We investigate a class of non-integrable two-particle Calogero-Moser systems modulated by a power-law external potential.The local well-posedness of the Cauchy problem is established under the strict initial separatio...We investigate a class of non-integrable two-particle Calogero-Moser systems modulated by a power-law external potential.The local well-posedness of the Cauchy problem is established under the strict initial separation condition for the particles.For suitably prepared initial configurations,local solutions can be extended globally via energy conservation;conversely,negative energy conditions induce(in)finite-time blowup.The linear(in)stability of stationary solutions is analyzed,with their energy serving as a threshold.Numerical investigations employ a fourth-order Runge-Kutta scheme with adaptive step-size control.Simulations demonstrate that the trajectories either converge to steady states or exhibit blowup,depending on the power exponent α and initial conditions.Increasingαaccelerates the convergence rate and dampens oscillatory dynamics,promoting a transition from periodic behavior to static equilibrium.展开更多
In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to...In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.展开更多
Objective] This study was conducted to further explore the diversity of Saccharomyces cerevisiae_from Chateau Changyu Moser XV and realize better de-velopment and utilization of Saccharomyces cerevisiae resources. [Me...Objective] This study was conducted to further explore the diversity of Saccharomyces cerevisiae_from Chateau Changyu Moser XV and realize better de-velopment and utilization of Saccharomyces cerevisiae resources. [Method] ln this study, the wine grape regions of Chateau Changyu Moser XV were taken as the research object. The Saccharomycetes_in the soil was isolated, screened and ob-served in the natural fermentation process of grape berry epidermis and the fruit. The 32 Saccharomycetes strains were preliminarily classified based on WL nutrient agar, and 26S rDNA D1/D2 sequence analysis was conducted. [Result] Total y, 4 kinds of Saccharomycetes were identified in this study, including Pichia kluyveri, Hanseniaspora uvarum, Saccharomyces cerevisiae_and Cryptococcus magnus. [Con-clusion] The main species of Saccharomycetes in the wine grape region of Chateau Changyu Moser XV were preliminarily determined, which provides theoretical basis and research basis for the brewing of wine with special characteristics.展开更多
We present universal construction for the Calogero-Moser system with two types spins interaction of trigonometric potential based on the root system of semi-simple Lie algebra. In this formalism, we successfully build...We present universal construction for the Calogero-Moser system with two types spins interaction of trigonometric potential based on the root system of semi-simple Lie algebra. In this formalism, we successfully build up the correct Lax pair as well as the R-matrix for this generalized Calogero-Moser models. Moreover using the property of root system, we make a concise explanation that in the quantized model, the R-matrix takes the same form as the classical one, which is the main new result of this paper.展开更多
基金Supported by National Natural Science Foundation of China(12201118)Guangdong Basic and Applied Basic Research Foundation(2023A1515010706)。
文摘We investigate a class of non-integrable two-particle Calogero-Moser systems modulated by a power-law external potential.The local well-posedness of the Cauchy problem is established under the strict initial separation condition for the particles.For suitably prepared initial configurations,local solutions can be extended globally via energy conservation;conversely,negative energy conditions induce(in)finite-time blowup.The linear(in)stability of stationary solutions is analyzed,with their energy serving as a threshold.Numerical investigations employ a fourth-order Runge-Kutta scheme with adaptive step-size control.Simulations demonstrate that the trajectories either converge to steady states or exhibit blowup,depending on the power exponent α and initial conditions.Increasingαaccelerates the convergence rate and dampens oscillatory dynamics,promoting a transition from periodic behavior to static equilibrium.
文摘In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.
基金Supported by Scientific Research Project of Ningxia Grape and Wine Technology Innovation Center(1505)District-level Undergraduate Innovation Program of Northem University for Nationalities(QJCX-2015-028)~~
文摘Objective] This study was conducted to further explore the diversity of Saccharomyces cerevisiae_from Chateau Changyu Moser XV and realize better de-velopment and utilization of Saccharomyces cerevisiae resources. [Method] ln this study, the wine grape regions of Chateau Changyu Moser XV were taken as the research object. The Saccharomycetes_in the soil was isolated, screened and ob-served in the natural fermentation process of grape berry epidermis and the fruit. The 32 Saccharomycetes strains were preliminarily classified based on WL nutrient agar, and 26S rDNA D1/D2 sequence analysis was conducted. [Result] Total y, 4 kinds of Saccharomycetes were identified in this study, including Pichia kluyveri, Hanseniaspora uvarum, Saccharomyces cerevisiae_and Cryptococcus magnus. [Con-clusion] The main species of Saccharomycetes in the wine grape region of Chateau Changyu Moser XV were preliminarily determined, which provides theoretical basis and research basis for the brewing of wine with special characteristics.
文摘We present universal construction for the Calogero-Moser system with two types spins interaction of trigonometric potential based on the root system of semi-simple Lie algebra. In this formalism, we successfully build up the correct Lax pair as well as the R-matrix for this generalized Calogero-Moser models. Moreover using the property of root system, we make a concise explanation that in the quantized model, the R-matrix takes the same form as the classical one, which is the main new result of this paper.
