Existence and Ulam-Hyers Stability of ODEs Involving Two Caputo Fractional Derivatives

In this paper, we study existence of solutions to a Cauchy problem for nonlinear ordinary differential equations involving two Caputo fractional derivatives. The existence and uniqueness of solutions are obtained by using monotonicity, continuity and explicit estimation of Mittag-Leffler functions via fixed point theorems. Further, we present Ulam-Hyers stability results by using direct analysis methods. Finally, examples are given to illustrate our theoretical results

On the center-stable manifolds for some fractional differential equations of Caputo type

This paper is devoted to study the existence of center-stable manifolds for some planar fractional differential equations of Caputo type with relaxation factor. After giving some necessary estimation for Mittag–Leffler functions, some existence results for center-stable manifolds are established under the mild conditions by virtue of a suitable Lyapunov–Perron operator. Moreover, an explicit example is given to illustrate the above result. Finally, high-dimensional case is considered

On the Hermite-Hadamard Inequalities for Convex Functions via Hadamard Fractional Integrals

In this paper, we establish new Hermite-Hadamard inequalitiesinvolving Hadamard fractional integrals, which are described byseries. To achieve our aim, we use fractional integral identitiesestablished, elementary inequalities in our previous works viaconvex functions and monotonicity. Finally, some applications tospecial means of real numbers are given

Distinctive Genes Determine Different Intramuscular Fat and Muscle Fiber Ratios of the longissimus dorsi Muscles in Jinhua and Landrace Pigs

Meat quality is determined by properties such as carcass color, tenderness and drip loss. These properties are closely associated with meat composition, which includes the types of muscle fiber and content of intramuscular fat (IMF). Muscle fibers are the main contributors to meat mass, while IMF not only contributes to the sensory properties but also to the plethora of physical, chemical and technological properties of meat. However, little is known about the molecular mechanisms that determine meat composition in different pig breeds. In this report we show that Jinhua pigs, a Chinese breed, contains much higher levels of IMF than do Landrace pigs, a Danish breed. We analyzed global gene expression profiles in the longissimus dorsi muscles in Jinhua and Landrace breeds at the ages of 30, 90 and 150 days. Cross-comparison analysis revealed that genes that regulate fatty acid biosynthesis (e.g., fatty acid synthase and stearoyl-CoA desaturase) are expressed at higher levels in Jinhua pigs whereas those that regulate myogenesis (e.g., myogenic factor 6 and forkhead box O1) are expressed at higher levels in Landrace pigs. Among those genes which are highly expressed in Jinhua pigs at 90 days (d90), we identified a novel gene porcine FLJ36031 (pFLJ), which functions as a positive regulator of fat deposition in cultured intramuscular adipocytes. In summary, our data showed that the up-regulation of fatty acid biosynthesis regulatory genes such as pFLJ and myogenesis inhibitory genes such as myostatin in the longissimus dorsi muscles of Jinhua pigs could explain why this local breed produces meat with high levels of IMF

Economic and ecological complexity in the wake of COVID-19 pandemic: evidence from 60 countries

The coronavirus disease 2019 is a deadly disease that globally infected millions of people. It enormously increases economies national healthcare bills and death tolls that deprive the global world. The negative environmental externality further strains the country’s healthcare sustainability agenda, causing to decline in global income. The study evaluates the different socio-economic and environmental factors to assess ecological complexity in a large, cross-country data set that includes 60 countries. The study used the following variables for estimation, i.e., coronavirus cases, cost of carbon emissions, per capita economic growth, foreign direct investment inflows, and population growth. Markov Switching Regression, VAR Granger causality and variance decomposition analysis applied on the given dataset. The results show that the COVID-19 cases have a rebound effect on environmental quality. Economic activities started after a lifted lockdown, and unsustainable production and consumption led to a deteriorating natural environment. The U-shaped relationship is found between carbon pollution and per capita income. On the other hand, the inverted U-shaped relationship is found between coronavirus cases and carbon pollution. The foreign direct investment inflows and population density increases carbon pollution. The study concludes that stringent environmental policies and incentive-based regulations help to minimize coronavirus cases and mitigate carbon pollution

Antigenic analysis of classical swine fever virus E2 glycoprotein using pig antibodies identifies residues contributing to antigenic variation of the vaccine C-strain and group 2 strains circulating in China

BACKGROUND: Glycoprotein E2, the immunodominant protein of classical swine fever virus (CSFV), can induce neutralizing antibodies and confer protective immunity in pigs. Our previous phylogenetic analysis showed that subgroup 2.1 viruses branched away from subgroup 1.1, the vaccine C-strain lineage, and became dominant in China. The E2 glycoproteins of CSFV C-strain and recent subgroup 2.1 field isolates are genetically different. However, it has not been clearly demonstrated how this diversity affects antigenicity of the protein. RESULTS: Antigenic variation of glycoprotein E2 was observed not only between CSFV vaccine C-strain and subgroup 2.1 strains, but also among strains of the same subgroup 2.1 as determined by ELISA-based binding assay using pig antisera to the C-strain and a representative subgroup 2.1 strain QZ-07 currently circulating in China. Antigenic incompatibility of E2 proteins markedly reduced neutralization efficiency against heterologous strains. Single amino acid substitutions of D705N, L709P, G713E, N723S, and S779A on C-strain recombinant E2 (rE2) proteins significantly increased heterologous binding to anti-QZ-07 serum, suggesting that these residues may be responsible for the antigenic variation between the C-strain and subgroup 2.1 strains. Notably, a G713E substitution caused the most dramatic enhancement of binding of the variant C-strain rE2 protein to anti-QZ-07 serum. Multiple sequence alignment revealed that the glutamic acid residue at this position is conserved within group 2 strains, while the glycine residue is invariant among the vaccine strains, highlighting the role of the residue at this position as a major determinant of antigenic variation of E2. A variant Simpson's index analysis showed that both codons and amino acids of the residues contributing to antigenic variation have undergone similar diversification. CONCLUSIONS: These results demonstrate that CSFV vaccine C-strain and group 2 strains circulating in China differ in the antigenicity of their E2 glycoproteins. Systematic site-directed mutagenesis of the antigenic units has revealed residues that limit cross-reactivity. Our findings may be useful for the development of serological differential assays and improvement of immunogenicity of novel classical swine fever vaccines

Preparation of poly(ethylene glycol)/polylactide hybrid fibrous scaffolds for bone tissue engineering

Polylactide (PLA) electrospun fibers have been reported as a scaffold for bone tissue engineering application, however, the great hydrophobicity limits its broad application. In this study, the hybrid amphiphilic poly(ethylene glycol) (PEG)/hydrophobic PLA fibrous scaffolds exhibited improved morphology with regular and continuous fibers compared to corresponding blank PLA fiber mats. The prepared PEG/PLA fibrous scaffolds favored mesenchymal stem cell (MSC) attachment and proliferation by providing an interconnected porous extracellular environment. Meanwhile, MSCs can penetrate into the fibrous scaffold through the interstitial pores and integrate well with the surrounding fibers, which is very important for favorable application in tissue engineering. More importantly, the electrospun hybrid PEG/PLA fibrous scaffolds can enhance MSCs to differentiate into bone-associated cells by comprehensively evaluating the representative markers of the osteogenic procedure with messenger ribonucleic acid quantitation and protein analysis. MSCs on the PEG/PLA fibrous scaffolds presented better differentiation potential with higher messenger ribonucleic acid expression of the earliest osteogenic marker Cbfa-1 and mid-stage osteogenic marker Col I. The significantly higher alkaline phosphatase activity of the PEG/PLA fibrous scaffolds indicated that these can enhance the differentiation of MSCs into osteoblast-like cells. Furthermore, the higher messenger ribonucleic acid level of the late osteogenic differentiation markers OCN (osteocalcin) and OPN (osteopontin), accompanied by the positive Alizarin red S staining, showed better maturation of osteogenic induction on the PEG/PLA fibrous scaffolds at the mineralization stage of differentiation. After transplantation into the thigh muscle pouches of rats, and evaluating the inflammatory cells surrounding the scaffolds and the physiological characteristics of the surrounding tissues, the PEG/PLA scaffolds presented good biocompatibility. Based on the good cellular response and excellent osteogenic potential in vitro, as well as the biocompatibility with the surrounding tissues in vivo, the electrospun PEG/PLA fibrous scaffolds could be one of the most promising candidates in bone tissue engineering

Economic determinants of national carbon emissions: perspectives from 119 countries

The study aims to analyze the economic determinants of national carbon emissions in a large cross-section of 119 countries. The study followed the ‘theory of sustainable development’ to assess the national sustainable developmental agenda. The study employed cross-sectional, robust least squares, and Markov switching regression for parameter estimates. The findings indicate that information disclosure, the cost of business start-up procedures, sustainable fuel imports, and renewable energy decrease emissions stock. In contrast, ease of doing business and logistics operations increase it. According to the ex-ante analysis, information disclosure, the cost of business start-up procedures, and environmentally friendly logistical operations would likely reduce emissions stock. Ease of doing business and lower renewable fuel expenditures will almost certainly increase emissions stock in the majority of subsequent years. Over time, information disclosure is expected to significantly impact carbon emissions, followed by renewable energy consumption, doing business, and logistical operations. Sustainable economic policies worldwide make it possible for green technology and environmentally friendly manufacturing to be put into place