A well known theorem of Duflo, the “annihilation theorem”, claims that the annihilator of a Verma module in the enveloping algebra of a complex semisimple Lie algebra is centrally generated. For the Lie superalgebra osp(1, 2l), this result does not hold. In this article, we introduce a “correct” analogue of the centre for which the annihilation theorem does hold in the case osp(1, 2l). This sub...

We derive conservation and balance laws for the translational gauge theory of dislocations by applying Noether’s theorem. We present an improved translational gauge theory of dislocations including the dislocation density tensor and the dislocation current tensor. The invariance of the variational principle under the continuous group of transformations is studied. Through Lie’s-infinitesimal in...

The first significant (leftmost nonzero) digit of seemingly random numbers often appears to conform to a logarithmic distribution, with more 1s than 2s, more 2s than 3s, and so forth, a phenomenon known as Benford's law. When humans try to produce random numbers, they often fail to conform to this distribution. This feature grounds the so-called Benford analysis, aiming at detecting fabricated ...

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

The ability to detect deception is of vital importance in human society, playing a crucial role in communication, cooperation, and trade between societies, businesses, and individuals. However, numerous studies have shown, remarkably consistently, that we are only slightly above chance when it comes to detecting deception. Here we investigate whether inconsistency between one's own opinion and ...

Patterns of brain activity during deception have recently been characterized with fMRI on the multi-subject average group level. The clinical value of fMRI in lie detection will be determined by the ability to detect deception in individual subjects, rather than group averages. High-dimensional non-linear pattern classification methods applied to functional magnetic resonance (fMRI) images were...

in this paper, lie group structure and lie algebra structure of unit complex 3-sphere     are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of     and the special complex unitary matrices    (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers    .  the relat...