SARS-CoV-2 Delta derivatives impact on neutralization of Covishield recipient sera

The emergence of SARS-CoV-2 Delta variant and its derivatives has created grave public health problem worldwide. The high transmissibility associated with this variant has led to daily increase in the number of SARS-CoV-2 infections. Delta variant has slowly dominated the other variants of concern. Subsequently, Delta has further mutated to Delta AY.1 to Delta AY.126. Of these, Delta AY.1 has been reported from several countries including India and considered to be highly infectious and probable escape mutant. Considering the possible immune escape, we had already evaluated the efficacy of the BBV152 against Delta and Delta AY.1 variants. Here, we have evaluated the neutralizing potential of sera of COVID-19 naive vaccinees (CNV) immunized with two doses of vaccine, COVID-19 recovered cases immunized with two doses of vaccine (CRV) and breakthrough infections (BTI) post immunization with two doses of vaccine against Delta, Delta AY.1 and B.1.617.3 using 50% plaque reduction neutralization test (PRNT50). Our study observed low NAb titer in CNV group against all the variants compared to CRV and BTI groups. Delta variant has shown highest reduction of 27.3-fold in NAb titer among CNV group compared to other groups and variants. Anti-S1-RBD IgG immune response among all the groups was also substantiated with NAb response. Compromised neutralization was observed against Delta and Delta AY.1 compared B.1 in all three groups. However, it provided protection against severity of the disease and fatality.

Time-scales Herglotz type Noether theorem for delta derivatives of Birkhoffian systems

The time-scales theory provides a powerful theoretical tool for studying differential and difference equations simultaneously. With regard to Herglotz type variational principle, this generalized variational principle can deal with non-conservative or dissipative problems. Combining the two tools, this paper aims to study time-scales Herglotz type Noether theorem for delta derivatives of Birkhoffian systems. We introduce the time-scales Herglotz type variational problem of Birkhoffian systems firstly and give the form of time-scales Pfaff–Herglotz action for delta derivatives. Then, time-scales Herglotz type Birkhoff’s equations for delta derivatives are derived by calculating the variation of the action. Furthermore, time-scales Herglotz type Noether symmetry for delta derivatives of Birkhoffian systems are defined. According to this definition, time-scales Herglotz type Noether identity and Noether theorem for delta derivatives of Birkhoffian systems are proposed and proved, which can become the ones for delta derivatives of Hamiltonian systems or Lagrangian systems in some special cases. Therefore, it is shown that the results of Birkhoffian formalism are more universal than Hamiltonian or Lagrangian formalism. Finally, the time-scales damped oscillator and a non-Hamiltonian Birkhoffian system are given to exemplify the superiority of the results.

Noether’s theorems for the relative motion systems on time scales

This paper propose Noether symmetries and the conserved quantities of the relative motion systems on time scales. The Lagrange equations with delta derivatives on time scales are presented for the system. Based upon the invariance of Hamilton action on time scales, under the infinitesimal transformations with respect to the time and generalized coordinates, the Hamilton’s principle, the Noether theorems and conservation quantities are given for the systems on time scales. Lastly, an example is given to show the application the conclusion.

Generalized Weighted Ostrowski, Trapezoid and Grüss Type Inequalities on Time Scales

In this article, using two parameters, we obtain generalizations of a weighted Ostrowski type inequality and its companion inequalities on an arbitrary time scale for functions whose first delta derivatives are bounded. Our work unifies the continuous and discrete versions and can also be applied to the quantum calculus case.

A New Algorithm for Solving Terminal Value Problems of q-Difference Equations

We propose a new algorithm for solving the terminal value problems on a q-difference equations. Through some transformations, the terminal value problems which contain the first- and second-order delta-derivatives have been changed into the corresponding initial value problems; then with the help of the methods developed by Liu and H. Jafari, the numerical solution has been obtained and the error estimate has also been considered for the terminal value problems. Some examples are given to illustrate the accuracy of the numerical methods we proposed. By comparing the exact solution with the numerical solution, we find that the convergence speed of this numerical method is very fast.

An Opial-Type Inequality on Time Scales

We establish some new Opial-type inequalities involving higher order delta derivatives on time scales. These extend some known results in the continuous case in the literature and provide new estimates in the setting of time scales.