Geometric and analytic quasiconformality in metric measure spaces

We prove the equivalence between geometric and analytic definitions of quasiconformality for a homeomorphism $f\colon X\rightarrow Y$ between arbitrary locally finite separable metric measure spaces, assuming no metric hypotheses on either space. When $X$ and $Y$ have locally $Q$-bounded geometry and $Y$ is contained in an Alexandrov space of curvature bounded above, the sharpness of our results implies that, as in the classical case, the modular and pointwise outer dilatations of \map are related by $K_O(f)= \operatorname{esssup} H_O(x,f)$.Comment: 15 pages. Flaw in covering argument for Theorem 1.2 corrected. Flaws in Remarks 4.3 and 4.4 corrected. Accepted for publication by the Proceedings of the American Mathematical Societ

Metric currents, differentiable structures, and Carnot groups

We examine the theory of metric currents of Ambrosio and Kirchheim in the setting of spaces admitting differentiable structures in the sense of Cheeger and Keith. We prove that metric forms which vanish in the sense of Cheeger on a set must also vanish when paired with currents concentrated along that set. From this we deduce a generalization of the chain rule, and show that currents of absolutely continuous mass are given by integration against measurable $k$-vector fields. We further prove that if the underlying metric space is a Carnot group with its Carnot-Carath\'eodory distance, then every metric current $T$ satisfies $T\lfloor_{\theta}=0$ and $T\lfloor_{d\theta}=0$, whenever $\theta \in \Omega^{1}(\mathbb{G})$ annihilates the horizontal bundle of $\mathbb G$. Moreover, this condition is necessary and sufficient for a metric current with respect to the Riemannian metric to extend to one with respect to the Carnot-Carath\'eodory metric, provided the current either is locally normal, or has absolutely continuous mass.Comment: 36 pages. To appear, Annali della Scuola Normale Superiore, Classe di Scienz

The Utilization of the Internet in the Advancement of Discipleship in the Traditional Black Church

Discipleship and technology are interrelated. Discipleship is the process of maturing in Christ through our actions, life, and words, as well as how we present ourselves to the world. This must become integral to the vitality and mission of the traditional Black Church. Technology is a resource that can assist the traditional Black Church to fulfill the Great Commission of Matthew 28:19-20. This thesis premise is supported by applied research (survey findings from pastoral leaders within the General Missionary Baptist Convention of Georgia), academic research (scholarly material from experts in the fields of theology, sociology, statistics, and church growth), and the Bible

A Memoir of the Archaeological Excavation of Fort Prince George, Pickens County, South Carolina Along with Pertinent Historical Documentation

https://scholarcommons.sc.edu/archanth_books/1201/thumbnail.jp

Optical BVRI Photometry of Common Proper Motion F/G/K+M Wide Separation Binaries

We present optical (BVRI) photometric measurements of a sample of 76 common proper motion wide separation main sequence binary pairs. The pairs are composed of a F-, G-, or K-type primary star and an M-type secondary. The sample is selected from the revised NLTT catalog and the LSPM catalog. The photometry is generally precise to 0.03 mag in all bands. We separate our sample into two groups, dwarf candidates and subdwarf candidates, using the reduced proper motion (RPM) diagram constructed with our improved photometry. The M subdwarf candidates in general have larger $V-R$ colors than the M dwarf candidates at a given $V-I$ color. This is consistent with an average metallicity difference between the two groups, as predicted by the PHOENIX/BT-Settl models. The improved photometry will be used as input into a technique to determine the metallicities of the M-type stars.Comment: 26 pages, 8 figures, accepted for publication in A

Controls on Saltwater Intrusion in a Shallow Coastal Aquifer: Wormsloe Historic Site, GA

The Wormsloe Historic site is situated on a barrier island located off the Georgia Coast. Four shallow monitoring wells were installed in an east-west transect to monitor the surficial aquifer for saltwater intrusion and to find what factors were most strongly controlling it. Previous studies have found strong indications for saltwater intrusion along the east coast, particularly in areas where the underlying Floridan aquifer has been extensively pumped. Temperature and conductivity data gathered show evidence for the lateral movement of saltwater into the surficial aquifer moving inland from a saline marsh, while tidal, precipitation, and Ground Penetrating Radar data reveal the timing and controls of it. Integration of the multiple lines of evidence indicates risks whereby lateral saltwater intrusion could eventually be conveyed downward under continued sea level rise, with the potential to impact the Upper Floridan aquifer or the regions potable water aquifer in the future

Deposition by Thomas Williams, signed by John Marshall. Date unknown.

In this deposition, the deponent Thomas Williams reports that he encouraged a girl to return a pocketbook to W. Minns. The girl later overhears W. Minns state the pocket book belonged to W. Thomas Reynolds, signed by John Marshall.https://digitalcommons.wofford.edu/littlejohnmss/1174/thumbnail.jp

Stretching single polysaccharide molecules using AFM: A potential method for the investigation of the intermolecular uronate distribution of alginate?

Illustrative examples of the way in which the molecular force-extension behaviour of polysaccharides is governed by the nature of the linkage between their constituent pyranose rings are presented for a series of standard homopolymers. These results agree with previously proposed general hypotheses regarding the possibility of generating force-induced conformational transitions, and with the predictions of a model in which the inter-conversion of pyranose conformers is assumed to be an equilibrium process on the timescale of the molecular stretching. Subsequently, we investigate the potential of the technique in the characterisation of co-polymeric polysaccharides in which the nature of the glycan linkages is different between the two distinct residue types. Specifically, we explore the possibility that the ratio of mannuronic acid (M) to guluronic acid (G) in alginate chains will be reflected in their single molecule stretching behaviour, owing to their contrasting equatorial and axial linkages. Furthermore, as the technique described interrogates the sample one polymer at a time we outline the promise of, and the obstacles to, obtaining a new level of characterisation using this methodology where differences observed in the single molecule stretching curves obtained from single alginate samples reflectsomething of the real intermolecular distribution of the M / G ratio

Point-by-point inscription of apodized fiber Bragg gratings

We demonstrate apodized fiber Bragg gratings inscribed with a point-by-point technique. We tailor the grating phase and coupling amplitude through precise control over the longitudinal and transverse position of each laser-inscribed modification. This method of apodization is facilitated by the highly-localized, high-contrast modifications generated by focussed IR femtosecond laser inscription. Our technique provides a simple method for the design and implementation of point-by-point fiber Bragg gratings with complex apodization profiles.Comment: 6 pages, 4 figures, article in revie