In this paper we will address the question of how many nonvanishing, linearly independent tangent vector fields can exist on a sphere Sn−1 ⊆ R. By this we mean the following, a tangent vector field on Sn−1 = {x ∈ R : ‖x‖ = 1} is a map v : Sn−1 → R such that v(x) ⊥ x for all x ∈ Sn−1. However, by assumption v is nonvanishing, so we can normalize such that ‖v(x)‖ = 1 and we obtain a map v : Sn−1 ...

−→ V, (v1, v2) −→ v1+v2, are smooth. Note that we can add v1, v2∈V only if they lie in the same fiber over M , i.e. π(v1)=π(v2) ⇐⇒ (v1, v2) ∈ V ×M V. The space V ×M V is a smooth submanifold of V ×V , as follows immediately from the Implicit Function Theorem or can be seen directly. The local triviality condition means that for every point m∈M there exist a neighborhood U of m in M and a diffeo...

We derive bounds on vector leptoquarks coupling to the first generation, using data from low energy experiments as well as from high energy accelerators. Similarly to the case of scalar leptoquarks, we find that the strongest indirect bounds arise from atomic parity violation and universality in leptonic π decays. These bounds are considerably stronger than the first direct bounds of HERA, rest...

In [1], Savage described a unified mathematical framework for strapdown inertial navigation algorithm design. The commenting note [2] showed that the " velocity translation vector " (VTV) in the Savage's framework is equivalent to the dual part of an appropriate screw vector in the dual quaternion representation [3] and significantly simplified the VTV rate equation by way of the screw vector r...

where n = dim M and 6» = ith Betti number of M ( = dim of Hi(M; Q)). Thus the geometric property of M having a nonzero vector field is expressed in terms of the algebraic invariant xM. We will discuss extensions of this idea to vector ^-fields, fields of ^-planes, and foliations of manifolds. All manifolds considered will be connected, smooth and without boundary; all maps will be continuous. F...

Orbispaces are spaces with extra structure. The main examples come from compact Lie group actionsX G and are denoted [X/G], their underlying space being X/G. By definition, every orbispace is locally of the form [X/G], but the group G might vary. To be more precise, an orbispace is a topological stack which is locally equivalent to [X/G] for G a Lie group and X a G-CW-complex [2] [4] [5]. Howev...

An intelligent system for monitoring the microgravity environment quality on-board the International Space Station is presented. The monitoring system uses a new approach combining Kohonen 's self-organizing feature map, learning vector quantization and back propagation neural network to recognize and classify the known and unknown patterns. Finally, fuzzy logic is used to assess the level of c...

Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$‎. ‎We investigate some operator theoretic properties of‎ ‎bilateral composition operator $C_{ph‎, ‎T}‎: ‎f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq‎ ‎+infty$.‎ ‎Compactness and weak compactness of $C_{ph‎, ‎T}$ on $H^p(X)$‎ ‎are characterized an...

In this paper, we establish weak and strong duality theorems for a pair of multiobjective symmetric dual problems. This removes several omissions in the paper "Symmetric and self duality in vector optimization problem, Applied Mathematics and Computation 183 (2006) 1121-1126".