• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.23-44
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• 2022

In this paper, we consider and introduce some new concepts of the biconvex functions involving an arbitrary bifunction and function. Some new relationships among various concepts of biconvex functions have been established. We have shown that the optimality conditions for the general biconvex functions can be characterized by a class of bivariational-like inequalities. Auxiliary principle technique is used to propose proximal point methods for solving general bivariational-like inequalities. We also discussed the conversance criteria for the suggested methods under pseudo-monotonicity. Our method of proof is very simple compared with methods. Several special cases are discussed as applications of our main concepts and results. It is a challenging problem to explore the applications of the general bivariational-like inequalities in pure and applied sciences.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.905-909
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• 1997

A characterization of Hilbert spaces is given in terms of four boundary points and two interior points of the unit sphere.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.533-537
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• 2004

A Banach space X is a Hilbert space if and only if E｜x + Y｜$geq$ 1 for all x $\epsilon$ X and all X-valued Bochner integrable functions Y satisfying EY = 0 and ｜Y｜$geq$ 1 a.e.

• Korean Journal of Optics and Photonics
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• v.24 no.5
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• pp.217-223
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• 2013

White light MTF(Modulation Transter Function)s of biconvex trial lenses from 10 to 20 diopter (D) were represented as a function of angular frequency and visual acuity, and then they were compared with AIM(Aerial Image Modulation) curves. All of the biconvex trial lenses evaluated in on-axis mode had MTF performance that could resolve Landolt's ring up to visual acuity 2.0. However, in a half field angle of five degrees, the trial lens of 10 diopters was able to resolve Landolt's ring up to visual acuity 0.9, and that of 20 diopter only up to visual acuity 0.8. This means that the trial lenses in the case of a half field angle of five degrees do not have sufficient resolution to measure visual acuity by 1.0.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.1
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• pp.182-189
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• 1993

To improve the resolution of complex flow field features, grid adaptation scheme of Anderson has been revised, which was based on the Poisson grid generator of Thompson. Anderson's original scheme adapts the grid to solution automatically, but if flow field is more or less complex, then the adaptivity is weak. So the technique of using threshold which is used in unstructured grid system is adopted. The regions of large variation in the solution are marked by marking function which has the property of total variation of the solution, and these regions have same values of weight but other regions are neglected. This updated method captures shocks clearly and sharpy. Four examples are demonstrated, (1) Hypersonic flow past a blunt body, (2) High speed inlet analysis, (3) Supersonic flow of M=1.4 over a 4% biconvex airfoil in a channel, (4) Hypersonic shock-on-shock interaction at M=8.03.

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.157-169
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• 2011

In this paper the time-dependent closed-form static solution of the suspended pre-stressed biconcave and biconvex cable trusses with unmovable, movable and elastic or viscoelastic yielding supports subjected to various types of vertical load is presented. Irvine's forms of the deflections and the cable equations are modified because the effects of the rheological behaviour needed to be incorporated in them. The concrete cable equations in the form of the explicit relations are derived and presented. From a solution of a vertical equilibrium equation for a loaded cable truss with rheological properties, the additional vertical deflection as a time-function is determined. The time-dependent closed-form model serves to determine the time-dependent response, i.e., horizontal components of cable forces and deflection of the cable truss due to applied loading at the investigated time considering effects of elastic deformations, creep strains, temperature changes and elastic supports. Results obtained by the present closed-form solution are compared with those obtained by FEM. The derived time-dependent closed-form computational model is used for a time-dependent simulation-based reliability assessment of cable trusses as is described in the second part of this paper.