The zeroth-order general Randic index, 0R?(G), of a connected graph G, is defined as 0 P R?(G) = ni =1 d?i , where di the degree vertex vi G and ? arbitrary real number. We consider linear combinations 0R?(G) form (? + ?)0R??1(G) ?? 0R??2(G) 2a 0R??1(G) a2 0R??2(G), an number, determine their bounds. As corollaries, various upper lower bounds indices that represent some special cases are obtain...

In Escherichia coli, protein degradation in synthetic circuits is commonly achieved by the ssrA-tagged degradation system. In this work, we show that the degradation kinetics for the green fluorescent protein fused with the native ssrA tag in each cell exhibits the zeroth-order limit of the Michaelis-Menten kinetics, rather than the commonly assumed first-order. When measured in a population, t...

First order logic without quantifiers, a.k.a. zeroth order logic, is more expressive than propositional logic. In this paper, we introduce two new operators for regular expressions allowing us to handle zeroth order boolean formula in order to increase the expressive power of expressions; We also extend the notion of interpretation and of realization using expression interpretation. We thus def...

For an integrable potential q on the unit interval, let λ0(q) be the zeroth Neumann eigenvalue of the Sturm–Liouville operator with the potential q. In this paper we will solve the minimization problem L̃1(r) = infq λ0(q), where potentials q have mean value zero and L1 norm r . The final result is L̃1(r)=−r/4. The approach is a combination of variational method and limiting process, with the help...

A compact Zeroth Order Resonator Antenna (ZORA) is implemented as a part of course work for Radio Frequency Integrated Circuits and Systems (E8-242). This work is based on [1] . Due to the unique properties of Compact Right/Left Handed (CRLH) transmission lines, the size of the antenna is independent of the frequency of operation. This compact structure is made of two unit cells each comprising...

We consider unconstrained stochastic optimization problems with no available gradient information. Such arise in settings from derivative-free simulation to reinforcement learning. propose an adaptive sampling quasi-Newton method where we estimate the gradients using finite differences of function evaluations within a common random number framework. develop modified versions norm test and inner...

It has been known that the Schwarzschild-de Sitter (Sch-dS) black hole may not be in thermal equilibrium and also found to thermodynamically unstable standard thermodynamics. In present work, we investigate possibility realize thermodynamical stability of Sch-dS as an effective system by using R\'{e}nyi statistics, which includes non-extensive nature holes. Our results indicate non-extensivity ...