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

The pedagogical training management of gifted high school teachers in the region of Red River Delta based on a competency approach

Pedagogical training for teachers is always an important issue of every education system. Teachers impart knowledge, give academic advice to students, and assist students in applying knowledge to develop society. This study investigated the gifted high school teacher pedagogical training management in the region of the Red River Delta according to the competency approach. Based on the available data, the research indicated three main things: (i) Professional pedagogical competence of gifted high school teachers; (ii) Pedagogical training activities for gifted high school teachers; (iii) Management of pedagogical training activities for gifted high school teachers. This study conducted a survey of 547 departmental and school managers in gifted high school teachers in nine provinces in Red River Delta, including Hanoi, Ha Nam, Thai Binh, Nam Dinh, Hai Duong, Hung Yen, Bac Ninh, Quang Ninh, and Vinh Phuc. These findings are only preliminary research, and they will be an important basis for proposing management solutions to improve the effectiveness of pedagogical training activities for gifted high school teachers

Musculoskeletal Pain and Work-related Risk Factors among Waste Collectors in Hanoi, Vietnam: A Cross-sectional Study

BACKGROUND: Musculoskeletal disorders (MSDs) are prevalent among waste collectors (WCs) in developing countries. AIM: This study aimed to investigate the prevalence of MSDs and the factors associated with the risk of persistent musculoskeletal pain among WCs in Hanoi, Vietnam. METHODS: A cross-sectional survey was utilized to study 468 WCs in 2017. The Örebro Musculoskeletal Pain Questionnaire and a questionnaire on demographic and work conditions were used to collect data. Descriptive and multivariate logistics regression analyzes were applied at a significance level of 0.05 to examine the factors related to the risk of persistent pain. FINDINGS: About 74.4% of the participants of this study experienced MSDs in at least one body region and 9.4% reported MSDs in all 10 body sites. The lower back was reported to be the most affected followed by the neck and shoulders. The risk of persistent musculoskeletal pain was significantly associated with age (odds ratio (OR) = 2.31, confidence interval (CI) = 1.05–5.09), gender (OR = 3.29, CI = 1.28–8.44), work hours (OR = 2.35, CI = 1.12–4.92), work shift (OR = 0.48, CI = 0.26–0.92), duration of poor postures of the neck (OR = 0.31, CI = 0.13–0.76), bent back (OR = 0.4 CI = 0.18–0.92) and for medial rotation (OR = 3.01, CI = 1.42–6.36), carrying heavy objects (OR = 2.94, CI = 1.15–7.48), and experience of work dissatisfaction (OR = 3.31, CI = 1.46-7.52), stress (OR = 7.14, CI = 3.14–16.24), or anxiety (OR = 6.37, CI = 3.07–13.21). CONCLUSIONS: High prevalence of MSDs among WCs and its association with self-assessed unfavorable work postures and work-related stress implies the need of mechanical and social support at work for WC to prevent the development of MSDs and persistent pain

On stability problem for the stationary Boussinesq system in Morrey-type spaces

In this paper we establish the asymptotic stability of steady solutions for the Boussinesq systems in the framework of Cartesian product of critical weak-Morrey spaces on $\mathbb{R}^n$, where $n \geqslant 3$. In our strategy, we first establish the continuity for the long time of the bilinear terms associated with the mild solutions of the Boussinesq systems, i.e., the bilinear estimates by using only the norm of the present spaces. As a direct consequence, we obtain the existence of global small mild solutions and asymptotic stability of steady solutions of the Boussinesq systems in the class of continuous functions from $[0, \infty)$ to the Cartesian product of critical weak-Morrey spaces. Our techniques consist interpolation of operators, duality, heat semigroup estimates , Holder and Young inequalities in block spaces (based on Lorentz spaces) that are preduals of Morrey-Lorentz spaces. Our results are generalized the previous ones of the steady Boussinesq systems in weak-$L^p$ spaces obtained by Hishida [T. Hishida, {\it On a class of Stable Steady flow to the Exterior Convection Problem}, Journal of Differential Equations, Vol. 141, Iss. 1 (1997), pages 54-85] and Ferreira et al. [L.C.F. Ferreira and E.J. Villamizar-Roa, {\it On the stability problem for the Boussinesq equations in weak-$L^p$ spaces}, Commun. Pure Appl. Anal. (2010), Vol. 9, No. 3, pages 667-684] and of the Navier-Stokes equations in Morrey spaces obtained by Kozono et al. [H. Kozono and M. Yamazaki, {\it The stability of small stationary solutions in Morrey Spaces of the Navier-Stokes equation}, Indiana University Mathematics Journal, Vol. 44, No. 4 (1995), pages 1307-1336].Comment: 17 page

Nonlinear analysis for proposing limit state criteria of reinforced concrete road bridge superstructures

In the research of long-time operating road bridge superstructures, it should note that when the internal forces in the beam elements reach specific values, the stiffness of the cross-section of these elements should decrease. Besides that, if there are damaged places in the beam-element of the road bridge superstructures, the element could not work normally, and the redistribution of internal forces between elements in the whole system would happen. This phenomenon was not taken into account in the initial design calculation. In practice, it shows that many road bridges are subjected to greater loads than the calculated loads in the design process, but they still normally operate. This article proposes the other limit state criteria in evaluating the load capacity reserve of road-bridge superstructures using nonlinear analysis based on nonlinear deformational models of modern construction codes. The proposed calculation procedure is established to explain the load capacity reserve of long-time operating road bridge superstructures in the case of the lack of experimental evaluation. From the obtained results, the suitable limit state criteria for road bridge superstructures are suggested, and the conclusions about the accuracy of the proposed approach of nonlinear structural analysis are recommended

Lax Compliance of Goodwill Impairment Accounting in the Early Year after IFRS Implementation

After some decades of discussing in recognizing, measuring and reporting goodwill in the financial reports, Hong Kong finally has promulgated HKAS 36 - Impairment of Assets, for the convergence of IFRS including IAS 36. This is absolutely applicable to all transactions of business combinations beginning on or after 1st January, 2005. The adoption of HKAS 36 has resulted in significant changes and more complexity in terms of techniques and in the nature of disclosures relating to goodwill and its impairment to the reporting first-time adopters. The traditional method by adopting “capitalize and amortize” has been replaced by impairment testing regime based on subjective assumptions. Therefore, it is more likely to have inconsistent compliance by the first-time adopters in their transition period under the new reporting approach. Thus, this study has the purpose of examining the compliance levels under a variety of provisions of HKAS 36. By using the data of annual reports of Hong Kong listed firms, first-time adopters, the research found the material levels of non-compliance and substantial changes in the quality of note-form disclosures bearing on impairment testing process. Further study on post transition period is identified and discussed. Keywords: Goodwill, Impairment, Financial Reporting Standard, Hong Kon

Contaminant spreading by natural convection in a box

In this paper the spreading of a contaminant accompanied  with natural convection in a box is numerically simulated. The box may be  considered as a cooking room or a working place where some sources of heat  and contaminant are in the simultaneous action. The box floor is supposed to  be divided into several domains with different boundary conditions for  temperature or heat flux. Here the purpose of the simulation is to  understand the contaminant spreading process in the box under the influence  of a convective motion. The model can be also applied for an enclosure with  separated parts differentially heated by the sunlight on its boundaries. A  good knowledge of this process is very useful for setting an efficient  ventilation scheme. In this paper the finite difference method based on the  Samarski scheme with ADI technique is applied for numerical simulation. Here  the box floor is divided into two domains of equal sizes but with different  temperature or heat flux. The contaminant source locates in the middle of  the box bottom. The simulation shows that over the part of the floor where  temperature or heat flux is greater the contaminant concentration is lager.  That result is in the accordance with the experiment done in the framework  of this~investigation

Dispersion and nonlinearity properties of small solid-core photonic fibers with As2Se3 substrate

Characteristics of As2Se3 photonic crystal fibers (PCFs) with a solid-core and small-core diameter are numerically investigated in the long-wavelength range (from 2 to 10 μm). A full modal analysis and optical properties of designed photonic crystal fibers with lattice constant Λ and filling factor d/Λ are presented in terms of chromatic dispersion, effective refractive index, nonlinear coefficients, and confinement loss. The simulation results show that a high nonlinear coefficient of 4410.303 W–1·km–1 and a low confinement loss of 10−20 dB·km–1 can simultaneously be achieved in the proposed PCFs at a 4.5 μm wavelength. Chromatic dispersions are flat. The values of dispersion increase with increasing filling factor d/Λ and decrease with the increase in lattice constant Λ. In particular, some chromatic dispersion curves also cut the zero-dispersion line at two points. The flat dispersion feature, high nonlinearity, and small confinement loss of the proposed photonic crystal fiber structure make it suitable for supercontinuum

flavonoids from Fissistigma acuminatissima

From the leaves of Fissistigma acuminatissima growing in Vietnam, two flavonoids, catechin and isorhamnetin-3-o-rutinoside were isolated. Their structures were characterized on the basis of MS and NMR spectra data and comparison with reported data.Keywords: Annonaeae; Fissistigma acuminatissima; catechin; isorhamnetin-3-o-rutinoside

NONLINEAR CHARACTERISTICS OF SQUARE SOLID-CORE PHOTONIC CRYSTAL FIBERS WITH VARIOUS LATTICE PARAMETERS IN THE CLADDING

Nonlinear characteristics of fused silica, solid-core photonic crystal fibers (PCFs) with a square array of air holes are studied numerically. We present a novel design that emphasizes the difference in air hole diameters in the photonic cladding. These PCFs have the advantages of flat dispersion, high nonlinearity, and low attenuation. Based on simulation results, three optimal structures, denoted #F1, #F2, and #F3, having anomalous and all-normal dispersions in the near-infrared range are selected to investigate characteristic properties at the pump wavelength. Such PCFs open up many possibilities for nonlinear optical applications, especially supercontinuum generation