest a new carrier recovery algorithm using $\theta-matching$ algorithm for multi-level QAM demodulation to overcome this problem and analysis the performance and implement it.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2003.09b
• /
• pp.45-48
• /
• 2003

We propose some properties of Bayesian fuzzy hypotheses testing by revision for prior possibility distribution and posterior possibility distribution using weighted fuzzy hypotheses H$\sub$0/($\theta$) versus H$_1$($\theta$) on $\theta$ with loss function.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2001.12a
• /
• pp.349-352
• /
• 2001

We propose one properties of Bayesian fuzzy hypotheses testing by revision for prior possibility distribution and posterior possibility distribution using weighted fuzzy hypotheses H$\sub$0/($\theta$) versus H$_1$($\theta$) on $\theta$.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.937-956
• /
• 2018

This article gives the foundations of the colored Jones polynomial for singular knots. We extend Masbum and Vogel's algorithm [26] to compute the colored Jones polynomial for any singular knot. We also introduce the tail of the colored Jones polynomial of singular knots and use its stability properties to prove a false theta function identity that goes back to Ramanujan.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.345-354
• /
• 2020

In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of ₂𝜓₂ series $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a,c;q)_n}{(b,d;q)_n}}z^n$$ and Ramanujan's sum $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a;q)_n}{(b;q)_n}}z^n$$.