This study investigated students' perceptions of explicit and implicit methods learning English tenses. It also sought to identify the method that is more effective in improving understanding The mixed approach was applied students Junior High School (SMP) DDI Mangkoso South Sulawesi Indonesia. samples comprised 18 from class VIII/a tenses through eight VIII/b using direct method. results showe...

The Strong Perfect Graph Conjecture (SPGC) was certainly one of the most challenging conjectures in graph theory. During more than four decades, numerous attempts were made to solve it, by combinatorial methods, by linear algebraic methods, or by polyhedral methods. The rst of these three approaches yielded the rst (and to date only) proof of the SPGC; the other two remain promising to consider...

The pre-coloring extension problem consists, given a graph G and a subset of nodes to which some colors are already assigned, in finding a coloring of G with the minimum number of colors which respects the pre-coloring assignment. This can be reduced to the usual coloring problem on a certain contracted graph. We prove that pre-coloring extension is polynomial for complements of Meyniel graphs....

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

The pre-coloring extension problem consists, given a graph G and a subset of nodes to which some colors are already assigned, in nding a coloring of G with the minimum number of colors which respects the pre-coloring assignment. This can be reduced to the usual coloring problem on a certain contracted graph. We prove that pre-coloring extension is polynomial for complements of Meyniel graphs. W...

An analysis of English tense and aspect is presented that specifies temporal precedence relations within a sentence. The relevant reference points for interpretation are taken to be the initial and terminal points of events in the world, as well as two "hypothetical" times: the perfect t ime (when a sentence contains perfect aspect) and the progressive or during time. A method for providing tem...

We obtain the characterization of saturation class and approximation spaces for perfect spline approximation. Also, a generalized perfect spline approximation is investigated.