• Title/Summary/Keyword: Stability of the curvature functional

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STABILITY AND TOPOLOGY OF TRANSLATING SOLITONS FOR THE MEAN CURVATURE FLOW WITH THE SMALL Lm NORM OF THE SECOND FUNDAMENTAL FORM

  • Eungmo, Nam;Juncheol, Pyo
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.1
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    • pp.171-184
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    • 2023
  • In this paper, we show that a complete translating soliton Σm in ℝn for the mean curvature flow is stable with respect to weighted volume functional if Σ satisfies that the Lm norm of the second fundamental form is smaller than an explicit constant that depends only on the dimension of Σ and the Sobolev constant provided in Michael and Simon [12]. Under the same assumption, we also prove that under this upper bound, there is no non-trivial f-harmonic 1-form of L2f on Σ. With the additional assumption that Σ is contained in an upper half-space with respect to the translating direction then it has only one end.

Design Evaluation Model Based on Consumer Values: Three-step Approach from Product Attributes, Perceived Attributes, to Consumer Values (소비자 가치기반 디자인 평가 모형: 제품 속성, 인지 속성, 소비자 가치의 3단계 접근)

  • Kim, Keon-Woo;Park, Do-Hyung
    • Journal of Intelligence and Information Systems
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    • v.23 no.4
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    • pp.57-76
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    • 2017
  • Recently, consumer needs are diversifying as information technologies are evolving rapidly. A lot of IT devices such as smart phones and tablet PCs are launching following the trend of information technology. While IT devices focused on the technical advance and improvement a few years ago, the situation is changed now. There is no difference in functional aspects, so companies are trying to differentiate IT devices in terms of appearance design. Consumers also consider design as being a more important factor in the decision-making of smart phones. Smart phones have become a fashion items, revealing consumers' own characteristics and personality. As the design and appearance of the smartphone become important things, it is necessary to examine consumer values from the design and appearance of IT devices. Furthermore, it is crucial to clarify the mechanisms of consumers' design evaluation and develop the design evaluation model based on the mechanism. Since the influence of design gets continuously strong, various and many studies related to design were carried out. These studies can classify three main streams. The first stream focuses on the role of design from the perspective of marketing and communication. The second one is the studies to find out an effective and appealing design from the perspective of industrial design. The last one is to examine the consumer values created by a product design, which means consumers' perception or feeling when they look and feel it. These numerous studies somewhat have dealt with consumer values, but they do not include product attributes, or do not cover the whole process and mechanism from product attributes to consumer values. In this study, we try to develop the holistic design evaluation model based on consumer values based on three-step approach from product attributes, perceived attributes, to consumer values. Product attributes means the real and physical characteristics each smart phone has. They consist of bezel, length, width, thickness, weight and curvature. Perceived attributes are derived from consumers' perception on product attributes. We consider perceived size of device, perceived size of display, perceived thickness, perceived weight, perceived bezel (top - bottom / left - right side), perceived curvature of edge, perceived curvature of back side, gap of each part, perceived gloss and perceived screen ratio. They are factorized into six clusters named as 'Size,' 'Slimness,' 'No-Frame,' 'Roundness,' 'Screen Ratio,' and 'Looseness.' We conducted qualitative research to find out consumer values, which are categorized into two: look and feel values. We identified the values named as 'Silhouette,' 'Neatness,' 'Attractiveness,' 'Polishing,' 'Innovativeness,' 'Professionalism,' 'Intellectualness,' 'Individuality,' and 'Distinctiveness' in terms of look values. Also, we identifies 'Stability,' 'Comfortableness,' 'Grip,' 'Solidity,' 'Non-fragility,' and 'Smoothness' in terms of feel values. They are factorized into five key values: 'Sleek Value,' 'Professional Value,' 'Unique Value,' 'Comfortable Value,' and 'Solid Value.' Finally, we developed the holistic design evaluation model by analyzing each relationship from product attributes, perceived attributes, to consumer values. This study has several theoretical and practical contributions. First, we found consumer values in terms of design evaluation and implicit chain relationship from the objective and physical characteristics to the subjective and mental evaluation. That is, the model explains the mechanism of design evaluation in consumer minds. Second, we suggest a general design evaluation process from product attributes, perceived attributes to consumer values. It is an adaptable methodology not only smart phone but also other IT products. Practically, this model can support the decision-making when companies initiative new product development. It can help product designers focus on their capacities with limited resources. Moreover, if its model combined with machine learning collecting consumers' purchasing data, most preferred values, sales data, etc., it will be able to evolve intelligent design decision support system.

The Comparative Analysis of Male and Female of Adult on the Base Crve, Power and Astigamtism of the Cornea (각막의 곡율반경, 굴절력, 난시에 대한 성인 남녀의 비교 분석)

  • Chio, Ho Seong;Kim, Douk Hoon
    • Journal of Korean Ophthalmic Optics Society
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    • v.5 no.2
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    • pp.27-31
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    • 2000
  • As the functional test of cornea. The clinical value of keratometric information was important for assessment the curvature of the cornea, the quality of the corneal surface, the stability of the corneal curvature, and the direction of the corneal astigmatism. This study was performed the comparative analysis of male and female of adult on the base curve, power and astigmatism of the Cornea. On the corneal base curve, the male right eye was 7.656 mm in vertical and 7.966 mm in horizontal. But, the male left cornea was 7.714 mm in vertical base curve and 8.026 mm in horizontal base curve. On the other hand, the female right eye cornea was 7.559 mm in vertical base curve and 7.695 mm in horizontal base curve. But, the female left eye cornea was 7.444 mm in vertical base curve and 7.742 mm in horizontal base curve. On the corneal diopter power, the male right eye was 44.063 diopter in vertical and 43.738 diopter in horizontal. But the male left eye was 44.046 diopter in vertical and 42.304 diopter in horizontal. On the other hand, the female right eye was 44.082 diopter in vertical and 43.77 diopter in horizontal. But, the female left eye was 44.347 diopter in vertical and 43.495 diopter in horizontal. According to the corneal astigmatism axis. The male right eye have 89.9% positive for with the - rule astigmatism, and 8.1 % positive for against - the - rule astigmatism. But, he male left eye have 91.89% positive for with - the - rule astigmatism, and 8.11 % positive for against - the - rule astigmatism. On the other hand, The female right eye have 76.92% positive for with - the - rule astigmatism, and 23.08 % positive for against - the - rule astigmatism. But, the female left have 80.76 % positive for with - the - rule astigmatism, and 17.31 % positive for against - the - rule as tigmatism. The diopter power of corneal astigmatism have 25.57% positive for behind 1 diopter, 44.89% positive for 1 diopter, 18.18% positive for 2 diopter, 5.11% positive for 3 diopter and 6.25% positive for over 4 diopter.

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