Finiteness of the number of compatibly-split subvarieties

We show that for a Frobenius split variety, there are only finitely many closed subvarieties which are compatibly-split.Comment: 3 page

Topology Driven Improvement of FDC Build Parameters

The likeliest failure origin for advanced ceramics parts, prepared by fused deposition, is a void from improper fill. Adequate filling of each cross-section is dependent upon the deposition toolpath. Cross-sectional spaces are conventionally filled with pre-defined parameters. We propose that adaptive build parameters will control variations in geometry and property of a part. Voids, overfilling, incomplete bonding and excess traversing can be suppressed by adjusting the fill parameters for cross-sectional areas. Improved build parameters and toolpath allows for faster build time and components ofj full density. Some implementations are discussed and presented.Mechanical Engineerin

Density of vector bundles periodic under the action of Frobenius

AbstractLet X be a proper and smooth curve of genus g⩾2 over an algebraically closed field k of positive characteristic. If k=F¯p, it follows from Hrushovski's work on the geometry of difference schemes that the set of rank r vector bundles with trivial determinant over X that are periodic under the action of Frobenius is dense in the corresponding moduli space. Using the equivalence between Frobenius periodicity of a stable vector bundle and its triviality after pull-back by some finite étale cover of X (due to Lange and Stuhler) on the one hand, and specialization of the fundamental group on the other hand, we prove that the same result holds for any algebraically closed field of positive characteristic

Semistability of Frobenius direct images over curves

Let $X$ be a smooth projective curve of genus $g \geq 2$ defined over an algebraically closed field $k$ of characteristic $p>0$. Given a semistable vector bundle $E$ over $X$, we show that its direct image $F\_*E$ under the Frobenius map $F$ of $X$ is again semistable. We deduce a numerical characterization of the stable rank-$p$ vector bundles $F\_*L$, where $L$ is a line bundle over $X$.Comment: 8 page

Gate Voltage Controllable Non-Equilibrium and Non-Ohmic Behavior in Suspended Carbon Nanotubes

In this work, we measure the electrical conductance and temperature of individual, suspended quasi-metallic single-walled carbon nanotubes under high voltage biases using Raman spectroscopy, while varying the doping conditions with an applied gate voltage. By applying a gate voltage, the high-bias conductance can be switched dramatically between linear (Ohmic) behavior and nonlinear behavior exhibiting negative differential conductance (NDC). Phonon populations are observed to be in thermal equilibrium under Ohmic conditions but switch to nonequilibrium under NDC conditions. A typical Landauer transport model assuming zero bandgap is found to be inadequate to describe the experimental data. A more detailed model is presented, which incorporates the doping dependence in order to fit this data

Biomarkers to Assess Liver Function in Various Types of Liver Diseases

Background: It is estimated that liver diseases are among the top ten killer diseases in India, causing deaths every year. Besides, there are those who suffered from chronic liver problems needing recurrent hospitalization and prolonged medical attention, which leaves them physically, mentally, emotionally and financially devastated. Methodology: The study included (n=80) various liver disease patients admitted to the General Medicine department and controls (n=20) subjects were having normal health within the age group of 30-55 years. Serum levels of bilirubin, Aspartate Transaminase, Alanine Amino Transferase, Alkaline Phosphatase and Gamma Glutamyl Transferase parameters were studied among the subjects suffering from cirrhosis, alcoholic liver disease, viral hepatitis, obstructive jaundice type of liver diseases. Result: The results of this study showed that the increase in serum levels of Bilirubin, AST, ALT, ALP and GGT in various types of liver diseases i.e Obstructive jaundice, Cirrhosis of the liver, Viral hepatitis, Alcoholic Liver disease when compared with controls. Conclusion: Biochemistry laboratory investigations i.e. Liver Function Test (LFT) are a simple, easy measure of tools which can early diagnose the various types of liver diseases. Keywords: Liver diseases; Liver Bio-markers;  Liver Function Test