A forgotten little chapter on isoperimetric inequalities. On the fraction of a convex and closed plane area lying outside a circle with which it shares a diameter

[EN]Often some interesting or simply curious points are left out when developing a theory. It seems that one of them is the existence of an upper bound for the fraction of area of a convex and closed plane area lying outside a circle with which it shares a diameter, a problem stemming from the theory of isoperimetric inequalities. In this paper such a bound is constructed and shown to be attained for a particular area. It is also shown that convexity is a necessary condition in order to avoid the whole area lying outside the circle

Thaumatrope (Magic Circle)

The thaumatrope consists of a circle of cardstock, 2.5 inches in diameter with 2 strings attached, one each at opposite points of the diameter. There were 2 images painted on the cardstock, one on each side, with their positions inverted. The outline of the image was usually printed and the color hand-painted in (Barnes 7).

Optical hysteresis of ridge waveguide magnetic garnet films and cavities in two-dimensional magneto-photonic crystal slabs

Magnetic iron garnets as well as magnetic photonic crystals are of great interests in magneto-optic applications such as isolators, current captors, circulators, TE-TM mode conversion, wavelength accordable filters, optical sensors and switches, all of which provide a promising platform for future integrated optical circuits. In the present work, two topics are studied based on magnetic iron garnet films. In the first part, the characteristics of the magnetization are investigated for ridge waveguides fabricated on (100) oriented iron garnet thin films. The magnetic response in magneto-optic waveguides patterned on epitaxial magnetic garnet films depends on the crystallographic orientation of the waveguides and the magnetic anisotropy of the material. These can be studied by polarization rotation hysteresis loops, which are related to the component of magnetization parallel to the light propagation direction and the linear birefringence. Polarization rotation hysteresis loops for low birefringence waveguides with different orientations are experimentally investigated. Asymmetric stepped curves are obtained from waveguides along, due to the large magnetocrystalline anisotropy in the plane. A model based on the free energy density is developed to demonstrate the motion of the magnetization and can be used in the design of magneto-optic devices. The second part of this thesis focuses on the design and fabrication of high-Q cavities in two-dimensional magneto-photonic crystal slabs. The device consists of a layer of silicon and a layer of iron garnet thin film. Triangular lattice elliptical air holes are patterned in the slab. The fundamental TM band gap overlaps with the first-order TE band gap from 0374~0.431(a/λ) showing that both TE and TM polarization light can be confined in the photonic crystals. A nanocavity is designed to obtain both TE and TM defect modes in the band gaps. Additional work is needed to overlap the TE and TM defect modes and obtain a high-Q cavity so as to develop miniaturized Faraday rotators.

The E-learning Circle – a holistic software design tool for e-learning

The article introduces the E-learning Circle, a tool developed to assure the quality of the software design process of e-learning systems, considering pedagogical principles as well as technology. The E-learning Circle consists of a number of concentric circles which are divided into three sectors. The content of the inner circles is based on pedagogical principles, while the outer circle specifies how the pedagogical principles may be implemented with technology. The circle’s centre is dedicated to the subject taught, ensuring focus on the specific subject’s properties. The three sectors represent the student, the teacher and the learning objectives. The strengths of the E-learning Circle are the compact presentation combined with the overview it provides, as well as the usefulness of a design tool dealing with complexity, providing a common language and embedding best practice. The E-learning Circle is not a prescriptive method, but is useful in several design models and processes. The article presents two projects where the E-learning Circle was used as a design tool.

Nonequilibrium hysteresis and spin relaxation in the mixed-anisotropy dipolar-coupled spin-glass LiHo0.5Er0.5F4

We present a study of the model spin-glass LiHo0.5Er0.5F4 using simultaneous ac susceptibility, magnetization, and magnetocaloric effect measurements along with small angle neutron scattering (SANS) at sub-Kelvin temperatures. All measured bulk quantities reveal hysteretic behavior when the field is applied along the crystallographic c axis. Furthermore, avalanchelike relaxation is observed in a static field after ramping from the zero-field-cooled state up to 200–300 Oe. SANS measurements are employed to track the microscopic spin reconfiguration throughout both the hysteresis loop and the related relaxation. Comparing the SANS data to inhomogeneous mean-field calculations performed on a box of one million unit cells provides a real-space picture of the spin configuration. We discover that the avalanche is being driven by released Zeeman energy, which heats the sample and creates positive feedback, continuing the avalanche. The combination of SANS and mean-field simulations reveal that the conventional distribution of cluster sizes is replaced by one with a depletion of intermediate cluster sizes for much of the hysteresis loop.

Generation of long, fully modified, and serum-resistant oligonucleotides by rolling circle amplification

Rolling Circle Amplification (RCA) is an isothermal enzymatic method generating single-stranded DNA products consisting of concatemers containing multiple copies of the reverse complement of the circular template precursor. Little is known on the compatibility of modified nucleoside triphosphates (dN*TPs) with RCA, which would enable the synthesis of long, fully modified ssDNA sequences. Here, dNTPs modified at any position of the scaffold were shown to be compatible with rolling circle amplification, yielding long (>1 kb), and fully modified single-stranded DNA products. This methodology was applied for the generation of long, cytosine-rich synthetic mimics of telomeric DNA. The resulting modified oligo-nucleotides displayed an improved resistance to fetal bovine serum.

4D/3D reduction of dualities: mirrors on the circle

We engineer a brane picture for the reduction of Seiberg dualities from 4D to 3D, valid also in the presence of orientifold planes. We obtain effective 3D dualities on the circle by T-duality, geometrizing the non-perturbative superpotential which is an affine Toda potential. When reducing to pure 3D, we define a double-scaling limit which creates a sector of interacting singlets, giving a unified mechanism for the brane reduction of dualities.

The Circle: Die neue Kolonisierung des inneren Menschen

Mit Hilfe des zeitgenössischen Romans 'The Circle' von Dave Eggers werden Entgrenzungs- und Verdichtungstendenzen moderner subjektivierter Arbeit illustriert, die einen Zusammenhang mit Burnout- und Erschöpfungsdepressionsdiagnosen plausibilisieren. Angesichts der Uneindeutigkeit der empirischen Evidenz wird vorgeschlagen, die Problematik der modernen Gestalt der Erwerbsarbeit – vor allem für diejenigen am unteren Ende der jeweiligen Hierarchien – nicht nur anhand ihrer Krankheitsträchtigkeit, sondern mit Hilfe des Konzepts der Lebensformen und ihrer normativen Aufladung zu kritisieren: Massiv entgrenzte und verdichtete Arbeit erscheint dann als Bruch des 'Arbeitsversprechens', das sich mit Entstehung der Arbeitsgesellschaft im 19. Jh. herausgebildet hat.