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

On the second gaussian map for curves on a K3 surface

By a theorem of Wahl, for canonically embedded curves which are hyperplane sections of K3 surfaces, the first gaussian map is not surjective. In this paper we prove that if C is a general hyperplane section of high genus (greater than 280) of a general polarized K3 surface, then the second gaussian map of C is surjective. The resulting bound for the genus g of a general curve with surjective second gaussian map is decreased to g >152.Comment: final version, to appear in Nagoya Mathematical Journa

An acoustic investigation of the developmental trajectory of lexical stress contrastivity in Italian

We examined whether typically developing Italian children exhibit adult-like stress contrastivity for word productions elicited via a picture naming task (n=25 children aged 3\u20135 years and 27 adults). Stimuli were 10 trisyllabic Italian words; half began with a weak\u2013strong (WS) pattern of lexical stress across the initial 2 syllables, as in patata, while the other half began with a strong\u2013weak (SW) pattern, as in gomito. Word productions that were identified as correct via perceptual judgement were analysed acoustically. The initial 2 syllables of each correct word production were analysed in terms of the duration, peak intensity, and peak fundamental frequency of the vowels using a relative measure of contrast\u2014the normalised pairwise variability index (PVI). Results across the majority of measures showed that children\u2019s stress contrastivity was adult-like. However, the data revealed that children\u2019s contrastivity for trisyllabic words beginning with a WS pattern was not adult-like regarding the PVI for vowel duration: children showed less contrastivity than adults. This effect appeared to be driven by differences in word-medial gemination between children and adults. Results are compared with data from a recent acoustic study of stress contrastivity in English speaking children and adults and discussed in relation to language-specific and physiological motor-speech constraints on production

Cassini's second and third laws

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

Higher Spin Gravity Amplitudes From Zero-form Charges

We examine zero-form charges in Vasiliev's four-dimensional bosonic higher spin gravities. These are classical observables given by integrals over noncommutative twistor space of adjoint combinations of the zero-form master fields, including insertions of delta functions in the deformed oscillators serving as gauge invariant regulators. The regularized charges admit perturbative expansions in terms of multi-linear functionals in the Weyl zero-form, which are Bose symmetric and higher spin invariant by construction, and that can be interpreted as basic building blocks for higher spin gravity amplitudes. We compute two- and three-point functions by attaching external legs given by unfolded bulk-to-boundary propagators, and identify the result with the two- and three-current correlation functions in theories of free conformal scalars and fermions in three dimensions. Modulo assumptions on the structure of the sub-leading corrections, and relying on the generalized Hamiltonian off-shell formulation, we are thus led to propose an expression for the free energy as a sum of suitably normalized zero-form chargesComment: V2: Typos corrected, references added, footnote and note added, discussion section improve