Maximal operators and Fourier restriction on the moment curve

Principles from origami art are applied in the design of mechanisms and robotics increasingly frequent. A large part of the application driven research of these origami-like mechanisms focuses on devices where the creases (hinge lines) are actuated and the facets are constructed as stiff elements. In this paper, a design tool is proposed in which hinge lines with torsional stiffness and flexible facets are used to design passive, instead of active mechanisms. The design tool is an extension of a model of a single vertex compliant facet origami mechanism (SV-COFOM) and is used to approximate a desired moment curve by optimizing the design variables of the mechanism. Three example designs are presented: a constant moment joint (CMJ), a gravity compensating joint (GCJ) and a zero moment joint (ZMJ). The CMJ design has been evaluated experimentally, resulting in a root-mean-squared error (RMSE) of 6.4 × 10−2 N·m on a constant moment value of 0.39 N·m. This indicates that the design tool is suitable for a course estimation of the moment curve of the SV-COFOM in early stages of a design process.

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The Polytope of $k$-Star Densities

The Electronic Journal of Combinatorics ◽

10.37236/4471 ◽

2017 ◽

Vol 24 (1) ◽

Cited By ~ 1

Author(s):

Johannes Rauh

Keyword(s):

Random Graph ◽

Exponential Random Graph Models ◽

Graph Models ◽

Moment Curve ◽

Cyclic Polytope ◽

Random Graph Models ◽

Exponential Random Graph ◽

Affine Symmetry ◽

Consecutive Integers ◽

The Moment

This paper describes the polytope $\mathbf{P}_{k;N}$ of $i$-star counts, for all $i\le k$, for graphs on $N$ nodes. The vertices correspond to graphs that are regular or as regular as possible. For even $N$ the polytope is a cyclic polytope, and for odd $N$ the polytope is well-approximated by a cyclic polytope. As $N$ goes to infinity, $\mathbf{P}_{k;N}$ approaches the convex hull of the moment curve. The affine symmetry group of $\mathbf{P}_{k;N}$ contains just a single non-trivial element, which corresponds to forming the complement of a graph.The results generalize to the polytope $\mathbf{P}_{I;N}$ of $i$-star counts, for $i$ in some set $I$ of non-consecutive integers. In this case, $\mathbf{P}_{I;N}$ can still be approximated by a cyclic polytope, but it is usually not a cyclic polytope itself.Polytopes of subgraph statistics characterize corresponding exponential random graph models. The elongated shape of the $k$-star polytope gives a qualitative explanation of some of the degeneracies found in such random graph models.

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A short proof of ℓ2 decoupling for the moment curve

American Journal of Mathematics ◽

10.1353/ajm.2021.0048 ◽

2021 ◽

Vol 143 (6) ◽

pp. 1983-1998

Author(s):

Shaoming Guo ◽

Zane Kun Li ◽

Po-Lam Yung ◽

Pavel Zorin-Kranich

Keyword(s):

Short Proof ◽

Moment Curve ◽

The Moment

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Tverberg Partitions of Points on the Moment Curve

Discrete & Computational Geometry ◽

10.1007/s00454-016-9813-3 ◽

2016 ◽

Vol 57 (1) ◽

pp. 56-70 ◽

Cited By ~ 1

Author(s):

Micha A. Perles ◽

Moriah Sigron

Keyword(s):

Moment Curve ◽

The Moment

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Almost Simplicial Polytopes: The Lower and Upper Bound Theorems

Canadian Journal of Mathematics ◽

10.4153/s0008414x18000123 ◽

2019 ◽

Vol 72 (2) ◽

pp. 537-556

Author(s):

Eran Nevo ◽

Guillermo Pineda-Villavicencio ◽

Julien Ugon ◽

David Yost

Keyword(s):

Lower Bound ◽

Upper Bound ◽

Independent Interest ◽

Upper Bound Theorem ◽

Moment Curve ◽

Simplicial Polytopes ◽

Cyclic Polytopes ◽

Bound Theorem ◽

The Moment

AbstractWe study $n$-vertex $d$-dimensional polytopes with at most one nonsimplex facet with, say, $d+s$ vertices, called almost simplicial polytopes. We provide tight lower and upper bound theorems for these polytopes as functions of $d,n$, and $s$, thus generalizing the classical Lower Bound Theorem by Barnette and the Upper Bound Theorem by McMullen, which treat the case where $s=0$. We characterize the minimizers and provide examples of maximizers for any $d$. Our construction of maximizers is a generalization of cyclic polytopes, based on a suitable variation of the moment curve, and is of independent interest.

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Serum and milk concentrations of enrofloxacin in cows intramammarily treated with a new enrofloxacin-polymorph

Medycyna Weterynaryjna ◽

10.21521/mw.5587 ◽

2016 ◽

Vol 72 (11) ◽

pp. 686-692 ◽

Cited By ~ 3

Author(s):

Ismael Martínez-Cortés ◽

Lilia Gutierrez ◽

Graciela Tapia ◽

Luis Ocampo ◽

Hector Sumano

Keyword(s):

Pharmaceutical Preparation ◽

Mammary Tissue ◽

Antibacterial Drug ◽

Positive Trend ◽

Moment Curve ◽

Maximum Serum ◽

California Mastitis Test ◽

Cell Counts ◽

Drug Concentrations ◽

The Moment

The success rate in treatment against Staphylococcus aureus mastitis with antibacterial drugs is marginal. Low antibacterial drug concentrations in the mammary tissue is part of the reason for this failure. Enrofloxacin has only been administered on few occasions through the intramammary route i.e., combined with gentamicin in an undisclosed vehicle or dose. A new solvate form of enrofloxacin (enrofloxacin hydrochloride-dihydrate [enro-C]) prepared as 1.5% suspension pH 5.5 was tested in a field mastitis outbreak due to coagulase-negative S. aureus (CNS) in F1 (Holstein/Zebu) cows aged 5-8 years destined to be culled. Enro-C was administered intramammarily daily (300 mg/infected quarter) for 8 days both to healthy and mastitic cows; milk and serum enro-C concentrations were determined on days 1 and 8. Maximum serum concentration (CMAX) values were similar in both groups (9.4 to 10.7 µg/mL). The area under the moment curve (AUMC) for enrofloxacin increased only by 11% in healthy cows and by 10% in infected cows from day 1 to day 8, a fact that suggests little accumulation with this dose regime. Peak concentrations in milk ranged from 18.5 to 19.8 µg/mL on day 1 and from 20.2 to 22 µg/mL on day 8. Cure rates on day 21 after treatment were 75% (12 out of 16 cows) or 69.4% (26 out of 36 glands). Somatic cell counts and California mastitis test showed a positive trend in cured animals. Uniquely high milk enrofloxacin and ciprofloxacin concentrations were obtained after intramammary administration of enro-C. These concentrations seem effective for treating CNS mastitis. The feasibility of incorporating this experimental pharmaceutical preparation of enrofloxacin is discussed.

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Area Under the Moment Curve (AUMC)

IUPAC Standards Online ◽

10.1515/iupac.76.0127 ◽

2016 ◽

Author(s):

Monica Nordberg ◽

John H. Duffus ◽

Douglas M. Templeton

Keyword(s):

Moment Curve ◽

The Moment

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