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It is our purpose here to announce the results of our study of the homology of the spaces in the £2-spectrum for complex cobordism and BrownPeterson cohomology. Let MU(n) be the standard Thorn complex. MUk = l im^^ ü,(~~)MU(n) is the 2k space in the £2-spectrum for complex cobordism. We will consider the space MU — hmn^_00 Iï ;>n MUf-. We find this product easier to study than the separate fact...

This study focuses on the problem Japanese learners have in distinguishing between Tone 2 and Tone 3 when learning tones in Mandarin. Acoustic experiments were carried out based on the four basic vowels in Mandarin. They were designed using continual sound stimuli, which gradually changed from Tone 2 to Tone 3 (i.e. turning point and ΔF0) and performed on Japanese learners and Chinese native sp...

We use the informational approach of Traub and Wozniakowski [9] to study the variational form of the second order elliptic Dirichlet problem Lu = f on ü C RN. For /e Hr(Q), where r> -1, a quasi-uniform finite element method using n linear functional Jaf^i nas T7'(ß)-norm error 0(n~<r+1)/'v). We prove that it is asymptotically optimal among all methods using any information consisting of any n l...