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Collagen fibril membranes (CFMs) with a high mechanical property were
fabricated with a lateral face evaporation method, in which type I
atelocollagen extracted from tilapia scales was used. The density and
thickness of the CFM obtained were 0.51 ± 0.04 mg/cm3 and 50 ± 5
μm. The collagen fibrils in the CFM had a similar periodic stripped pattern
of 67 nm with native collagen fibrils. The CFM was crosslinked in gaseous
glutaraldehyde for different duration in order to increase the mechanical
property. The crosslinking degrees of the CFMs analyzed by free amino groups
gradually increased to 70.3 % against the exposure duration until 6 hours,
and reached a plateau. The denaturation temperatures of the CFMs with the
crosslinking degrees at 20.4 % to 43% were linearly increased from 49°C to
75°C. The tensile strength of the CFMs was slightly improved until the
crosslinking degree at 33.3 % and then the tensile strength rapidly
increased to be 68 MPa. It was suggested that a percolation phenomenon took
place in the CFMs by crosslinking of collagen fibrils with polymerized GA
The main purpose of this paper is to study the mean value properties of certain Hardy sums over a short interval by using the mean-value theorems of the Dirichlet $L$-functions. Our main result is a mean-value formula for these sums.
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