We generated an anatomically detailed, three-dimensional (3-D) reconstruction of a human foot from 286 computerized topographic (CT) images. For each bone, 2-D cross-sectional data were obtained and aligned to form a stacked image model. We calculated the inertial matrix of each bone from the stacked image model and used it to determine the principal axes. Relative angles between the principal ...

We obtain a complete characterization for doubly commuting mixed invariant subspaces of the Hardy space over unit polydisc. say closed subspace Q H2(Dn) is if Mzj(Q)⊆Q 1≤j≤k and Mzj⁎(Q)⊆Q, k+1≤j≤n some integer k∈{1,2,…,n−1}. prove that only ifQ=ΘH2(Dk)⊗Qθ1⊗⋯⊗Qθn−k, where Θ∈H∞(Dk) inner function Qθj either Jordan block H2(D)⊖θjH2(D) θj or H2(D). Furthermore, an explicit representation commutant ...

in this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)d^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the banach algebras. this proof is given in two cases of the continuous and discontinuous function $g$, under the generalized lipschitz and caratheodory conditions.

The categorical concept of Kan extensions form a more general notion of both limits and adjoints. The general definition of Kan extensions is given and motivated by several concrete examples. After providing the necessary background on some basic categorical objects and theorems, the relationship between Kan extensions, limits, and adjoints is expressed through two theorems from [3]. 1. Some Pr...

We study Darboux-type transformations associated with the focusing nonlinear Schrödinger equation (NLS−) and their effect on spectral properties of the underlying Lax operator. The latter is a formally J -selfadjoint (but non-self-adjoint) Dirac-type differential expression of the form M(q) = i d dx −q −q − d dx , satisfying JM(q)J = M(q), where J is defined by J = 0 1 1 0 C, and C denotes the ...

Geometric puncturing is a method to construct new codes from a given [n, k, d]q code by deleting the coordinates corresponding to some geometric object in PG(k − 1, q). We construct [gq(4, d), 4, d]q and [gq(4, d)+1, 4, d]q codes for some d by geometric puncturing, where gq(k, d) = ∑k−1 i=0 ⌈

We classify all embeddings θ : PG(n, q) −→ PG(d, q), with d ≥ n(n+3) 2 , such that θ maps the set of points of each line to a set of coplanar points and such that the image of θ generates PG(d, q). It turns out that d = 1 2n(n+3) and all examples are related to the quadric Veronesean of PG(n, q) in PG(d, q) and its projections from subspaces of PG(d, q) generated by sub-Veroneseans (the point s...

We propose new formulas for extracting a difference of the polarized light sea–quark density, ∆d̄(x)−∆ū(x), from polarized deep–inelastic semi–inclusive data. We have estimated the value of it from the present experimental data measured by SMC and HERMES groups. Although the data might suggest a violation of polarized light flavor sea–quark symmetry, the precision of the present data is not enou...

DEFINITION A relational query language Q is BP-complete if for each relational database D, the set of all relations defined by the queries of Q on D is equal to the set of all first-order definable relations over D. More formally, fix some infinite universe U of atomic data elements. A relational database schema S is a finite set of relation names, each with an associated arity. A relational da...