Differential Forms in Electromagnetics

Doppler Shift from a Composition of Boosts with Thomas Rotation: a Spacetime Algebra Approach

“…One should stress that spacetime algebra provides an invariant formulation of physics -as opposed to the paravector covariant model of the so-called algebra of physical space advocated by William E. Baylis [27]. Other problems of electromagnetic waves and applications can be addressed within geometric algebra [28], providing a geometric treatment for special relativity that is coordinate-free and generalizes the more elementary ordinary vector analysis stemming from the works of Gibbs and Heaviside, without meandering into more mathematically involved formalisms -such as differential forms [29][30][31] or just classical plain tensors.…”

Spinor and Hertzian Differential Forms in Electromagnetism

“…Following De Rham [6] {see [7] for the physical applications} and Meetz-Engl [8], Deschamps [9] introduced in electromagnetism the notion of exterior differential forms, gene-rating numerous works [10][11][12][13][14][15][16] on this subject. Exterior means that the algebra of differential forms is endowed with the Cartan exterior derivative d assigning to a p-form w (in this Note, differential forms are represented by underlined expressions) a (p + 1)-form dw such that d is linear and…”

“…Then, the 2-form G is changed into * F (a notation introduced by analogy with the Hodge star operator [8][9][10][11][12][13][14][15][16]…”

Public-Key Steganography with Active Attacks

“…But any PDR-CCA-secure cryptosystem can be turned into one with pseudorandom ciphertexts using the following method, suggested by Lindell [13]: Take the ciphertext output by the PDR-CCA-secure encryption algorithm and encrypt it again, using a second cryptosystem with pseudorandom ciphertexts, which is secure against chosen-plaintext attacks. Decryption proceeds analogously, by first applying the decryption operation of the second cryptosystem and then the decryption operation of the PDR-CCA-secure cryptosystem.…”