1,112 research outputs found
An easily verifiable proof of the Brouwer fixed point theorem
We give a remarkably elementary proof of the Brouwer fixed point theorem. The
proof is verifiable for most of the mathematicians.Comment: 4 page
ISOLATlON AND PROPERTIES OF THE ENZYME OF LEUCONOSTOC MESENTEROIDES. PRODUCING RIBOFLAVINYLGLUCOSIDE
Quantization of Conductance Minimum and Index Theorem
We discuss the minimum value of the zero-bias differential conductance
in a junction consisting of a normal metal and a nodal
superconductor preserving time-reversal symmetry. Using the quasiclassical
Green function method, we show that is quantized at in the limit of strong impurity scatterings in the
normal metal. The integer represents the number of perfect
transmission channels through the junction. An analysis of the chiral symmetry
of the Hamiltonian indicates that corresponds to the
Atiyah-Singer index in mathematics.Comment: 5 pages, 1 figur
An Elementary Proof of The 2-Dimensional Version of The Brouwer Fixed Point Theorem
We give an elementary proof of the 2-dimensional version of the Brouwer fixed point theorem. The proof can be extended to the n-dimensional version naturally. In our proof, we only use the Bolzano-Weierstrass theorem and the fact that an odd number plus an even number is odd
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