Simple Cusp Research Articles

Teichmüller curves in the space of two-genus double covers of flat tori

This paper focuses on Teichmuller curves in the space of two-genus double covers of flat tori, identifying all of them, counting them with respect to their triangular areas, formulating the numbers of their cusps, and characterizing the ones without a simple cusp. Some applications are also discussed.

Discussion

Dr Derek R. Brinster (New York, NY). Dr Lau, excellent presentation, excellent results at the Cornell group. You said that VSRR can be done on patients with BAV with a simple cusp repair. Can you define what simple versus complex cusp repair is and whether any complex cusp repairs were being performed?

On the Spatial Uniformity of the Degree of Ionization in a Helium ECR Plasma Produced under a Simple Cusp Field

Production of a plasma that has a large degree of ionization (DOI), volume, and spatial and temporal uniformities is a challenge for the improvement of the performance of plasma-based vapor deposition processes. As a potential candidate for the discharge, we investigate plasma parameters arising in helium electron cyclotron resonance (ECR) discharges due to a simple cusp field. Two-dimensional distributions of helium atom emission-line intensities were measured using spectroscopy with multiple viewing chords and then de-convoluted by Abel inversion. The local plasma parameters, including the atomic density, were evaluated using collisional-radiative model analysis. The DOI calculated from the electron and atomic densities reached up to 35% and, in most of the region inside the ECR surface, it was more than 10%.

Spectroscopic measurement of the degree of ionization in a helium electron cyclotron resonance discharge in a simple cusp field

For an electron cyclotron resonance (ECR) discharge, a simple cusp field can improve electron confinement and enhance the degree of ionization (DOI) without sacrificing accessibility to the plasma. In this study, the spatial distribution of the DOI is experimentally revealed in a helium plasma produced with widely used 2.45 GHz and 800 W microwaves. The DOI is evaluated from the electron density and ground state atom density measured using HeI emission line intensities and by collisional-radiative model analysis. It is found that the DOI increases to more than 15% within a reasonably large volume surrounded by the ECR surface and locally reaches as high as 25%.

Measurement of linear polarization in the HeI 21P–31D emission line in an electron cyclotron resonance discharge plasma

The magnitude and direction of linear polarization in the HeI 21P–31D emission line are simultaneously measured using a beam-splitting-type polarization spectroscopy system. The polarization measured in the steady-state phase of an electron cyclotron resonance (ECR) discharge produced in a simple cusp field is directed closely perpendicular to the magnetic field at the ECR surface, and the degree of polarization increases up to 8% when the neutral pressure is reduced to less than 23 mPa. These results suggest that the cause of the polarization is attributable to impact excitation by high-energy electrons produced at the ECR surface.

Numerical continuation of solution at singular points of codimension one

Numerical continuation of a solution through some singular points of the curve of solutions to algebraic or transcendental equations with a parameter is considered. Singular points of codimension one are investigated. An algorithm for constructing all the branches of the curve at a simple bifurcation point is proposed. A special regularization that allows one to pass simple cusp points as limit points is obtained. For the regularized simple cusp point, a bound on the norm of the inverse Jacobian matrix in a neighborhood of this point is found. Using this bound, the convergence of the continuation process in a neighborhood of the simple cusp point is proved; an algorithm for the discrete continuation of the solution at the singular point along a smooth curve is obtained and its validity is proved. Based on a unified approach, a bound on the norm of the inverse Jacobian matrix and results on the convergence of continuation process in the case of the simple bifurcation point are also obtained. The operation of computational programs is demonstrated on benchmarks, which proves their effectiveness and confirms theoretical results. The effectiveness of software is investigated by solving the applied problem of three-rod truss stability.

Nuclear cusp conditions and their fulfillment in molecular calculations with SLATER basis sets

A short revision of the main antecedents on the nuclear cusp conditions is followed by a derivation of the general expressions of the conditions which must be accomplished by wave functions and densities. It is stressed that in case of the molecular densities, besides Kato's cusp condition, there are also simple cusp conditions for the three dipole‐type terms of the densities but not for terms of order higher than dipole. The degree of fulfillment of standard atomic and molecular calculations with Slater basis sets is tested, concluding that errors of spherical terms usually affect the third or fourth significant figures, being smaller as nuclear charges increase, and the errors of dipole‐type components are greater than those of the spherical terms. In practice, improvements in the computational method or in the basis set do not guarantee a better fulfillment of the cusp conditions. Hydrogen is a special case which can yield poor results. © 2014 Wiley Periodicals, Inc.

Repair of the Regurgitant Bicuspid or Tricuspid Aortic Valve

The treatment of severe aortic valve regurgitation (AR) has been moving ahead quickly and has undergone a fundamental transition over the past few decades. Mechanical or bioprosthetic aortic valve replacement has been the standard of care for many years for most types of AR. Although still restricted to patients with well-defined pathological aortic valve and root anatomy, the number of accepted indications for reconstructive aortic valve surgery is growing. The cusp tissue, aortic annulus, tissue of the sinus of Valsalva, commissures, subcommissural tissue, and sinotubular junction constitute the functional unit of what is generally called the aortic root. Reconstructive surgery for severe aortic valve insufficiency today includes a wide variety of procedures on all of those components, from simple cusp plication to complex valve-sparing aortic root replacement (V-SARR). It is ultimately aimed not only at improving symptoms of congestive heart failure and increasing life expectancy but also at giving the patient a chance to live a normal life because it renders lifelong anticoagulation unnecessary. V-SARR procedures have recently been discussed not only as adequate correction for aneurysms but even as supplementary procedures to prolong the longevity of a valve repair. Our article gives an overview of the background and principles of reconstructive aortic valve procedures for AR in the setting of both a bicuspid and a tricuspid aortic valve. It explains the principles, describes the techniques, and reviews the reported current outcomes after reconstruction of the different components of the aortic root. This overview should help clinicians evaluate the status and relevance of frequently discussed current techniques for the treatment of patients with different types of thoracic aortic aneurysms and AR. The need for lifelong anticoagulation remains the main drawback of prosthetic aortic valve replacement for many young patients living an active lifestyle. In addition to sparing the patient’s native …

Cusp algebras

We consider simple cusp algebras, that is certain subalgebras of the algebra of holomorphic functions on a disk that are annihilated by some distributions living on a singleton. We determine when these algebras can be holized in two dimensions, and when these holizations are globally biholomorphic.

Is self-fertilization possible in nudibranchs?

Is self-fertilization possible in nudibranchs?

Repair of Flail Leaflet of the Tricuspid Valve by a Simple Cusp Remodeling Technique

The approach of repairing tricuspid valve insufficiency caused by congenital lack of chordae or traumatic rupture of chordae is often complicated and difficult. We try to present an alternative method and midterm results. Between April 1997 and December 2004, eight patients (5 males, 3 females; mean age 23.9 +/- 5.8 years; range: 8 to 57 years) with severe tricuspid regurgitation (congenital lack of chordae in 5 cases and traumatic rupture of chordae in 3 cases) underwent surgical repair at Fu Wai Hospital. Four patients were in NYHA (New York Heart Association) class III, and 4 in class IV. Eight flail anterior leaflets and one flail septal leaflet of the tricuspid valve with massive tricuspid regurgitation were identified by echocardiography and the spaces of the free edges of the flail leaflets ranged from 20 to 30 mm. Tricuspid repair was performed under hypothermic cardiopulmonary bypass. The free edge of the affected cusp segment was sutured in folio, the segment of annulus devoid of leaflet was plicated, and the neo-annulus was fixed with a flexible annuloplasty ring. All patients survived and recovered after the operation. Echocardiography showed good coaptation with no regurgitation of the tricuspid valve in five patients and a mild residual tricuspid regurgitation in three patients. A remarkable decrease in the diameter of the right ventricle was observed, from a mean of 42.6 +/- 12.5 mm to a mean of 23.6 +/- 5.3mm (p < 0.01). Mean follow up was 50 +/- 42.9 months. Six patients were in NYHA class I, and two in class II and III. Except for one patient who had a mild-to-moderate increase in tricuspid regurgitation a year later, all the other patients were doing well. The procedure provided a simple and valuable option for repair of flail leaflet of tricuspid valve caused by congenital lack of chordae or traumatic rupture of chordae.

Stratifiable Families of Extremals and Sufficient Conditions for Optimality in Optimal Control Problems

It is shown that, if a parametrized family of extremals F can be stratified in a way compatible with the flow map generated by F, then those trajectories of the family which realize the minimal values of the cost in F are indeed optimal in comparison with all trajectories which lie in the region R covered by the trajectories of F. It is not assumed that F is a field covering the state space injectively. As illustration, an optimal synthesis is constructed for a system where the flow of extremals exhibits a simple cusp singularity.

ECR Plasma in a Stuffed Cusp Field

A stuffed cusp field with a torus ECR surface is obtained by adding a toroidal stuffer field onto a simple cusp field. Results of the production of ECR plasma in this field is described. With sweeping the stuffer current, Iis start to increase when the ECR surface forms closed torus, and reaches up several times of one without the stuffer current. Only in this closed case, X-rays (> 3 keV) are detected by NaI scintillator. These disappear when an obstacle is inserted inside ECR torus, suggesting that the ECR torus is of primary importance to produce and maintain energetic electrons. A peak density and temperature measured by a floating double probe reach up to ne ≃ 2 × 1012cm–3 and Te ≃ 25eV at a low Ar pressure of p ≃ 7.3 × 10–6Torr with the microwave power of 380W.

Parametrized Families of Extremals and Singularities in Solutions to the Hamilton--Jacobi--Bellman Equation

We analyze the effect which a fold and simple cusp singularity in the flow of a parametrized family of extremal trajectories of an optimal control problem has on the corresponding parametrized cost or value function. A fold singularity in the flow of extremals generates an edge of regression of the value implying the well-known results that trajectories stay strongly locally optimal until the fold-locus is reached, but lose optimality beyond. Thus fold points correspond to conjugate points. A simple cusp point in the parametrized flow of extremals generates a swallow-tail in the parametrized value. More specifically, there exists a region in the state space which is covered 3:1 with both locally minimizing and maximizing branches. The changes from the locally minimizing to the maximizing branch occur at the fold-loci and there trajectories lose strong local optimality. However, the branches intersect and generate a cut-locus which limits the optimality of close-by trajectories and eliminates these trajectories from optimality near the cusp point prior to the conjugate point. In the language of partial differential equations, a simple cusp point generates a shock in the solutions to the Hamilton--Jacobi--Bellman equation while fold points will not be part of the synthesis of optimal controls near the simple cusp point.

Fourier integral operators with cusp singularities

We study the boundedness properties, on Lebesgue and Sobolev spaces, of Fourier integral operators associated with canonical relations such that at least one of the projections is a simple (Whitney) cusp. In the process, we obtain decay estimates for oscillatory integral operators whose symplectic relations have the same singular structure. Such singularities occur generically for averages over lines and curves in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]. On L 2 , we show that the operators lose 1/3 derivative. To obtain sharp results off of L 2 , we need to impose an additional transversality condition, satisfied by many geometric averaging operators, which leads to the notion of a strong cusp. These estimates can be further improved if we impose curvature conditions on the cusp surface. One application is the L 2 comp → L 2 1/6, loc and L 12/7 comp → L 2 loc boundedness of restrictions of the X-ray transform on [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] to four-dimensional families of lines satisfying a natural curvature and torsion condition.

Catastrophic misconceptions in science education

The article is an attempt to model the ideas of children's misconceptions and subsequent acceptance of conventional scientific thought on the simple cusp of catastrophe theory. The cusp catastrophe occurs in systems whose bimodal behaviour is dependent upon two control factors or constraints. The model may lack precise description and prediction, but it may help to organise information more clearly in a qualitative way and give new language to the interaction of the factors involved in the provision of useful learning experiences in teaching from children's alternative frameworks to conventionally acceptable views of science. It is possible that the model may stimulate research in terms of the type and quantity of learning experience necessary.

Design Study and Supporting Experiments for an Axially Symmetric Anchor for a Tandem Mirror

In order to determine if a simple magnetic cusp, which is axisymmetric. can be used as an end cell (anchor and plug) for a tandem mirror reactor, a large {50 em) bore, supereondueting, magnetic cusp is being buflt at the University of Missouri. Prior to the construction of this device, an approximately half seale normal magnetic cusp was built, and experiments invol­ ving ECRF heating were conducted. to better establish the design conditions for the large, high field (4-Tesla) cusp.

Catastrophe theory: A topological reconceptualization of sexual orientation

The classical model of sexual orientation as a continuum is examined and hypotheses regarding the sequential patterning of sexual partner choices are considered. Data are reviewed which suggest that these patterns are often discontinuous: shifts from one orientation to the other are observed without a transitional period and bisexuality is rare as a lifestyle in which contacts with both male and female partners are regular, concurrent, ongoing activities. Catastrophe theory, a mathematical model of discontinuity, is explained with the simple example of aggression in dogs and then the simple cusp catastrophe is applied as a starting place for this topological reconceptualization of sexual orientation. Behavioral predictions and implications for future research are discussed.

Ecological outbreak dynamics and the cusp catastrophe

Many ecological processes exhibit trajectories which can be suitably represented by stable equilibria or smooth limit cycles. However, a third kind of ecological process involves intermittent, abrupt, and drastic changes in densities, here termed ‘outbreak dynamics’, which require different modelling frameworks. One such framework, the cusp catastrophe, is used here in a modelling study of a particular outbreak insect, the forest tent caterpillar. This model is then generalized to cover a set of related ecological systems. The particular form of the model for each system depends on whether the major controlling ecological variables are externally imposed, or are incorporated in the model equations. It is concluded that the simple cusp catastrophe is an appropriate metaphor for understanding outbreak dynamics.

Exact universal uniqueness criteria for the adiabatic tubular packed bed reactor

Exact, universal a priori bounds and regions of multiplicity for the entire tubular packed bed reactor are developed by application of a technique reported in Chang and Calo, Chem. Engng Sci. 1979 34 285 to a cascade two-phase cell model for an nth order chemical reaction with interphase resistance to mass and heat transport, Le ≠ 1 (or Le = 1) and either lumped parameter catalyst particles or with intraparticle concentration gradients with uniform temperature. Both the more common case of interphase heat transfer greater than interphase mass transfer rate and the inverse case of particle over-temperature have been considered. In all cases it has been shown that the reactor conservation equations can be decoupled at certain points along the bed determined by the Lewis number, and that questions of multiplicity and uniqueness reduce to consideration of a single algebraic equation which is actually a form of the two-phase adiabatic CSTR. Also as for the CSTR, the topology of the adiabatic packed bed reactor is shown to be the simple cusp catastrophe. The application of the resultant criteria is quite simple and represents a practical step in the design procedure for highly exothermic reactions in packed beds. A flow chart of a suggested procedure is included.