• Honam Mathematical Journal
• /
• v.41 no.4
• /
• pp.781-798
• /
• 2019

This paper is designed to introduce a Hermite-based-poly-Bernoulli numbers and polynomials with q-parameter. By making use of their generating functions, we derive several summation formulae, identities and some properties that is connected with the Stirling numbers of the second kind. Furthermore, we derive symmetric identities for Hermite-based-poly-Bernoulli polynomials with q-parameter by using generating functions.

• Journal of Mechanical Science and Technology
• /
• v.18 no.12
• /
• pp.2158-2173
• /
• 2004

In this paper, the higher order terms in the crack tip stress fields are investigated macroscopically for more realistic assessment of structural material behaviors. For reactor pressure vessel material of A533B ferritic steel, effects of crack size and temperature have been evaluated using 3-point SENB specimens through a series of finite element analyses, tensile tests and fracture toughness tests. The T-stress, Q-parameter and q-parameter as well as the K and J-integral are calculated and mutual relationships are investigated also. Based on the evaluation, it has proven that the effect of crack size from standard length (a/W=0.53) to shallow length (a/W=0.11) is remarkable whilst the effect of temperature from -20$^{\circ}C$ to -60$^{\circ}C$ is negligible. Finally, the cleavage fracture toughness loci as a function of the promising Q-parameter or q-parameter are developed using specific test results as well as finite element analysis results, which can be applicable for structural integrity evaluation considering constraint effects.

• Kyungpook Mathematical Journal
• /
• v.55 no.4
• /
• pp.983-996
• /
• 2015

In the paper A new parameter for Ramanujan's theta-functions and explicit values, Arab J. Math. Sc., 18 (2012), 105-119, Saikia studied the parameter $A_{k,n}$ involving Ramanujan's theta-functions ${\phi}(q)$ and ${\psi}(q)$ for any positive real numbers k and n and applied it to find explicit values of ${\psi}(q)$. As more application to the parameter $A_{k,n}$, in this paper we prove a new general theorem for explicit evaluation of Ramanujan-$G{\ddot{o}}llnitz$-Gordon continued fraction K(q) in terms of the parameter $A_{k,n}$ and give examples. We also find some new explicit values of the parameter $A_{k,n}$ and offer reciprocity theorems for the continued fraction K(q).

• Journal of the Mineralogical Society of Korea
• /
• v.10 no.2
• /
• pp.97-104
• /
• 1997

Based on the method of determination for relative stability of each phase from the difference among the interaction parameters of the phases consisting the mixed layer, the types of interactions between layers were specified and interaction parameter between layers in ordered domain was analytically derived as a function parameter between layers in ordered domain was analytically derived as a function of not only temperature and mole fraction of layers but also ordering parameter. Interaction parameter between the different layers in ordered phase, L is as follows:{{{{ {L }_{1 } (X,Q,T)= { C} over { Q} -4(1-2Q) { L}^{2 } - { RT} over {2} ln { 1} over {2 } - { 2RT} over { { X}_{ s} } ln { { 4QX}`_{s } ^{2 } } over {(1- { X}_{s }- { QX}_{s })( { X}_{s }- {QX }_{s } ) } }}}}L2 is the interaction parameter between ordered and disordered phase in domain and is the mole fraction of the domain which represent the infinite length of mixed layer mineral and Q and C are the reaction progress parameter and arbitrary constant, respectively. This equation was used for the I/S mixed layer clay minerals to infer the relative stability of R1 type I/S mixed layer in the temperature range from 373K to 450K. The result of calculation suggest that, owing to the decrease in interaction parameter with increasing temperature. The interaction parameter decreases more rapidly with decreasing mole fraction of smectite in domain, which is consistent with the fact that the probability of finding the series smectite layer is lo in the domain with small mole fraction of smectite layers in natural system.

• Journal of the Korean Mathematical Society
• /
• v.48 no.5
• /
• pp.913-926
• /
• 2011

The family of q-Laguerre polynomials $\{L_n^{(\alpha)}({\cdot};q)\}_{n=0}^{\infty}$ is usually defined for 0 < q < 1 and ${\alpha}$ > -1. We extend this family to a new one in which arbitrary complex values of the parameter ${\alpha}$ are allowed. These so-called generalized q-Laguerre polynomials fulfil the same three term recurrence relation as the original ones, but when the parameter ${\alpha}$ is a negative integer, no orthogonality property can be deduced from Favard's theorem. In this work we introduce non-standard inner products involving q-derivatives with respect to which the generalized q-Laguerre polynomials $\{L_n^{(-N)}({\cdot};q)\}_{n=0}^{\infty}$, for positive integers N, become orthogonal.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.12 no.1
• /
• pp.21-32
• /
• 2002

In this paper, for any prime q, new cyclic difference sets with Singer parameter equation omitted are constructed by using the q-ary sequences (d-homogeneous functions) of period $q_n$-1. When q is a power of 3, new cyclic difference sets with Singer parameter equation omitted are constructed from the ternary sequences of period $q_n$-1 with ideal autocorrealtion found by Helleseth, Kumar and Martinsen.

• Journal of information and communication convergence engineering
• /
• v.8 no.3
• /
• pp.307-311
• /
• 2010

EPCglobal Class-1 Gen-2 protocol has been proposed for UHF-band RFID systems. In Gen-2 standard, Q-algorithm was proposed to select a frame size for the next query round without estimating the number of tags. Therefore, the Q-algorithm has advantage that the reader's algorithm is simpler than other algorithms. However, it is impossible to allocate the optimized frame size. Also, the original Q-algorithm did not define an optimized parameter C for adjusting the frame size. In this paper, we propose an adaptive Q-algorithm with the different parameter $C_c$ and $C_i$ in accordance with the status of reply slot. Simulation results show that the proposed adaptive Q-algorithm outperforms the original Gen-2 Q-algorithm.

• Journal of KSNVE
• /
• v.8 no.5
• /
• pp.964-973
• /
• 1998

In this paper we propose a levitation and imbalance compensation controller design methodology of magnetic bearing system. In order to achieve levitation and elimination of unbalance vibartion in some operation speed we use the discrete-time Q-parameterization control. When rotor speed p = 0 there are no rotor unbalance, with frequency equals to the rotational speed. So in order to make levitatiom we choose the Q-parameterization controller free parameter Q such that the controller has poles on the unit circle at z = 1. However, when rotor speed p $\neq$ 0 there exist sinusoidal disturbance forces, with frequency equals to the rotational speed. So in order to achieve asymptotic rejection of these disturbance forces, the Q-parameterization controller free parameter Q is chosen such that the controller has poles on the unit circle at z = $exp^{ipTs}$ for a certain speed of rotation p ( $T_s$ is the sampling period). First, we introduce the experimental setup employed in this research. Second, we give a mathematical model for the magnetic bearing in difference equation form. Third, we explain the proposed discrete-time Q-parameterization controller design methodology. The controller free parameter Q is assumed to be a proper stable transfer function. Fourth, we show that the controller free parameter which satisfies the design objectives can be obtained by simply solving a set of linear equations rather than solving a complicated optimization problem. Finally, several simulation and experimental results are obtained to evaluate the proposed controller. The results obtained show the effectiveness of the proposed controller in eliminating the unbalance vibrations at the design speed of rotation.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.7 no.6
• /
• pp.59-70
• /
• 2003

We estimated the spectrum decay parameter $\chi$ and the stress parameter ($\Delta$$\sigma$) in southeastern Korea. Especially, we propose a procedure to compute site-independent $\chi$$_{q}$ and dependent $\chi$$_{s}$ values, separately, This procedure is to use the coda normalization method for the computation of site independent Q or corresponding $\chi$$_{q}$ value as the first step followed by the next step, the computation of $\chi$$_{s}$ values for each site using the given $\chi$$_{q}$ value evaluated at the first step, For the estimation of stress parameter, we used seismic data monitored from three earthquakes occurred near Gyeongju in 1999 with the method of Jo and Baag, In addition, we simulated strong ground motion using the $\chi$ value and the stress parameter, In this case, we calculated the $\chi$ value with conventional method. The $\chi$ value of 0.016+0.000157R and the stress parameter of 92-bar was applied to the stochastic simulation, At last, we derived seismic attenuation equation using results of the stochastic prediction, and compared these results with some others reported previously.ported previously.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.13 no.12
• /
• pp.2541-2546
• /
• 2009

In the anti-collision scheme proposed by EPCglobal Class-1 Gen-2 standard, the frame size for a query round is determined by Q-algorithm. In the Q-algorithm, the reader calculates a frame size without estimating the number of tags in it's identification range. It uses only the slot status. Therefore, the Q-algorithm has advantage that the reader's algorithm is simpler than other DFSA algorithms. However, the standard does not define an optimized parameter value for adjusting the frame size. In this paper, we propose the optimized parameter values for minimizing the identification time by various computer simulations.