Stability for the Boussinesq system on real hyperbolic Manifolds and application

In this paper we study the global existence and stability of mild solution for the Boussinesq system on the real hyperbolic manifold $\mathbb{H}^d(\mathbb{R})$ ($d \geqslant 2$). We will consider a couple of Ebin-Marsden's Laplace and Laplace-Beltrami operators associated with the corresponding linear system which provides a vectorial heat semigoup. First, we prove the existence and the uniqueness of the bounded mild solution for the linear system by using certain dispersive and smoothing estimates of the vectorial heat semigroup. Next, using the fixed point arguments, we can pass from the linear system to the semilinear system to establish the existence of the bounded mild solution. We will prove the exponential stability of such solution by using the cone inequality. Finally, we give an application of stability to the existence of periodic mild solution for the Boussinesq system.Comment: 23 pages. arXiv admin note: substantial text overlap with arXiv:2209.0780

On asymptotically almost periodic solutions to the Navier-Stokes equations in hyperbolic manifolds

In this paper we extend a recent work \cite{HuyXuan2020} to study the forward asymptotically almost periodic (AAP-) mild solution of Navier-Stokes equation on the real hyperbolic manifold $\mathbb{H}^d(\mathbb{R})$ with dimension $d \geq 2$. Using the dispertive and smoothing estimates for Stokes equation \cite{Pi} we invoke the Massera-type principle to prove the existence and uniqueness of the AAP- mild solution for the Stokes equation in $L^p(\Gamma(TM)))$ space with $p>d$. We then establish the existence and uniqueness of the small AAP- mild solutions of the Navier-Stokes equation by using the fixed point argument. The asymptotic behaviour (exponential decay and stability) of these small solutions are also related. Our results extend also \cite{FaTa2013} for the forward asymptotic mild solution of the Navier-Stokes equation on the curved background.Comment: 21 page

Agricultural restructure policy in Vietnam and practical application for sustainable development in agriculture

Recently, effective agricultural policies necessitate sustainable development in the agricultural sector, which necessitates frequent research and the attention of policymakers. Consequently, this study investigates the effect of agricultural restructuring policies on agricultural import, agricultural export, agricultural employment, agricultural irrigation land, and agricultural land on the sustainable development of agriculture in Vietnam. From 1991 to 2021, the researchers extracted secondary data from secondary sources such as World Development Indicators (WDI). The researchers also used the non-linear autoregressive distributed lag (NARDL) method to examine the relationships between the variables. The results revealed that agricultural restructuring policies regarding agricultural import, agricultural exports, agricultural employment, agricultural irrigation land, and agricultural land have a positive correlation with Vietnam's agriculture's sustainable development. The research assists policymakers in formulating regulations for achieving sustainable agricultural development by implementing effective agricultural restructuring policies.Mai Thi Huyen (Bac Giang Agriculture and Forestry University (BAFU)), Nguyen Thi Xuan Huong (Viet Nam National University of Forestry (VNUF)), Nguyen Van Song (Viet Nam National University of Agriculture (VNUA)), Nguyen Thi Hai Yen (College of Economics, Vinh University (VU)), Nguyen Dang Que National Academy of Public Administration (NAPA))Includes bibliographical references

Complex Monge-Amp\`ere equations for plurifinely plurisubharmonic functions

This paper studies the complex Monge-Amp\`ere equations for $\mathcal F$-plurisubharmonic functions in bounded $\mathcal F$-hyperconvex domains. We give sufficient conditions for this equation to solve for measures with a singular part

On attractor's dimensions of the modified Leray-alpha equation

The primary objective of this paper is to investigate the modified Leray-alpha equation on the two-dimensional sphere $\mathbb{S}^2$, the square torus $\mathbb{T}^2$ and the three-torus $\mathbb{T}^3$. In the strategy, we prove the existence and the uniqueness of the weak solutions and also the existence of the global attractor for the equation. Then we establish the upper and lower bounds of the Hausdorff and fractal dimensions of the global attractor on both $\mathbb{S}^2$ and $\mathbb{T}^2$. Our method is based on the estimates for the vorticity scalar equations and the stationary solutions around the invariant manifold that are constructed by using the Kolmogorov flows. Finally, we will use the results on $\mathbb{T}^2$ to study the lower bound for attractor's dimensions on the case of $\mathbb{T}^3$.Comment: 24 page

Research and Design of an X-Band UHF Power Amplifier

Introduction. A method for designing power amplifiers for use in the transmitting channels of X-band transceiver modules is investigated. The design process was aimed at optimizing the relationship between the basic amplifier characteristics, including the operating frequency band, output power level, output linearity, high harmonics suppression, etc.  Aim. Investigation of a method for designing an X-band UHF power amplifier, which is capable of optimizing the relationship between its main characteristics.  Materials and methods. Theoretical calculations were combined with experimental studies into the design of a UHF power amplifier. The stages of the design process are described in detail, including major ideas, principal circuits, and strip circuits. Evaluations were conducted using the Keysight ADS high frequency circuit simulation tool.  Results. A method for designing X-band UHF power amplifiers on the basis of a close combination of theory, simulation, and experimental adjustment was described in detail.  Conclusion. A prototype of an X-band PA was developed; an approach to developing a methodology for manufacturing, measuring, and testing X-band PAs is described.Introduction. A method for designing power amplifiers for use in the transmitting channels of X-band transceiver modules is investigated. The design process was aimed at optimizing the relationship between the basic amplifier characteristics, including the operating frequency band, output power level, output linearity, high harmonics suppression, etc.  Aim. Investigation of a method for designing an X-band UHF power amplifier, which is capable of optimizing the relationship between its main characteristics.  Materials and methods. Theoretical calculations were combined with experimental studies into the design of a UHF power amplifier. The stages of the design process are described in detail, including major ideas, principal circuits, and strip circuits. Evaluations were conducted using the Keysight ADS high frequency circuit simulation tool.  Results. A method for designing X-band UHF power amplifiers on the basis of a close combination of theory, simulation, and experimental adjustment was described in detail.  Conclusion. A prototype of an X-band PA was developed; an approach to developing a methodology for manufacturing, measuring, and testing X-band PAs is described

Periodic solutions for Boussinesq systems in weak-Morrey spaces

We prove the existence and polynomial stability of periodic mild solutions for Boussinesq systems in critical weak-Morrey spaces for dimension $n\geqslant3$. Those systems are derived via the Boussinesq approximation and describe the movement of an incompressible viscous fluid under natural convection filling the whole space $\mathbb{R}^{n}$. Using certain dispersive and smoothing properties of heat semigroups on Morrey-Lorentz spaces as well as Yamazaki-type estimate on block spaces, we prove the existence of bounded mild solutions for the linear equations corresponding to the Boussinesq system. Then, we establish a Massera-type theorem to obtain the existence and uniqueness of periodic solutions to corresponding linear equations on the half-line by using a mean-ergodic method. Next, using fixed point arguments, we can pass from linear equations to prove the existence uniqueness and polynomial stability of such solutions for Boussinesq systems. Finally, we apply the results to Navier-Stokes equations.Comment: 18 page

Driving Factors for Green Innovation in Vietnamese Construction Enterprises

Purpose: The aim of this study is to examine the influences of different factors on green innovation in Vietnamese construction enterprises.   Theoretical framework: The theoretical framework is built upon the resource-based view, the model of organizational innovation, and stakeholder theory.   Design/methodology/approach: The research carries out a literature survey related to construction enterprises, then empirical analysis is conducted among 450 employees and managers at all level working in this field with the results analyzed using Cronbach’s Alpha analysis, exploratory factor analysis, pearson correlation analysis, linear regression analysis and One - way ANOVA analysis.   Findings: The results demonstrate that using renewable energy is well represented for green innovation in the Vietnamese construction industry and quantitative results also show positive impacts of all factors studied on green innovation: Green dynamic capabilities, Green creativity, Green knowledge sharing, Corporate environmental ethics, Pressure from industry competitors and regulators. In addition, the result affirmed there are statistically significant differences in the level of green innovation between construction enterprises of size and age, but not types of firm.   Research, Practical & Social implications: The study proposes solutions for both enterprises and regulators – one of the external stakeholders to develop green innovation in the construction sector. 

Asymptotically almost periodic solutions to parabolic equations on the real hyperbolic manifold

In this work we study the existence and the asymptotic behaviour of the asymptotically almost periodic mild solutions of the vectorial parabolic equations on the real hyperbolic manifold $\mathbb{H}^d(\mathbb{R})$ ($d \geqslant 2$). We will consider the vectorial laplace operator in the sense of Ebin-Marsden's laplace operator. Our method is based on certain dispertive and smoothing estimates of the semigroup generated by the linearized vectorial heat equation and the fixed point argument. First, we prove the existence and the uniqueness of the asymptotically almost periodic mild solution for the linearized equations. Next, using the fixed point argument, we can pass from linearized equations to semilinear equations to prove the existence, uniqueness, exponential decay and stability of the solutions. Our abstract results will be applied to the incompressible Navier-Stokes equation and the semilinear vectorial heat equation.Comment: 20 pages. arXiv admin note: text overlap with arXiv:2101.0330

Studying of The Viability of Selected Probioitcs in Soy Milk to Develop A Functional Beverage Product

In this research, Lactobacillus casei (L.casei) and  Lactobacillus plantarum (L.plantarum) were added into two soymilk products. The number of survival probiotics as well as the effects of probiotic strains, soymilk brands and additives to the quality of final product were also studied. The initial number was added around 107 to 108(CFU/ml) into Fami and Vinasoy soy milk. The number of survival probiotics was stable during the first four weeks with about 107 (CFU/ml) and then decreased to around 106 (CFU/ml) in the sixth week. In term of soymilk’s quality, the pH decreased dramatically while the Brix fell slowly after storing seven days in both soymilk products. The influence of food additive-fructose oligosaccharides adding to microencapsulate probiotics was also examined to increase storage time and final product quality