The Running Intersection Relaxation of the Multilinear Polytope

2021 ◽  
Author(s):  
Alberto Del Pia ◽  
Aida Khajavirad
Keyword(s):  
Convex Hull ◽  
Extended Formulation ◽  
New Class ◽  
Polynomial Size

The multilinear polytope of a hypergraph is the convex hull of a set of binary points satisfying a collection of multilinear equations. We introduce the running intersection inequalities, a new class of facet-defining inequalities for the multilinear polytope. Accordingly, we define a new polyhedral relaxation of the multilinear polytope, referred to as the running intersection relaxation, and identify conditions under which this relaxation is tight. Namely, we show that for kite-free beta-acyclic hypergraphs, a class that lies between gamma-acyclic and beta-acyclic hypergraphs, the running intersection relaxation coincides with the multilinear polytope and it admits a polynomial size extended formulation.

Computational Geometry on the Sphere With Application to Automated Machining

1992 ◽  
Vol 114 (2) ◽  
pp. 288-295 ◽  
Author(s):  
Lin-Lin Chen ◽  
T. C. Woo
Keyword(s):  
Computational Geometry ◽  
Convex Hull ◽  
Unit Sphere ◽  
Degrees Of Freedom ◽  
Cutting Tools ◽  
Numerical Control ◽  
Geometric Algorithms ◽  
New Class

Based on observations made on the geometry of the cutting tools and the degrees of freedom in 3-, 4-, 5-axis numerical control machines, a new class of geometric algorithms is induced on the unit sphere. Spherical algorithms are useful for determining the type of tool, its path, workpiece fixturing, and the type of machine. Basic to these algorithms are four that are presented here: detection of convexity on the sphere, computation for spherically convex hull, determination of the spherical convexity of a union, and the intersection of hemispheres. These four algorithms are related by duality and the sharing of partial results.

scholarly journals A New Class of Curves of Rational B-Spline Type

2021 ◽  
Author(s):  
Mohamed ALLAOUI ◽  
Jamal ADETOLA ◽  
Wilfrid HOUEDANOU ◽  
Aurélien GOUDJO
Keyword(s):  
Convex Hull ◽  
Continuous Functions ◽  
B Spline ◽  
B Splines ◽  
Rational Bézier Curves ◽  
New Class ◽  
Rational Parametrization ◽  
New Family ◽  
Depth Analysis ◽  
Approximation Of Continuous Functions

A new class of rational parametrization has been developed and it was used to generate a new family of rational k functions B-splines which depends on an index α ∈ ]−∞ , 0[ ∪ ]1 , +∞[. This family of functions verifies, among other things, the properties of positivity, of partition of the unit and, for a given degree k, constitutes a true basis approximation of continuous functions. We loose, however, the regularity classical optimal linked to the multiplicity of nodes, which we recover in the asymptotic case, when α → ∞. The associated B-splines curves verify the traditional properties particularly that of a convex hull and we see a certain “conjugated symmetry” related to α. The case of open knot vectors without an inner node leads to a new family of rational Bezier curves that will be separately, object of in-depth analysis.

Computational Geometry on the Sphere With Application to Automated Machining

1990 ◽  
Author(s):  
Lin-Lin Chen ◽  
Tony C. Woo
Keyword(s):  
Computational Geometry ◽  
Convex Hull ◽  
Unit Sphere ◽  
Degrees Of Freedom ◽  
Cutting Tools ◽  
Numerical Control ◽  
Geometric Algorithms ◽  
New Class

Abstract Based on observations made on the geometry of the cutting tools and the degrees of freedom in 3-, 4-, 5-axis numerical control machines, a new class of geometric algorithms is induced — on the unit Sphere. Spherical algorithms are useful for determining the type of tool, its path, workpiece fixturing, and the type of machine. Basic to these algorithms are four that are presented here: detection of convexity on the sphere, computation for spherically convex hull, determination of the spherical convexity of a union and the intersection of hemispheres. These four algorithms are related by duality and the sharing of partial results.

In Situ microscopy of the anodic etching of silicon

1995 ◽  
Vol 53 ◽  
pp. 232-233
Author(s):  
Frances M. Ross ◽  
Peter C. Searson
Keyword(s):  
Composite Structures ◽  
High Surface ◽  
High Surface Area ◽  
Chemical Properties ◽  
Selective Etching ◽  
Silicon On Insulator ◽  
Second Phase ◽  
Porous Layers ◽  
New Class ◽  
Porous Semiconductors

Porous semiconductors represent a relatively new class of materials formed by the selective etching of a single or polycrystalline substrate. Although porous silicon has received considerable attention due to its novel optical properties1, porous layers can be formed in other semiconductors such as GaAs and GaP. These materials are characterised by very high surface area and by electrical, optical and chemical properties that may differ considerably from bulk. The properties depend on the pore morphology, which can be controlled by adjusting the processing conditions and the dopant concentration. A number of novel structures can be fabricated using selective etching. For example, self-supporting membranes can be made by growing pores through a wafer, films with modulated pore structure can be fabricated by varying the applied potential during growth, composite structures can be prepared by depositing a second phase into the pores and silicon-on-insulator structures can be formed by oxidising a buried porous layer. In all these applications the ability to grow nanostructures controllably is critical.

The microtubule associated protein (MAP) tau forms a new class of triple-stranded left-hand helical fibrous protein polymer

1992 ◽  
Vol 50 (1) ◽  
pp. 540-541
Author(s):  
G. C. Ruben ◽  
K. Iqbal ◽  
I. Grundke-Iqbal ◽  
H. Wisniewski ◽  
T. L. Ciardelli ◽  
...  
Keyword(s):  
Axial Ratio ◽  
Normal Structure ◽  
Paired Helical Filaments ◽  
Left Hand ◽  
New Class ◽  
Protein Polymer ◽  
Fibrous Protein ◽  
Protein Map ◽  
Neurotransmitter Transport ◽  
Alzheimer Neurofibrillary Tangles

In neurons, the microtubule associated protein, tau, is found in the axons. Tau stabilizes the microtubules required for neurotransmitter transport to the axonal terminal. Since tau has been found in both Alzheimer neurofibrillary tangles (NFT) and in paired helical filaments (PHF), the study of tau's normal structure had to preceed TEM studies of NFT and PHF. The structure of tau was first studied by ultracentrifugation. This work suggested that it was a rod shaped molecule with an axial ratio of 20:1. More recently, paraciystals of phosphorylated and nonphosphoiylated tau have been reported. Phosphorylated tau was 90-95 nm in length and 3-6 nm in diameter where as nonphosphorylated tau was 69-75 nm in length. A shorter length of 30 nm was reported for undamaged tau indicating that it is an extremely flexible molecule. Tau was also studied in relation to microtubules, and its length was found to be 56.1±14.1 nm.

Study of segregation in La1.8Sr0.2CuO4 superconductor by STEM-EDS microanalysis

1987 ◽  
Vol 45 ◽  
pp. 54-55
Author(s):  
T. F. Kelly ◽  
P. J. Lee ◽  
E. E. Hellstrom ◽  
D. C. Larbalestier
Keyword(s):  
Rare Earth ◽  
High Field ◽  
Transport Current ◽  
Total Thickness ◽  
New Class ◽  
Ceramic Superconductors ◽  
Current Densities ◽  
Group Ii ◽  
Eds Microanalysis

Recently there has been much excitement over a new class of high Tc (>30 K) ceramic superconductors of the form A1-xBxCuO4-x, where A is a rare earth and B is from Group II. Unfortunately these materials have only been able to support small transport current densities 1-10 A/cm2. It is very desirable to increase these values by 2 to 3 orders of magnitude for useful high field applications. The reason for these small transport currents is as yet unknown. Evidence has, however, been presented for superconducting clusters on a 50-100 nm scale and on a 1-3 μm scale. We therefore planned a detailed TEM and STEM microanalysis study in order to see whether any evidence for the clusters could be seen.A La1.8Sr0.2Cu04 pellet was cut into 1 mm thick slices from which 3 mm discs were cut. The discs were subsequently mechanically ground to 100 μm total thickness and dimpled to 20 μm thickness at the center.

Electronic structure studies of conducting polymers by electron energy-loss spectroscopy

1996 ◽  
Vol 54 ◽  
pp. 160-161
Author(s):  
J. Fink
Keyword(s):  
Electronic Structure ◽  
Conducting Polymers ◽  
Conjugated Polymers ◽  
Electron Acceptors ◽  
Electron Donors ◽  
Light Emitting ◽  
One Dimensional ◽  
New Class ◽  
Electrical Conductivities ◽  
Electron Energy Loss

Conducting polymers comprises a new class of materials achieving electrical conductivities which rival those of the best metals. The parent compounds (conjugated polymers) are quasi-one-dimensional semiconductors. These polymers can be doped by electron acceptors or electron donors. The prototype of these materials is polyacetylene (PA). There are various other conjugated polymers such as polyparaphenylene, polyphenylenevinylene, polypoyrrole or polythiophene. The doped systems, i.e. the conducting polymers, have intersting potential technological applications such as replacement of conventional metals in electronic shielding and antistatic equipment, rechargable batteries, and flexible light emitting diodes.Although these systems have been investigated almost 20 years, the electronic structure of the doped metallic systems is not clear and even the reason for the gap in undoped semiconducting systems is under discussion.

Mechanochemical changes on cyclometalated Ir(iii) acyclic carbene complexes – design and tuning of luminescent mechanochromic transition metal complexes

2020 ◽  
Vol 7 (3) ◽  
pp. 786-794 ◽  
Author(s):  
Jingqi Han ◽  
Kin-Man Tang ◽  
Shun-Cheung Cheng ◽  
Chi-On Ng ◽  
Yuen-Kiu Chun ◽  
...  
Keyword(s):  
Transition Metal ◽  
Metal Complexes ◽  
Transition Metal Complexes ◽  
Carbene Complexes ◽  
New Class

A new class of luminescent cyclometalated Ir(iii) complexes with readily tunable mechanochromic properties derived from the mechanically induced trans-to-cis isomerization have been developed.

Amino-functional polyethers: versatile, stimuli-responsive polymers

2020 ◽  
Vol 11 (24) ◽  
pp. 3940-3950 ◽  
Author(s):  
Patrick Verkoyen ◽  
Holger Frey
Keyword(s):  
Ring Opening ◽  
Review Article ◽  
Stimuli Responsive ◽  
New Class ◽  
Stimuli Responsive Polymers ◽  
Responsive Polymers

Amino-functional polyethers have emerged as a new class of “smart”, i.e. pH- and thermoresponsive materials. This review article summarizes the synthesis and applications of these materials, obtained from ring-opening of suitable epoxide monomers.

Sign in / Sign up

Export Citation Format

Share Document