On Fractional Geometry of Curves

Fractional Differential Geometry of curves is discussed, with the help of a new fractional derivative, the Λ-fractional derivative, with the corresponding Λ-fractional space. Λ-Fractional derivative completely conforms with the demands of Differential Topology, for the existence of a differential. Therefore Fractional Differential Geometry is established in that Λ-space. The results are pulled back to the initial space

On the fractional deformation of a linearly elastic bar

Fractional derivatives have non-local character, although they are not mathematical derivatives, according to differential topology. New fractional derivatives satisfying the requirements of differential topology are proposed, that have non-local character. A new space, the Λ-space corresponding to the initial space is proposed, where the derivatives are local. Transferring the results to the initial space through Riemann-Liouville fractional derivatives, the non-local character of the analysis is shown up. Since fractional derivatives have been established, having the mathematical properties of the derivatives, the linearly elastic fractional deformation of an elastic bar is presented. The fractional axial stress along the distributed body force is discussed. Fractional analysis with horizon is also introduced and the deformation of an elastic bar is also presented

On Fractional Geometry of Curves

Fractional Differential Geometry of curves is discussed, with the help of a new fractional derivative, the Λ-fractional derivative, with the corresponding Λ-fractional space. Λ-Fractional derivative completely conforms with the demands of Differential Topology, for the existence of a differential. Therefore Fractional Differential Geometry is established in that Λ-space. The results are pulled back to the initial space

Immune response (IgG) following full inoculation with BNT162b2 COVID-19 mRNA among healthcare professionals

Soon after the beginning of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic in December, 2019, numerous research teams, assisted by vast capital investments, achieved vaccine development in a fraction of time. However, almost 8 months following the initiation of the European vaccination programme, the need for prospective monitoring of the vaccine-induced immune response, its determinants and related side-effects remains a priority. The present study aimed to quantify the immune response following full vaccination with the BNT162b2 coronavirus disease 2019 (COVID-19) mRNA vaccine by measuring the levels of immunoglobulin G (IgG) titers in healthcare professionals. Moreover, common side-effects and factors associated with IgG titers were identified. For this purpose, blood samples from 517 individuals were obtained and analysed. Blood sampling was performed at a mean period of 69.0 +/- 23.5 days following the second dose of the vaccine. SARS-CoV-2 IgG titers had an overall mean value of 4.23 +/- 2.76. Females had higher titers than males (4.44 +/- 2.70 and 3.89 +/- 2.84, respectively; P=0.007), while non-smokers had higher titers than smokers (4.48 +/- 2.79 and 3.80 +/- 2.64, respectively; P=0.003). An older age was also associated with lower antibody titers (P<0.001). Moreover, the six most prevalent adverse effects were pain at the injection site (72.1%), generalized fatigue (40.5%), malaise (36.3%), myalgia (31,0%), headache (25.8%) and dizziness/weakness (21.6%). The present study demonstrated that the immune response after receiving the BNT162b2 COVID-19 mRNA vaccine is dependent on various modifiable and non-modifiable factors. Overall, the findings of the present study highlight two key aspects of the vaccination programs: First, the need for prospective immunosurveillance studies in order to estimate the duration of immunity, and second, the need to identify those individuals who are at a greater risk of developing low IgG titers in order to evaluate the need for a third dose of the vaccine

Improved strategies to counter the COVID-19 pandemic:Lockdowns vs. primary and community healthcare

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