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Solved
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...
2 days ago
Solved
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...
2 days ago
Solved
Specific Fuel Consumption
Brake-specific fuel consumption (BSFC) measures how efficiently an engine converts fuel mass into useful work. Lower is better...
2 days ago
Solved
Piston Mean Speed
Mean piston speed is a critical mechanical stress indicator — it sets limits on valve timing, bearing loads, and material fatigu...
2 days ago
Solved
Engine Displacement
Engine displacement is the total swept volume of all cylinders. It is determined by bore (cylinder diameter), stroke (piston tra...
2 days ago
Solved
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 ...
2 days ago
Solved
Volumetric efficiency
Volumetric efficiency measures how well an engine breathes. The ratio of the actual air mass drawn in per cycle to the theoreti...
2 days ago
Solved
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...
2 days ago
Solved
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...
2 days ago
Solved
Engine Thermal Efficiency
The thermal efficiency of an ideal Otto cycle engine depends only on the compression ratio. A higher compression ratio yields gr...
2 days ago
Solved
Determine connected components of a graph
Adjacency matrix of an undirected graph is given. Return the number of connected components in the graph.
8 days ago
Solved
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. ...
8 days ago
Solved
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...
8 days ago
Solved
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...
8 days ago
Solved
Create a figure and plot data
Given two data vectors (x,y), open a new figure and plot the data. Return the figure handle.
8 days ago
Solved
Tell me the slope
Tell me the slope, given a vector with horizontal run first and vertical rise next. Example input: x = [10 2];
8 days ago
Solved
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...
10 days ago
Solved
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 ...
11 days ago
Solved
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 : ...
11 days ago
Solved
Euclid primes
Historical context Euclid, the greek mathematician proved at his time that the prime numbers set is an infinite. By the way he ...
11 days ago
Solved
Fermat primes
Historical context The french mathematician Pierre de Fermat found the formula to find some prime numbers. He thought / co...
11 days ago
Solved
Ulam primes first formula
Historical context The polish-american mathematician Stanislaw Ulam found the formula to give the first 760 prime numbers ...
11 days ago
Solved
Ulam primes second formula
Historical context The polish-american mathematician Stanislaw Ulam found the formula to give some prime numbers not given...
12 days ago
Solved
Euler primes
Historical context The great swiss mathematician Leonhard Euler found the formula to give some prime numbers. Problem...
12 days ago
Solved
Frequencies of prime gaps
Problem statement Given two positive integers n and , write a function which computes the frequency of the gap between two ...
12 days ago
Solved
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...
12 days ago
Solved
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...
12 days ago
Solved
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...
12 days ago
Solved
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...
12 days ago
Solved
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 ...
12 days ago
