Spatial skills have been shown in various longitudinal studies to be related to multiple science, technology, engineering, and math (STEM) achievement and retention. The specific nature of this relation has been probed in only a few domains, and has rarely been investigated for calculus, a critical topic in preparing students for and in STEM majors and careers. We gathered data on paper-and-pen...

We classify functions $$f:(a,b)\rightarrow \mathbb {R}$$ which satisfy the inequality $$\begin{aligned} {\text {tr}}f(A)+f(C)\ge {tr}}f(B)+f(D) \end{aligned}$$ when $$A\le B\le C$$ are self-adjoint matrices, $$D= A+C-B$$ , so-called trace minmax functions. (Here B$$ if $$B-A$$ is positive semidefinite, and f evaluated via functional calculus.) A function only its derivative analytically continu...

Let A be a generator of a bounded C 0-group, resp. of a positive contraction semi-group, on L p ((), 1 < p < 1. By means of the transference principle of Coifman and Weiss it is shown that A admits an H 1-calculus on each cone C = f 2 C : j arg =2j < g, > 0 resp. on each sector = f 2 C : j arg j < g with > =2. Several applications of these results are included.

We deene a category of games G, and its extensional quotient E. A model of the lazy-calculus, a type-free functional language based on evaluation to weak head normal form, is given in G, yielding an extensional model in E. This model is shown to be fully abstract with respect to applicative simulation. This is, so far as we know, the rst purely semantic construction of a fully abstract model fo...

Boomborg-PC is a proof-checker of Calculus of Constructions that runs on a bu er of GNU Emacs. Calculus of Constructions, proposed by Thierry Coquand and G erard Huet [2], is one of the so-called higher-order typed -calculi [1]. A typed -calculus is a formal system for writing typed -terms, and Boomborg-PC is a program that typechecks -terms written by the rules of Calculus of Constructions. A ...

Many programming languages in the OO tradition now support pattern matching some form. Historical examples include Scala and Ceylon, with more recent additions of Java, Kotlin, TypeScript, Flow. But on generic class hierarchies currently results puzzling type errors most these languages. Yet this combination features occurs naturally many scenarios, such as when manipulating typed ASTs. To it p...

Gir71] J.-Y. Girard. Une extension dy syst eme de fonctionelles recursives de G del et son application aux fondements de l'analyse. 2. An operational semantics (big step semantics, evaluation function) should be deened for the-operator (or an extension thereof), and Plotkin's program should be carried out (standardization, machine-calculus correspondence.) Given a notion of operational equivale...

In this paper, fractal calculus, which is called Fα-calculus, reviewed. Fractal calculus implemented on interpolation functions and Weierstrass functions, may be non-differentiable non-integrable in the sense of ordinary calculus. Graphical representations are presented.

Realizing free semicircular elements on the full Fock space, we prove an equivalence between rationality of operators obtained from them and finiteness rank their commutators with right annihilation operators. This is analogue result for reduced $C^*$-algebra group by G. Duchamp C. Reutenauer which was extended PA. Linnel to densely defined unbounded affiliated factor. Although motivated quanti...