Amwoga KhalwaleInverse problems in geophysics involve determining the physical properties of the Earth’s subsurface (like density, velocity, or conductivity) based on indirect observations, such as seismic waves, gravity measurements, or magnetic fields. Unlike forward problems, where you start with a known model and predict the data (e.g., how seismic waves propagate through a given structure), inverse … Read more
Fourier Transform is a mathematical tool or operation that transforms or breaks down a function or a signal into its constituent frequencies. In essence, it decomposes a complex signal into its constituent sinusoidal components, each with a specific frequency, amplitude, and phase. Think of it like a prism splitting light into a spectrum of colors—except … Read more
Lanchester’s Square Laws, formulated by British engineer and mathematician Frederick W. Lanchester during World War I, are a set of mathematical principles that describe the relationship between the combat effectiveness of opposing forces in warfare. These laws aim to quantify how the size and organization of military forces influence the outcome of battles, particularly in … Read more
Trading futures versus forex (foreign exchange) pits two dynamic, leveraged markets against each other, each with unique structures, opportunities, and challenges. Both attract traders seeking high returns, but they differ significantly in mechanics, accessibility, risk profiles, and focus. Let’s explore every angle—market structure, contracts, liquidity, volatility, trading hours, leverage, costs, risks, rewards, and suitability—to give … Read more
Trading stocks versus trading forex (foreign exchange) is a decision many investors and traders face, and each market offers distinct characteristics that cater to different goals, risk tolerances, and lifestyles. Let’s dive into a comprehensive comparison across various aspects—market structure, accessibility, liquidity, volatility, trading hours, leverage, costs, focus, risks, rewards, and more—to help you understand … Read more
The inverse geodesic problem is a concept in differential geometry and related fields, particularly on curved surfaces or manifolds. It involves finding a geodesic—a shortest path between two points—given certain constraints, but in reverse. Instead of starting with two points and finding the geodesic between them (the direct geodesic problem), the inverse problem typically involves … Read more
In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1). In Other words, The Chinese Remainder Theorem (CRT) … Read more
What It Is Bayes’ Theorem is a fundamental principle in probability theory that describes how to update the probability of a hypothesis based on new evidence. Named after the 18th-century mathematician Thomas Bayes, it provides a mathematical framework for reasoning under uncertainty, flipping the perspective from “what’s the chance of evidence given a hypothesis” to … Read more
Multilevel modeling (MLM), also known as hierarchical linear modeling (HLM) or mixed-effects modeling, is a statistical technique used to analyze data with a nested or hierarchical structure—where observations are grouped within higher-level units. Think of students nested within classrooms, patients within hospitals, or repeated measurements within individuals. Traditional statistical methods like linear regression assume all … Read more
The Heikin-Ashi Technique is a charting method used in technical analysis to smooth out price data and highlight trends more clearly than traditional candlestick charts. Originating from Japan (“Heikin-Ashi” translates to “average bar” in Japanese), it modifies raw price data—open, high, low, close (OHLC)—into a format that filters noise, making it easier to spot trend … Read more