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The purpose of this study is to investigate the assessment expertise of Mathematics' teachers, focusing on the competence in designing assessment item development. In this present research, I analysed how the teachers' competence appears in designing assessment items development when they generated problems the given problem into a new one. To examine this assumption, the following research questions were posed and investigated in the present study : How do Pre-service and In-service Teachers in primary schools develop the assessment item when generating problems the given problems into new problems? The result from the case study of metamorphosing the given problem into a new problem teachers used similar patterns switching numbers or changing units in order to develop new problems. Also, teachers in primary schools tend to develop problems as commonly as in the mathematics workbooks. In-service teachers tend to have better skills developing assessment items, but there were quite much of variability between individuals.
In this paper, we provide some properties of several left regular functions in Clifford analysis. We find the corresponding Cauchy-Riemann system and conjugate harmonic functions of the harmonic functions, for each left regular function in the sense of several complex variables. And we investigate certain properties of generalized quaternions in Clifford analysis.
In this paper, we initiate the study of zero symmetric and constant parts of near-rings, and then apply these to self map near-rings. Next, we investigate that every near-ring can be embedded into some self map near-ring, and every zero symmetric near-ring can be embedded into some zero symmetric self map near-ring.
For a ring R of imaginary quadratic integers, using a concept of a unitary number system in place of the Motzkin's universal side divisor, we show that the following statements are equivalent: (1) R is Euclidean. (2) R has a unitary number system. (3) R is norm-Euclidean. Through an application of the above theorem we see that R admits binary or ternary number systems if and only if R is Euclidean.
We introduce the fundamental theorem of upper and lower solutions for a class of singular (p1,p2)-Laplacian systems and give the proof by using the Schauder fixed point theorem. It will play an important role to study the existence of solutions.
Due to Bell, a ring R is usually said to be IFP if ab = 0 implies aRb = 0 for a; b 2 R. It is shown that if f(x)g(x) = 0 for f(x) = a0+a1x and g(x) = b0+ +bnxn in R[x], then (f(x)R[x])2n+2g(x) = 0. Motivated by this results, we study the structure of the IFP when proper ideals are taken in place of R, introducing the concept of insertion-of- ideal-factors-property (simply, IIFP) as a generalization of the IFP. A ring R will be called an IIFP ring if ab = 0 (for a; b 2 R) implies aIb = 0 for some proper nonzero ideal I of R, where R is assumed to be non- simple. We in this note study the basic structure of IIFP rings.
Let (X; S) be an association scheme where X is a nite set and S is a partition of X X. The size of X is called the order of (X; S). We de ne C to be the set of positive integers m such that each association scheme of order m is commutative. It is known that each prime is belonged to C and it is conjectured that each prime square is belonged to C. In this article we give a su cient condition for a scheme of order pq to be commutative where p and q are primes, and obtain a partial answer for the conjecture in case where p = q.
The approximate solvability of a generalized system for re- laxed cocoercive extended general variational inequalities is studied by using the project operator technique. The results presented in this paper are more general and include many previously known results as special cases.
A remarkably large number of integral formulas have been investigated and developed. Certain large number of integral formulas are expressed as derivatives of some known functions. Here we choose to recall such a formula to present explicit expressions in terms of Gamma function, Psi function and Polygamma functions. Some simple interesting special cases of our main formulas are also considered. It is also pointed out that the same argument can establish explicit integral formulas for other those expressed in terms of derivatives of some known functions.