Dynamic Algebra is “doing algebraic calculations on a computer by direct manipulation”. We have implemented Dynamic Algebra in the Epsilonwriter application. For that purpose, a “Theory of Movements in Formulas” (TMF) has been elaborated. It describes, in a precise context, how we can move a sub-expression in a formula with preservation of equivalence. It has been implemented in Epsilonwriter f...

In order to support Web-based collaborative design in terms of transferring or updating models dynamically and efficiently, new incremental modelling and local updating strategies have been developed for simulation modelling application since simulation is more focused on visualisation effects than on geometry details. Based on an assembly connection concept, a drag-and-drop assembly method has...

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In this note we shall show how Carlitz in 1954 could have reached an analogue of the Voronoi congruence in the more difficult case of p≡1(mod4): h(-4p) ≡B(p+1)/2(x4)(mod p), where B(p+1)/2(x4) is the generalized Bernoulli number with x4 being the Kronecker symbol associated to the Gaussian field Q(√-4).

We consider discrete nonlinear hyperbolic equations on quad-graphs, in particular on Z2. The fields are associated to the vertices and an equation Q(x1, x2, x3, x4) = 0 relates four fields at one quad. Integrability of equations is understood as 3Dconsistency. The latter is a possibility to consistently impose equations of the same type on all the faces of a three-dimensional cube. This allows ...

On wall-size displays with pen or touch input, users can have difficulties reaching display contents located too high, too low, or too far away. Drag-and-drop interactions can be further complicated by bezels separating individual display units. Researchers have proposed a variety of interaction techniques to address this issue, such as extending the user’s reach (e.g., push-andthrow) and bring...

When a liquid drop impacts a smooth, solid, dry surface, the drop forms a radially spreading lamella, which can lead to a splash. Previous studies have focused almost exclusively on impacts perpendicular to a surface; yet it is common for drops to impact on angled or moving surfaces. The asymmetry of such impacts leads to an azimuthal variation of the ejected rim, and under certain conditions o...

and Applied Analysis 3 Theorem 1.1. The double inequality α1H a, b 1 − α1 Q a, b < M a, b < β1H a, b ( 1 − β1 ) Q a, b 1.7 holds for all a, b > 0with a/ b if and only if α1 ≥ 2/9 0.2222 . . . and β1 ≤ 1−1/ √ 2 log 1 √ 2 0.1977 . . . . Theorem 1.2. The double inequality α2G a, b 1 − α2 Q a, b < M a, b < β2G a, b ( 1 − β2 ) Q a, b 1.8 holds for all a, b > 0with a/ b if and only if α2 ≥ 1/3 0.3333...

Limburg dialects of Dutch have two distinctive tonal contours on syllables with primary stress. These tones are traditionally called Schleifton (‘dragging tone’) and Stosston (‘bumping tone’), but here we will use the terms ‘level high tone’ and ‘falling tone’.1 The tones fall on the stressed syllable in the word, and serve to distinguish between minimal pairs. The following examples are from t...

With regard to the second law of thermodynamics, as given by equation (6), it should be noted that the sign "is greater than" applies to the case of a system which is approaching the condition of thermodynamic equilibrium and implies a difference between "forward" and "backward" directions for the time-like coordinate x4. The equality sign, on the other hand, may characterize either a system wh...