120,939 research outputs found
Binomial coefficients, Catalan numbers and Lucas quotients
Let be an odd prime and let be integers with and . In this paper we determine
mod for ; for example,
where is the Jacobi symbol, and is the Lucas
sequence given by , and for
. As an application, we determine modulo for any integer , where denotes the
Catalan number . We also pose some related conjectures.Comment: 24 pages. Correct few typo
Generalized linear isotherm regularity equation of state applied to metals
A three-parameter equation of state (EOS) without physically incorrect
oscillations is proposed based on the generalized Lennard-Jones (GLJ) potential
and the approach in developing linear isotherm regularity (LIR) EOS of Parsafar
and Mason [J. Phys. Chem., 1994, 49, 3049]. The proposed (GLIR) EOS can include
the LIR EOS therein as a special case. The three-parameter GLIR, Parsafar and
Mason (PM) [Phys. Rev. B, 1994, 49, 3049], Shanker, Singh and Kushwah (SSK)
[Physica B, 1997, 229, 419], Parsafar, Spohr and Patey (PSP) [J. Phys. Chem. B,
2009, 113, 11980], and reformulated PM and SSK EOSs are applied to 30 metallic
solids within wide pressure ranges. It is shown that the PM, PMR and PSP EOSs
for most solids, and the SSK and SSKR EOSs for several solids, have physically
incorrect turning points, and pressure becomes negative at high enough
pressure. The GLIR EOS is capable not only of overcoming the problem existing
in other five EOSs where the pressure becomes negative at high pressure, but
also gives results superior to other EOSs.Comment: 9 pages, 3 figure
Why Students Drop Out of School: A Review of 25 Years of Research
Reviews research on the underlying causes of the high school dropout crisis -- individual and institutional characteristics that predict whether a student is likely to drop out of high school. Discusses student engagement, deviance, and other models
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UV-Photolithography Fabrication of Poly-Ethylene Glycol Hydrogels Encapsulated with Hepatocytes
The development of biomanufacturing technologies particularly, layered manufacturing has
advanced cell encapsulation processes in an effort to mimic the cellular microenvironment for invitro studies. This paper illustrates an inexpensive UV-photolithographic method for
encapsulation of human hepatocytes in three dimensional structures using poly-ethylene
diacrylate (PEGDA) hydrogels as candidate substrates. In order to further develop this
technology for layered fabrication, we have quantified the long-term effects of the photo-initiator
concentration and UV light exposure on the metabolic rates of encapsulated human hepatocytes
under a 21 day study. The photoinitator toxicity was observed immediately after polymerization
with no significant cytotoxicity on a long term basis. A cellular viability is examined and
reported for the UV photopolymerization process. Cell phenotype maintenance was observed by
measuring the amount of urea produced over a 1 week time period. This photo encapsulation
process may find use in the fabrication of spatially complex 3D scaffolds for tissue engineering
applications, elucidation of the 3D structure-pharmacokinetic response relationship and the
fabrication of complex multi-compartment liver tissue analog devices for drug screening
applications.Mechanical Engineerin
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Precision Extrusion Deposition of Polycaprolactone/Hydroxyapatite Tissue Scaffolds
Freeform fabrication provides an effective process tool to manufacture advanced tissue scaffolds
with specific designed properties. Our research focuses on using a novel Precision Extrusion
Deposition (PED) process technique to directly fabricate Polycaprolactone (PCL) and composite
PCL/ Hydroxyapatite (HA) tissue scaffolds. The scaffold morphology and the mechanical
properties were evaluated using SEM and mechanical testing. In vitro biological studies were
conducted to investigate the cellular responses of the composite scaffolds. Results and
characterizations demonstrate the viability of the PED process as well as the good mechanical
property, structural integrity, controlled pore size, pore interconnectivity, and the biological
compatibility of the fabricated scaffolds.Mechanical Engineerin
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