Second order tangent bundles of infinite dimensional manifolds

The second order tangent bundle $T^{2}M$ of a smooth manifold $M$ consists of the equivalent classes of curves on $M$ that agree up to their acceleration. It is known that in the case of a finite $n$-dimensional manifold $M$, $T^{2}M$ becomes a vector bundle over $M$ if and only if $M$ is endowed with a linear connection. Here we extend this result to $M$ modeled on an arbitrarily chosen Banach space and more generally to those Fr\'{e}chet manifolds which can be obtained as projective limits of Banach manifolds. The result may have application in the study of infinite-dimensional dynamical systems.Comment: 8 page

The sectional curvature remains positive when taking quotients by certain nonfree actions

We study some cases when the sectional curvature remains positive under the taking of quotients by certain nonfree isometric actions of Lie groups. We consider the actions of the groups $S^1$ and $S^3$ such that the quotient space can be endowed with a smooth structure using the fibrations $S^3/S^1{\simeq}S^2$ and $S^7/S^3\simeq S^4$. We prove that the quotient space carries a metric of positive sectional curvature, provided that the original metric has positive sectional curvature on all 2-planes orthogonal to the orbits of the action.Comment: 26 pages, 1 figure. Changed the spelling of the author's nam

The Berwald-type linearisation of generalised connections

We study the existence of a natural `linearisation' process for generalised connections on an affine bundle. It is shown that this leads to an affine generalised connection over a prolonged bundle, which is the analogue of what is called a connection of Berwald type in the standard theory of connections. Various new insights are being obtained in the fine structure of affine bundles over an anchored vector bundle and affineness of generalised connections on such bundles.Comment: 25 page

The Ursinus Weekly, March 23, 1959

Student-faculty show was well received by Ursinus • Students urged to take SS test, April 30 • U.C. students can enter public speaking contest • Ursinus to host annual county science fair • MSGA discusses new projects March 16 • Dr. Schmoyer to discuss growth of liturgy • Mrs. P. Streich to talk this Wednesday • May Day boasts long history; featured at Ursinus since 1905 • Campus Chest ends; Campaign is successful • Art seminars to begin on April 8 • S-P Jaycees to sponsor Easter sunrise service • Editorial: That\u27s it • Our escape from the communists • Letters to the editor • Antics • Girls finish b-ball season; Win 81-31 • Track team practices for opener • Baseball team begins practice for \u2759 season • Men\u27s tennis team getting into shape • APO sells paperbacks • Dean\u27s list • Museum presents recent print sequenceshttps://digitalcommons.ursinus.edu/weekly/1381/thumbnail.jp

Projective dynamics and first integrals

We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltrami's theorem about projectively flat Riemannian manifolds. We set the ground for a new and simple theory of the integrable systems having only quadratic first integrals. This theory begins with two centered quadrics related by central projection, each quadric being a model of a space of constant curvature. Finally, we present an extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure

Spectral unmixing for label-free, in-liquid characterization of biomass microstructure and biopolymer content by coherent Raman imaging

Characterization of lignocellulosic biomass microstructure with chemical specificity and under physiological conditions could provide invaluable insights to our understanding of plant tissue development, microstructure, origins of recalcitrance, degradation, and solubilization. However, most methods currently available are either destructive, are not compatible with hosting a physiological environment, or introduces exogenous probes, complicating their use for studying changes in microstructure and mechanisms of plant development, recalcitrance, or degradation in situ. To address these challenges, we here present a multi-modal chemically specific imaging technique based on coherent anti-Stokes Raman scattering (CARS) microspectroscopy with simplex maximization and entropy-based spectral unmixing enabling label-free, chemically specific characterization of plant microstructure in liquid. We describe how spatial drift of samples suspended in liquid can introduce artifacts in spectral unmixing procedures for single-frequency CARS and propose a mitigative strategy toward these effects using simultaneously acquired forward-scattered CARS signals and epi-detected autofluorescence. We further apply the technique for chemical and microstructural characterization of untreated and liquid hot water pretreated rapeseed straw by CARS and show how the framework can be extended for 3D imaging with chemical specificity. Finally, we provide examples of the intricate chemical and microstructural details recovered by this hybrid imaging technique, including discerning between primary and secondary cell walls, localization of aqueous components to cell lumina, and the presence of funnel-type pits in samples ofBrassica napus

Raman Computed Tomography (Raman-CT) System and Method

The invention relates to an optical tomography scanning system (1) for 3D imaging of an object (100), for example an experimental rodent or a patient, using Raman scattered light from the object. A laser (10) and an optical configuration (20) for fixating the object and arranged for rotation (Θ) is provided, and an optical receiving part (30) receives Raman scattered light. The optical receiving part has a detector array (35) for receiving the Raman scattered light in two spatial dimensions (X, Z), and optical guide means (37) convey Raman scattered light to a spectrometer (38), where multiple spectra are recorded for the two spatial dimensions for each relative rotational position (Θ) of the object. A 3D image reconstruction of the object based on the multiple spectra at a plurality of relative rotational positions (Θ) of the object enables 3D tomographic imaging of the object, such as an experimental rat.</p

Raman Computed Tomography (Raman-CT) System and Method

The invention relates to an optical tomography scanning system (1) for 3D imaging of an object (100), for example an experimental rodent or a patient, using Raman scattered light from the object. A laser (10) and an optical configuration (20) for fixating the object and arranged for rotation (Θ) is provided, and an optical receiving part (30) receives Raman scattered light. The optical receiving part has a detector array (35) for receiving the Raman scattered light in two spatial dimensions (X, Z), and optical guide means (37) convey Raman scattered light to a spectrometer (38), where multiple spectra are recorded for the two spatial dimensions for each relative rotational position (Θ) of the object. A 3D image reconstruction of the object based on the multiple spectra at a plurality of relative rotational positions (Θ) of the object enables 3D tomographic imaging of the object, such as an experimental rat.</p