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Γ-CONVERGENCE FOR AN OPTIMAL DESIGN PROBLEM WITH VARIABLE EXPONENT
HAMDI ZORGATI 한국산업응용수학회 2023 Journal of the Korean Society for Industrial and A Vol.27 No.4
In this paper, we derive the Γ-limit of functionals pertaining to some optimal material distribution problems that involve a variable exponent, as the exponent goes to infinity. In addition, we prove a relaxation result for supremal optimal design functionals with respect to the weak-∗ L∞(Ω; [0, 1]) × W 1,p0 (Ω; Rm ) weak topology.
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Cultural Distance and Corporate Internationalization: Evidence from Emerging Economies
ELMOEZ, Zaabi,ZORGATI, Imen,ALESSA, Adlah A. Korea Distribution Science Association 2021 The Journal of Asian Finance, Economics and Busine Vol.8 No.3
This study investigates the relationship between cultural distance and entry mode choice, where the foreign investor firm and the host country are both from emergent economies. Within this framework, research is limited and the issue is whether companies, regardless of their specific situations, have the same strategy when they meet a high degree of uncertainty in the host environment. In this study, we focused on the influence of informal institutional factors: cultural distance, that has been extensively analyzed in international business, measured by Kogut and Singh index and defined according to Hofstede, Globe Project and Schwartz approaches. The general trend derived from prior research proves that when a company from a developed country is involved; overall more enthusiasm is shown for wholly-owned subsidiaries rather than joint venture. This result still stands validated for corporations from this emergent economy area. Our analysis of a sample of 163 FDI in the Kingdom of Saudi Arabia (KSA) using logistic binary regression model reveals that the foreign firms prefer to establish wholly-owned subsidiaries in the host country over entering into a joint venture with a local firm, taking into consideration the large cultural distance.
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COMPACTNESS AND DIRICHLET’S PRINCIPLE
JIN KEUN SEO,HAMDI ZORGATI 한국산업응용수학회 2014 Journal of the Korean Society for Industrial and A Vol.18 No.2
In this paper we explore the emergence of the notion of compactness within its historical beginning through rigor versus intuition modes in the treatment of Dirichlet‘s principle. We emphasize on the intuition in Riemann‘s statement on the principle criticized byWeierstrass‘ requirement of rigor followed by Hilbert‘s restatement again criticized by Hadamard, which pushed the ascension of the notion of compactness in the analysis of PDEs. A brief overview of some techniques and problems involving compactness is presented illustrating the importance of this notion. Compactness is discussed here to raise educational issues regarding rigor vs intuition in mathematical studies. The concept of compactness advanced rapidly afterWeierstrass’s famous criticism of Riemann’s use of the Dirichlet principle. The rigor of Weierstrass contributed to establishment of the concept of compactness, but such a focus on rigor blinded mathematicians to big pictures. Fortunately, Poincar´e and Hilbert defended Riemann’s use of the Dirichlet principle and found a balance between rigor and intuition. There is no theorem without rigor, but we should not be a slave of rigor. Rigor (highly detailed examination with toy models) and intuition (broader view with real models) are essentially complementary to each other.
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