Recovering unitary calculus from calculus with reality

By analogy with complex $K$--theory and $K$--theory with reality, there are theories of unitary functor calculus and unitary functor calculus with reality, both of which are generalisations of Weiss' orthogonal calculus. In this paper we show that unitary functor calculus can be completely recovered from the unitary functor calculus with reality, in analogy to how complex topological $K$--theory is completely recovered from $K$--theory with reality via forgetting the $C_2$--action.Comment: Updated title and reference

Pengembangan Buku Kerja Berbasis Pendekatan Analogi Pada Mata Kuliah Kalkulus II Di Iain Sts Jambi

Developing An Analogy Approach-Based Work Book in Calculus II Subject at Institut Agama Islam Negeri Sultan Thaha Saipudin (IAIN STS) Jambi. One of the problems encountered in teaching Calculus II subject at IAIN STS Jambi was the lecture had out ye accommodated the needs of the students t study actively. Analogy approach was assumed as one of the alternative approaches which could be applied in teaching and learning process that could help the students to get involved actively. Therefore, an analogy approach-based work book was developed. The aim of this research was to develop an analogy approach-based work book which was valid. This was a developmental research which used 4-D model that consisted of defining, designing, developing and disseminating. The work book which had been developed was validated by scientists in Calculus education and language. The practicality of the book was seen through observation and questionnaire. The data gotten was analyzed descriptively

Newton-Cartan supergravity with torsion and Schr\"odinger supergravity

We derive a torsionfull version of three-dimensional N=2 Newton-Cartan supergravity using a non-relativistic notion of the superconformal tensor calculus. The "superconformal" theory that we start with is Schr\"odinger supergravity which we obtain by gauging the Schr\"odinger superalgebra. We present two non-relativistic N=2 matter multiplets that can be used as compensators in the superconformal calculus. They lead to two different off-shell formulations which, in analogy with the relativistic case, we call "old minimal" and "new minimal" Newton-Cartan supergravity. We find similarities but also point out some differences with respect to the relativistic case.Comment: 30 page

Generalized symmetric nonextensive thermostatistics and q-modified structures

We formulate a convenient generalization of the q-expectation value, based on the analogy of the symmetric quantum groups and q-calculus, and show that the q->q^{-1} symmetric nonextensive entropy preserves all of the mathematical structure of thermodynamics just as in the case of non-symmetric Tsallis statistics. Basic properties and analogies with quantum groups are discussed.Comment: 9 pages, 1 figure. To appear in Mod. Phys. Lett.

Gravito-electromagnetism

We develop and apply a fully covariant 1+3 electromagnetic analogy for gravity. The free gravitational field is covariantly characterized by the Weyl gravito-electric and gravito-magnetic spatial tensor fields, whose dynamical equations are the Bianchi identities. Using a covariant generalization of spatial vector algebra and calculus to spatial tensor fields, we exhibit the covariant analogy between the tensor Bianchi equations and the vector Maxwell equations. We identify gravitational source terms, couplings and potentials with and without electromagnetic analogues. The nonlinear vacuum Bianchi equations are shown to be invariant under covariant spatial duality rotation of the gravito-electric and gravito-magnetic tensor fields. We construct the super-energy density and super-Poynting vector of the gravitational field as natural U(1) group invariants, and derive their super-energy conservation equation. A covariant approach to gravito-electric/magnetic monopoles is also presented.Comment: 14 pages. Version to appear in Class. Quant. Gra

Cartan calculus on the superalgebra calO(mathbbCq2vert1){cal O}({mathbb C}_q^{2vert1})

In analogy with the classical case, the noncommutative differential calculus on a quantum superspace can be extended to the Cartan calculus by introducing inner derivations and Lie derivatives. So, to give a Cartan calculus on the algebra of functions on quantum (2+1)-superspace ${mathbb C}_q^{2vert1}$, we first introduce two left-covariant differential calculi over ${cal O}({mathbb C}_q^{2vert1})$ and extend one of these calculi by adding inner derivations and Lie derivatives to the calculus. We also introduce tensor product realization of the wedge product of forms