A general theorem of existence of quasi absolutely minimal Lipschitz extensions

In this paper we consider a wide class of generalized Lipschitz extension problems and the corresponding problem of finding absolutely minimal Lipschitz extensions. We prove that if a minimal Lipschitz extension exists, then under certain other mild conditions, a quasi absolutely minimal Lipschitz extension must exist as well. Here we use the qualifier "quasi" to indicate that the extending function in question nearly satisfies the conditions of being an absolutely minimal Lipschitz extension, up to several factors that can be made arbitrarily small.Comment: 33 pages. v3: Correction to Example 2.4.3. Specifically, alpha-H\"older continuous functions, for alpha strictly less than one, do not satisfy (P3). Thus one cannot conclude that quasi-AMLEs exist in this case. Please note that the error remains in the published version of the paper in Mathematische Annalen. v2: Several minor corrections and edits, a new appendix (Appendix A

Aerodynamic analysis of several high throat Mach number inlets for the quiet clean short-haul experimental engine

The results of an analytical study to investigate internal and external surface Mach numbers on several inlet geometries for possible application to the nacelle of the Quiet Clean Short-Haul Experimental Engine (QCSEE) are presented. The effects of external forebody geometry and internal lip geometry were illustrated at both low-speed and cruise conditions. Boundary-layer analyses were performed on several geometries to determine if lip flow separation might exist. The results indicated that inner-surface Mach number level and gradient could be reduced with inlets at a 50 deg incidence angle by blunting the external forebody geometry. The external Mach numbers at cruise conditions indicated that a compromise in the external forebody bluntness might be required to satisfy both low-speed and cruise conditions. For a fixed value of bluntness parameter, no lip flow separation was indicated for the 1.46- and 1.57-area-contraction-ratio inlets at low-speed conditions. However, a lip separation condition was obtained with the 1.37-contraction-ratio inlet. The QCSEE nacelle design takeoff operating condition (incidence angle of 50 deg and free-stream Mach number of 0.12) resulted in higher peak surface Mach numbers than the design crosswind (incidence angle of 90 deg and free-stream Mach number of 0.05) or static condition

Legislatively Overturning Fort Stewart Schools: The Trump Administration\u27s Assault on Federal Employee Collective Bargaining

In his Fiscal Year 2019 Budget Submission, President Trump noted that about 60 percent of Federal employees belong to a union and lamented that dealing with Federal employee unions ostensibly “consume[s] considerable management time and taxpayer resources, and may negatively impact efficiency, effectiveness, cost of operations, and employee accountability and performance.” Although he acknowledged that Federal employee unions can negotiate over fewer matters than can unions in the private sector, he nonetheless claimed that collective bargaining contracts can negatively impact agency performance, workplace productivity, and employee satisfaction. The President told Congress that “[a]gency managers will be encouraged to restore management prerogatives that have been ceded to Federal labor unions,” and that “[t]he Administration sees an opportunity for progress on this front and intends to overhaul labor-management relations.” The Administration took such an opportunity this past April when it submitted proposed legislation to the House and Senate Armed Services Committees that would revamp the statutes that authorize the Department of Defense (DOD) to operate schools on bases in the United States and overseas for military dependents. In 1990, the Supreme Court unanimously ruled in Fort Stewart Schools v. Federal Labor Relations Authority that teachers and other educational personnel in DOD’s domestic dependents schools could collectively bargain over wages because, unlike the majority of Federal employees, their salaries are not set by statute. DOD’s new legislative proposal contains a provision that would statutorily overturn the Fort Stewart Schools decision by granting the Secretary of Defense sole and exclusive discretion to set compensation rates in the DOD dependents schools. Under the Federal Labor-Management Relations Statute, the 1.2 million Federal employees represented by labor unions have the right to “engage in collective bargaining with respect to conditions of employment.” “Conditions of employment” is defined as “personnel policies, practices, and matters, whether established by rule, regulation, or otherwise, affecting working conditions, except that such term does not include policies, practices, and matters . . . to the extent such matters are specifically provided for by Federal statute.” The essential holding of Fort Stewart Schools was that wages are a “condition of employment” for Federal employees and, as such, are negotiable unless they are set by statute. Most “white collar” Federal employees’ salaries are set by the Classification Act of 1949, and the salaries of employees in the skilled crafts and trades and unskilled labor positions are set by the Prevailing Rate Systems Act. But depending on the degree of disaggregation, there are over forty other separate pay systems that vary considerably in numbers of employees covered and method of determining pay. As of 2010, over 250,000 Federal employees were covered by pay plans unique to their agency. To the extent that Congress has left the head of an agency with discretion to set salaries that is not sole and exclusive, the employees in that agency may collectively bargain over wages as a result of Fort Stewart Schools. This article argues that those bargaining rights are at risk if the Administration succeeds in eliminating the right of teachers in DOD schools to bargain over pay. It will first explain that the right of some Federal employees to bargain over wages predated the enactment of the Federal Service Labor-Management Relations Statute (FSLMR Statute). This article will then describe the debate over whether Congress intended for Federal employees to bargain over pay when it enacted the statute as part of the Civil Service Reform Act of 1978, and how that debate was resolved by the Supreme Court in the Fort Stewart Schools case. It will then explain how the legislation proposed by the DOD will eliminate the right of DOD teachers to bargain over pay and will identify other groups of Federal employees who may stand to lose their bargaining rights if the Administration succeeds in rolling back the Fort Stewart Schools decision

On the Evaluation of Gluon Condensate Effects in the Holographic Approach to QCD

In holographic QCD the effects of gluonic condensate can be encoded in a suitable deformation of the 5D metric. We develop two different methods for the evaluation of first order perturbative corrections to masses and decay constants of vector resonances in 5D Hard-Wall models of QCD due to small deformations of the metric. They are extracted either from a novel compact form for the first order correction to the vector two-point function, or from perturbation theory for vector bound-state eigenfunctions: the equivalence of the two methods is shown. Our procedures are then applied to flat and to AdS 5D Hard-Wall models; we complement results of existing literature evaluating the corrections to vector decay constant and to two-pion-one-vector couplings: this is particularly relevant to satisfy the sum rules. We concentrate our attention on the effects for the Gasser-Leutwyler coefficients; we show that, as in the Chiral Quark model, the addition of the gluonic condensate improves the consistency, the understanding and the agreement with phenomenology of the holographic model.Comment: 23 pages, three figures, sign error in pion wave function fixed, numerical analysis extended, general conclusions unchange

Distinguishing among Technicolor/Warped Scenarios in Dileptons

Models of dynamical electroweak symmetry breaking usually include new spin-1 resonances, whose couplings and masses have to satisfy electroweak precision tests. We propose to use dilepton searches to probe the underlying structure responsible for satisfying these. Using the invariant mass spectrum and charge asymmetry, we can determine the number, parity, and isospin of these resonances. We pick three models of strong/warped symmetry breaking, and show that each model produces specific features that reflect this underlying structure of electroweak symmetry breaking and cancellations.Comment: Added missing referenc

It is a Graviton! or maybe not

The discovery of Kaluza-Klein (KK) gravitons is a smoking gun of extra dimensions. Other scenarios, however, could give rise to spin-two resonances of a new strongly-coupled sector and act as impostors. In this paper we prove that a spin-two resonance does not couple to the Standard Model through dimension-four operators. We then show that the massive graviton and its impostor both couple to the Standard Model through the same dimension-five operators. Therefore the spin determination is identical. Nevertheless, we also show that one can use the ratio of branching ratios to photons and to jets for distinguishing between KK gravitons and their impostors. The capacity to distinguish between KK gravitons and impostors is a manifestation of the breakdown of the duality between AdS and strongly-coupled theories.Comment: 14 pages, 3 figures, 1 table. References added, typos correcte