• The Mathematical Education
• /
• v.47 no.1
• /
• pp.11-25
• /
• 2008

The characteristics of the pseudo-conceptual or the pseudo-analytical behaviors according to the achievement level(i.e. advanced group, proficient group, basic group, and below-basic group) in grade 9 are as follows. The pseudo-conceptual or pseudo-analytical behaviors to get credit from teachers become conspicuous in lower achievement level. The high achieving students showed more pseudo-conceptual or pseudo-analytical behaviors without undergoing the process of reflection or control. The proficient group was short of control in computation, and the advanced group didn't control well in representation. The proficient group tended to depend on a past successful algorithm and behave habitually. Therefore, it is needed to teach mathematics according to the characteristic of pseudo-conceptual or pseudo-analytic behaviors shown in each achievement level.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.207-218
• /
• 2020

Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group G with a maximal torus T is expressed as the ring of invariants, H*(BG; ℚ) ≅ H*(BT; ℚ)^W(G), which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups Sp(n) and for the alternating groups A_n as the subgroup of W(SU(n)). We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space. For n = 3, 4, the rings under a conjugate of W(Sp(n)) are shown to be polynomial, and for n = 6, 8, they are non-polynomial. The structures of H*(BT^n-1; 𝔽_p)^A_n will be also discussed for n = 3, 4.

• Journal of Positioning, Navigation, and Timing
• /
• v.13 no.1
• /
• pp.85-92
• /
• 2024

This study develops a Global Positioning System (GPS) Code Multipath Grid Map (CMGM) of each individual domestic reference station from the extracted code multipath of measurement data. Multipath corresponds to signal reflection/refraction caused by obstacles around the receiver antenna, and it is a major source of error that cannot be eliminated by differencing. From the receiver-independent exchange format (RINEX) data for two days, the associated code multipath of a satellite tracking arc is extracted. These code multipath data go through bias correction and interpolation to yield the CMGM with respect to the azimuth and elevation angles. The effect of the CMGM on multipath mitigation is then quantitatively analyzed to improve the Root Mean Square (RMS) of averaged pseudo multipath. Furthermore, the single point positioning (SPP) accuracy is analyzed in terms of the RMS of the horizontal and vertical errors. During two weeks in February 2023, the RMSs of the averaged pseudo multipath for five reference stations decreased by about 40% on average after CMGM application. Also, the SPP accuracies increased by about 7% for horizontal errors and about 10% for vertical errors on average after CMGM application. The overall quantitative analysis indicates that the proposed approach will reduce the convergence time of Differential Global Navigation Satellite System (DGNSS), Real-Time Kinematic (RTK), and Precise Point Positioning (PPP)-RTK correction information in real-time to use measurement data whose code multipath is corrected and mitigated by the CMGM.