An Instruction Idea Connecting Integral Concepts In Senior High School With Irregular Area Measurement In Elementary School

The topic integral has been taught in Senior High School (SMA) as an anti differentiation only. This makes the learning process merely consists of symbol manipulation. This makes the students focus merely on developing their rote skills for solving repetitive exercises. This implies the student do not understand the integral whole idea. This research has a goal to design mathematics learning on integral idea. In addition the proposed alternative learning activity must grow the students’ intrinsic motivation to learn and improve their mathematics skills. The proposed learning plan is naturally connected to the measurement of irregular regions in elementary school math activities. Keyword: Idea Learning, Integral, Area

Enumerations of lattice animals and trees

We have developed an improved algorithm that allows us to enumerate the number of site animals on the square lattice up to size 46. We also calculate the number of lattice trees up to size 44 and the radius of gyration of both lattice animals and trees up to size 42. Analysis of the resulting series yields an improved estimate, $\lambda = 4.062570(8)$, for the growth constant of lattice animals, and, $\lambda_0 = 3.795254(8)$, for the growth constant of trees, and confirms to a very high degree of certainty that both the animal and tree generating functions have a logarithmic divergence. Analysis of the radius of gyration series yields the estimate, $\nu = 0.64115(5)$, for the size exponent.Comment: 14 pages, 2 eps figures, corrections to some series coefficients and reference

The Interaction of Yer Deletion and Nasal Assimilation in Optimality Theory1

The problem of opacity presents a challenge for generative phonology. This paper examines the process of Nasal Assimilation in Polish rendered opaque by the process of Vowel Deletion in Optimality Theory (Prince & Smolensky, 1993), which currently is a dominating model for phonological analysis. The opaque interaction of the two processes exposes the inadequacy of standard Optimality Theory arising from the fact that standard OT is a non-derivational theory. It is argued that only by introducing intermediate levels can Optimality Theory deal with complex cases of opaque interactions

Analytical Expression for Sound Transmission Loss Calculation: An Improvement to the Existing Method after Singh and Katra

An analytical expression for measuring of sound transmission loss (TL) has been developed by using two microphones, an impedance tube and an impulse sound source as a proposed improvement to the existing procedure after Singh and Katra (1978). The calculation procedure is based on the autospectrum of short-time signals captured by the two microphones placed on two opposite positions from test sample while the sound source is on its surface. No spectral decomposition is required and the TL is calculated directly from the autospectrums of captured signals

Two-point coordinate rings for GK-curves

Giulietti and Korchm\'aros presented new curves with the maximal number of points over a field of size q^6. Garcia, G\"uneri, and Stichtenoth extended the construction to curves that are maximal over fields of size q^2n, for odd n >= 3. The generalized GK-curves have affine equations x^q+x = y^{q+1} and y^{q^2}-y^q = z^r, for r=(q^n+1)/(q+1). We give a new proof for the maximality of the generalized GK-curves and we outline methods to efficiently obtain their two-point coordinate ring.Comment: 16 page