3,118 research outputs found
What is the probability that a random integral quadratic form in variables has an integral zero?
We show that the density of quadratic forms in variables over that are isotropic is a rational function of , where the rational
function is independent of , and we determine this rational function
explicitly. When real quadratic forms in variables are distributed
according to the Gaussian Orthogonal Ensemble (GOE) of random matrix theory, we
determine explicitly the probability that a random such real quadratic form is
isotropic (i.e., indefinite).
As a consequence, for each , we determine an exact expression for the
probability that a random integral quadratic form in variables is isotropic
(i.e., has a nontrivial zero over ), when these integral quadratic
forms are chosen according to the GOE distribution. In particular, we find an
exact expression for the probability that a random integral quaternary
quadratic form has an integral zero; numerically, this probability is
approximately .Comment: 17 pages. This article supercedes arXiv:1311.554
Antidiarrhoeal Activity of Leaf Extract of Moringa Oleifera In Experimentally Induced Diarrhoea In Rats
To evalauate the antidiarrhoeal activity of the hydroalcoholic extract of moringa oleifera leaves. The hydroalchoholic extract was evaluated using rodent animal models of diarrhoea like the castor oil and magnesium sulfate induced gastrointestinal motility, in a model of enteropooling induced by the administration of castor oil and PGE2, Charcoal meal test. Acute toxicity and phytochemical constituents were also been evaluated using standardized methods. The results of the present study indicates that the hydroalcoholic extract of moringa oleifera leaves was effective in inducing a significant protection against experimentally induced diarrhoea by castor oil and magnesium sulfate, as evidenced by a decrease in the number of frequency, weight of stools after 4 hours with respect to control. The extract also prevented the enteropooling induced by castor oil and PGE2 at all the doses tested. Acute toxicity studies indicated that the extract is safe till 2500 mg/kg. The antidiarrhoeal activity though, not ascribed to any particular phytochemical present, general tests performed indicated the presence of flavonoids, tannis which were reported to produce antidiarrhoeal activity. These results showed that Moringa oleifera leaves possess anti-diarrheal properties mediated through inhibition of hyper secretion and gastrointestinal motility that substantiate its use in the treatment of diarrhea in traditional medicines or folklore use. Keywords: enteropooling, hyper secretion, Moringa oleifer
Arithmetical Congruence Preservation: from Finite to Infinite
Various problems on integers lead to the class of congruence preserving
functions on rings, i.e. functions verifying divides for all
. We characterized these classes of functions in terms of sums of rational
polynomials (taking only integral values) and the function giving the least
common multiple of . The tool used to obtain these
characterizations is "lifting": if is a surjective morphism,
and a function on a lifting of is a function on such that
. In this paper we relate the finite and infinite notions
by proving that the finite case can be lifted to the infinite one. For -adic
and profinite integers we get similar characterizations via lifting. We also
prove that lattices of recognizable subsets of are stable under inverse
image by congruence preserving functions
Correlating the Energetics and Atomic Motions of the Metal-Insulator Transition of M1 Vanadium Dioxide
Materials that undergo reversible metal-insulator transitions are obvious
candidates for new generations of devices. For such potential to be realised,
the underlying microscopic mechanisms of such transitions must be fully
determined. In this work we probe the correlation between the energy landscape
and electronic structure of the metal-insulator transition of vanadium dioxide
and the atomic motions occurring using first principles calculations and high
resolution X-ray diffraction. Calculations find an energy barrier between the
high and low temperature phases corresponding to contraction followed by
expansion of the distances between vanadium atoms on neighbouring sub-lattices.
X-ray diffraction reveals anisotropic strain broadening in the low temperature
structure's crystal planes, however only for those with spacings affected by
this compression/expansion. GW calculations reveal that traversing this barrier
destabilises the bonding/anti-bonding splitting of the low temperature phase.
This precise atomic description of the origin of the energy barrier separating
the two structures will facilitate more precise control over the transition
characteristics for new applications and devices.Comment: 11 Pages, 8 Figure
Analysis of rolling contact spall life in 440 C steel bearing rims
The results of a two year study of the mechanisms of spall failure in the HPOTP bearings are described. The objective was to build a foundation for detailed analyses of the contact life in terms of: cyclic plasticity, contact mechanics, spall nucleation, and spall growth. Since the laboratory rolling contact testing is carried out in the 3 ball/rod contact fatigue testing machine, the analysis of the contacts and contact lives produced in this machine received attention. The results from the experimentally observed growth lives are compared with calculated predictions derived from the fracture mechanics calculations
Dual-acting stapled peptides target both HIV-1 entry and assembly
Background:
Previously, we reported the conversion of the 12-mer linear and cell-impermeable peptide CAI to a cell-penetrating peptide NYAD-1 by using an i,i + 4 hydrocarbon stapling technique and confirmed its binding to the C-terminal domain (CTD) of the HIV-1 capsid (CA) protein with an improved affinity (Kd ~ 1 μM) compared to CAI (Kd ~ 15 μM). NYAD-1 disrupts the formation of both immature- and mature-like virus particles in in vitro and cell-based assembly assays. In addition, it displays potent anti-HIV-1 activity in cell culture against a range of laboratory-adapted and primary HIV-1 isolates.<p></p>
Results:
In this report, we expanded the study to i,i + 7 hydrocarbon-stapled peptides to delineate their mechanism of action and antiviral activity. We identified three potent inhibitors, NYAD-36, -66 and -67, which showed strong binding to CA in NMR and isothermal titration calorimetry (ITC) studies and disrupted the formation of mature-like particles. They showed typical α-helical structures and penetrated cells; however, the cell penetration was not as efficient as observed with the i,i + 4 peptides. Unlike NYAD-1, the i,i + 7 peptides did not have any effect on virus release; however, they impaired Gag precursor processing. HIV-1 particles produced in the presence of these peptides displayed impaired infectivity. Consistent with an effect on virus entry, selection for viral resistance led to the emergence of two mutations in the gp120 subunit of the viral envelope (Env) glycoprotein, V120Q and A327P, located in the conserved region 1 (C1) and the base of the V3 loop, respectively.<p></p>
Conclusion:
The i,i + 7 stapled peptides derived from CAI unexpectedly target both CA and the V3 loop of gp120. This dual-targeted activity is dependent on their ability to penetrate cells as well as their net charge. This mechanistic revelation will be useful in further modifying these peptides as potent anti-HIV-1 agents.<p></p>
Periodic harmonic functions on lattices and points count in positive characteristic
This survey addresses pluri-periodic harmonic functions on lattices with
values in a positive characteristic field. We mention, as a motivation, the
game "Lights Out" following the work of Sutner, Goldwasser-Klostermeyer-Ware,
Barua-Ramakrishnan-Sarkar, Hunzikel-Machiavello-Park e.a.; see also 2 previous
author's preprints for a more detailed account. Our approach explores harmonic
analysis and algebraic geometry over a positive characteristic field. The
Fourier transform allows us to interpret pluri-periods of harmonic functions on
lattices as torsion multi-orders of points on the corresponding affine
algebraic variety.Comment: These are notes on 13p. based on a talk presented during the meeting
"Analysis on Graphs and Fractals", the Cardiff University, 29 May-2 June 2007
(a sattelite meeting of the programme "Analysis on Graphs and its
Applications" at the Isaac Newton Institute from 8 January to 29 June 2007
Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems
We determine explicit orbit representatives of reducible Jordan algebras and
of their corresponding Freudenthal triple systems. This work has direct
application to the classification of extremal black hole solutions of N = 2, 4
locally supersymmetric theories of gravity coupled to an arbitrary number of
Abelian vector multiplets in D = 4, 5 space-time dimensions.Comment: 18 pages. Updated to match published versio
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