Co-Teaching in Today\u27s Schools

Co-teaching in today\u27s schools varies based on the model that schools choose and the teachers providing the support. This literature review examined the wide variety of co-teaching models and established that co-teaching is most effective when the co-teachers share a similar philosophy and are well prepared through efficient planning. It is also necessary for the classroom size to be small enough for teachers to be able to meet with students individually or in small groups. This research focused on how co-teachers view their arrangement and how it has been implemented in the schools in which they teach. Surveys were anonymously sent to teachers in two elementary school settings: one a small suburban school and the other a city school

The mixed Hodge structure on the fundamental group of hyperelliptic curves and higher cycles

In this paper we give a geometrical interpretation of an extension of mixed Hodge structures (MHS) obtained from the canonical MHS on the group ring of the fundamental group of a hyperelliptic curve modulo the fourth power of its augmentation ideal. We show that the class of this extension coincides with the regulator image of a canonical higher cycle in a hyperelliptic jacobian. This higher cycle was introduced and studied by Collino.Comment: 22 pages, 3 figures. To appear in: Journal of Algebraic Geometr

On power series expansions of the S-resolvent operator and the Taylor formula

The $S$-functional calculus is based on the theory of slice hyperholomorphic functions and it defines functions of $n$-tuples of not necessarily commuting operators or of quaternionic operators. This calculus relays on the notion of $S$-spectrum and of $S$-resolvent operator. Since most of the properties that hold for the Riesz-Dunford functional calculus extend to the S-functional calculus it can be considered its non commutative version. In this paper we show that the Taylor formula of the Riesz-Dunford functional calculus can be generalized to the S-functional calculus, the proof is not a trivial extension of the classical case because there are several obstructions due to the non commutativity of the setting in which we work that have to be overcome. To prove the Taylor formula we need to introduce a new series expansion of the $S$-resolvent operators associated to the sum of two $n$-tuples of operators. This result is a crucial step in the proof of our main results,but it is also of independent interest because it gives a new series expansion for the $S$-resolvent operators. This paper is devoted to researchers working in operators theory and hypercomplex analysis

Cassini's second and third laws

Cassinis second and third laws of moons rotational motion extended and applied to earth satellite, Mercyry, and Iapetu

Passing to the limit in maximal slope curves: from a regularized Perona-Malik equation to the total variation flow

We prove that solutions of a mildly regularized Perona-Malik equation converge, in a slow time scale, to solutions of the total variation flow. The convergence result is global-in-time, and holds true in any space dimension. The proof is based on the general principle that "the limit of gradient-flows is the gradient-flow of the limit". To this end, we exploit a general result relating the Gamma-limit of a sequence of functionals to the limit of the corresponding maximal slope curves.Comment: 19 page

Prym map and second gaussian map for Prym-canonical line bundles

We show that the second fundamental form of the Prym map lifts the second gaussian map of the Prym-canonical bundle. We prove, by degeneration to binary curves, that this gaussian map is surjective for the general point [C,A] of R_g for g > 19.Comment: Final version. To appear in Advances in Mathematic

Study of certain tether safety issues and the use of tethers for payload orbital transfer. Continuation of investigation of electrodynamic stabilization and control of long orbiting tethers

Tether safety issues are summarized