The Profile of Cognitive Conflict with Intervention in Understanding Algebra of Students at Pangkep State Polytechnic of Agriculture

ABSTRACTThe study aims at obtaining information on the profile of cognitive conflict of students by giving intervention on understanding Algebra of students at Pangkep State Polytechnic of Agriculture. The research method employed descriptive qualitative. The study involved the students who experienced cognitive conflict as a sample. The instruments used in collecting the data were written test and interview. Each of the students delivered his or her answer; he or she would be given new information that could trigger cognitive conflict.The result of the study reveal that (1) the students experienced cognitive conflict in determining set of completion on inequality that did not have a zero divisor. Based on students understanding, quadratic inequality that difficult to be factored or the factors were not integers that did not have solutions, (2) the students experienced cognitive conflict in solving equation that had infinite solutions. The students tended to work procedurally without identifying relational elements formed by the expressions. The subjects did not see the objects produce in first step that showed experession on the left was equal to the expression on the right side, (3) the students experienced cognitive conflict in determining set of completion on inequality segment.ABSTRAK Penelitian ini bertujuan untuk memperoleh informasi tentang profil konflik kognitif mahasiswa dengan pemberian intervensi terhadap pemahaman aljabar mahasiswa Politeknik Pertanian Negeri Pangkep. Metode penelitian yang digunakan adalah deskriptif kualitatif. Penelitian ini melibatkan mahasiswa yang mengalami konflik kognitif sebagai sampel. Untuk pengumpulan data, instrumen yang digunakan adalah soal tertulis dan wawancara. Setiap mahasiswa selesai menyampaikan jawaban, akan diberikan informasi baru yang dapat memicu terjadinya konflik kognitif.Hasil penelitian menunjukkan bahwa: (1) Mahasiswa mengalami konflik kognitif dalam menentukan himpunan penyelesaian pada pertidaksamaan yang tidak memiliki pembuat nol dan faktor-faktornya bukan bilangan real. Menurut pemahaman mahasiswa pertidaksamaan kuadrat yang sulit untuk difaktorkan tidak memiliki solusi (2) Mahasiswa mengalami konflik kognitif dalam menyelesaikan persamaan yang memiliki solusi yang tak berhingga. Mahasiswa cenderung bekerja secara prosedural tanpa mengindentifikasi elemen-elemen relasional yang dibentuk pada ekspresi tersebut. Subjek tidak memandang objek yang dihasilkan pada langkah pertama yang memperlihatkan bahwa ekspresi di ruas kiri sama dengan ekspresi di ruas kanan (3) Mahasiswa mengalami konflik kognitif dalam menentukan himpunan penyelesaian pada pertidaksamaan setelah diintervensi dengan informasi baru dengan menarik akar pada kedua ruas pertidaksamaan.

Markov’s Inequality and $$C^{\infty }$$ Functions on Certain Algebraic Hypersurfaces

It is known that if E is a $$C^{\infty }$$ C ∞ determining set, then E is a Markov set if and only if it has Bernstein’s property. This article provides the equivalent of this result for compact subsets of some algebraic varieties.

On realization of effect algebras

A well known fact is that there is a finite orthomodular lattice with an order determining set of states which is not order embeddable into the standard quantum logic, the latticeWe show that a finite generalized effect algebra is order embeddable into the standard effect algebraAs an application we obtain an algorithm, which is based on the simplex algorithm, deciding whether such an order embedding exists and, if the answer is positive, constructing it.

Infinite Graphs with Finite 2-Distinguishing Cost

A graph $G$ is said to be 2-distinguishable if there is a labeling of the vertices with two labels such that only the trivial automorphism preserves the labels. Call the minimum size of a label class in such a labeling of $G$ the cost of 2-distinguishing $G$.We show that the connected, locally finite, infinite graphs with finite 2-distinguishing cost are exactly the graphs with countable automorphism group. Further we show that in such graphs the cost is less than three times the size of a smallest determining set. We also another, sharper bound on the 2-distinguishing cost, in particular for graphs of linear growth.

Symmetry Breaking in Tournaments

We provide upper bounds for the determining number and the metric dimension of tournaments. A set of vertices $S \subseteq V(T)$ is a determining set for a tournament $T$ if every nontrivial automorphism of $T$ moves at least one vertex of $S$, while $S$ is a resolving set for $T$ if every two distinct vertices in $T$ have different distances to some vertex in $S$. We show that the minimum size of a determining set for an order $n$ tournament (its determining number) is bounded by $\lfloor n/3 \rfloor$, while the minimum size of a resolving set for an order $n$ strong tournament (its metric dimension) is bounded by $\lfloor n/2 \rfloor$. Both bounds are optimal.

The determining number of Kneser graphs

Graph Theory International audience A set of vertices S is a determining set of a graph G if every automorphism of G is uniquely determined by its action on S. The determining number of G is the minimum cardinality of a determining set of G. This paper studies the determining number of Kneser graphs. First, we compute the determining number of a wide range of Kneser graphs, concretely Kn:k with n≥k(k+1) / 2+1. In the language of group theory, these computations provide exact values for the base size of the symmetric group Sn acting on the k-subsets of 1,..., n. Then, we establish for which Kneser graphs Kn:k the determining number is equal to n-k, answering a question posed by Boutin. Finally, we find all Kneser graphs with fixed determining number 5, extending the study developed by Boutin for determining number 2, 3 or 4.

Financial phantasmagoria: corporate image-work in times of crisis

Our purpose in this article is to relate the real movements in the economy during 2008 to the ‘image-work’ of financial institutions. Over the period January—December 2008 we collected 241 separate advertisements from 61 financial institutions published in the Financial Times. Reading across the ensemble of advertisements for themes and evocative images provides an impression of the financial imaginaries created by these organizations as the global financial crisis unfolded. In using the term ‘phantasmagoria’ we move beyond its colloquial sense of a set of strange images designed to dazzle towards the more technical connotation used by Rancière (2004) who suggested that words and images can offer a trace of an overall determining set-up if they are torn from their obviousness so they become phantasmagoric figures. The key phantasmagoric figure we identify here is that of the financial institution as timeless, immortal and unchanging; a coherent and autonomous entity amongst other actors. This notion of uniqueness belies the commonality of thinking which precipitated the global financial crisis as well as the limited capacity for control of financial institutions in relation to market events. It also functions as a powerful naturalizing force, making it hard to question certain aspects of the recent period of ‘capitalism in crisis’.

TYPE DECOMPOSITION OF A PSEUDOEFFECT ALGEBRA

Effect algebras, which generalize the lattice of projections in a von Neumann algebra, serve as a basis for the study of unsharp observables in quantum mechanics. The direct decomposition of a von Neumann algebra into types I, II, and III is reflected by a corresponding decomposition of its lattice of projections, and vice versa. More generally, in a centrally orthocomplete effect algebra, the so-called type-determining sets induce direct decompositions into various types. In this paper, we extend the theory of type decomposition to a (possibly) noncommutative version of an effect algebra called a pseudoeffect algebra. It has been argued that pseudoeffect algebras constitute a natural structure for the study of noncommuting unsharp or fuzzy observables. We develop the basic theory of centrally orthocomplete pseudoeffect algebras, generalize the notion of a type-determining set to pseudoeffect algebras, and show how type-determining sets induce direct decompositions of centrally orthocomplete pseudoeffect algebras.