COMPUTING MINKOWSKI SUMS OF PLANE CURVES

1995 ◽  
Vol 05 (04) ◽  
pp. 413-432 ◽  
Author(s):  
ANIL KAUL ◽  
RIDA T. FAROUKI
Keyword(s):  
Algebraic Curve ◽  
Numerical Procedure ◽  
The Other ◽  
Minkowski Sum ◽  
Plane Curves ◽  
Parametric Curves ◽  
Implicit Equation ◽  
Minkowski Sums ◽  
High Degree ◽  
The Given

The Minkowski sum of two plane curves can be regarded as the area generated by sweeping one curve along the other. The boundary of the Minkowski sum consists of translated portions of the given curves and/or portions of a more complicated curve, the “envelope” of translates of the swept curve. We show that the Minkowski-sum boundary is describable as an algebraic curve (or subset thereof) when the given curves are algebraic, and illustrate the computation of its implicit equation. However, such equations are typically of high degree and do not offer a practical basis for tracing the boundary. For the case of polynomial parametric curves, we formulate a simple numerical procedure to address the latter problem, based on constructing the Gauss maps of the given curves and using them to identifying “corresponding” curve segments that are to be summed. This yields a set of discretely-sampled arcs that constitutes a superset of the Minkowski-sum boundary, and can be regarded as a planar graph. To extract the true boundary, we present a method for identifying and “trimming” away extraneous arcs by systematically traversing this graph.

scholarly journals Diameter, Decomposability, and Minkowski Sums of Polytopes

2018 ◽  
Vol 62 (4) ◽  
pp. 741-755
Author(s):  
Antoine Deza ◽  
Lionel Pournin
Keyword(s):  
The Other ◽  
Minkowski Sum ◽  
Minkowski Sums ◽  
Bounded Below

AbstractWe investigate how the Minkowski sum of two polytopes affects their graph and, in particular, their diameter. We show that the diameter of the Minkowski sum is bounded below by the diameter of each summand and above by, roughly, the product between the diameter of one summand and the number of vertices of the other. We also prove that both bounds are sharp. In addition, we obtain a result on polytope decomposability. More precisely, given two polytopes $P$ and $Q$, we show that $P$ can be written as a Minkowski sum with a summand homothetic to $Q$ if and only if $P$ has the same number of vertices as its Minkowski sum with $Q$.

The acquisition of Hungarian recursive PPs

2018 ◽  
Vol 4 (1) ◽  
pp. 105-123
Author(s):  
Ágnes Langó-Tóth
Keyword(s):  
Language Acquisition ◽  
Functional Element ◽  
The Other ◽  
Functional Head ◽  
Experiment Subject ◽  
The Given

Abstract In this study an experiment is presented on how Hungarian children interpret two word orders of recursive PPs (subject-PP-verb and PP-subject-verb order). According to the research of Roeper (2011) and Hollebrandse and Roeper (2014), children tend to give conjunctive interpretation to multiple embedded sentences at the beginning of language acquisition. This interpretation later turns into an adult-like, recursive interpretation. Our aim is to discover (i) whether Hungarian children start with conjunction as well, and whether (ii) the apparently more salient functional head lévő appearing in Hungarian recursive PPs can help them to acquire the correct, recursive interpretation early. We also want to find out whether (iii) the word orders in recursive PPs have an influence on the acquisition of children. In this paper two experiments are presented conducted with 6 and 8-year-olds and adults, in which the participants were asked to choose between two pictures. One of the pictures depicted recursive and the other one depicted conjunctive interpretation of the given sentence. In the first experiment subject-PP-verb order was tested, but in the second one sentences were tested with PP-subject-verb order. We will claim that lévő, which is (arguably) a more salient Hungarian functional element than -i, does not help children to acquire the embedded reading of recursive sentences, because both of them are overt functional heads. However, the two types of word orders affect the acquisition of recursive PPs. PP-subject-verb order is easier to compute because the order of the elements in the sentences and the order of the elements in the pictures matches.

Growth Characteristics of Activated Sludges Acclimated to para-Nitrophenol in Batch and Continuous Modes

1994 ◽  
Vol 29 (7) ◽  
pp. 327-333
Author(s):  
Y. Matsui ◽  
F. Yamaguchi ◽  
Y. Suwa ◽  
Y. Urushigawa
Keyword(s):  
Growth Characteristics ◽  
The Other ◽  
Operational Mode ◽  
Continuous Mode ◽  
Relative Resistance ◽  
Batch Mode ◽  
The Given ◽  
Operational Modes ◽  
Very High ◽  
Sensitive Group

Activated sludges were acclimated to p-nitrophenol (PNP) in two operational modes, a batch and a continuous. The operational mode of the PNP acclimation of activated sludges strongly affected the physiological characteristics of predominant microorganisms responsible for PNP degradation. Predominant PNP degraders in the sludge in batch mode (Sludge B) had lower PNP affinity and were relatively insensitive to PNP concentration. Those of the sludge in continuous mode (Sludge C), on the other hand, had very high PNP affinity and were sensitive to PNP. MPN enumeration of PNP degraders in sludge B and C using media with different PNP concentrations (0.05, 0.2,0.5 and 2.0 mM) supported the above results. Medium with 0.2 mM of PNP did not recover PNP degraders in sludge C well, while it recovered PNP degraders in sludge B as well as the medium with 0.05 mM did. When switching from one operational mode to the other, the predominant population in sludge B shifted to the sensitive group, but that of sludge C did not shift at the given loading of PNP, showing relative resistance to inhibitive concentration.

C-Terminal amino acid sequence of chicken pepsinogen and its homology with sequences of other acid proteases

1980 ◽  
Vol 45 (4) ◽  
pp. 1144-1154 ◽  
Author(s):  
Miroslav Baudyš ◽  
Helena Keilová ◽  
Vladimír Kostka
Keyword(s):  
Amino Acid ◽  
Amino Acid Sequence ◽  
The Other ◽  
Terminal Sequence ◽  
Terminal Part ◽  
Terminal Amino Acid ◽  
Tryptic Peptides ◽  
Terminal Amino ◽  
High Degree ◽  
Terminal Amino Acid Sequence

To determine the primary structure of the C-terminal part of the molecule of chicken pepsinogen the tryptic, chymotryptic and thermolytic digest of the protein were investigated and peptides derived from this region were sought. These peptides permitted the following 21-residue C-terminal sequence to be determined: ...Ile-Arg-Glu-Tyr-Tyr-Val-Ile-Phe-Asp-Arg-Ala-Asn-Asn-Lys-Val-Gly-Leu-Ser-Pro-Leu-Ser.COOH. A comparison of this structure with the C-terminal sequential regions of the other acid proteases shows a high degree of homology between chicken pepsinogen and these proteases (e.g., the degree of homology with respect to hog pepsinogen and calf prochymosin is about 66%). Additional tryptic peptides, derived from the N-terminal part of the zymogen molecule whose amino acid sequence has been reported before, were also obtained in this study. This sequence was extended by two residues using an overlapping peptide. An ancillary result of this study was the isolation of tryptic peptides derived from other regions of the zymogen molecule.

Giving and Promising

2018 ◽  
Author(s):  
Jean-Yves Lacoste ◽  
Oliver O’Donovan
Keyword(s):  
The Other ◽  
Face To Face ◽  
Present Experience ◽  
The World ◽  
The Given

Giving and promise must be thought together. Being-in-the world entails being-with the other, who is both “given” and bearer of a gift promised. But any disclosure may be understood as a gift; it is not anthropomorphic to speak of “self-giving” with a wider reference than person-to-person disclosure. Which implies that no act of giving can exhaust itself in its gift. Present experience never brings closure to self-revealing. Yet giving is crystallized into “the given,” the closure of gift. “The given” is what it is, needing no gift-event to reveal it. But the given, too, is precarious, and can be destabilized when giving brings us face to face with something unfamiliar. Nothing appears without a promise of further appearances, and God himself can never be “given.”

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

scholarly journals Involvement of loop 5 lysine residues and the N-terminal β-hairpin of the ribotoxin hirsutellin A on its insecticidal activity

2016 ◽  
Vol 397 (2) ◽  
pp. 135-145 ◽  
Author(s):  
Miriam Olombrada ◽  
Lucía García-Ortega ◽  
Javier Lacadena ◽  
Mercedes Oñaderra ◽  
José G. Gavilanes ◽  
...  
Keyword(s):  
Active Sites ◽  
Structural Changes ◽  
The Other ◽  
Spatial Proximity ◽  
Ribonucleolytic Activity ◽  
The Family ◽  
Lysine Residues ◽  
Hirsutella Thompsonii ◽  
Close Spatial Proximity ◽  
High Degree

Abstract Ribotoxins are cytotoxic members of the family of fungal extracellular ribonucleases best represented by RNase T1. They share a high degree of sequence identity and a common structural fold, including the geometric arrangement of their active sites. However, ribotoxins are larger, with a well-defined N-terminal β-hairpin, and display longer and positively charged unstructured loops. These structural differences account for their cytotoxic properties. Unexpectedly, the discovery of hirsutellin A (HtA), a ribotoxin produced by the invertebrate pathogen Hirsutella thompsonii, showed how it was possible to accommodate these features into a shorter amino acid sequence. Examination of HtA N-terminal β-hairpin reveals differences in terms of length, charge, and spatial distribution. Consequently, four different HtA mutants were prepared and characterized. One of them was the result of deleting this hairpin [Δ(8-15)] while the other three affected single Lys residues in its close spatial proximity (K115E, K118E, and K123E). The results obtained support the general conclusion that HtA active site would show a high degree of plasticity, being able to accommodate electrostatic and structural changes not suitable for the other previously known larger ribotoxins, as the variants described here only presented small differences in terms of ribonucleolytic activity and cytotoxicity against cultured insect cells.

Methylene. III. Gas phase reactions with 1-chloropropane

1969 ◽  
Vol 312 (1509) ◽  
pp. 141-161 ◽  
Keyword(s):  
Gas Phase ◽  
Rate Constants ◽  
Hydrogen Abstraction ◽  
The Other ◽  
Gas Phase Reactions ◽  
Other Hand ◽  
Chlorine Substituent ◽  
High Degree ◽  
Singlet Methylene

The work described in this and the following paper is a continuation of that in parts I and II, devoted to elucidation of the mechanism of the reactions of methylene with chloroalkanes, with particular reference to the reactivities of singlet and triplet methylene in abstraction and insertion processes. The products of the reaction between methylene, prepared by the photolysis of ketene, and 1-chloropropane have been identified and estimated and their dependence on reactant pressures, photolysing wavelength and presence of foreign gases (oxygen and carbon mon­oxide) has been investigated. Both insertion and abstraction mechanisms contribute significantly to the over-all reaction, insertion being relatively much more important than with chloroethane. This type of process appears to be confined to singlet methylene. If, as seems likely, there is no insertion into C—Cl bonds under our conditions (see part IV), insertion into C2—H and C3—H bonds occurs in statistical ratio, approximately. On the other hand, the chlorine substituent reduces the probability of insertion into C—H bonds in its vicinity. As in the chloroethane system, both species of methylene show a high degree of selectivity in their abstraction reactions. We find that k S Cl / k S H >7.7, k T Cl / k T H < 0.14, where the k ’s are rate constants for abstraction, and the super- and subscripts indicate the species of methylene and the type of atom abstracted, respectively. Triplet methylene is discriminating in hydrogen abstraction from 1-C 3 H 7 Cl, the overall rates for atoms attached to C1, C2, C3 being in the ratios 2.63:1:0.

Development of Advanced CNC Interpolation Algorithm With Consideration of Command and Dynamic Errors

2015 ◽  
Author(s):  
Meng-Shiun Tsai ◽  
Ying-Che Huang
Keyword(s):  
The Other ◽  
Contour Error ◽  
Interpolation Algorithm ◽  
Interpolation Scheme ◽  
Error Equation ◽  
The Past ◽  
Cnc Interpolation ◽  
Dynamic Errors ◽  
Simulation Results ◽  
The Given

In this paper, an integrated acceleration/deceleration with dynamics interpolation scheme is proposed to confine the maximum contour error at the junction of linear junction. The dynamic contour error equation is derived analytically and then it is utilized for the interpolation design. Based on the derived formulations which could predict the command and dynamic errors, the advanced interpolation design could adjust the connecting velocity of the two blocks to confine the overall contour errors under the given tolerance. Simulation results validate the proposed algorithm can achieve higher accurate trajectory as compared to the other interpolation algorithm proposed in the past.

scholarly journals (Symplectic) leaves and (5d Higgs) branches in the Poly(go)nesian Tropical Rain Forest

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Marieke van Beest ◽  
Antoine Bourget ◽  
Julius Eckhard ◽  
Sakura Schäfer-Nameki
Keyword(s):  
Rain Forest ◽  
Tropical Rain Forest ◽  
Gauge Theories ◽  
Edge Coloring ◽  
Field Theories ◽  
Minkowski Sum ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Minkowski Sums ◽  
Symplectic Leaves

Abstract We derive the structure of the Higgs branch of 5d superconformal field theories or gauge theories from their realization as a generalized toric polygon (or dot diagram). This approach is motivated by a dual, tropical curve decomposition of the (p, q) 5-brane-web system. We define an edge coloring, which provides a decomposition of the generalized toric polygon into a refined Minkowski sum of sub-polygons, from which we compute the magnetic quiver. The Coulomb branch of the magnetic quiver is then conjecturally identified with the 5d Higgs branch. Furthermore, from partial resolutions, we identify the symplectic leaves of the Higgs branch and thereby the entire foliation structure. In the case of strictly toric polygons, this approach reduces to the description of deformations of the Calabi-Yau singularities in terms of Minkowski sums.

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