On a Kirchhoff-Carrier equation with nonlinear terms containing a finite number of unknown values

summary:We consider problem (P) of Kirchhoff-Carrier type with nonlinear terms containing a finite number of unknown values $u(\eta _{1},t),\cdots ,u(\eta _{q},t)$ with $0\leq \eta _{1}<\eta _{2}<\cdots <\eta _{q}<1.$ By applying the linearization method together with the Faedo-Galerkin method and the weak compact method, we first prove the existence and uniqueness of a local weak solution of problem (P). Next, we consider a specific case $({\rm P}_{q})$ of (P) in which the nonlinear term contains the sum $S_{q}[u^{2}](t)=q^{-1}\sum _{i=1}^{q}u^{2}(\frac{(i-1)}{q},t)$. Under suitable conditions, we prove that the solution of $({\rm P}_{q})$ converges to the solution of the corresponding problem $({\rm P}_{\infty })$ as $q\rightarrow \infty$ (in a certain sense), here $({\rm P}_{\infty })$ is defined by $({\rm P}_{q})$ in which $S_{q}[u^{2}](t)$ is replaced by $\int _{0}^{1}u^{2}( y,t) {\rm d}y.$ The proof is done by using the compactness lemma of Aubin-Lions and the method of continuity with a priori estimates. We end the paper with remarks related to similar problems

New records and morphological assessments of long-nosed fruit bats (chiroptera: pteropodidae: Macroglossus spp.) from Vietnam

Long-nosed fruit bat is a common name of the genus Macroglossus which comprises two species: Dagger-toothed long-nosed fruit bat (M. minimus) and Greater long-nosed fruit bat (M. sobrinus). These two species were rarely recorded from Vietnam or neighboring countries. Within Vietnam, M. minimus has been recorded only from two localities in southern Vietnam while M. sobrinus was known from all northern, central and southern regions of the country. Morphological features of these species in Vietnam were poorly documented in previous publications. With results from a rapid examination of all specimens and recently captured individuals, we here confirm that M. sobrinus is distinctively larger than M. minimus in all external and craniodental measurements. Two species are also distinguishable by their nostril shapes and mandible symphyses. This paper provides new distributional records of both M. sobrinus and M. minimus from Vietnam with remarks on their ecology and habitats.

Effects of calpastain (CAST) polymorphisms on carcass and meat quality traits in Mongcai pigs

Calpastain (CAST) activity plays a major role in muscle growth and proteolytic changes post-mortem and the CAST gene has been considered as a candidate gene for carcass and pork quality characteristics. The aim of this study was to analyze the association of two polymorphisms namely CAST_HinfI (allele A and B) and CAST_MspI (allele C and D) with carcass and meat quality traits in Mongcai, a Vietnamese indigenous pig breed. Polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) was used to genotype the animals at these loci. Results indicate that the CAST_HinfI single nucleotide polymorphism (SNP) had a low frequency of allele A as compared to allele B, while the C and D allele distribution was almost the same for the CAST_MspI SNP. In the association analysis, significant effects on dressing percentage of carcass were detected. The CAST_HinfI locus was associated with the pH24, while the CAST_MspI position was in association with pH45 min, drip loss48 and redness color. Additional analysis showed a variation in muscle fiber type composition with higher proportion of IIx fiber in pigs with AB genotype (P &lt; 0.05). Three constructed haplotypes namely AB/CD, AB/DD and BB/CC also had significant effects on carcass, type IIa and IIb fiber percentages.Keywords: Association, carcass, pork quality, Vietnamese local pi

On a Kirchhoff-Carrier equation with nonlinear terms containing a finite number of unknown values

We consider problem (P) of Kirchhoff-Carrier type with nonlinear terms containing a finite number of unknown values $u(\eta_1,t),\cdots,u(\eta_q,t)$ with 0\leq\eta_1<\eta_2<\cdots<\eta_q<1. By applying the linearization method together with the Faedo-Galerkin method and the weak compact method, we first prove the existence and uniqueness of a local weak solution of problem (P). Next, we consider a specific case $({\rm P}_q)$ of (P) in which the nonlinear term contains the sum S_q[u^2](t)=q^{-1}\sum_{i=1}^qu^2(\frc{(i-1)}q,t). Under suitable conditions, we prove that the solution of $({\rm P}_q)$ converges to the solution of the corresponding problem $({\rm P}_{\infty})$ as $q\rightarrow\infty$ (in a certain sense), here $({\rm P}_{\infty})$ is defined by $({\rm P}_q)$ in which $S_q[u^2](t)$ is replaced by $\int_0^1u^2( y,t) {\rm d}y.$ The proof is done by using the compactness lemma of Aubin-Lions and the method of continuity with a priori estimates. We end the paper with remarks related to similar problems

Conditional expectation with regularization for missing data imputation

Missing data frequently occurs in datasets across various domains, such as medicine, sports, and finance. In many cases, to enable proper and reliable analyses of such data, the missing values are often imputed, and it is necessary that the method used has a low root mean square error (RMSE) between the imputed and the true values. In addition, for some critical applications, it is also often a requirement that the imputation method is scalable and the logic behind the imputation is explainable, which is especially difficult for complex methods that are, for example, based on deep learning. Based on these considerations, we propose a new algorithm named "conditional Distribution-based Imputation of Missing Values with Regularization" (DIMV). DIMV operates by determining the conditional distribution of a feature that has missing entries, using the information from the fully observed features as a basis. As will be illustrated via experiments in the paper, DIMV (i) gives a low RMSE for the imputed values compared to state-of-the-art methods; (ii) fast and scalable; (iii) is explainable as coefficients in a regression model, allowing reliable and trustable analysis, makes it a suitable choice for critical domains where understanding is important such as in medical fields, finance, etc; (iv) can provide an approximated confidence region for the missing values in a given sample; (v) suitable for both small and large scale data; (vi) in many scenarios, does not require a huge number of parameters as deep learning approaches; (vii) handle multicollinearity in imputation effectively; and (viii) is robust to the normally distributed assumption that its theoretical grounds rely on

Network-Aided Intelligent Traffic Steering in 6G O-RAN: A Multi-Layer Optimization Framework

To enable an intelligent, programmable and multi-vendor radio access network (RAN) for 6G networks, considerable efforts have been made in standardization and development of open RAN (O-RAN). So far, however, the applicability of O-RAN in controlling and optimizing RAN functions has not been widely investigated. In this paper, we jointly optimize the flow-split distribution, congestion control and scheduling (JFCS) to enable an intelligent traffic steering application in O-RAN. Combining tools from network utility maximization and stochastic optimization, we introduce a multi-layer optimization framework that provides fast convergence, long-term utility-optimality and significant delay reduction compared to the state-of-the-art and baseline RAN approaches. Our main contributions are three-fold: i) we propose the novel JFCS framework to efficiently and adaptively direct traffic to appropriate radio units; ii) we develop low-complexity algorithms based on the reinforcement learning, inner approximation and bisection search methods to effectively solve the JFCS problem in different time scales; and iii) the rigorous theoretical performance results are analyzed to show that there exists a scaling factor to improve the tradeoff between delay and utility-optimization. Collectively, the insights in this work will open the door towards fully automated networks with enhanced control and flexibility. Numerical results are provided to demonstrate the effectiveness of the proposed algorithms in terms of the convergence rate, long-term utility-optimality and delay reduction.Comment: 15 pages, 10 figures. A short version will be submitted to IEEE GLOBECOM 202

Synthesis of para-menthane 3,8 - diol from Eucalyptus citriodora essential oil for application in mosquito repellent products

To repel mosquitoes, there have been many highly effective chemical repellent products, but they carry the potential risk of being unsafe for humans and harmful to the environment. Insect repellent products derived from natural sources that are safe for humans and environmentally friendly are becoming increasingly popular. PMD is a broad-spectrum and effective insect repellent but is present in small amounts in the Eucalyptus citriodora essential oil (EO). In this study, we investigated and evaluated the conditions for synthesizing PMD from EO raw materials in an acidic environment to achieve the highest synthesis efficiency of 76.3%, and the PMD product was 96.4% pure after being converted for 5 hours at 50°C in a 0.25% H2SO4 solution. Additionally, the study also separated the two cis and trans isomers of PMD by column chromatography and determined their structures using infrared spectroscopy (IR) and nuclear magnetic resonance (NMR)

Enabling Intelligent Traffic Steering in A Hierarchical Open Radio Access Network

peer reviewedIn this paper, we aim to enable an intelligent traffic (TS) steering application in the open radio access network (O-RAN) by jointly optimizing the flow-split distribution, congestion control and scheduling (i.e. so-called JFCS). To do so, we develop a multi-layer optimization framework based on network utility maximization and stochastic optimization methods. The proposed algorithm provides fast convergence, long-term utility-optimality and significantly low latency compared to state-of-the-art RAN approaches. In particular, our main contributions are as follows: i) we propose the novel JFCS framework to efficiently and adaptively route traffic to indented users in appropriate radio units, and ii) we develop low-complexity algorithms to effectively solve the JFCS problem in different time scales, enabling a closed-loop control of the TS in the O-RAN context. The insights presented in this work will pave the way for O-RAN that are completely automated, offering improved control and flexibility

New records of bats (Mammalia: Chiroptera) from Cu Lao Cham and Ly Son archipelagos, central Vietnam

Cu Lao Cham and Ly Son are two well-known archipelagos of Vietnam for their specular landscapes and varied ecosystems including forest, cave, and agriculture. However, their bat fauna has received little attention. Between July 2017 and August 2018, we conducted a series of mammal surveys with emphasis on bats of the two archipelagos. Bats were captured by mist nets and harp traps. Echolocation calls of microchiropteran species were recorded using the PCTape system then analysed by Selena software. With reference to all available literatures and specimens from the recent surveys, we obtained confirmed records of 9 bat species from Cu Lao Cham and 3 species from Ly Son. Of these, Megaderma spasma and Taphozous melanopogon are new to Cu Lao Cham while Rhinolophus macrotis is new to Ly Son. These three species were rarely recorded from other islands of Vietnam and also uncommon within Cu Lao Cham and Ly Son. These new records not only expand the known distributional range, but also provide worthwhile notes on a narrow geographical variation in morphology and echolocation of each species