102,685 research outputs found

### The Lawson-Yau formula and its generalization

AbstractThe Euler characteristic of Chow varieties of algebraic cycles of a given degree in complex projective spaces was computed by Blaine Lawson and Stephen Yau by using holomorphic symmetries of cycles spaces. In this paper we compute this in a direct and elementary way and generalize this formula to the l-adic Eulerâ€“PoincarÃ© characteristic for Chow varieties over any algebraically closed field. Moreover, the Euler characteristic for Chow varieties with certain group action is calculated. In particular, we calculate the Euler characteristic of the space of right quaternionic cycles of a given dimension and degree in complex projective spaces

### Exactly $n$-resolvable Topological Expansions

For $\kappa$ a cardinal, a space X=(X,\sT) is $\kappa$-{\it resolvable} if
$X$ admits $\kappa$-many pairwise disjoint \sT-dense subsets; (X,\sT) is
{\it exactly} $\kappa$-{\it resolvable} if it is $\kappa$-resolvable but not
$\kappa^+$-resolvable.
The present paper complements and supplements the authors' earlier work,
which showed for suitably restricted spaces (X,\sT) and cardinals
$\kappa\geq\lambda\geq\omega$ that (X,\sT), if $\kappa$-resolvable, admits an
expansion \sU\supseteq\sT, with (X,\sU) Tychonoff if (X,\sT) is
Tychonoff, such that (X,\sU) is $\mu$-resolvable for all $\mu<\lambda$ but is
not $\lambda$-resolvable (cf. Theorem~3.3 of \cite{comfhu10}). Here the "finite
case" is addressed. The authors show in ZFC for $1<n<\omega$: (a) every
$n$-resolvable space (X,\sT) admits an exactly $n$-resolvable expansion
\sU\supseteq\sT; (b) in some cases, even with (X,\sT) Tychonoff, no choice
of \sU is available such that (X,\sU) is quasi-regular; (c) if
$n$-resolvable, (X,\sT) admits an exactly $n$-resolvable quasi-regular
expansion \sU if and only if either (X,\sT) is itself exactly
$n$-resolvable and quasi-regular or (X,\sT) has a subspace which is either
$n$-resolvable and nowhere dense or is $(2n)$-resolvable. In particular, every
$\omega$-resolvable quasi-regular space admits an exactly $n$-resolvable
quasi-regular expansion. Further, for many familiar topological properties
\PP, one may choose \sU so that (X,\sU)\in\PP if (X,\sT)\in\PP

### Tychonoff Expansions with Prescribed Resolvability Properties

The recent literature offers examples, specific and hand-crafted, of
Tychonoff spaces (in ZFC) which respond negatively to these questions, due
respectively to Ceder and Pearson (1967) and to Comfort and Garc\'ia-Ferreira
(2001): (1) Is every $\omega$-resolvable space maximally resolvable? (2) Is
every maximally resolvable space extraresolvable? Now using the method of
${\mathcal{KID}}$ expansion, the authors show that {\it every} suitably
restricted Tychonoff topological space (X,\sT) admits a larger Tychonoff
topology (that is, an "expansion") witnessing such failure. Specifically the
authors show in ZFC that if (X,\sT) is a maximally resolvable Tychonoff space
with S(X,\sT)\leq\Delta(X,\sT)=\kappa, then (X,\sT) has Tychonoff
expansions \sU=\sU_i ($1\leq i\leq5$), with \Delta(X,\sU_i)=\Delta(X,\sT)
and S(X,\sU_i)\leq\Delta(X,\sU_i), such that (X,\sU_i) is: ($i=1$)
$\omega$-resolvable but not maximally resolvable; ($i=2$) [if $\kappa'$ is
regular, with S(X,\sT)\leq\kappa'\leq\kappa] $\tau$-resolvable for all
$\tau<\kappa'$, but not $\kappa'$-resolvable; ($i=3$) maximally resolvable, but
not extraresolvable; ($i=4$) extraresolvable, but not maximally resolvable;
($i=5$) maximally resolvable and extraresolvable, but not strongly
extraresolvable.Comment: 25 pages, 0 figure

### An Isocurvature Mechanism for Structure Formation

We examine a novel mechanism for structure formation involving initial number
density fluctuations between relativistic species, one of which then undergoes
a temporary downward variation in its equation of state and generates
superhorizon-scale density fluctuations. Isocurvature decaying dark matter
models (iDDM) provide concrete examples. This mechanism solves the
phenomenological problems of traditional isocurvature models, allowing iDDM
models to fit the current CMB and large-scale structure data, while still
providing novel behavior. We characterize the decaying dark matter and its
decay products as a single component of ``generalized dark matter''. This
simplifies calculations in decaying dark matter models and others that utilize
this mechanism for structure formation.Comment: 4 pages, 3 figures, submitted to PRD (rapid communications

### Hiding dark energy transitions at low redshift

We show that it is both observationally allowable and theoretically possible
to have large fluctuations in the dark energy equation of state as long as they
occur at ultra-low redshifts z<0.02. These fluctuations would masquerade as a
local transition in the Hubble rate of a few percent or less and escape even
future, high precision, high redshift measurements of the expansion history and
structure. Scalar field models that exhibit this behavior have a sharp feature
in the potential that the field traverses within a fraction of an e-fold of the
present. The equation of state parameter can become arbitrarily large if a
sharp dip or bump in the potential causes the kinetic and potential energy of
the field to both be large and have opposite sign. While canonical scalar field
models can decrease the expansion rate at low redshift, increasing the local
expansion rate requires a non-canonical kinetic term for the scalar field.Comment: 4 pages, 2 figures; submitted to Phys. Rev. D (Brief Report

### Aerodynamics of F1 car side mirror

This study investigates the aerodynamic performance of a Formula 1 carrear view side mirror when the location of its glass is varied inside its frame. Bothexperimental and computational studies have been carried out for a simplifiedtwo-dimensional model of a typical Formula 1 mirror at different Reynoldsnumbers. Experimental results showed strong correlation between the mirrorâ€™sglass location and its drag over all investigated Reynolds number range of1.1 Ã— 105 to 2.6 Ã— 105 â€“ as the mirrorâ€™s glass is located further inside its frame areduction in the drag is achieved with a maximum of 10%-11%. No change is foundin the mirrorâ€™s vortex shedding frequency at all investigated Reynolds numberswhich implies no structural impact of this modification. However thecomputational results obtained using Fluent failed to predict the changes in flowcharacteristics and drag caused by the proposed modification, more calculationsare needed using higher order numerical methods should be performed toinvestigate this phenomenon further to confirm the experimental findings

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