Scaling by 5 on a 1/4-Cantor Measure

Each Cantor measure (\mu) with scaling factor 1/(2n) has at least one associated orthonormal basis of exponential functions (ONB) for L^2(\mu). In the particular case where the scaling constant for the Cantor measure is 1/4 and two specific ONBs are selected for L^2(\mu), there is a unitary operator U defined by mapping one ONB to the other. This paper focuses on the case in which one ONB (\Gamma) is the original Jorgensen-Pedersen ONB for the Cantor measure (\mu) and the other ONB is is 5\Gamma. The main theorem of the paper states that the corresponding operator U is ergodic in the sense that only the constant functions are fixed by U.Comment: 34 page

Quadratic Word Equations with Length Constraints, Counter Systems, and Presburger Arithmetic with Divisibility

Word equations are a crucial element in the theoretical foundation of constraint solving over strings, which have received a lot of attention in recent years. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant strings that equate the left and right hand sides of the equation. While the problem of solving word equations is decidable, the decidability of the problem of solving a word equation with a length constraint (i.e., a constraint relating the lengths of words in the word equation) has remained a long-standing open problem. In this paper, we focus on the subclass of quadratic word equations, i.e., in which each variable occurs at most twice. We first show that the length abstractions of solutions to quadratic word equations are in general not Presburger-definable. We then describe a class of counter systems with Presburger transition relations which capture the length abstraction of a quadratic word equation with regular constraints. We provide an encoding of the effect of a simple loop of the counter systems in the theory of existential Presburger Arithmetic with divisibility (PAD). Since PAD is decidable, we get a decision procedure for quadratic words equations with length constraints for which the associated counter system is \emph{flat} (i.e., all nodes belong to at most one cycle). We show a decidability result (in fact, also an NP algorithm with a PAD oracle) for a recently proposed NP-complete fragment of word equations called regular-oriented word equations, together with length constraints. Decidability holds when the constraints are additionally extended with regular constraints with a 1-weak control structure.Comment: 18 page

Coupling of vortex breakdown and stability in a swirling flow

Swirling flows are ubiquitous over a large range of length scales and applications including micron-scale microfluidic devices up to geophysical flows such as tornadoes. As the viscous dissipation, shear, and centrifugal stresses interact, such flows can often exhibit unexpected fluid dynamics. Here, we use microfluidic experiments and numerical simulations to study the flow in a vortex T-mixer: a T-shaped channel with staggered, offset inlets. The vortex T-mixer flow is characterized by a single dominant vortex, the stability of which is closely coupled to the appearance of vortex breakdown. Specifically, at a Reynolds number of Re≈90, a first vortex breakdown region appears in the steady-state solution, rendering the vortex pulsatively unstable. A second vortex breakdown region appears at Re≈120, which restabilizes the vortex. Finally, a third vortex breakdown region appears at Re≈180, which renders the vortex helically unstable. Thus, a counterintuitive flow regime exists for the vortex T-mixer in which increasing the Reynolds number has a stabilizing effect on the steady-state flow. The pulsatively unstable vortex evolves into a periodically pulsating state with a Strouhal number of St≈0.5, and the helically unstable vortex evolves into a helically oscillating state with St≈1.75. These transitions can be explained within the framework of linear hydrodynamic stability. In addition, the vortex T-mixer flow exhibits multistability; multiple flow states are stable over various ranges of Re, including a narrow range of tristability for 160≤Re≤170, in which the steady state, the pulsatile oscillation, and the helical oscillation are all stable. This study provides experimental and numerical evidence of the close coupling between vortex breakdown and flow stability, including the restabilization of the flow with increasing Reynolds number due to the appearance of a vortex breakdown region, which will provide new insights into how vortex breakdown can affect the stability of a swirling flow

Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach

We consider the problem of soft gluon resummation for gauge theory amplitudes and cross sections, at next-to-eikonal order, using a Feynman diagram approach. At the amplitude level, we prove exponentiation for the set of factorizable contributions, and construct effective Feynman rules which can be used to compute next-to-eikonal emissions directly in the logarithm of the amplitude, finding agreement with earlier results obtained using path-integral methods. For cross sections, we also consider sub-eikonal corrections to the phase space for multiple soft-gluon emissions, which contribute to next-to-eikonal logarithms. To clarify the discussion, we examine a class of log(1 - x) terms in the Drell-Yan cross-section up to two loops. Our results are the first steps towards a systematic generalization of threshold resummations to next-to-leading power in the threshold expansion.Comment: 66 pages, 19 figure

Another weak first order deconfinement transition: three-dimensional SU(5) gauge theory

We examine the finite-temperature deconfinement phase transition of (2+1)-dimensional SU(5) Yang-Mills theory via non-perturbative lattice simulations. Unsurprisingly, we find that the transition is of first order, however it appears to be weak. This fits naturally into the general picture of "large" gauge groups having a first order deconfinement transition, even when the center symmetry associated with the transition might suggest otherwise.Comment: 17 pages, 8 figure

Evaluation of the chemical constituents and the antimicrobial activity of the volatile oil of Citrus reticulata fruit(Tangerine fruit peel) from South West Nigeria

The volatile oil of tangerine fruit (Citrus reticulata) was extracted by steam distillation and assessed for antibacterial and antioxidant activity. The volatile oil was tested against some Gram-negative organisms (Escherichia coli ATCC 35218, E. coli, Pseudomonas aeruginosa, Klebsiella pneumoniae, Salmonella paratyphi, Proteus mirabilis and Citrobacter spp); Gram-positive organisms such as Staphylococcus aureus ATCC 25923, S. aureus, Enterococcus faecalis and a fungus (Candida albicans). The minimum inhibitory concentration (MIC) was determined with concentrations of oil extract ranging from 0.87 to 445 mg/ml. Result of the study showed that the oil has a broad spectrum antibacterial activity. MIC recorded were S. aureus (0.74 mg/ml), S. aureus ATTC 25923 (2.46 mg/ml), E. faecalis (1.26 mg/ml), S. typhi (2.07 mg/ml), K. pneumoniae (0.56 mg/ml), E. coli ATTC 35218 (0.19 mg/ml), E. coli (1.95 mg/ml), P. aeruginosa (0.97 mg/ml), C. albicans (0.68 mg/ml). Antioxidant screening with 2,2-diphenyl-1-picrylhydrazyl (DPPH) was negative. Analysis of the chemical constituent by GC-MS showed the presence of D-limonene as the major constituent. Other constituents found were a-pinene and β-pinene

Factors associated with the decision to investigate child protective services referrals: a systematic review

Background: Limited resources for child protection create challenging decision situations for child protective services (CPS) workers at the point of intake. A body of research has examined the factors associated with worker decisions and processes using a variety of methodological approaches to gain knowledge on decision-making. However, few attempts have been made to systematically review this literature. Objective: As part of a larger project on decision-making at intake, this systematic review addressed the question of the factors associated with worker decisions to investigate alleged maltreatment referrals. Methods: Quantitative studies that examined factors associated with screening decisions in CPS practice settings were included in the review. Database and other search methods were used to identify research published in English over a 35-year period (1980-2015). Findings: Of 1,147 identified sources, 18 studies were selected for full data extraction. The studies were conducted in the U.S., Canada, and Sweden and varied in methodological quality. Most studies examined case factors with few studies examining other domains. Conclusions: To inform CPS policy and practice, additional research is needed to examine the relationships between decision-making factors and case outcomes. Greater attention needs to be given to the organizational and external factors that influence decision-making