László Márk

A Unified System of Tensor Invariants and Their Integral Reduction Theorems

This paper organizes the complete operator set and the integral theorems of classical vector analysis into a single unified system. The starting point is algebraic: the second-order tensor invariant of an arbitrary third-order tensor, given by the general epsilon-dual formula (th...

The Unified System of Tensor Invariants — Complete Teaching Edition

This edition contains everything the academic article does – the full five-dimensional invariant table, all theorems, the ideas behind the proofs and the research directions – but in teaching language: before every formula it states what the formula will claim and why it is true....

Tensor Invariants and Integral Theorems — Made Understandable (lecture notes)

Short introductory notes for university students on the unified system of tensor invariants. The many formulas of a vector analysis course – grad, div, rot, the Gauss and Stokes theorems, the Laplacian, the Green identities, Maxwell's equations – are in fact different faces of a...

Sector-Switching Curl on the Klein Bottle — numerical verification report

Verification of the sharp statement formulated at the meeting point of the tensor-invariant system (jet/jad/dev) and the Möbius-Klein transform framework: on the Klein bottle the curl of a genuine (sigma-equivariant) vector field lives in the other sector (it is a twisted scalar)...

The Unified System of Tensor Invariants — Complete Teaching Edition

This edition contains everything the academic article does – the full five-dimensional invariant table, all theorems, the ideas behind the proofs and the research directions – but in teaching language: before every formula it states what the formula will claim and why it is true....

Tensor Invariants and Integral Theorems — Made Understandable (lecture notes)

Short introductory notes for university students on the unified system of tensor invariants. The many formulas of a vector analysis course – grad, div, rot, the Gauss and Stokes theorems, the Laplacian, the Green identities, Maxwell's equations – are in fact different faces of a...

One Twist, Two Views — the connection between the tensor-invariant system and the Möbius–Klein transform

Two independently built frameworks – the unified tensor-invariant system of vector analysis (jet/jad/dev operators, dimensional ladder) and the spectral theory of non-orientable surfaces (Möbius and Klein transforms, sector decomposition) – rest on a single common actor: orientat...

One Twist, Two Views — the connection between the tensor-invariant system and the Möbius–Klein transform

Two independently built frameworks – the unified tensor-invariant system of vector analysis (jet/jad/dev operators, dimensional ladder) and the spectral theory of non-orientable surfaces (Möbius and Klein transforms, sector decomposition) – rest on a single common actor: orientat...