The classical result that r-fold vector cross products exist only for d-dimensional vector spaces with r = 1 and d even; r = 2 and d = 3 or 7; r = 3 and d = 8; and r = d − 1 for arbitrary d will be explained. Vector cross products will then be used to construct exceptional Lie superalgebras. 1. Bilinear vector cross products We all are familiar with the usual vector cross product × in R3, which...

As an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of ...

We propose the first Key-policy Attribute-based Encryption (KP-ABE) scheme for (monotone) Boolean circuits based on bilinear maps. The construction is based on secret sharing and just one bilinear map, and can be viewed as an extension of the KP-ABE scheme in [7]. Selective security of the proposed scheme in the standard model is proved, and comparisons with the scheme in [5] based on leveled m...

  In present PET/CT scanners, PET attenuation correction is performed by relying on the information given by CT scan. In the CT-based attenuation correction methods, dual-energy technique (DECT) is the most accurate approach, which has been limited due to the increasing patient dose. In this feasibility study, we have introduced a new method that can implement dual-en...

Bilinear systems in input/output form are introduced, and represented by means of suitable rational functions in two indeterminates. Necessary and sufficient conditions for BIBO stability are derived, and compared with analogous results on 2D systems stability. Several features of the output evolutions, corresponding to finite support as well as to periodic input sequences, are discussed, and r...

In this submission, we propose an efficient identity-based and implicitly authenticated key agreement protocol IDAK based on pairing techniques. Though both Weil and Tate pairing could be used for IDAK, we recommend Tate pairing for IDAK to avoid extra ephemeral value validation process. The security of IDAK was formally proved in [22] in Bellare-Rogaway model with random oracle. In additon, ID...

We show that the quantum field theoretical formulation of the τ function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we prove that i) the partial charge transformations preserving the neutral sector are Laplace transformations, ii) the basic vertex operators are Lévy and adjoint Lévy transformations and iii) the diagonal s...

Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...