• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.21 no.3
• /
• pp.51-57
• /
• 2021

In this paper, the relevance between Einstein's special theory of relativity (1905) and Bernoulli's fluid mechanics (1738), which motivates Shannon's theorem (1948), was derived from the AB=A/A=I dimension, and the Shannon's theorem channel code was simulated. When Bernoulli's fluid mechanics ΔP=pgh was applied to the Hallasan volcano Magma eruption, the dimensions and heights matched the measured values. The relationship between Einstein's special theory of relativity, Shannon's information theory, and the stack effect theory of fluid mechanics was analyzed, and the relationship between volcanic eruptions was mathematically proven. Einstein's and Bernoulli's conservation of energy and conservation of mass were the same in terms of bandwidth and power efficiency in Shannon's theorem.

• Honam Mathematical Journal
• /
• v.34 no.3
• /
• pp.311-326
• /
• 2012

The purpose of this paper is to introduce and investigate two new classes of generalized Bernoulli and Apostol-Bernoulli polynomials based on the definition given recently by the authors [29]. In particular, we obtain a new addition formula for the new class of the generalized Bernoulli polynomials. We also give an extension and some analogues of the Srivastava-Pint$\acute{e}$r addition theorem [28] for both classes. Finally, by making use of the new adition formula, we exhibit several interesting relationships between generalized Bernoulli polynomials and other polynomials or special functions.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.3
• /
• pp.831-845
• /
• 2014

In this paper, we obtain new generating functions involving families of pairs of inverse functions by using a generalization of the Srivastava's theorem [H. M. Srivastava, Some generalizations of Carlitz's theorem, Pacific J. Math. 85 (1979), 471-477] obtained by Tremblay and Fug$\grave{e}$ere [Generating functions related to pairs of inverse functions, Transform methods and special functions, Varna '96, Bulgarian Acad. Sci., Sofia (1998), 484-495]. Special cases are given. These can be seen as generalizations of the generalized Bernoulli polynomials and the generalized degenerate Bernoulli polynomials.

• Advances in nano research
• /
• v.12 no.2
• /
• pp.139-150
• /
• 2022

This paper presents sets of explicit analytical equations that compute the static displacements of nanobeams by adopting the nonlocal elasticity theory of Eringen within the framework of Euler Bernoulli and Timoshenko beam theories. Castigliano's theorem is applied to an equivalent Virtual Local Beam (VLB) made up of linear elastic material to compute the displacements. The first derivative of the complementary energy of the VLB with respect to a virtual point load provides displacements. The displacements of the VLB are assumed equal to those of the nonlocal beam if nonlocal effects are superposed as additional stress resultants on the VLB. The illustrative equations of displacements are relevant to a few types of loadings combined with a few common boundary conditions. Several equations of displacements, thus derived, matched precisely in similar cases with the equations obtained by other analytical methods found in the literature. Furthermore, magnitudes of maximum displacements are also in excellent agreement with those computed by other numerical methods. These validated the superposition of nonlocal effects on the VLB and the accuracy of the derived equations.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.915-929
• /
• 2007

The main result of this paper is to construct the derivative twisted p-adic (h, q)-L-functions at s = 0. We obtain twisted version of Theorem 4 in [17]. We also obtain twisted (h, q)-extension of Proposition 1 in [3].

• Journal of the Semiconductor & Display Technology
• /
• v.21 no.4
• /
• pp.163-167
• /
• 2022

In this paper, an optimization design method of a diffuser using Bernoulli's theorem was reviewed. The aspect ratio of the cylindrical diffuser chamber and the diameter ratio of the air inlet and outlet were used as design parameters. For the optimal design of the cylindrical diffuser chamber, the air flow inside the chamber was simulated using ANSYS while changing the aspect ratio of the chamber. In order to confirm the simulation results, the diffuser manufactured using the laser processing machine was measured. Through ANSYS simulation and measurement, it was found that the optimal design condition was when the aspect ratio (chamber height/radius) of the diffuser chamber was 1/2 and the diameter ratio of the air inlet and outlet was also 1/2.

• Journal of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.57-72
• /
• 2016

We establish maximal moment inequalities of partial sums under ${\psi}$-weak dependence, which has been proposed by Doukhan and Louhichi [P. Doukhan and S. Louhichi, A new weak dependence condition and application to moment inequality, Stochastic Process. Appl. 84 (1999), 313-342], to unify weak dependence such as mixing, association, Gaussian sequences and Bernoulli shifts. As an application of maximal moment inequalities, a functional central limit theorem is developed for linear processes with ${\psi}$-weakly dependent innovations.

• Journal of the Korean Vacuum Society
• /
• v.22 no.3
• /
• pp.111-118
• /
• 2013

The influence of gas flow on the plasma generation in the atmospheric plasma jet is described with the theory of hydrodynamics. The plasma discharge is affected by the gas-flow streams with Reynolds number (Re) as well as the gas pressure with Bernoulli's theorem according to the gas flow rate inserted into the glass tube. The length of plasma column is varied with the flow types such as the laminar flow of Re<2,000 and the turbulent flow of Re>4,000 as it has been known in a general fluid experiments. In the laminar flow, the plasma column length is increased as the increase of flow rate. Since the pressure in the glass tube becomes low as the increase of flow velocity by the Bernoulli's theorem, the breakdown voltage of plasma discharge is reduced by the Paschen's law. Therefore, the plasma length is increased as the increasing flow rate with the fixed operation voltage. In the transition of laminar and turbulent flows, the plasma length is decreased. When the flow becomes turbulent as the flow rate is increasing, the plasma length becomes short and the discharge is shut down ultimately. In the discharge of laminar flow, the diameter of plasma beam exposed on the substrate surface is kept less than the glass diameter, since the gas flow is kept to the distinct distance from the nozzle of glass tube.

• Honam Mathematical Journal
• /
• v.36 no.2
• /
• pp.263-273
• /
• 2014

Ever since Euler solved the so-called Basler problem of ${\zeta}(2)=\sum_{n=1}^{\infty}1/n^2$, numerous evaluations of ${\zeta}(2n)$ ($n{\in}\mathbb{N}$) as well as ${\zeta}(2)$ have been presented. Very recently, Ritelli [61] used a double integral to evaluate ${\zeta}(2)$. Modifying mainly Ritelli's double integral, here, we aim at evaluating certain interesting alternating series.

• Steel and Composite Structures
• /
• v.39 no.5
• /
• pp.543-564
• /
• 2021

In this study free vibration analysis of a cracked Goland composite wing is investigated. The wing is modelled as a cantilevered beam based on Euler- Bernoulli equations. Also, composite material is modelled based on lamina fiber-reinforced. Edge crack is modelled by additional boundary conditions and local flexibility matrix in crack location, Castigliano's theorem and energy release rate formulation. Governing differential equations are extracted by Hamilton's principle. Using the separation of variables method, general solution in the normalized form for bending and torsion deflection is achieved then expressions for the cross-sectional rotation, the bending moment, the shear force and the torsional moment for the cantilevered beam are obtained. The cracked beam is modelled by separation of beam into two interconnected intact beams. Free vibration analysis of the beam is performed by applying boundary conditions at the fixed end, the free end, continuity conditions in the crack location of the beam and dynamic stiffness matrix determinant. Also, the effects of various parameters such as length and location of crack and fiber angle on natural frequencies and mode shapes are studied. Modal analysis results illustrate that natural frequencies and mode shapes are affected by depth and location of edge crack and coupling parameter.