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Geometric Compression Ratio
The geometric compression ratio CR is the ratio of the total cylinder volume at BDC to the clearance volume at TDC. It is one of...
15日 前
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Swept Volume and Clearance Volume
The swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre...
15日 前
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Specific Fuel Consumption
Brake-specific fuel consumption (BSFC) measures how efficiently an engine converts fuel mass into useful work. Lower is better...
15日 前
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Piston Mean Speed
Mean piston speed is a critical mechanical stress indicator — it sets limits on valve timing, bearing loads, and material fatigu...
15日 前
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Engine Displacement
Engine displacement is the total swept volume of all cylinders. It is determined by bore (cylinder diameter), stroke (piston tra...
15日 前
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Fuel-Air Equivalence Ratio (Lambda)
Lambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. λ = 1 is perfect stoichiometry, λ < 1 is ...
15日 前
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Volumetric efficiency
Volumetric efficiency measures how well an engine breathes. The ratio of the actual air mass drawn in per cycle to the theoreti...
15日 前
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Brake Mean Effective Pressure (BMEP)
BMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different siz...
15日 前
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Engine torque and RPM
Torque and power are related through rotational speed. Knowing brake power and engine RPM, you can back-calculate the torque del...
15日 前
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Engine Thermal Efficiency
The thermal efficiency of an ideal Otto cycle engine depends only on the compression ratio. A higher compression ratio yields gr...
15日 前
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Determine connected components of a graph
Adjacency matrix of an undirected graph is given. Return the number of connected components in the graph.
20日 前
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Plotting Practice
Plot cos(x) vs x as shown in the figure below. Include the appropriate title, x-label, and y-label. Note, it is case sensitive. ...
20日 前
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Sieve of Eratosthenes - 02
"Sift the Two's and Sift the Three's, The Sieve of Eratosthenes. When the multiples sublime, The numbers that remain a...
21日 前
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Travelling Salesman Problem (TSP)
Find a short way through given points. This is the travelling salesman problem. But the solution should be a fast and small func...
21日 前
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Create a figure and plot data
Given two data vectors (x,y), open a new figure and plot the data. Return the figure handle.
21日 前
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Tell me the slope
Tell me the slope, given a vector with horizontal run first and vertical rise next. Example input: x = [10 2];
21日 前
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Rule of mixtures (composites) - lower and upper bounds
The <http://en.wikipedia.org/wiki/Rule_of_mixtures rule of mixtures> is used in the mechanical design of composite structures to...
23日 前
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Check the integers additive decomposition conjecture
Problem statement A conjecture (I rediscovered ?) related to Goldbach's one states that every integer above 2 can be written ...
24日 前
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Check p² = 24k + 1, p > 3, the 'golden prime squares' equation
Historical context In december 2023, I / Nicolas Douillet was working on prime squares properties and I found* the formula : ...
24日 前
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Euclid primes
Historical context Euclid, the greek mathematician proved at his time that the prime numbers set is an infinite. By the way he ...
24日 前
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Fermat primes
Historical context The french mathematician Pierre de Fermat found the formula to find some prime numbers. He thought / co...
24日 前
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Ulam primes first formula
Historical context The polish-american mathematician Stanislaw Ulam found the formula to give the first 760 prime numbers ...
24日 前
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Ulam primes second formula
Historical context The polish-american mathematician Stanislaw Ulam found the formula to give some prime numbers not given...
25日 前
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Euler primes
Historical context The great swiss mathematician Leonhard Euler found the formula to give some prime numbers. Problem...
25日 前
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Frequencies of prime gaps
Problem statement Given two positive integers n and , write a function which computes the frequency of the gap between two ...
25日 前
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Find the first occurence of a given gap between two consecutive prime numbers
Problem statement Given a gap = p' - p between the two consecutive prime numbers p and p', find its first occurence, f. E...
25日 前
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Prime numbers which are the difference of two consecutive cubes
Problem statement Given a positive integer n greater than 2, find the prime numbers less or equal to n and which are the diff...
25日 前
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Simulate full-stop emergency braking scenario.
Emergency braking events demand rapid deceleration to bring the vehicle safely to rest. Given initial vehicle speed and constant...
25日 前
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Compute optimal regenerative and friction brake torque blending.
Electric and hybrid vehicles combine regenerative braking with traditional friction braking to maximize energy recovery while en...
25日 前
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Estimate brake disc temperature rise during braking.
During braking, kinetic energy is converted into thermal energy, causing brake discs to heat up. Excessive temperature rise can ...
25日 前
