In this paper, we present algebroids and crossed modules of algebroids. We also define pullbackcrossed module of algebroids.

In this paper, we present algebroids and crossed modules of algebroids. We also define pullbackcrossed module of algebroids.

The efficiency of induction motors decreases at light loads. Efficiency optimizer control systemsadjust the motor flux value to achieve the best efficiency in a wide range of load variations. Reduced fluxoperation has some other benefits such as power factor improvement and torque ripple reduction. The latter isan important issue in a direct torque controlled induction motor drive. In this paper, the effect of fluxreference value on the torque ripple of a direct torque controlled induction motor is analyzed. The effect offlux value on torque ripple in a wide range of speed variations is investigated. Simulation and theexperimental results presented justify the validity of the theoretical analysis about torque ripple.

Here, the concept of electric capacity on Finsler spaces is introduced and the fundamentalconformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact Finslermanifold is conformal invariant. This work enables mathematicians and theoretical physicists to become morefamiliar with the global Finsler geometry and one of its new applications.

V. Dannon showed that spherical curves in E4 can be given by Frenet-like equations, and he thengave an integral characterization for spherical curves in E4 . In this paper, Lorentzian spherical timelike andspacelike curves in the space time 41 R are shown to be given by Frenet-like equations of timelike andspacelike curves in the Euclidean space E3 and the Minkowski 3-space 31 R . Thus, finding an integralcharacterization for a Lorentzian spherical 41 R -timelike and spacelike curve is identical to finding it for E3curves and 31 R -timelike and spacelike curves. In the case of E3 curves, the integral characterizationcoincides with Dannon’s.Let {T, N, B}be the moving Frenet frame along the curve α (s) in the Minkowski space 31 R . Letα (s) be a unit speed C4 -timelike (or spacelike) curve in 31 R so that α '(s) = T . Then, α (s) is a Frenetcurve with curvature κ (s) and torsion τ (s) if and only if there are constant vectors a and b so that(i) { [ ] } 0'( ) ( ) cos ( ) sin ( ) cos ( ) ( ) ( ) ( ) , s T s =κ s a ξ s + b ξ s + ∫ ξ s −ξ δ T δ κ δ dδ T is timelike,(ii) { ( ) } 0'( ) ( ) cosh ( ) ( ) ( ) ( ) s T s =κ s aeξ +be−ξ + ∫ ξ s −ξ δ T δ κ δ dδ , N is timelike,where0( ) ( ) . s ξ s = ∫ τ δ dδ

In this paper we introduce the concept of Dirac structures on (Hermitian) modules and vectorbundles and deduce some of their properties. Among other things we prove that there is a one to onecorrespondence between the set of all Dirac structures on a (Hermitian) module and the group of allautomorphisms of the module. This correspondence enables us to represent Dirac structures on (Hermitian)modules and on vector bundles in a very suitable form and define induced Dirac structures in a natural way.

We study the exponential decay of global solution for an n-dimensional thermo-elasticity systemin a bounded domain of ℜn . By using the multiplier technique and constructing an energy functional welladapted to the system, the exponential decay is proved.

On a Finsler manifold, we define conformal vector fields and their complete lifts and prove that incertain conditions they are homothetic.

Let A be a unital algebra over a field of characteristic zero. We show that every derivation from( ) n M A into its dual ( ) n M A ∗ is the sum of an inner derivation and a derivation induced by a derivationfrom A into A∗

We introduce some new concepts of topological spaces which say α − separable topologicalspace and O-topological group, α − first axiom, α − second axiom, and we find some relations betweenthem with some applications in normed spaces.

Let X ,..., Xn 1 be a random sample from a distribution with sample mean X and samplevariance S 2. In this paper we consider certain very general properties of the so-called “Z-scores”X X S i n i ( − )/ : = 1,...., . A representation theorem is then given for Z-scores obtained from an underlyingnormal population, together with a theorem for their limiting distribution as the sample size tends to infinity.Finally, two applications involving grading and testing for an outlier are presented.