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We prove the existence of a Lipschitz continuous selector SX(m) : Km(X)→X for an arbitrary Banach space X.
The kinetic results showed that the free lipase had the same affinity for both substrates (Km(Et)=1.79 M, Km(Ol)=1.80 M) while the lipase in its immobilised form had higher affinity for oleic acid (Km,app(Et)=1.20 M, Km,app(Ol)=1.16×10−8 M).
The output of the transmitter s[ m] can be written as s [ m ] = ∑ k = 0 M − 1 ∑ n = − ∞ ∞ d k n M 2 a m − n M 2 e j 2 π M km (3).
where â k, k ′ [ m ] = a [ m ] e j 2 π M km ∗ a [ m ] e j 2 π M k ′ m (5). is the convolution of the prototype filters on subcarriers k and k′ (we use ∗ to denote a convolution).
(ii) TCR display of the input signal: TCR patterns of the input signal x(n) are obtained by computing and displaying a bilinear TCR distribution derived in [49], which can also be viewed as a modified version of the CPF: MCP F x ( n, 2 k / M ) = ∑ m = 0 ( N - 1 ) 2 x ( n + m ) x ( n - m ) e - j 4 π M km, (41).
Table 1 System parameters Parameter name Parameter value Macro BS power 43 dBm Pico BS power 24 dBm Bandwidth 10 MHz Carrier frequency 2.1 GHz Noise power −174 dBm/Hz Macro cell radius 1000 m Pico cell radius 100 m Path loss (macro) 128.1+37.6log10(R m (km)) dB Path loss (pico) 140.7+36.7log10(R p (km)) dB Shadowing standard deviation (macro) 8 dB Shadowing standard deviation (pico) 10 dB.
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Chinese Kun Ming (KM) mouse were obtained from the Laboratory Animal Research Center of Guangzhou University of Traditional Chinese Medicine.
Four threshold travel distance values from the demand location were selected: 500 m, 1 Km, 2 Km and 3 Km.
A "walkable" distance is commonly used in built environment and active living research to define "neighbourhood" buffers (e.g., 800 m, 1 km, 1.6 km).
Figure 10 shows the simulated average data rate for three different cable lengths, 100 m, 1 km, and 10 km.
The spatial units used were map-grid-based squares of 250×250 m, 1×1 km and 10×10 km and administrative measures of town and zip-code areas.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com