• International Journal of Computer Science & Network Security
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• v.24 no.1
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• pp.85-94
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• 2024

In this paper, we present the very first time the generalized notion of (α, β, γ, δ) - convex (concave) function in mixed kind, which is the generalization of (α, β) - convex (concave) functions in 1^st and 2^nd kind, (s, r) - convex (concave) functions in mixed kind, s - convex (concave) functions in 1^st and 2^nd kind, p - convex (concave) functions, quasi convex(concave) functions and the class of convex (concave) functions. We would like to state the well-known Ostrowski inequality via SVN-Riemann Integrals for (α, β, γ, δ) - convex (concave) function in mixed kind. Moreover we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are (α, β, γ, δ)-convex (concave) functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases with respect to convexity of function.

• Proceedings of the Korean Geotechical Society Conference
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• 2005.03a
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• pp.1335-1342
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• 2005

In this paper, there is intended to introduce the new tunnel face shape, that is concave shaped face, and discusses its effects on the tunnel stabilization. Therefore, a comparative analysis in which the stability of a concave face was compared to that of a conventional plane face on the basis of displacement patterns in the tunnel face was conducted using a model test. In order to check and confirm displacement patterns on the concave face according to the radius of curvature as well as those around the face according to lateral pressure coefficient(k), two experimental concave models, produced at a scale of 1:2 and 1:5(tunnel radius), of the forefront of the curved area extended from plane face was built and tested.

• International Journal of Fluid Machinery and Systems
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• v.4 no.1
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• pp.33-46
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• 2011

Concave surface boundary-layer flows are subjected to centrifugal instability which results in the formation of streamwise counter-rotating vortices. Such boundary layer flows have been experimentally investigated on concave surfaces of 1 m and 2 m radius of curvature. In the experiments, to obtain uniform vortex wavelengths, thin perturbation wires placed upstream and perpendicular to the concave surface leading edge, were used to pre-set the wavelengths. Velocity contours were obtained from hot-wire anemometer velocity measurements. The most amplified vortex wavelengths can be pre-set by the spanwise spacing of the thin wires and the free-stream velocity. The velocity contours on the cross-sectional planes at several streamwise locations show the growth and breakdown of the vortices. Three different vortex growth regions can be identified. The occurrence of a secondary instability mode is also shown as mushroom-like structures as a consequence of the non-linear growth of the streamwise vortices. Wall shear stress measurements on concave surface of 1 m radius of curvature reveal that the spanwise-averaged wall shear stress increases well beyond the flat plate boundary layer values. By pre-setting much larger or much smaller vortex wavelength than the most amplified one, the splitting or merging of the streamwise vortices will respectively occur.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.11 s.254
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• pp.1433-1438
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• 2006

A systematic approach to socket shape design of a concave piston assembly for a high pressure hydraulic pump of an excavator is presented in this paper. A design model is given and a methodology of socket shape design is proposed. An axisymmetric rigid-plastic finite element method is employed for predicting the approximate socket shape formed by a rotary forming process as well as for simulating the test process for separating the shoe from the piston assembly designed. It is verified that the predictions are in good agreement with the experiments. The approach is successfully applied to developing an optimal concave piston assembly.

• 한국전산유체공학회:학술대회논문집
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• 2009.04a
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• pp.170-175
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• 2009

Shock focusing is related with explosive release of shock wave energy on a narrow spot in a short duration of time triggering a spontaneous high pressure near the focal point. It is well known that reflection of planar incident shock wave from the metallic concave mirror such as ellipsoidal, paraboloidal or hemispherical cavities will focus on a focal point. We intend to improve the computational results using a wave propagation algorithm and to resolve the mushroom-like structure. For computation of the concave cavity flow, it is not easy to use a single-block mesh because of the many singular points in geometry and coordinates. We have employed a uniform Cartesian-grid method for the wave propagation algorithm.

• The Journal of the Korea institute of electronic communication sciences
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• v.12 no.5
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• pp.731-736
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• 2017

In this paper, we report the fabrication of concave surface fiber tips for optical resonators. It was confirmed that the radius of curvature on fiber end can be controlled by introducing the hydrofluoric acid solution and the wavelength of $1.55{\mu}m$ laser which is absorbed well in the etchant to induce the photothermal effect. Using the microscope images, we observed the proposed concave fiber tip fabrication method is effective to make the controllable concave tips. We also observed changes in the size of the beam emitted from the tips with the various radius of curvature using the beam profiler. The authors believe that the proposed method will be applied to resonators for optical communications.

• Laser Solutions
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• v.18 no.1
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• pp.18-22
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• 2015

In this paper, controlling shape of optical fiber tip for endoscope was investigated for eliminating blind spot. The blind spot of endoscope is generated by divergence angle of optical fiber, so it is easy to generate blind spot when tightly focusing. In order to eliminate this region, fiber tip is necessary to be controlled as convex or concave. Illumination simulation of convex and concave type of fiber tip in the endoscope was in progress, so the distance of non- blind region was investigated in each case. As well as the simulation, the tip was fabricated as concave shape by UV laser machining. Then the beam radiation was measured to observe the blind region. The result showed that controlling the fiber tip as convex or concave shape makes the narrow blind region of illumination in endoscope.

• Journal of Biosystems Engineering
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• v.10 no.2
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• pp.36-46
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• 1985

This study was intended to develop the mathematical model of the head-fed type threshing unit. As the first step, the physical model of the threshing phenomena was considered to consist of four separate processes as 1) detachment process of grains, 2) movement of grains between the cylinder and concave, 3) grain penetration through stems of bundle, and 4) grain passing through concave. The mathematical and computer models were developed based on the physical models. Threshing experiments were performed and determined the distribution of grain accumulation along the cylinder shaft by varying the moisture content of grains, feeding rate, and cylinder speed. It was found that the model developed coincided very well with the experimental results for the varied operational conditions. Greater concentration of grains passing through concave toward the thresher inlet was equally true for the model and experiment work for the threshing of grains with higher moisture content and with higher cylinder-speed. The model could be used for obtaining the optimized design or for optimizing the performance of the head-fed type threshing unit if term as to power requirement for threshing may be additionally included in the developed model.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1461-1484
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• 2021

We deal with the following elliptic equations: $\{-div({\varphi}^{\prime}(\left|{\nabla}z\right|^2){\nabla}z)+V(x)\left|z\right|^{{\alpha}-2}z={\lambda}{\rho}(x)\left|z\right|^{r-2}z+h(x,z),\\z(x){\rightarrow}0,\;as\;\left|x\right|{\rightarrow}{\infty},$ in ℝ^N , where N ≥ 2, 1 < p < q < N, 1 < α ≤ p^*q'/p', α < q, 1 < r < min{p, α}, φ(t) behaves like t^q/2 for small t and t^p/2 for large t, and p' and q' the conjugate exponents of p and q, respectively. Here, V : ℝ^N → (0, ∞) is a potential function and h : ℝ^N × ℝ → ℝ is a Carathéodory function. The present paper is devoted to the existence of at least two distinct nontrivial solutions to quasilinear elliptic problems of Schrödinger type, which provides a concave-convex nature to the problem. The primary tools are the well-known mountain pass theorem and a variant of Ekeland's variational principle.

• Smart Structures and Systems
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• v.16 no.4
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• pp.701-723
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• 2015

Friction isolators are one of the most important types of bearings used to mitigate damages of earthquakes. The adaptive behavior of these isolators allows them to achieve multiple levels of performances and predictable seismic behavior during different earthquake hazard levels. There are three main types of friction isolators. The first generation with one sliding surface is known as Friction Pendulum System (FPS) isolators. The double concave friction pendulum (DCFP) with two sliding surfaces is an advanced form of FPS, and the third one, with fully adaptive behavior, is named as triple concave friction pendulum (TCFP). The current study has been conducted to investigate and compare seismic responses of these three types of isolators. The structure is idealized as a two-dimensional single degree of freedom (SDOF) resting on isolators. The coupled differential equations of motion are derived and solved using state space formulation. Seismic responses of isolated structures using each one of these isolators are investigated under seven near fault earthquake motions. The peak values of bearing displacement and base shear are studied employing the variation of essential parameters such as superstructure period, effective isolation period and effective damping of isolator. The results demonstrate a more efficient seismic behavior of TCFP isolator comparing to the other types of isolators. This efficiency depends on the selected effective isolation period as well as effective isolation damping. The investigation shows that increasing the effective isolation period or decreasing the effective isolation damping improves the seismic behavior of TCFP compared to the other isolators. The maximum difference in seismic responses, the base shear and the bearing displacement, for the TCFP isolator are calculated 26.8 and 13.4 percent less than the DCFP and FPS in effective isolation damping equal to10%, respectively.