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We study the spontaneous out-of-plane bending of a planar untwisted ribbon composed of nematic polymer networks activated by a change in temperature. Our theory accounts for both stretching and bending energies, which compete to establish equilibrium. We show that when equilibrium is attained these energy components obey a complementarity relation: one is maximum where the other is minimum. Moreover, we identify a bleaching regime: for sufficiently large values of an activation parameter (which measures the mismatch between the degrees of order in polymer organization in the reference and current configurations), the ribbon's deformation is essentially independent of its thickness. [ABSTRACT FROM AUTHOR]

We present a theory of deformation of ribbons made of nematic polymer networks (NPNs). These materials exhibit properties of rubber and nematic liquid crystals, and can be activated by external stimuli of heat and light. A two-dimensional energy for a sheet of such a material has already been derived from the celebrated neo-classical energy of nematic elastomers in three space dimensions. Here, we use a dimension reduction method to obtain the appropriate energy for a ribbon from the aforementioned sheet energy. We also present an illustrative example of a rectangular NPN ribbon that undergoes in-plane serpentine deformations upon activation under an appropriate set of boundary conditions. [ABSTRACT FROM AUTHOR]

Abstract We define a ribbon category Sp (β) , depending on a parameter β , which encompasses Cautis, Kamnitzer and Morrison's spider category, and describes for β = m − n the monoidal category of representations of U q (gl m | n) generated by exterior powers of the vector representation and their duals. We identify this category Sp (β) with a direct limit of quotients of a dual idempotented quantum group U ˙ q (gl r + s) , proving a mixed version of skew Howe duality in which exterior powers and their duals appear at the same time. We show that the category Sp (β) gives a unified natural setting for defining the colored gl m | n link invariant (for β = m − n) and the colored HOMFLY-PT polynomial (for β generic). [ABSTRACT FROM AUTHOR]

Abstract A one-to-one correspondence is proved between the N -rooted ribbon graphs, or maps, with e edges and the (e − N + 1) -loop Feynman diagrams of a certain quantum field theory. This result is used to obtain explicit expressions and relations for the generating functions of N -rooted maps and for the numbers of N -rooted maps with a given number of edges using the path integral approach applied to the corresponding quantum field theory. [ABSTRACT FROM AUTHOR]

A challenge in the dry granulation (DG) process is the generation of an excessive amount of fines during milling, which can cause problems in die filling due to poor flowability and content uniformity of tablets. Using a design of experiments (DOE) approach, we show that the amount of fines generated during milling decreases with either increasing ribbon density or screen size, while impeller speed has negligible effect. Moreover, under identical milling conditions, the percent fines can be accurately predicted from ribbon density. Thus, controlling ribbon density and screen size is important for optimizing the amount of fines produced during DG process. Because density has a central role in the outcome, it is a critical ribbon property that needs to be controlled to improve robustness of the DG process. [ABSTRACT FROM AUTHOR]

In [K. Kishimoto, T. Shibuya and T. Tsukamoto, Simple-ribbon fusions and genera of links, J. Math. Soc. Japan68 (2016) 1033–1045], we introduced a special kind of fusions, the simple-ribbon fusions. In this paper, we give a sufficient condition for simple-ribbon fusions to produce a prime knot. [ABSTRACT FROM AUTHOR]

In this article the new properties of relative retracts in the context of relative homotopy are studied. The results of the studies are particularly applied to the characterization of connected and locally connected spaces and absolute neighborhood retracts. [ABSTRACT FROM AUTHOR]

We present a new set of axioms for 2D TQFT formulated on the category of cell graphs with edge-contraction operations as morphisms. We construct a functor from this category to the endofunctor category consisting of Frobenius algebras. Edge-contraction operations correspond to natural transformations of endofunctors, which are compatible with the Frobenius algebra structure. Given a Frobenius algebra A , every cell graph determines an element of the symmetric tensor algebra defined over the dual space A ⁎ . We show that the edge-contraction axioms make this assignment depending only on the topological type of the cell graph, but not on the graph itself. Thus the functor generates the TQFT corresponding to A . [ABSTRACT FROM AUTHOR]

In this paper, we present a novel MEMS orthogonal fluxgate sensor fabricated by standard micro fabricated technology. The sensor mainly consists of a three-dimensional solenoid pick-up coil and a meander-shaped Co-based amorphous ribbon core. The experimental results demonstrate that the sensitivity and noise can be optimized by tuning operation conditions with excitation current amplitude and frequency. The fabricated sensor exhibits a maximum sensitivity of 575 V/T, a wide linear range of ± 480 μT, and a perming below 0.8 μT for 90 mA rms sinusoidal excitation current at 500 kHz frequency. The equivalent magnetic noise is 0.20 nT/√Hz at 1 Hz, and the RMS noise is 1.09 nT in the frequency range of 0.1–10 Hz under the same excitation. In comparison with other micro fabricated fluxgates in similar dimensions, this device possesses relatively high sensitivity and low noise spectral density. [ABSTRACT FROM AUTHOR]

Inner hair cells (IHCs) in the cochlea are the mammalian phono-receptors, transducing sound energy into graded changes in membrane potentials, the so called "receptor potentials." Ribbon synapses between IHCs and auditory nerve neurons are responsible for converting receptor potentials into spike rates. The characteristics of auditory nerve responses to sound have been described extensively. For instance, persistent acoustic stimulation produces sensory adaptation, which is revealed as a reduction in neuronal spike rate with time constants in the range of milliseconds to seconds. Since the amplitude of IHC receptor potentials is invariant during this period, the classic hypothesis pointed to vesicle depletion at the IHC as responsible for auditory adaptation. In this study, we observed that fast synaptic depression occurred in responses to stimuli of varying intensities. Nevertheless, release continued after this initial depression, via synaptic vesicles with slower exocytotic kinetics. Heterogeneity in kinetic elements, therefore, favored synaptic responses with an early peak and a sustained phase. The application of cyclothiazide (CTZ) revealed that desensitization of postsynaptic receptors contributed to synaptic depression, which was more pronounced during stronger stimulation. Thus, desensitization had a twofold effect: It abbreviated signaling between IHC and the auditory nerve and also balanced differences in decay kinetics between responses to different stimulation strengths. We therefore propose that both pre- and postsynaptic mechanisms at the IHC ribbon synapse contribute to synaptic depression at the IHC ribbon synapse and spike rate adaptation in the auditory nerve. [ABSTRACT FROM AUTHOR]

Savar, one of the suburbs of Dhaka is undergoing tremendous development due to rapid urbanisation. Better access due to Dhaka Aricha Highway integrating with the development process has led augmentation of ribbon development. This type of development is very much attractive to developers in the sense that they do not have to waste money or plot space for constructing roads and can attract trade from the traffic on arterial roads. But the emergence of fringe zones and their complex, as well as unplanned ribbon development along Dhaka Aricha Highway, has led to serious land use problems such as haphazard urban growth, loss of agricultural lands, encroachment of water bodies, unauthorised urban sprawl, the rapid increase in land values, speculation in land and other related problems. Besides, the option for future planned development and provision of service along the Dhaka Aricha Highway is being jeopardized. In this consequence, this study attempts to focus on the trend of ribbon development along Dhaka-Aricha Highway to show the impact on the land use. To assess the trend in land use change, satellite image of four base years (2007, 2010, 2013 and 2016) of the study area were analysed by Geographical Information System (GIS) tool. Finally, a number of recommendations have been formulated to reduce the adverse impact of ribbon development. [ABSTRACT FROM AUTHOR]

We give an excluded minor characterisation of the class of ribbon graphs that admit partial duals of Euler genus at most one. [ABSTRACT FROM AUTHOR]

A ribbon is a first-order thickening of a non-singular curve. We show that a compactification of the moduli space of generalized line bundles on a ribbon is given by the Simpson moduli space of semi-stable sheaves. We then describe the geometry of this space, determining the irreducible components, connectedness, and the smooth locus. [ABSTRACT FROM AUTHOR]

Given a ribbon graph $$\Gamma $$ with some extra structure, we define, using constructible sheaves, a dg category $$\mathrm {CPM}(\Gamma )$$ meant to model the Fukaya category of a Riemann surface in the cell of Teichmüller space described by $$\Gamma .$$ When $$\Gamma $$ is appropriately decorated and admits a combinatorial 'torus fibration with section,' we construct from $$\Gamma $$ a one-dimensional algebraic stack $$\widetilde{X}_\Gamma $$ with toric components. We prove that our model is equivalent to $$\mathcal {P}\mathrm {erf}(\widetilde{X}_\Gamma )$$ , the dg category of perfect complexes on $$\widetilde{X}_\Gamma $$ . [ABSTRACT FROM AUTHOR]

The fundamental quandles and biquandles are invariants of classical knots and surface knots. It is unknown whether there exist classical or surface knots which have isomorphic fundamental quandles and distinct fundamental biquandles. We show that ribbon 2-knots or ribbon torus-knots with isomorphic fundamental quandles have isomorphic fundamental biquandles. For this purpose, we give a method for obtaining a presentation of the fundamental biquandle of a ribbon 2-knot/torus-knot from its fundamental quandle. [ABSTRACT FROM AUTHOR]

Abstract: Ribbon graphs embedded on a Riemann surface provide a useful way to describe the double-line Feynman diagrams of large N computations and a variety of other QFT correlator and scattering amplitude calculations, e.g. in MHV rules for scattering amplitudes, as well as in ordinary QED. Their counting is a special case of the counting of bi-partite embedded graphs. We review and extend relevant mathematical literature and present results on the counting of some infinite classes of bi-partite graphs. Permutation groups and representations as well as double cosets and quotients of graphs are useful mathematical tools. The counting results are refined according to data of physical relevance, such as the structure of the vertices, faces and genus of the embedded graph. These counting problems can be expressed in terms of observables in three-dimensional topological field theory with gauge group which gives them a topological membrane interpretation. [Copyright &y& Elsevier]