Optimality Conditions of Interval-Valued Optimization Problems by Using Subdifferantials

Karaman, Emrah

doi:10.35378/gujs.619160

Cited by 4 publications

(3 citation statements)

References 20 publications

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“…The seven universal design criteria and fourteen biophilic design patterns are examined jointly. Rockwood Retirement South Hill, an outstanding project, met the pattern requirements in the table to a large degree [36]. The biophilic design standards, shown to have a favorable effect on users across psychological, physiological, and social domains, and the universal design criteria, which are both simple access for the elderly, are assessed in this research.…”

Section: Biophilic Design For Co-improving Physical Conditionsmentioning

confidence: 99%

Biophilic architecture and designs for mental well-being

Alam

2023

IOP Conf. Ser.: Earth Environ. Sci.

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There is a growing recognition that people who stay in contact with nature are more likely to enjoy fulfilling, fruitful lives. More recently, architects and designers have begun to recognize the importance of biophilic design, which incorporates natural elements into built environments. However, as urbanization spreads around the globe, attention must be redirected to city size, with an emphasis on planning for and making progress toward “biophilic cities.” Biophilic communities are ones that aim to foster a sense of appreciation and stewardship for the natural world among their citizens by providing them with enough opportunities to experience nature both inside and beyond the city limits. Employing deconstructive discourse analysis on different uses of biophilic concepts, the present paper aims to review the contribution of biophilic architecture and designs to the improved physical space for mental well-being.

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Section: Biophilic Design For Co-improving Physical Conditionsmentioning

confidence: 99%

Biophilic architecture and designs for mental well-being

Alam

2023

IOP Conf. Ser.: Earth Environ. Sci.

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“…In order to prove these properties, the norm on the set of gH-continuous bounded linear IVFs is defined and the idea of sequences with their convergence on the set of n-tuple of compact intervals is described. Although the author of [25] provided the concept of subgradients for IVFs in terms of linear functions, our concept is more general (please see Remark 6 of this article for details).…”

Section: Motivation and Contributionmentioning

confidence: 99%

“…Remark 6. It is noteworthy that (i) the author of [25] in Definition 2 has proposed the concept of subgradient for IVFs by considering L as linear real valued function. However, in Definition 3.1 of the present article, we consider L x as linear IVF.…”

Section: Subdifferentiability Of Ivfsmentioning

confidence: 99%

Generalized-Hukuhara Subgradient and its Application in Optimization Problem with Interval-valued Functions

Debnath¹,

Ghosh²,

Mesiar³

et al. 2021

Preprint

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In this article, the concepts of gH-subgradients and gH-subdifferentials of interval-valued functions are illustrated. Several important characteristics of the gH-subdifferential of a convex interval-valued function, e.g., closeness, boundedness, chain rule, etc. are studied. Alongside, we prove that gHsubdifferential of a gH-differentiable convex interval-valued function only contains gH-gradient of that interval-valued function. It is observed that the gH-directional derivative of a convex intervalvalued function in each direction is maximum of all the products of gH-subgradients and the direction. Importantly, we show that a convex interval-valued function is gH-Lipschitz continuous if it has gHsubgradients at each point in its domain. Furthermore, the relations between efficient solutions of an optimization problem with interval-valued function and its gH-subgradients are derived.

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Flexible and Tough Superelastic Co–Cr Alloys for Biomedical Applications

2022

Advanced Materials

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present, the three dominant metallic alloys used as biomaterials are Co-Cr alloys, stainless steels, and Ti alloys, and Mg alloys provide a biodegradable option. [1][2][3] There are basically three qualities required of a metallic biomaterial: good biocompatibility, high corrosion resistance, and good wear resistance. Recently, the need for a low Young's modulus similar to that of human bones has been highlighted. A large difference in the Young's modulus of the implant and the bone has been shown to result in the loosening of implants and bone atrophy due to the "stress shielding effect." [2,4] At 190-240 GPa, the Young's modulus of the Co-Cr alloys and stainless steels commonly used at present is much higher than that of the 10-30 GPa of human bones. [2,5] Many kinds of β-type Ti alloys with a body-centered-cubic (BCC) structure and a relatively low Young's modulus have been developed. [1] The Young's modulus of these polycrystalline alloys is typically in the range of 50-80 GPa. [1,2] The Young's modulus of a single-crystal Ti-Nb-Ta-Zr has been reported to be 35 GPa in the <001> direction, [6] and a low apparent Young's modulus of 20 GPa has been shown for some Ti-Nb-based alloys when stress-induced martensitic transformation is involved. [7] While these alloys are appropriate for use as the stems and the acetabular cups of totalThe demand for biomaterials has been increasing along with the increase in the population of elderly people worldwide. The mechanical properties and high wear resistance of metallic biomaterials make them well-suited for use as substitutes or as support for damaged hard tissues. However, unless these biomaterials also have a low Young's modulus similar to that of human bones, bone atrophy inevitably occurs. Because a low Young's modulus is typically associated with poor wear resistance, it is difficult to realize a low Young's modulus and high wear resistance simultaneously. Also, the superelastic property of shape-memory alloys makes them suitable for biomedical applications, like vascular stents and guide wires. However, due to the low recoverable strain of conventional biocompatible shape-memory alloys, the demand for a new alloy system is high. The novel body-centered-cubic cobalt-chromium-based alloys in this work provide a solution to both of these problems. The Young's modulus of <001>-oriented single-crystal cobalt-chromium-based alloys is 10-30 GPa, which is similar to that of human bone, and they also demonstrate high wear and corrosion resistance. They also exhibit superelasticity with a huge recoverable strain up to 17.0%. For these reasons, the novel cobalt-chromium-based alloys can be promising candidates for biomedical applications.

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Optimality Conditions of Interval-Valued Optimization Problems by Using Subdifferantials

Cited by 4 publications

References 20 publications

Biophilic architecture and designs for mental well-being

Biophilic architecture and designs for mental well-being

Generalized-Hukuhara Subgradient and its Application in Optimization Problem with Interval-valued Functions

Flexible and Tough Superelastic Co–Cr Alloys for Biomedical Applications

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