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In mathematics, a rational number is any number that can be expressed as the quotient
or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q
may be equal to 1, every integer is a rational number. The set of all rational numbers,
often referred to as ”the rationals”, is usually denoted by a boldface Q (or blackboard
bold , Unicode ); it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian
for ”quotient”. The decimal expansion of a rational number always either terminates
after a finite number of digits or begins to repeat the same finite sequence of digits over
and over. Moreover, any repeating or terminating decimal represents a rational number.
These statements hold true not just for base 10, but also for any other integer base (e.g.
binary, hexadecimal). A real number that is not rational is called irrational. Irrational
numbers include √2, , e, and . The decimal expansion of an irrational number continues
without repeating. Since the set of rational numbers is countable, and the set of real
numbers is uncountable, almost allreal numbers are irrational.

Vibration control is crucially important in ensuring a smooth ride for vehicle passengers. This study sought to design a suspension system for a car such that its mode of vibration would be predominantly bouncing at lower speeds, and primarily pitching at higher speeds. Our study used analytical and numerical methods to choose appropriate springs and dampers for the front and rear suspension. After an initial miscalculation, we succeeded in arriving at appropriate shocks for the vehicle with the desired modes of vibration at the specified frequencies. We then assessed the maximum bouncing and pitching that the vehicle would experience under a specific set of conditions: travel at 40 km/hr over broken, rough terrain. Our testing showed moderate success in our suspension design. We successfully damped the force being transmitted to both the front and rear quarter car somewhat, while ensuring that the modes of vibration fell into the desired shapes at the desired frequency ranges.

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Calculating the value of Ck ∈ {1, ∞} class of smoothness real-valued function's derivative in point of R+ in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and q-difference operator. (P,q)-power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using q-difference and p,q-power difference is shown.

Se pretende describir el decaimiento de una partícula α encontrando los niveles de energía Eα correspondientes a los estados ligados de la partícula producto de la desintegración. Los niveles de energía y los estados ligados se encuentran mediante dos métodos de aproximación: WKB y diferencias finitas. Posteriormente se halla el tiempo de vida medio τ, se comparan los resultados con los de la literatura y se decide el mejor método de solución acorde con la literatura.