This study explores the self-efficacy and problem-solving skills of middle school mathematics students. The students – 111 9th graders who were studying a unit for analysis function given instruction that was based on either dynamic or static visualization. Findings revealed positive impact visualization involved use technological GeoGebra application, compared to exposed displayed high levels in real time. Improvement these shown both immediately after intervention three months later,...

We show how to construct a sequence of isomorphisms between two descriptions the fundamental group compact Riemann surface.

In this paper, we reconstruct matrices from their minors, and give explicit formulas for the reconstruction of orders 2 × 3, 4, n, 3 6 m n. We also formulate Plücker relations, which are conditions existence a matrix related to its given minors.

Abstract We investigate the topological structures of Galois covers a union two Zappatic surfaces type $$R_k$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:math> . prove that such are simply connected general type. also compute their Chern numbers and indices.

This is the final paper in a series of four, concerning surface 𝕋 × embedded ℂℙ 8 , where one-dimensional torus. In this we compute fundamental group Galois cover with respect to generic projection onto 2 and show that it nilpotent class 3. first time such presented as surface.

Let T be the complex projective torus, and X surface CP 1 × .Let Gal its Galois cover with respect to a generic projection 2 .In this paper we compute fundamental group of , using degeneration regeneration techniques, Moishezon-Teicher braid monodromy algorithm calculations.We show that π (X ) = Z 10 .

Two arrangements with the same combinatorial intersection lattice but whose complements have different fundamental groups are called a Zariski pair. This work finds that there at most nine such pairs amongst all ten line points doubles or triples. result is obtained by considering moduli space of given configuration table which describes lattice. A complete classification this type under suitable assumption, producing list seventy-one described in table, do not explicitly appear literature....

Let C(T) be a generalized Coxeter group, which has natural map onto one of the classical groups, either B n or D . C Y (T) quotient C(T), and if is simply-laced (which means all relations between generators order 2 3), too. A t,n group contains t Abelian groups generated by elements. The main result in this paper that isomorphic to ⋊ , depends on whether signed graph T loops not, other words number cycles T. This extends results Rowen, Teicher Vishne have groups.

In this article, we compute the braid monodromy of two algebraic curves defined over ℝ. These are complex level not bigger than 6, and they unions lines conics. We use different techniques for computing their monodromies. results will be applied to computations fundamental groups complements in [Formula: see text] text].

Let T be a complex torus, and X the surface CP 1 × .If is embedded in n-1 then may 2n-1 .Let Gal its Galois cover with respect to generic projection 2 .In this paper we compute fundamental group of , using degeneration regeneration techniques, Moishezon-Teicher braid monodromy algorithm calculations.We show that π (X ) = Z 4n-2 .

ABSTRACT Let X be the surface 𝕋 × 𝕋, where is complex torus. This article third in a series studying fundamental group of Galois cover with respect to generic projection onto ℂℙ2. Van Kampen Theorem gives presentation complement branch curve, 54 generators and more than 2000 relations. Here we introduce certain natural quotient (obtained by identifying pairs generators), prove it Coxeter related degeneration X, show that this virtually nilpotent. Communicated C. Pedrini.

This paper is the second in a series of papers concerning Hirzebruch surfaces. In first this series, fundamental group Galois covers surfaces F k (a, b), where a, b are relatively prime, was shown to be trivial. For general case, conjecture stated that [Formula: see text] c = gcd b) and n 2ab + kb 2 . paper, we degenerate surface 1 (2, 2), compute braid monodromy factorization branch curve ℂ , verify that, holds: cover 2) with respect generic projection isomorphic text].

In this paper we calculate fundamental groups (and some of their quotients) complements four toric varieties branch curves. For these calculations, study properties and degenerations the braid monodromies curves in $\mathbb{CP}^2$. The related to first three turn be quotients Artin $\mathcal{B}_5$, $\mathcal{B}_6$, $\mathcal{B}_4$, while fourth one is a certain quotient group $\tilde{\mathcal{B}}_6 = \mathcal{B}_6/$, where $X, Y$ are transversal. all by normal subgroups generated squares...

In this paper, we investigate the fundamental groups of Galois covers planar Zappatic deformations type [Formula: see text]. Using Moishezon–Teicher’s algorithm, prove that generic fiber text] are simply-connected; also compute their Chern numbers.

We investigate the local contribution of braid monodromy factorization in context links obtained by closure these braids. consider plane curves which are arrangements lines and conics as well some algebraic surfaces, where former occur configurations degenerated regenerated surfaces latter. In particular we focus on degenerations involve intersection points multiplicity two three. demonstrate when same arise even different.