We present some conditions for the asymptotic equilibrium of nonlinear differential equations and, in particular, a linear inhomogeneous equation in Banach spaces. We also discuss analogous problems for a linear equation with unbounded operator. Some obtained results are applied to problems of asymptotic equivalence.Hanoi, Vietnam.
This paper is concerned with the existence of almost periodic solutions of neutral functional differential equations of the form d dt Dxt = Lxt + f (t), where D, L are bounded linear operators from Cf is an almost (quasi) periodic function. We prove that if the set of imaginary solutions of the characteristic equations is bounded and the equation has a bounded, uniformly continuous solution, then it has an almost (quasi) periodic solution with the same set of Fourier exponents as f .
Southeast Asia played an important role in global trade networks from before to the 15th century AD. This article aims to analyze the changes in maritime networks in the classical period of Southeast Asia and their influence on the development of ports and political centers in this region. The research method used is the historical method by utilizing relevant secondary sources. The analysis results show that long before Christ, the Southeast Asian region had become an arena of maritime networks with India and was followed by China at the beginning of the century AD. The sea transportation network connecting India, China, and the Middle East has influenced the growth of ports in Southeast Asia, which has implications for economic development and political power in the classical kingdoms. The initial trading network that China built until the mid-6th century AD gave birth to the development of the Funan kingdom with the port of Oc-Eo. Meanwhile, the China-Malacca Strait direct network shut down Funan’s ports with the shipping technology revolution. It encouraged the development of owned ports in the archipelago in succession in different periods, namely Sriwijaya, Majapahit, and Malacca, influencing economic and political consequences. These countries. The implications of this finding are the basis for generalizing the development of Pacific Asia trade and the economic and cultural interactions between maritime nations and regions worldwide. Asia Tenggara memainkan peran penting dalam jaringan perdagangan global dari sebelum hingga abad ke-15 Masehi. Artikel ini bertujuan untuk menganalisis perubahan jaringan maritim pada periode klasik Asia Tenggara dan pengaruhnya terhadap perkembangan pelabuhan dan pusat politik di kawasan ini. Metode penelitian yang digunakan adalah metode sejarah dengan memanfaatkan sumber-sumber sekunder yang relevan. Hasil analisis menunjukkan bahwa jauh sebelum Masehi, kawasan Asia Tenggara telah menjadi arena jaringan maritim dengan India dan diikuti oleh Cina pada awal abad Masehi. Jaringan transportasi laut yang menghubungkan India, Cina, dan Timur Tengah telah mempengaruhi pertumbuhan pelabuhan di Asia Tenggara, yang berimplikasi pada perkembangan ekonomi dan kekuatan politik di kerajaan-kerajaan klasik. Jaringan perdagangan awal yang dibangun Tiongkok hingga pertengahan abad ke-6 M melahirkan perkembangan kerajaan Funan dengan pelabuhan Oc-Eo. Sementara itu, jaringan langsung Selat Malaka-China menutup pelabuhan Funan dengan revolusi teknologi perkapalan. Hal tersebut mendorong berkembangnya pelabuhan-pelabuhan milik di Nusantara secara berturut-turut pada periode yang berbeda, yaitu Sriwijaya, Majapahit, dan Malaka, sehingga mempengaruhi konsekuensi ekonomi dan politik. Negara-negara ini. Implikasi dari temuan ini adalah dasar untuk menggeneralisasi perkembangan perdagangan Asia Pasifik dan interaksi ekonomi dan budaya antara negara dan wilayah maritim di seluruh dunia.Cite this article: Man, N.M., Chi, N.T.P., Wasino, Hartatik, E.S. (2022). Ports, Maritime Networks, and Its Effect on the Development of the Ancient Kingdom of Southeast Asia. Paramita: Historical Studies Journal, 32(2), 202-211. http://dx.doi.org/10.15294/paramita.v32i2.37833
This paper is concerned with the existence of invariant manifolds for dynamical equations on a periodic time scale when the nonlinear perturbation has a small global Lipschitz constant. Particularly, for time-varying non-regressive dynamical equations, which have exponential dichotomies on a periodic time scale with bounded graininess, we use the method of graph transforms as in [1] to prove that there exists a unique integral manifold of that systems.
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