scholarly journals Higher order extension of Löwner’s theory: Operator $k$-tone functions

2014 ◽  
Vol 366 (6) ◽  
pp. 3043-3074 ◽  
Author(s):  
Uwe Franz ◽  
Fumio Hiai ◽  
Éric Ricard
Keyword(s):  
Higher Order ◽  
Order Extension ◽  
Theory Operator

scholarly journals Memoized zipper-based attribute grammars and their higher order extension

2019 ◽  
Vol 173 ◽  
pp. 71-94 ◽  
Author(s):  
João Paulo Fernandes ◽  
Pedro Martins ◽  
Alberto Pardo ◽  
João Saraiva ◽  
Marcos Viera
Keyword(s):  
Higher Order ◽  
Attribute Grammars ◽  
Order Extension

scholarly journals HIGHER ORDER KORTEWEG-DE VRIES MODELS FOR INTERNAL WAVES

2003 ◽  
Vol 2 (2) ◽  
pp. 15
Author(s):  
J. JAHARUDDIN
Keyword(s):  
Free Surface ◽  
Evolution Equation ◽  
Linear Theory ◽  
Internal Waves ◽  
Solvability Condition ◽  
Vries Equation ◽  
Asymptotic Methods ◽  
Higher Order ◽  
De Vries ◽  
Order Extension

By using asymptotic methods, evolution equation is derived for the internal waves in density stratified fluid. This evo- lution equation arise as a solvability condition. A higher-order extension of the familiar Korteweg-de Vries equation is produced for internal waves in a density stratified flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed via integrals of the modal function for the linear theory of long internal waves.

scholarly journals Higher-Order Spreadsheets with Spilled Arrays

2020 ◽  
pp. 743-769 ◽  
Author(s):  
Jack Williams ◽  
Nima Joharizadeh ◽  
Andrew D. Gordon ◽  
Advait Sarkar
Keyword(s):  
Functional Programming ◽  
Iterative Process ◽  
Object Oriented ◽  
Higher Order ◽  
Formal Calculus ◽  
Order Extension

AbstractWe develop a theory for two recently-proposed spreadsheet mechanisms: gridlets allow for abstraction and reuse in spreadsheets, and build on spilled arrays, where an array value spills out of one cell into nearby cells. We present the first formal calculus of spreadsheets with spilled arrays. Since spilled arrays may collide, the semantics of spilling is an iterative process to determine which arrays spill successfully and which do not. Our first theorem is that this process converges deterministically. To model gridlets, we propose the grid calculus, a higher-order extension of our calculus of spilled arrays with primitives to treat spreadsheets as values. We define a semantics of gridlets as formulas in the grid calculus. Our second theorem shows the correctness of a remarkably direct encoding of the Abadi and Cardelli object calculus into the grid calculus. This result is the first rigorous analogy between spreadsheets and objects; it substantiates the intuition that gridlets are an object-oriented counterpart to functional programming extensions to spreadsheets, such as sheet-defined functions.

scholarly journals ON IDEMPOTENT ULTRAFILTERS IN HIGHER-ORDER REVERSE MATHEMATICS

2015 ◽  
Vol 80 (1) ◽  
pp. 179-193 ◽  
Author(s):  
ALEXANDER P. KREUZER
Keyword(s):  
Reverse Mathematics ◽  
Higher Order ◽  
Hindman’S Theorem ◽  
Image Position ◽  
Idempotent Ultrafilter ◽  
Order Extension

AbstractWe analyze the strength of the existence of idempotent ultrafilters in higher-order reverse mathematics.Let $\left( {{{\cal U}_{{\rm{idem}}}}} \right)$ be the statement that an idempotent ultrafilter on ℕ exists. We show that over $ACA_0^\omega$, the higher-order extension of ACA0, the statement $\left( {{{\cal U}_{{\rm{idem}}}}} \right)$ implies the iterated Hindman’s theorem (IHT) and we show that $ACA_0^\omega + \left( {{{\cal U}_{{\rm{idem}}}}} \right)$ is ${\rm{\Pi }}_2^1$-conservative over $ACA_0^\omega + IHT$ and thus over $ACA_0^ +$.

New Extension of Affine Arithmetic: Complex Form

2012 ◽  
Vol 3 (1) ◽  
pp. 11
Author(s):  
Ahmed Elaraby Ahmed ◽  
Hassan El-Owny
Keyword(s):  
Arbitrary Order ◽  
Complex Form ◽  
Higher Order ◽  
Computational Approach ◽  
High Order ◽  
Affine Arithmetic ◽  
First Order ◽  
Order Extension

In this paper we present the new complex form for affine arithmetic (AA) which is a self-verifying computational approach that keeps track of first-order correlation between uncertainties in the data and intermediate and final results. In this paper we propose a higher-order extension satisfying the requirements of genericity, arbitrary-order and self-verification, comparing the resulting method with other wellknown high-order extensions of AA

Sign in / Sign up

Export Citation Format

Share Document