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For example, the nitrogen atom ground state has three unpaired electrons of parallel spin, so that the total spin is 3/2 and the multiplicity is 4. The lower energy and increased stability of the atom arise because the high-spin state has unpaired electrons of parallel spin, which must reside in different spatial orbitals according to the Pauli ...
All India Secondary School Examination, commonly known as the class 10th board exam, is a centralized public examination that students in schools affiliated with the Central Board of Secondary Education, primarily in India but also in other Indian-patterned schools affiliated to the CBSE across the world, taken at the end of class 10.
Pairing-based cryptography is used in the KZG cryptographic commitment scheme. A contemporary example of using bilinear pairings is exemplified in the BLS digital signature scheme. [3] Pairing-based cryptography relies on hardness assumptions separate from e.g. the elliptic-curve cryptography, which is older and has been studied for a longer time.
Since ε 2 = 0 for dual numbers, exp(aε) = 1 + aε, all other terms of the exponential series vanishing. Let F = {1 + εr : r ∈ H}, ε 2 = 0. Note that F is stable under the rotation q → p −1 qp and under the translation (1 + εr)(1 + εs) = 1 + ε(r + s) for any vector quaternions r and s. F is a 3-flat in the eight-dimensional space of ...
A BLS digital signature, also known as Boneh–Lynn–Shacham [1] (BLS), is a cryptographic signature scheme which allows a user to verify that a signer is authentic.. The scheme uses a bilinear pairing:, where ,, and are elliptic curve groups of prime order , and a hash function from the message space into .
A pairing is called perfect if the above map is an isomorphism of R-modules and the other evaluation map ′: (,) is an isomorphism also. In nice cases, it suffices that just one of these be an isomorphism, e.g. when R is a field, M,N are finite dimensional vector spaces and L=R .
In chemistry and physics, the exchange interaction is a quantum mechanical constraint on the states of indistinguishable particles.While sometimes called an exchange force, or, in the case of fermions, Pauli repulsion, its consequences cannot always be predicted based on classical ideas of force. [1]
Reciprocity is useful in optics, which (apart from quantum effects) can be expressed in terms of classical electromagnetism, but also in terms of radiometry. There is also an analogous theorem in electrostatics , known as Green's reciprocity , relating the interchange of electric potential and electric charge density .