Determine the source term of a two-dimensional heat equation

Let $\Omega$ be a two-dimensional heat conduction body. We consider the problem of determining the heat source $F(x,t)=\varphi(t)f(x,y)$ with $\varphi$ be given inexactly and $f$ be unknown. The problem is nonlinear and ill-posed. By a specific form of Fourier transforms, we shall show that the heat source is determined uniquely by the minimum boundary condition and the temperature distribution in $\Omega$ at the initial time $t=0$ and at the final time $t=1$. Using the methods of Tikhonov's regularization and truncated integration, we construct the regularized solutions. Numerical part is given.Comment: 18 page

Determination of the body force of a two-dimensional isotropic elastic body

Let $\Omega$ represent a two$-$dimensional isotropic elastic body. We consider the problem of determining the body force $F$ whose form $\phi(t)(f_1(x),f_2(x))$ with $\phi$ be given inexactly. The problem is nonlinear and ill-posed. Using the Fourier transform, the methods of Tikhonov's regularization and truncated integration, we construct a regularized solution from the data given inexactly and derive the explicitly error estimate. Numerical part is givenComment: 23 page

“False Patellar Duplication†Originated from Synovial Osteochondromatosis in Knee Joint: A Rare Case Report

BACKGROUND: “False patellar duplication†is a situation where there are two pieces in the position of a knee-joint like patella. It can derive from cartilage tumors, soft tissue tumors, or gout tumors, or due to the heterotopic ossification, forming a sub patella in the knee joint. CASE REPORT: A woman, 57 years old, healthy history, she has hospitalized for right knee joint pain since 2 years. Diagnosis: the synovial osteochondromatosis of the right knee. We decided to conduct and arthroscopy and removal. After 18 months surgery, the patient knee joint is currently good, range of motion (ROM) (-10)°- 0°-160°, Lysholm Knee Scoring Scale 85/100 point. CONCLUSION: This is the second case in the world and the first case in Vietnam. This is an experience in the process of diagnosis, arthroscopic treatment and differentiation from the "double patellae" status

Anatomical Study of Femoral Condylar Index in Magnetic Resonance Imaging: Implication to Total Knee Replacement Surgery for Vietnamese People

BACKGROUND: The femoral rotation angle is important element in total knee replacement (TKR). AIM: To measure this angle, we determine through the axes: the transepicondylar axis (cTEA and sTEA), the posterior condylar axis (PCA), the anteroposterior axis (APA – Whiteside axis). METHODS: Measuring the angles created by the four axes: cTEA, sTEA, PCA and APA in magnetic resonance imaging (MRI); determining the femoral rotation angle and application TKR. RESULTS: the angle between APA and cTEA: 90.41° ± 3.35°, the angle between APA and sTEA: 94.47° ± 3.31°, the angle between APA and PCA: 96.40° ± 4.59°, the angle between cTEA and sTEA: 4.00° ± 1.02°, the angle between cTEA and PCA: 6.53° ± 2.55°, the angle between sTEA and PCA: 3.48° ± 1.91°. CONCLUSION: The angle between sTEA and PCA is the angle that best represents the femoral rotation angle. However, in case of sTEA or PCA is difficult to identify, it can be measure via the APA or cTEA. These angles don’t differ by age, gender and place of knee joint

Multifactorial Evolutionary Algorithm For Clustered Minimum Routing Cost Problem

Minimum Routing Cost Clustered Tree Problem (CluMRCT) is applied in various fields in both theory and application. Because the CluMRCT is NP-Hard, the approximate approaches are suitable to find the solution for this problem. Recently, Multifactorial Evolutionary Algorithm (MFEA) has emerged as one of the most efficient approximation algorithms to deal with many different kinds of problems. Therefore, this paper studies to apply MFEA for solving CluMRCT problems. In the proposed MFEA, we focus on crossover and mutation operators which create a valid solution of CluMRCT problem in two levels: first level constructs spanning trees for graphs in clusters while the second level builds a spanning tree for connecting among clusters. To reduce the consuming resources, we will also introduce a new method of calculating the cost of CluMRCT solution. The proposed algorithm is experimented on numerous types of datasets. The experimental results demonstrate the effectiveness of the proposed algorithm, partially on large instance

Evaluation of Lecture Hall Service and Infrastructures Construction Rules of Vietnam Universities Via A Case of Neu in Hanoi

Building a university design regulations and standards is not only necessary for units in the industry but also contributes to bringing to society modern educational models, suitable to the economic conditions of the country. The standard applies to the design, renovation and new design of university buildings throughout Vietnam, based on the document issued by the Ministry of Construction No. TCVN 3981:1985. This paper also suggest: Improve the quality of the teaching /lecture service staff. First, Develop a reasonable monitoring, evaluation and reward mechanism to motivate people to work hard; Second, Each faculty member on duty has a job description with clear responsibilities, rights and obligations; Third, Conduct ongoing training. It is necessary to regularly organize training and training courses on serving, communicating, and dealing with customers

EROSION FEATURES ALONG CUA DAI BEACH, HOI AN CITY, QUANG NAM PROVINCE, VIETNAM

Hoi An is a famous tourist city in Central Vietnam with Cua Dai beach which is a long beautiful swimming beach. In recent years, tourism of the city is developing very fast. The southern part of Cua Dai beach was covered by many resorts which were located close to the beach and protected by hard structures such as seawall, revetment, groin,… At present, all properties closed to the beach and hard protection structures of resort system were destroyed by wave action. And the northern part of Cua Dai beach (public beach) was seriously eroded and has been protected by “Soft structure”. Cua Dai coast erosion problem becomes the hot topic in communication system from central to local governments and it becomes the big concern of Vietnamese and international scientists. This paper presents the initial study results of Cua Dai beach erosion features. Study results show that Cua Dai beach erosion/deposition phenomenon occurred for a long time but the rate of accretion was larger than that of erosion. From the year of 2000 to present the rate of erosion was larger than that of accretion. The main causes of Cua Dai beach erosion are the interaction between hard protection structures and wave action, dredging operation in Thu Bon river mouth... which reduced the longshore sediment transport rate from Thu Bon river mouth to eroded beach

The Temperature-sensitivity of a Critical Electric Field Induced Magnetic Easy-axis Reorientation Ferromagnetic/ferroelectric Layered Heterostructures

We have investigated the effects of temperature on the magnetic easy axis reorientation (EARs) in polycrystalline ferromagnetic (FM) nano-scale thin films, i.e. (001)-oriented cubic films such as Fe, Ni, CFO and (0001)-oriented hexagonal films such as Co, grown on ferroelectric (FE) substrates, for example PZT, BTO substrates. The model of FM/FE bilayered heterostructures has been applied to study the total free energy of the FM films. By minimizing this energy, we have shown that temperature has a significant effect on a critical electric field induced magnetic reorientation

BoMb-OT: On Batch of Mini-batches Optimal Transport

Mini-batch optimal transport (m-OT) has been successfully used in practical applications that involve probability measures with intractable density, or probability measures with a very high number of supports. The m-OT solves several sparser optimal transport problems and then returns the average of their costs and transportation plans. Despite its scalability advantage, the m-OT does not consider the relationship between mini-batches which leads to undesirable estimation. Moreover, the m-OT does not approximate a proper metric between probability measures since the identity property is not satisfied. To address these problems, we propose a novel mini-batching scheme for optimal transport, named Batch of Mini-batches Optimal Transport (BoMb-OT), that finds the optimal coupling between mini-batches and it can be seen as an approximation to a well-defined distance on the space of probability measures. Furthermore, we show that the m-OT is a limit of the entropic regularized version of the BoMb-OT when the regularized parameter goes to infinity. Finally, we carry out extensive experiments to show that the BoMb-OT can estimate a better transportation plan between two original measures than the m-OT. It leads to a favorable performance of the BoMb-OT in the matching and color transfer tasks. Furthermore, we observe that the BoMb-OT also provides a better objective loss than the m-OT for doing approximate Bayesian computation, estimating parameters of interest in parametric generative models, and learning non-parametric generative models with gradient flow.Comment: 36 pages, 20 figure

Biocontrol of Alternaria alternata YZU, a causal of stem end rot disease on pitaya, with soil phosphate solubilizing bacteria

Stem end rot is the most destructive disease caused by Alternaria alternata YZU in pitaya-growing regions of Vietnam. This study was conducted to characterize antagonistic phosphate-solubilizing bacteria (PSB) from rhizosphere soil for their biocontrol activities against A. alternata YZU and evaluate the effect of temperature, pH, and water activity on that antagonism. Among seven PSB isolated from 45 rhizosphere soil samples, PSB31 (identified as Bacillus sp. strain IMAU61039, Accession number: MF803700.1) exhibited the highest antagonistic activity against A. alternata YZU with an average inhibition diameter of 0.65 ± 0.05 cm. The results also show that the strain PSB31 controlled the mycelial growth of A. alternata YZU by secreting antifungal metabolites. The most potent inhibitory activity was identified under in vitro conditions of 25 °C, pH 7, and aw 1. The isolated PSB31 could be a potential biological control agent against A. alternata YZU