Lebesgue integration is a fundamental concept in many mathematical theories, such as real analysis, probability and information theories. Reported higher-order-logic formalizations of the Lebesgue integral either do not include, or have a limited support for the Borel algebra, which is the canonical sigma algebra used on any metric space over which the Lebesgue integral is defined. In this repo...

An ultra-small-area, low-power analog front-end (AFE) for high-density neural recording is presented in this brief. It features an 11-bit incremental delta-sigma analog-to-digital converter ( $\Delta \Sigma $ ADC) enhanced with offset-rejecting event-driven input biasing network. This network avoids saturation of the ADC ca...

A logical structure of propositions associated with a physical system,which can be xperimentally tested,form in the clasical case a Boolean algebra and in a quantum mechanical case an orthomodular lattice or poset (a quantum logic). Recently new logical structures for the presence of propositions, properties,questions or events with fuzziness,uncertainity or unsharpness has been introduced: Eff...

Let A be a complex unital Banach algebra with unit 1. An element $$a\in A$$ is said to of $$G_{1}$$ -class if $$\begin{aligned} \Vert (z-a)^{-1}\Vert =\frac{1}{\text {d}(z,\sigma (a))} \quad \forall z\in {\mathbb {C}}\setminus \sigma (a). \end{aligned}$$ Here $$d(z, (a))$$ denotes the distance between z and spectrum $$\sigma (a)$$ a. Some examples such elements are given also some properties pr...

Na+-K+-stimulated adenosine triphosphat s (Na+-K+ATPase) activities were measured in 12 human brain tumors and surrounding tissue (white matter and cortex) by the colorimetric deter mination of hydrolyzed inorganic phosphorus (Pi) from adenosine triphosphate (ATP). In glioma cases, the brain microvessels, filial component, and neurons were isolated fr...

In this paper, model sets for continuous{time linear time invariant systems that are spanned by xed pole orthonormal bases are investigated. These bases gen-eralise the well known Laguerre and Kautz bases. It is shown that the obtained model sets are complete in all of the Hardy spaces H p ((); 1 p < 1 and the right half plane algebra A(() provided that a mild condition on the choice of basis p...

The topic of sets with fuzzy order relations valuated in complete lattices with additional structure has been quite active in the recent decade, and a number of papers have been published (see [3, 5, 6] among many others). Based on a quantale-valued order relation and subset membership, counterparts to common order-theoretic notions can be defined, like monotone mappings, adjunctions, joins and...

This is an expository account of R. McKenzie’s recent refutation of the RS conjecture. We adopt the usual conventions: if S is an algebra then S denotes the universe of S, |S| denotes the cardinality of S, and |S| denotes the successor cardinal to |S|. For an algebra A, let Vsi(A) denote the class of all nontrivial subdirectly irreducible members of V(A), and (following McKenzie) define κ(A) = ...