LetW (A) andWe(A) be the joint numerical range and the joint essential numerical range of an m-tuple of self-adjoint operators A = (A1, . . . , Am) acting on an infinite dimensional Hilbert space, respectively. In this paper, it is shown that We(A) is always convex and admits many equivalent formulations. In particular, for any fixed i ∈ {1, . . . ,m}, We(A) can be obtained as the intersection ...

aim: abnormal joint mobility is an important factor in movement dysfunction and physical disability. a general lack of descriptive details exists for measurements of hip rotation range of motion (rom). this study was designed to establish the influence of hip position on active and passive range of motion of the hip in external and internal rotation(ext & int rot). material & methods: ...

EINSTEIN’S equations (1936) yield maximum likelihood estimates of the w regional frequency distribution of crossovers in the tetrads from which a given sample of strands was derived, one per tetrad. But clearly, as with all estimates of universe parameters from sample statistics, other values within a certain range cannot be rejected; that range can be ascertained, for each tetrad-rank separate...

We study rank 2 bundles E on a two dimensional neighborhood of an irreducible curve C ≃ P1 with C2 = −k. Section 1 calculates bounds on the numerical invariants of E. Section 2 describes “balancing”, and proves the existence of families of bundles with prescribed numerical invariants. Section 3 studies rank 2 bundles on OP1(−k), giving an explicit construction of their moduli as stratified spaces.

It is a long open problem to combinatorially characterize the 3D bar-joint rigidity of graphs. The problem is at the intersection of combinatorics and algebraic geometry, and crops up in practical algorithmic applications ranging from mechanical computer aided design to molecular modeling. The problem is equivalent to combinatorially determining the generic rank of the 3D bar-joint rigidity mat...

This paper studies the possibilities of the Linear Matrix Inequality (LMI) characterization of the matrix cones formed by nonnegative complex Hermitian quadratic functions over specific domains in the complex space. In its real case analog, such studies were conducted in Sturm and Zhang [11]. In this paper it is shown that stronger results can be obtained for the complex Hermitian case. In part...

‎let $v$ be an $n$-dimensional complex inner product space‎. ‎suppose‎ ‎$h$ is a subgroup of the symmetric group of degree $m$‎, ‎and‎ ‎$chi‎ :‎hrightarrow mathbb{c} $ is an irreducible character (not‎ ‎necessarily linear)‎. ‎denote by $v_{chi}(h)$ the symmetry class‎ ‎of tensors associated with $h$ and $chi$‎. ‎let $k(t)in‎ (v_{chi}(h))$ be the operator induced by $tin‎ ‎text{end}(v)$‎. ‎the...

let ‎x be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎cartesian decomposition ‎‎x = a + i ‎b‎‎‎‎‎, ‎where ‎‎a ‎and ‎‎b ‎are ‎‎‎n ‎‎times n‎ ‎hermitian ‎matrices. ‎it ‎is ‎known ‎that ‎‎$vert x vert_p^2 ‎leq 2(vert a vert_p^2 + vert b vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎vert . vert_p$ ‎is ‎the ‎schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎in this paper‎, this inequality and some of its improvements ...