Transformation Groups and the Method of Darboux

In the study of partial differential equations (PDE), one is often concerned as to whether or not explicit solutions can be obtained via various integration techniques. One such technique, known as the method of Darboux, has had particular success in solving nonlinear problems as demonstrated by the classical works of Goursat. Recently, Anderson, Fels, and Vassiliou provided a far-reaching generalization of Vessiot’s group-theoretic interpretation of the method of Darboux. This generalization allows for the characterization of Darboux integrable systems in terms of fundamental geometric invariants as well as the construction of Darboux integrable systems in general. In this work, we refine the theory of Anderson, Fels, and Vassiliou by providing conditions for which their construction gives rise to various classes of second-order PDE in the plane of the form F(x,y,u,ux,uy,uxx,uxy,uyy) = 0. We use this refinement to completely characterize all linear Darboux integrable PDE in the plane and provide a simple proof concerning the classification of all PDE equivalent to the wave equation uxy = 0. We then study the fundamental invariants associated to several classes of Darboux integrable equations, in particular, f-Gordon equations of the form uxy= f(x,y,u,ux,uy). In doing so, we construct several new examples of Darboux integrable f-Gordon equations with interesting geometric structure

Disseminated cutaneous gout: a rare manifestation of a common disease

Disseminated cutaneous gout is a rare atypical cutaneous manifestation of gout in which widespread dermal and subcutaneous tophi develop at extra-articular body sites. Given the lack of joint involvement that is typically a feature in tophaceous gout, the diagnosis may not be initially suspected. We present the case of a 50-year-old Hispanic man with poorly controlled gout who was evaluated for several years of firm papulonodules over the trunk and upper and lower extremities, sparing the joints; histopathology confirmed, the diagnosis of disseminated cutaneous gout. Per our literature review, disseminated cutaneous gout presents with polymorphous papules and nodules that can mimic other, more common cutaneous diseases. There is a preponderance of cases in males, Asians, and patients with longstanding gout. The lower extremities are involved in nearly all reports. Uric acid-lowering therapy with allopurinol has been reported to decrease the size and number of lesions in a minority of treated patients

Marshall University Music Department Presents a Senior Recital, Ashley Gilbert, clarinet, accompanied by Mila Markun, piano, and, Junior Recital, Brandon Layman, trumpet, accompanied by Alanna Cushing, piano

https://mds.marshall.edu/music_perf/1455/thumbnail.jp

Building Collegiate E-Loyalty: The Role Of Perceived Value In The Quality-Loyalty Linkage In Online Higher Education

E-service quality of online higher education reflects the student’s perception of quality of online exchanges across four dimensions: fulfillment, efficiency, system availability and privacy.  This study links e-service quality to intentions to remain loyal as mediated by perceived value in an online higher education environment.  AMOS is used to examine the structural model based on responses to a student self-report online survey (n=127).  Results indicate a strong causal linkage between e-S-QUAL and Loyalty Intentions as mediated by Perceived Value.  Further, the direct linkage between e-S-QUAL and Loyalty Intentions was found to be insignificant, substantiating the proposed full mediation model

Intensive Cultural Resources Survey For Portions Of The Proposed 17-Mile El Paso Natural Gas Mainline Expansion Project On Public Lands In El Paso And Hudspeth Counties, Texas

On behalf of El Paso Natural Gas Company, LLC (EPNG), SWCA Environmental Consultants (SWCA) conducted an intensive cultural resources survey on a portion of the proposed 17.0-mile-long (27.4- kilometer [km]) EPNG Mainline Expansion Project (Project) that crosses public lands administered by the Texas General Land Office (GLO) and the Clint Independent School District (CISD) in El Paso and Hudspeth Counties, Texas. Investigations were conducted in support of EPNG’s filing of a standard 7c application with the Federal Energy Regulatory Commission (FERC). The 17-mile proposed project is one component of a larger project that includes construction in the states of Arizona, New Mexico, and Texas. Project activities would occur at three distinct locations along the EPNG’s existing South Mainline system including construction and operation of a new 17-mile-long loop line and construction and operation of two new compressor stations. In Texas, the proposed project consists of the construction of an approximate 17-mile, 30-inch outside diameter loop line extension in El Paso and Hudspeth Counties, Texas. This report addresses only the portions of the 17-mile loop extension on Texas public lands. The public lands component of the project includes 1.85 miles of 300-foot-wide corridor (67.3 acres) on three GLO properties (i.e., parcels 0003.000.00.00-HU-TX, 0004.000.00.00-HU-TX, and 0125.000.00.00-EP-TX) and 0.15 mile of 300-foot-wide corridor (5.5 acres) on one CISD property (parcel 0064.000.00.00-EP-TX). Cultural resources investigations were conducted on the public lands to comply with the Antiquities Code of Texas, as the agencies administering those lands are political subdivisions of the State of Texas. Additionally, as the project is subject to FERC review and the project may cross waters of the U.S. under jurisdiction of the U.S. Army Corps of Engineers, work was performed in support of EPNG’s compliance with Section 106 of the National Historic Preservation Act (54 U.S.C. 306108) and its implementing regulations (36 Code of Federal Regulations [CFR] 800). Impacts associated with the construction of the pipeline will occur within a variable width construction right-of-way (ROW) measuring 60 feet wide in residential areas and 180 feet wide in dunal areas, but averaging 90 feet wide. For the 2.0 miles of cultural resources survey on public lands, SWCA investigated a 300-foot-wide corridor to give EPNG options for the ultimate centerline placement. The anticipated typical depth of construction impacts is approximately 6 feet below ground surface, although, in dunal areas, the depth of impacts will be approximately 9 feet; however, subsurface impacts are anticipated to extend up to 12 feet below ground surface via subsurface bores to avoid impacts to areas with existing infrastructure and drainages. The project area of potential effects (APE) on public lands consists of approximately 10,500 feet (2.0 miles) of 300-foot-wide survey corridor encompassing 72.7 acres, which includes 7.3 acres of permanent 30-foot-wide ROW and 12.1 acres of construction corridor. Included within the 300-foot-wide survey corridor are proposed access roads for the project that consist of existing 15- to 25-foot-wide gravel access roads for several previously constructed pipelines that parallel the current APE. Investigations included a cultural resources background review and literature search of the APE and an intensive pedestrian survey of the APE augmented with shovel testing. SWCA’s background review indicated that 11 previous cultural resources surveys have been conducted within a 1-mile radius of the APE. Seven of the 11 previously surveyed project areas intersect the APE or are adjacent to (within 300 feet of) the APE; the remainder of the previous survey areas are within the 1-mile buffer, but due to their distance to the APE, will not be traversed by the planned construction. None of the seven previous cultural surveys intersect or are adjacent to the four public land parcels discussed in this report. The review also indicates that 40 previously recorded archaeological sites are within a 1-mile buffer of the APE; however, only four sites (i.e., 41EP868, 41EP4768, 41EP5490, and 41HZ234) appear to be intersected by, or within 300 feet of, the APE. None of these four sites are located within any of the public lands. The closest previous site to a public land parcel is 41HZ234, which is located just within the northern boundary of the 300-foot-wide survey corridor but is several hundred feet outside the northern boundary of parcel 0004.000.00.00-HU-TX on private property. Because of the current survey effort, SWCA recorded one new archaeological site (41HZ803). Owing to the paucity or commonality of recovered assemblages, lack of features, lack of unique character, and/or lack of contextual integrity, this resource possesses negligible research value and is unlikely to contribute new or important information regarding local and/or regional prehistory. Consequently, no further work is recommended for 41HZ803

Student Privacy: A Key Piece of the Online Student Satisfaction Puzzle

This quantitative study examines linkages from online student perceptions of privacy in the satisfaction puzzle across 5 university administrative/student touch-points. The importance of categorizing the quality dimensions of online learning is paramount as learners are exposed to multiple quality touch-points prior to, during, and after the completion of an online learning experience (Ehlers, 2004; Frydenberg, 2002). Facing a greater competitive environment in student recruitment, academic institutions are increasingly aware of external evaluator rankings, accreditors, and resulting student perceptions. ANOVA results are reported, along with considerations and issues for addressing perceptions of privacy among online students

The Pursuit Of Excellence: 3rd-Party Rankings And Positioning Of Online Programs Through Quality And Value

Third-party ranking agencies (e.g., US News and World Report, Center for Online Education, CollegeChoice.net) produce rankings that are a popular publicly accessible search option for potential students as they sort online degree options. While higher education administration is keen to the possibility that most or all ranking systems risk methodological flaws, potential students are still on board with rankings and seem significantly steered by their results (Barkhorn, 2014). Monitoring rankings has become a positioning consideration for academic institutions. The disparity amongst ranking factors across time and across assessor, along with the mismatch between ranking methods used and suggested methodologies from research on higher education begs the question: which attributes are colleges and universities supposed to leverage? This study reports a fully mediated SEM using data from online student feedback across multiple quality touch points: faculty, LMS and course on student loyalty as mediated by perceived value

Tuning the Nigerian Slit Gong

An experimental and theoretical investigation of the Nigerian slit gong is reported. It is shown that in tuning the gong the artisan ensures that the frequencies of the two lowest mechanical resonances are nearly coincident with the frequencies of two of the acoustic resonances of the internal cavity. Four possible tuning parameters are identified and the effects of changing these parameters is discussed

Research on the Chytrid Fungus in NH Amphibian Populations

The chytrid fungus (Batrachochytrium Dendrobatidis) has caused significant decline of amphibians all over the United States, Central America, and Australia. Chytridiomycosis is the fatal disease that infects the skin of amphibians disrupting their ability for water intake, and the ability to exchange ions and function properly. NH specimens were swabbed and PCR analysis was completed to determine if Chytrid DNA was present in NH waterbodies. Samples were obtained from NH water bodies such as Dorrs Pond, Marsh Pond, Lynxfield Pond, Carter Hill Orchard, etc. Thirty six samples were tested over the course of the Fall 2021 and Spring 2022 semesters. The chytrid fungus could potentially cause significant problems to amphibians all over the world, if something is not done before this fungus reaches all water bodies

Utilizing pHluorin-Tagged Receptors to Monitor Subcellular Localization and Trafficking

Understanding membrane protein trafficking, assembly, and expression requires an approach that differentiates between those residing in intracellular organelles and those localized on the plasma membrane. Traditional fluorescence-based measurements lack the capability to distinguish membrane proteins residing in different organelles. Cutting edge methodologies transcend traditional methods by coupling pH-sensitive fluorophores with total internal reflection fluorescence microscopy (TIRFM). TIRF illumination excites the sample up to approximately 150 nm from the glass-sample interface, thus decreasing background, increasing the signal to noise ratio, and enhancing resolution. The excitation volume in TIRFM encompasses the plasma membrane and nearby organelles such as the peripheral ER. Superecliptic pHluorin (SEP) is a pH sensitive version of GFP. Genetically encoding SEP into the extracellular domain of a membrane protein of interest positions the fluorophore on the luminal side of the ER and in the extracellular region of the cell. SEP is fluorescent when the pH is greater than 6, but remains in an off state at lower pH values. Therefore, receptors tagged with SEP fluoresce when residing in the endoplasmic reticulum (ER) or upon insertion in the plasma membrane (PM) but not when confined to a trafficking vesicle or other organelles such as the Golgi. The extracellular pH can be adjusted to dictate the fluorescence of receptors on the plasma membrane. The difference in fluorescence between TIRF images at neutral and acidic extracellular pH for the same cell corresponds to a relative number of receptors on the plasma membrane. This allows a simultaneous measurement of intracellular and plasma membrane resident receptors. Single vesicle insertion events can also be measured when the extracellular pH is neutral, corresponding to a low pH trafficking vesicle fusing with the plasma membrane and transitioning into a fluorescent state. This versatile technique can be exploited to study localization, expression, and trafficking of membrane proteins