(2) ([25%]) Prove that if a regular surface in R³ contains a straight line, then the surface has non-positive Gauss curvature at all the points of this line.

(3) ([30%]) Consider a regular surface S where and the inversion Φ :R3＼  given by Compare the mean curvature and the Gauss urvatures of S and of the image surface S' = Φ(S). More precisely, show that and where N(p) is the unit normal of S at p, H'(Φ(p) is the mean curvature of s' at Φ(p), K'(Φ(p) is the Gauss curvature of S' at Φ(p).

(4) ([25%]) Prove that if S is a regular surface that is diffeomorphic to a cylinder and has Gaussian curvature K< O, then S has at most one simple closed geodesic (up to reparametrization).

一、組織結構的設計會受到哪些情境變數的影響？請解釋其內涵，並且舉例說明。

二、請比較企業倫理的四種觀點。你覺得管理者最常採取哪一種？為甚麼？

三、閱讀下文，作者闡述有關影響行銷標準化決策的因素是甚麼？請說明。此外，提出你的評論。       The three market conditions that influence the standardization decision are cultural differences,economic differences, and differences in customer perceptions in foreign markets.      Culture influences every aspect of marketing. The products people buy, the attributes they value, and the principals whose opinions they accept are all culture-based choices. For example, different levels of awareness, knowledge, familiarity, and affect with people, products in general, and specific brands may result in differential attitudes toward similar products. Cultural differences influence consumer acculturation which, in turn, affects acceptance of standardized products. Hence, where a product is culturally compatible with the society, it is likely to be more suitable for standardization.      Poor economic means may prevent masses in LDCs from buying the variety of products that U.S.consumers consider essential. To bring such products as automobiles and appliances within the reach of the middle class in developing countries, for example, the products must be appropriately modified to cut cost without reducing functional quality. Finally, the decision on product standardization should be based on the psychological meaning of the product in different markets. Foreign products in many cultures are perceived as high quality products. In such cases, standardization would be desirable. In contrast, if the image of a country’s products is weak, it would be strategically desirable to adapt a product so that it could be promoted as different from, rather than typical of, that country’s products.                                                                                     （source: Subhash C. Jain, Journal of Marketing）

四、閱讀下文，請以安索夫的產品－市場矩陣（參考下圖） ，分析法蘭瓷進入中國電商市場是屬於甚麼成長策略？請說明理由。並且，請分析法蘭瓷應擬定甚麼行銷策略最為適當？      法藍瓷產品融合中西方文化及結合浮雕的獨特設計，深受歐美人士的喜愛，所以能定位在藝術禮品市場的高級品。十數年的發展，法藍瓷開發全球 56 個國家市場，拓展 6000 多個零售據點，年營收最高 20 億元，坐穩全球陶瓷市場第四大品牌。2008 年，法藍瓷將經營重心轉至中國，主要是因為歐美市場受金融海嘯而萎縮，而且中國的經濟的快速成長，讓法藍瓷在中國市場的業績得以快速成長。近年來，中國市場也受到全球經濟不景氣影響，2015 和 2016 年法藍瓷連續兩年虧損。於是法藍瓷計劃將資源分配到中國電商市場，想要進入一個銷售低價的杯、盤、相框、項鍊等年輕化商品的電子商務市場。

(a). 獨佔廠商沒有供給線。

(b). 若廠商的生產具有規模經濟，則隱含其生產技術具有規模報酬遞增之特性。

(c). 劣等財必為季芬財，反之則否。

(d). 根據貨幣中立性，政府無法透過擴大支出來影響實質所得。

110年 - 110 國立臺灣大學_碩士班招生考試_數學研究所:幾何#101955