DMCA Notice & Procedure

This page outlines the procedure for submitting a formal notice regarding alleged copyright infringement on this website. If you believe that your copyrighted material has been used without permission, you may request its removal by following the steps listed below.

How to Submit a DMCA Notice

Please include all of the following information in your request:

  • Your full legal name or the name of the rights holder you represent.
  • Contact information, including a valid email address.
  • Identification of the copyrighted work that you believe has been infringed. If the work exists online, include any relevant URLs.
  • The exact URL on this website that contains the material you are reporting.
  • A good-faith statement that the use of the material is not authorised by the copyright owner, its agent, or the law.
  • A statement confirming the accuracy of your notice and that you are the copyright owner or are authorised to act on their behalf.
  • Your electronic signature (typing your full legal name is acceptable).

Where to Send Your Notice

All DMCA notices should be sent to:

Email: tiago.hands@tutanota.com

Only properly completed and legitimate notices will be reviewed.

Procedure After Submission

Once your notice is received:

  • Your request will be evaluated.
  • If valid, the material will be removed or access will be restricted.
  • If additional details are required, you will be contacted.

Please note that submitting false or misleading notices may result in legal consequences under applicable copyright law.

Popular posts from this blog

The Method of Differences — A Clean Proof of the Sum of Cubes

The Method of Differences — A Clean Proof of the Sum of Cubes The method of differences is a remarkably elegant tool for evaluating finite sums. When each term of a series can be written in the form f(r+1) − f(r) , the sum “collapses” — all interior terms cancel, leaving only a boundary expression. This behaviour is called a telescoping sum . 1) Telescoping Sums Assume the general term u r can be written as: u r = f(r+1) − f(r). Then the finite sum from r = 1 to r = n becomes: Σ u r = Σ ( f(r+1) − f(r) ). To see what happens, write out a few terms: u₁ = f(2) − f(1) u₂ = f(3) − f(2) u₃ = f(4) − f(3) ⋮ uₙ = f(n+1) − f(n) When these are added, everything cancels except the first and last pieces: Σ u r = f(n+1) − f(1). This is the essence of the method: interior structure disappears, leaving just the difference between the final and initial states. 2) A Classic Application — The Sum of Cubes We will use this technique to prove the well-known ...
Read more

2×2 Orthogonal Matrix Mastery — A Generalised Construction

Image
2×2 Orthogonal Matrix Mastery — A Generalised Construction Orthogonal matrices in two dimensions reveal one of the cleanest structures in linear algebra. A 2×2 matrix is orthogonal when its columns (and rows) satisfy two conditions: They are perpendicular (their dot product is zero); They have unit length (their magnitude is one). This article presents a clear generalisation: any pair of perpendicular vectors with equal magnitude can be normalised to form an orthogonal matrix. 1. Begin with two perpendicular vectors Let the first vector be: (a, b) A perpendicular vector can be chosen as: (−b, a) Their dot products confirm orthogonality: (a, b) · (−b, a) = −ab + ab = 0 (a, −b) · (b, a) = ab − ab = 0 2. Compute their shared magnitude Both vectors have the same length: |(a, b)| = √(a² + b²) We can therefore normalise each one by dividing by √(a² + b²). 3. Form the matrix using the normalised vectors Place the two normalised vectors...
Read more

The Maclaurin Series — A Clean Derivation

Image
The Maclaurin Series — A Clean Derivation Many smooth functions can be written as an infinite polynomial. When this expansion is centred at x = 0 , we obtain the Maclaurin series . This article derives the Maclaurin formula directly from repeated differentiation, showing precisely why the coefficients involve derivatives and factorials. 1) Begin with a General Power Series Suppose a function f(x) can be expressed as f(x) = a₀ + a₁x + a₂x² + a₃x³ + … + aᵣxʳ + … The constants aᵣ are real coefficients whose values we wish to determine. 2) Evaluate at x = 0 f(0) = a₀ so a₀ = f(0). 3) Differentiate Once f′(x) = a₁ + 2a₂x + 3a₃x² + … + r·aᵣxʳ⁻¹ + … Setting x = 0 eliminates all higher powers: f′(0) = a₁. Thus, a₁ = f′(0). 4) Differentiate Again f″(x) = 2·1·a₂ + 3·2·a₃x + … + r(r−1)aᵣxʳ⁻² + … Evaluate at x = 0 : f″(0) = 2! · a₂ Hence a₂ = f″(0) / 2!. 5) The General Pattern Differentiate repeatedly. After r differentiations, a...
Read more