Some properties of sinc-approximations of continuous functions on a segment are studied. For the first time, the sinc-approximations arose in the work of Pleynet. Later, in connection with developments in signals coding theory, E. Borel and E. T. Whittaker introduced the notions of a cardinal function and a truncated cardinal function, the restriction of which to [0, π] looks like this:

1. Notations and Assumptions 2 2. Error calculus 2 2.1. Ulp calculus 2 2.2. Relative error analysis 4 2.3. Generic error of addition/subtraction 4 2.4. Generic error of multiplication 5 2.5. Generic error of inverse 5 2.6. Generic error of division 6 2.7. Generic error of square root 7 2.8. Generic error of the exponential 7 2.9. Generic error of the logarithm 8 2.10. Ulp calculus vs relative e...

In this paper, we demonstrate a miniature magnetic-force-based, three-axis, AC magnetic sensor with piezoelectric/vibrational energy-harvesting functions. For magnetic sensing, the sensor employs a magnetic-mechanical-piezoelectric configuration (which uses magnetic force and torque, a compact, single, mechanical mechanism, and the piezoelectric effect) to convert x-axis and y-axis in-plane and...

CORDIC algorithm is used for calculation of complex functions in signal processing and wireless communication applications. These functions are the combination of sine and cosine terms that are linked to complex analysis. Pipeline architectures are used in CORDIC algorithm to reduce the critical path, increases the clock speed. An angle recoding method is used to reduce the latency and obtain t...

The Mahler measure of a polynomial in several variables has been a subject of much study over the past thirty years — very few closed forms are proven but more are conjectured. In the case of multiple Mahler measures more tractable but interesting families exist. Using values of log-sine integrals we provide systematic evaluations of various higher and multiple Mahler measures. The evaluations ...

In this study, the second type of Green and Naghdi's thermoelasticity theory is applied to present the vibration of a nanobeam subjected to rectified sine wave heating based upon the nonlocal thermoelasticity theory. Both Young's modulus and thermal conductivity are considered to be linear functions of the temperature. The Laplace transform domain is adopted to solve the governing partial diffe...

SINEs (short interspersed elements) are transposable elements that typically originate independently in each taxonomic clade (order/family). However, some SINE families share a highly similar central sequence and are thus categorized as a SINE superfamily. Although only four SINE superfamilies (CORE-SINEs, V-SINEs, DeuSINEs, and Ceph-SINEs) have been reported so far, it is expected that new SIN...