Two Temperature Extension of Phonon Hydrodynamics

2020 ◽  
Vol 45 (3) ◽  
pp. 291-304 ◽  
Author(s):  
Bing-Yang Cao ◽  
Miroslav Grmela ◽  
Zeng-Yuan Guo ◽  
Yu-Chao Hua ◽  
Ben-Dian Nie
Keyword(s):  
Mathematical Structure ◽  
State Variables ◽  
Qualitative Properties ◽  
Physical Content ◽  
Independent State ◽  
Energy Field ◽  
The Status ◽  
Qualitative Properties Of Solutions ◽  
Generic Equation ◽  
Two Temperature

AbstractPhonon hydrodynamics uses the fields of the total energy and the heat flux as state variables. We extend it by promoting the microscopic internal energy field into the status of an extra independent state variable. The governing equations of both the phonon and the extended (two temperature) phonon hydrodynamics are formulated as particular realizations of the abstract GENERIC equation. Such unified formulation makes both theories manifestly compatible with mechanics and thermodynamics. Also differences and similarities (in the physical content, in the mathematical structure, and in qualitative properties of solutions) between the two heat transfer theories, as well as their mutual compatibility, become manifestly displayed.

The Crisis of the Ryukyus (1877–82)

2018 ◽  
Author(s):  
Patrick Sze-lok Leung ◽  
Anthony Carty
Keyword(s):  
International Law ◽  
Colonial Power ◽  
Independent State ◽  
The People ◽  
The Us ◽  
The Status ◽  
Historical Viewpoint

Okinawa is now considered as Japanese territory, without challenge from most world powers. However, this is debatable from a historical viewpoint. The Ryukyu Kingdom which dominated the islands was integrated into Japan in 1879. The transformation is seen by Wang Hui as a process of modernization. This chapter argues the issue from an international law perspective. It shows that Ryukyu was an independent State as demonstrated by the 1854 Ryukyu–US Treaty, although it sent regular tributes to China. The Japanese integration by coercion is not justifiable. The people of Ryukyu were willing to continue being a tributary State rather than part of Japan. Britain, as the greatest colonial power, did not object. China and the US attempted to intervene in this affair, but no treaty has so far been concluded. Therefore, the status of Ryukyu/Okinawa remains unresolved and may need to be revisited, while putting the history context into consideration.

Qualitative properties of solutions to set optimization problems

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Lam Quoc Anh ◽  
Nguyen Huu Danh ◽  
Pham Thanh Duoc ◽  
Tran Ngoc Tam
Keyword(s):  
Optimization Problems ◽  
Set Optimization ◽  
Qualitative Properties ◽  
Qualitative Properties Of Solutions

Old and New Results for First Order Periodic ODEs without Uniqueness: a Comprehensive Study by Lower and Upper Solutions

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Franco Obersnel ◽  
Pierpaolo Omari
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Lower And Upper Solutions ◽  
Elementary Approach ◽  
Qualitative Properties ◽  
First Order ◽  
The Past ◽  
The Cauchy Problem ◽  
Qualitative Properties Of Solutions ◽  
Comprehensive Study

AbstractAn elementary approach, based on a systematic use of lower and upper solutions, is employed to detect the qualitative properties of solutions of first order scalar periodic ordinary differential equations. This study is carried out in the Carathéodory setting, avoiding any uniqueness assumption, in the future or in the past, for the Cauchy problem. Various classical and recent results are recovered and generalized.

scholarly journals Radially symmetric solutions to the Hénon–Lane–Emden system on the critical hyperbola

2014 ◽  
Vol 16 (03) ◽  
pp. 1350030 ◽  
Author(s):  
Roberta Musina ◽  
K. Sreenadh
Keyword(s):  
Variational Methods ◽  
Existence Results ◽  
Qualitative Properties ◽  
Radially Symmetric Solutions ◽  
Qualitative Properties Of Solutions

We use variational methods to study the existence of non-trivial and radially symmetric solutions to the Hénon–Lane–Emden system with weights, when the exponents involved lie on the "critical hyperbola". We also discuss qualitative properties of solutions and non-existence results.

scholarly journals Approximation of customers’ rights institution concerning retail purchase-sale to the European Union provisions

2020 ◽  
pp. 452-457
Author(s):  
Danylo Demchenko
Keyword(s):  
European Union ◽  
The European Union ◽  
Complete Understanding ◽  
Independent State ◽  
Association Agreement ◽  
Rights Protection ◽  
Consumer Rights ◽  
The Status ◽  
The Subject ◽  
Official Evaluation

In the article the meaning of the customer rights protection is researched regarding the minor purchase and sale, as a fundamentalfor the capitalist economy. Separately, it is noted that the adoption of the law “on consumer rights protection” was one of the first when Ukraine received the status of an independent state and fixed the basic principle of consumer rights protection in Part 2 of Article 50of the Constitution of Ukraine. The importance of the association agreement between Ukraine and the European Union for updating theappropriate level of attention to consumer protection is considered. The Annex XXXIX to the 20 agreement regarding association isdefined, being fundamental for the purposes of the research, in which 15 provisions that concern the subject of the research are outlined.The special attention is devoted to the results that were already accomplished, even without the use of systematic approach by the legalauthorities. Three main spheres are found out, which will undergo swift development, as a consequence of continuation of work onapproximation of Ukrainian legislation to the European sample. Each of the streams is processed specifically and in detail. The optionsof future implementation are provided in the process of analysis. For a more complete understanding, separate statistical analysis wasmade. Special attention is paid to problematic issues that do not allow the executive authorities to approach the legislation with thehigher intensity and more effectively. The author’s vision of the Conception of the governmental policy in the sphere of customer’srights protection for the 2020 period is laid out. The critical remarks are being made regarding the inactivity of the executive authoritiesin attraction of European Committee for the official evaluation of the appropriateness of the Ukrainian legislation to the provisions ofthe European Union. Based on the analysis, the methodological concepts of transformation of the institution of the consumer rights protectionin the Ukrainian legislation are worked out.

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