We address the question of what physical resources are required and sufficient to store classical information. While there is no lower bound on the required energy or space to store information, we find that there is a nonzero lower bound for the product P = of these two resources. Specifically, we prove that any physical system of mass m and d degrees of freedom that stores S bits of i...

‎In this paper we give an upper bound for Noetherian dimension of all injective modules with Krull dimension on arbitrary rings‎. ‎In particular‎, ‎we also give an upper bound for Noetherian dimension of all Artinian modules on Noetherian duo rings.

The Bell–Clauser–Horne–Shimony–Holt inequality can be used to show that no local hidden-variable theory reproduce the correlations predicted by quantum mechanics (QM). It proved certain QM lead a violation of classical bound established inequality, while all correlations, and classical, respect (the Tsirelson bound). Here, we these well-known results depend crucially on assumption values physic...

in this article, the immobilization of microsomal membranes on fractosil and hexadecylfractosil by hydrophobic adsorption is reported. microsomes were prepared from rat brain and thecatalytic activity of antimycin a insensitive nadh-cytochrome c reductase (nccr), one of themembrane bound enzymes in the microsomal electron transport chain, was chosen as a representative ofthe microsomal membrane...

Causality and the generalized laws of black hole thermodynamics imply a bound, known as Bekenstein-Hod universal on information emission rate perturbed system. Using time-domain ringdown analysis, we investigate whether remnant holes produced by coalescences observed Advanced LIGO Virgo obey this bound. We find that bound is verified astrophysical population with 94% probability, providing firs...

In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

We give further results on the question of code optimality for linear codes over finite Frobenius rings for the homogeneous weight. This article improves on the existing Plotkin bound derived in an earlier paper [6], and suggests a version of a Singleton bound. We also present some families of codes meeting these new bounds.