Shaped superconductor cylinder retains intense magnetic field

The curve of the inner walls of a superconducting cylinder is plotted from the flux lines of the magnetic field to be contained. This shaping reduces maximum flux densities and permits a stronger and more uniform magnetic field

The Fecal Fermentation Profile of Infants with Different Feeding Modalities

Introduction/Background Research indicates nutrition and environment in the first year of a child\u27s life are crucial in their development and growth and can contribute to lower chances of developing obesity and other health concerns. Key factors that can determine these outcomes include the bacteria and resulting short chain fatty acids (SCFAs) present in the gut. This composition may be affected by feeding modality (formula feeding vs breastfeeding), exposure to the mother’s microbiota, weight status of the child, and type of delivery. This research aims to identify the impact of infant feeding modality on toddlers\u27 fecal fermentation profile, and if there are associations between weight status and microbiome, fecal fermentation profile. Methods/ Procedures Participants (n=40) were recruited during well-child pediatric appointments at ETSU’s Pediatric primary care clinic. Researchers explained the requirements of the study and participants were provided with a 90-question food frequency questionnaire (FFQ) for children ages 2-7, including 90 questions and asks about a child\u27s typical intake over the previous 6-month period. The food list was developed from NHANES III dietary recall data. The child’s history was obtained, including current age, birth length and weight, delivery type (C-section or vaginal), feeding method (breast, bottle fed, or both) and duration. The child’s weight and height were obtained, and body mass index (BMI) calculated. Participant-provided stool samples were freeze-dried and ground, and SCFAs were extracted using a procedure developed by Schwiertz et al. that was modified. One mL of the SCFA extraction solution, containing Oxalic acid (0.1 mol/L), Sodium Azide (40 mmol/L), and Caproic acid (0.1 mmol/L) (internal standard) was added to 80 mg of a freeze-dried stool sample in a 16 x 100 mm disposable culture tube, and analyzed using a Shimadzu GC2010 gas chromatograph with SigmaAldrich ZB-Wax Plus capillary column. Samples were run in duplicate, and values for each participant were averaged. Data analysis was generated using SAS software, Version 9.4 of the SAS System, Copyright © 2013 SAS Institute Inc. Results Initial findings showed no significant differences in the SCFA composition of obese vs non-obese toddlers in the sample. However, there were significant differences in the amount of specific SCFAs (isobutyrate, isovaleric acid, and octanoic acid) in toddlers who were formula fed as infants versus toddlers who were breastfed, and those fed a combination of breastmilk, and formula (p \u3c 0.05). Further analysis will determine if these initial results may be contributed to overall dietary intake, and more specifically fiber intake

Coupled KdV equations of Hirota-Satsuma type

It is shown that the system of two coupled Korteweg-de Vries equations passes the Painlev\'e test for integrability in nine distinct cases of its coefficients. The integrability of eight cases is verified by direct construction of Lax pairs, whereas for one case it remains unknown

Slowly rotating charged fluid balls and their matching to an exterior domain

The slow-rotation approximation of Hartle is developed to a setting where a charged rotating fluid is present. The linearized Einstein-Maxwell equations are solved on the background of the Reissner-Nordstrom space-time in the exterior electrovacuum region. The theory is put to action for the charged generalization of the Wahlquist solution found by Garcia. The Garcia solution is transformed to coordinates suitable for the matching and expanded in powers of the angular velocity. The two domains are then matched along the zero pressure surface using the Darmois-Israel procedure. We prove a theorem to the effect that the exterior region is asymptotically flat if and only if the parameter C_{2}, characterizing the magnitude of an external magnetic field, vanishes. We obtain the form of the constant C_{2} for the Garcia solution. We conjecture that the Garcia metric cannot be matched to an asymptotically flat exterior electrovacuum region even to first order in the angular velocity. This conjecture is supported by a high precision numerical analysis.Comment: 11 pages, 2 figure

Zero curvature representation for a new fifth-order integrable system

In this brief note we present a zero-curvature representation for one of the new integrable system found by Mikhailov, Novikov and Wang in nlin.SI/0601046.Comment: 2 pages, LaTeX 2e, no figure

Properties of equations of the continuous Toda type

We study a modified version of an equation of the continuous Toda type in 1+1 dimensions. This equation contains a friction-like term which can be switched off by annihilating a free parameter \ep. We apply the prolongation method, the symmetry and the approximate symmetry approach. This strategy allows us to get insight into both the equations for \ep =0 and \ep \ne 0, whose properties arising in the above frameworks are mutually compared. For \ep =0, the related prolongation equations are solved by means of certain series expansions which lead to an infinite- dimensional Lie algebra. Furthermore, using a realization of the Lie algebra of the Euclidean group $E_{2}$, a connection is shown between the continuous Toda equation and a linear wave equation which resembles a special case of a three-dimensional wave equation that occurs in a generalized Gibbons-Hawking ansatz \cite{lebrun}. Nontrivial solutions to the wave equation expressed in terms of Bessel functions are determined. For \ep\,\ne\,0, we obtain a finite-dimensional Lie algebra with four elements. A matrix representation of this algebra yields solutions of the modified continuous Toda equation associated with a reduced form of a perturbative Liouville equation. This result coincides with that achieved in the context of the approximate symmetry approach. Example of exact solutions are also provided. In particular, the inverse of the exponential-integral function turns out to be defined by the reduced differential equation coming from a linear combination of the time and space translations. Finally, a Lie algebra characterizing the approximate symmetries is discussed.Comment: LaTex file, 27 page

On application of Liouville type equations to constructing B\"acklund transformations

It is shown how pseudoconstants of the Liouville-type equations can be exploited as a tool for construction of the B\"acklund transformations. Several new examples of such transformations are found. In particular we obtained the B\"acklund transformations for a pair of three-component analogs of the dispersive water wave system, and auto-B\"acklund transformations for coupled three-component KdV-type systems.Comment: 11 pages, no figure

Slowly, rotating non-stationary, fluid solutions of Einstein's equations and their match to Kerr empty space-time

A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in angular speed parameter. It is shown that the match applies to any previously known non-rotating fluid source made to rotate slowly for which a zero pressure boundary surface exists. The method is applied to the dust source of Robertson-Walker and in outline to an interior solution due to McVittie describing gravitational collapse. The applicability of the method to additional examples is transparent. The differential angular velocity of the rotating systems is determined and the induced rotation of local inertial frame is exhibited

Solution generating with perfect fluids

We apply a technique, due to Stephani, for generating solutions of the Einstein-perfect fluid equations. This technique is similar to the vacuum solution generating techniques of Ehlers, Harrison, Geroch and others. We start with a ``seed'' solution of the Einstein-perfect fluid equations with a Killing vector. The seed solution must either have (i) a spacelike Killing vector and equation of state P=rho or (ii) a timelike Killing vector and equation of state rho+3P=0. The new solution generated by this technique then has the same Killing vector and the same equation of state. We choose several simple seed solutions with these equations of state and where the Killing vector has no twist. The new solutions are twisting versions of the seed solutions