Energy-Consumption Factors of Air-Stream Moulding Machines

In this article, an outline of the key questions connected with the essential problems of energy-consumption of air-stream mouldingmachines has been presented. Research results and calculations of requisite parameters appraisable of energy-consumption of air-streammoulding machines have been supplemented also by the data analysis of offer of the moulding machines manufacturers. The attention onconstructional and technological factors which are favourable for the diminution of energy-consuming of the moulding process has beenpaid

Direct measurement of diurnal polar motion by ring laser gyroscopes

We report the first direct measurements of the very small effect of forced diurnal polar motion, successfully observed on three of our large ring lasers, which now measure the instantaneous direction of Earth's rotation axis to a precision of 1 part in 10^8 when averaged over a time interval of several hours. Ring laser gyroscopes provide a new viable technique for directly and continuously measuring the position of the instantaneous rotation axis of the Earth and the amplitudes of the Oppolzer modes. In contrast, the space geodetic techniques (VLBI, SLR, GPS, etc.) contain no information about the position of the instantaneous axis of rotation of the Earth, but are sensitive to the complete transformation matrix between the Earth-fixed and inertial reference frame. Further improvements of gyroscopes will provide a powerful new tool for studying the Earth's interior.Comment: 5 pages, 4 figures, agu2001.cl

Four problems regarding representable functors

Let $R$, $S$ be two rings, $C$ an $R$-coring and ${}_{R}^C{\mathcal M}$ the category of left $C$-comodules. The category ${\bf Rep}\, ( {}_{R}^C{\mathcal M}, {}_{S}{\mathcal M} )$ of all representable functors ${}_{R}^C{\mathcal M} \to {}_{S}{\mathcal M}$ is shown to be equivalent to the opposite of the category ${}_{R}^C{\mathcal M}_S$. For $U$ an $(S,R)$-bimodule we give necessary and sufficient conditions for the induction functor $U\otimes_R - : {}_{R}^C\mathcal{M} \to {}_{S}\mathcal{M}$ to be: a representable functor, an equivalence of categories, a separable or a Frobenius functor. The latter results generalize and unify the classical theorems of Morita for categories of modules over rings and the more recent theorems obtained by Brezinski, Caenepeel et al. for categories of comodules over corings.Comment: 16 pages, the second versio

Strong Connections on Quantum Principal Bundles

A gauge invariant notion of a strong connection is presented and characterized. It is then used to justify the way in which a global curvature form is defined. Strong connections are interpreted as those that are induced from the base space of a quantum bundle. Examples of both strong and non-strong connections are provided. In particular, such connections are constructed on a quantum deformation of the fibration $S^2 -> RP^2$. A certain class of strong $U_q(2)$-connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with the q-dependent hermitian metric. A particular form of the Yang-Mills action on a trivial U\sb q(2)-bundle is investigated. It is proved to coincide with the Yang-Mills action constructed by A.Connes and M.Rieffel. Furthermore, it is shown that the moduli space of critical points of this action functional is independent of q.Comment: AMS-LaTeX, 40 pages, major revision including examples of connections over a quantum real projective spac

Towards Spinfoam Cosmology

We compute the transition amplitude between coherent quantum-states of geometry peaked on homogeneous isotropic metrics. We use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in 1/volume. We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex yields the Friedmann equation in the appropriate limit.Comment: 8 page

Quantum Bundle Description of the Quantum Projective Spaces

We realise Heckenberger and Kolb's canonical calculus on quantum projective (n-1)-space as the restriction of a distinguished quotient of the standard bicovariant calculus for Cq[SUn]. We introduce a calculus on the quantum (2n-1)-sphere in the same way. With respect to these choices of calculi, we present quantum projective (N-1)-space as the base space of two different quantum principal bundles, one with total space Cq[SUn], and the other with total space Cq[S^(2n-1)]. We go on to give Cq[CP^n] the structure of a quantum framed manifold. More specifically, we describe the module of one-forms of Heckenberger and Kolb's calculus as an associated vector bundle to the principal bundle with total space Cq[SUn]. Finally, we construct strong connections for both bundles.Comment: 33 pages; minor changes, to appear in Comm. Math. Phy

A differential U-module algebra for U=U_q sl(2) at an even root of unity

We show that the full matrix algebra Mat_p(C) is a U-module algebra for U = U_q sl(2), a 2p^3-dimensional quantum sl(2) group at the 2p-th root of unity. Mat_p(C) decomposes into a direct sum of projective U-modules P^+_n with all odd n, 1<=n<=p. In terms of generators and relations, this U-module algebra is described as the algebra of q-differential operators "in one variable" with the relations D z = q - q^{-1} + q^{-2} z D and z^p = D^p = 0. These relations define a "parafermionic" statistics that generalizes the fermionic commutation relations. By the Kazhdan--Lusztig duality, it is to be realized in a manifestly quantum-group-symmetric description of (p,1) logarithmic conformal field models. We extend the Kazhdan--Lusztig duality between U and the (p,1) logarithmic models by constructing a quantum de Rham complex of the new U-module algebra.Comment: 29 pages, amsart++, xypics. V3: The differential U-module algebra was claimed quantum commutative erroneously. This is now corrected, the other results unaffecte

Twisted partial actions of Hopf algebras

In this work, the notion of a twisted partial Hopf action is introduced as a unified approach for twisted partial group actions, partial Hopf actions and twisted actions of Hopf algebras. The conditions on partial cocycles are established in order to construct partial crossed products, which are also related to partially cleft extensions of algebras. Examples are elaborated using algebraic groups

Getting them through the door: Social and behavioral determinants of uptake and engagement in an obesity intervention

Using data from a large-scale screening program (N = 19634), we aimed to prospectively identify factors predicting uptake (i.e. acceptance of the invitation) and engagement (i.e. participation in at least two sessions) in a multi-component-intensive-behavioral-intervention for obesity-management (MBIOM) intervention targeting adolescents (n = 2862; 12–14 years; BMI ≥90th percentile). Approximately one third of adolescents most in need of weight management declined the initial invitation to enter the MBIOM. Poor diet, sedentary behavior, and parental education predicted willingness to enter and stay in the intervention, however measured body mass index did not matter. Perceived family support, instead of initial motivation, facilitated engagement. Our results provide new insights on the importance of regional socio-geographical factors including trust in local authorities