When aiming to produce a target chemical at high yield, titer, and productivity, various combinations of genetic parts available to build the target pathway can generate a large number of strains for characterization. This engineering approach will become increasingly laborious and expensive when seeking to develop desirable strains for optimal production of a large space of biochemicals due to...

The purpose of this paper is to present a new approach to study the existence of fixed points for multivalued F-contraction in the setting of modular metric spaces. In establishing this connection, we introduce the notion of multivalued F-contraction and prove corresponding fixed point theorems in complete modular metric space with some specific assumption on the modular. Then we apply our resu...

in this paper, we investigate duality of modular g-riesz bases and g-riesz basesin hilbert c*-modules. first we give some characterization of g-riesz bases in hilbert c*-modules, by using properties of operator theory. next, we characterize the duals of a giveng-riesz basis in hilbert c*-module. in addition, we obtain sucient and necessary conditionfor a dual of a g-riesz basis to be again a g...

‎In this paper‎, ‎first we introduce the notion of $frac{1}{2}$-modular metric spaces and weak $(alpha,Theta)$-$omega$-contractions in this spaces and we establish some results of best proximity points‎. ‎Finally‎, ‎as consequences of these theorems‎, ‎we derive best proximity point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces‎. ‎We present an ex...

We investigate differential operators and their compatibility with subgroups of SL2(R) n. In particular, we construct Rankin–Cohen brackets for Hilbert modular forms, and more generally, multilinear differential operators on the space of Hilbert modular forms. As an application, we explicitly determine the Rankin– Cohen bracket of a Hilbert–Eisenstein series and an arbitrary Hilbert modular for...

Modular graph functions arise in the calculation of low-energy expansion closed-string scattering amplitudes. For toroidal world-sheets, they are ${\rm SL}(2,\mathbb{Z})$-invariant torus complex structure that have to be integrated over moduli space inequivalent tori. We use methods from resurgent analysis construct non-perturbative corrections arising when argument modular function approaches ...

The main analysis techniques for critical systems use state space exploration. However, one is often quickly limited by the so-called state space explosion problem, even if the systems models are relatively small. Several methods have been proposed to tackle this problem in order to get a manageable state space. One of these takes advantage of the modular structure of the model in order to buil...

graham higman has defined coset diagrams for psl(2,ℤ). these diagrams are composed of fragments, and the fragments are further composed of two or more circuits. q. mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...