A compound exhibits (prototropic) tautomerism if it can be represented by two or more structures that are related by a formal intramolecular movement of a hydrogen atom from one heavy atom position to another. When the movement of the proton is accompanied by the opening or closing of a ring it is called ring-chain tautomerism. This type of tautomerism is well observed in carbohydrates, but it ...

In this paper, we study fuzzy calculus in two main branches differential and integral.  Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating  $gH$-derivative of a composite function.  Two techniques namely,  Leibniz's rule and integration by parts are introduced for ...

This paper shows that the commutativity condition [A(t), A′(t)] = 0 is often not necessary to guarantee the chain rules for matrix functions: d dtf(A(t)) = A ′(t)f ′(A(t)) and d dtf(A(t)) = f ′(A(t))A′(t), where A(t) is a square matrix of differentiable functions and f is an analytic function. A further question on the chain rules is presented and discussed.

In many healthcare settings, intuitive decision rules for risk stratification can help effective hospital resource allocation. This paper introduces a novel variant of decision tree algorithms that produces a chain of decisions, not a general tree. Our algorithm, α-Carving Decision Chain (ACDC), sequentially carves out “pure” subsets of the majority class examples. The resulting chain of decisi...

τ-chain (pronounced tau-chain) is a decentralized peer-to-peer network having three unified faces: Rules, Proofs, and Computer Programs, allowing a generalization of virtually any centralized or decentralized P2P network , together with many new abilities, as we present on this note. " If law-making is a game, then it is a game in which changing the rules is a move. "-Peter Suber presenting Nom...