Shot Noise in Gravitational-Wave Detectors with Fabry-Perot Arms

Shot-noise-limited sensitivity is calculated for gravitational-wave interferometers with Fabry–Perot arms, similar to those being installed at the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the Italian–French Laser Interferometer Collaboration (VIRGO) facility. This calculation includes the effect of nonstationary shot noise that is due to phase modulation of the light. The resulting formula is experimentally verified by a test interferometer with suspended mirrors in the 40-m arms

A Limited Habitable Zone for Complex Life

The habitable zone (HZ) is commonly defined as the range of distances from a host star within which liquid water, a key requirement for life, may exist on a planet's surface. Substantially more CO2 than present in Earth's modern atmosphere is required to maintain clement temperatures for most of the HZ, with several bars required at the outer edge. However, most complex aerobic life on Earth is limited by CO2 concentrations of just fractions of a bar. At the same time, most exoplanets in the traditional HZ reside in proximity to M dwarfs, which are more numerous than Sun-like G dwarfs but are predicted to promote greater abundances of gases that can be toxic in the atmospheres of orbiting planets, such as carbon monoxide (CO). Here we show that the HZ for complex aerobic life is likely limited relative to that for microbial life. We use a 1D radiative-convective climate and photochemical models to circumscribe a Habitable Zone for Complex Life (HZCL) based on known toxicity limits for a range of organisms as a proof of concept. We find that for CO2 tolerances of 0.01, 0.1, and 1 bar, the HZCL is only 21%, 32%, and 50% as wide as the conventional HZ for a Sun-like star, and that CO concentrations may limit some complex life throughout the entire HZ of the coolest M dwarfs. These results cast new light on the likely distribution of complex life in the universe and have important ramifications for the search for exoplanet biosignatures and technosignatures.Comment: Revised including additional discussion. Published Gold OA in ApJ. 9 pages, 5 figures, 5 table

Existence of an Antisymmetric Solution of a Boundary Value Problem with Antiperiodic Boundary Conditions

In this work, an application is made of a recent extension of the Leggett-Williams fixed point theorem, commonly referred to as an Avery type fixed point theorem, to a second order boundary value problem with antiperiodic boundary conditions. Under certain conditions and with the use of concavity, an antisymmetric solution to the boundary value problem is shown to exist. In conclusion, a non-trivial example is provided

Symmetric mixed states of nn qubits: local unitary stabilizers and entanglement classes

We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states into six classes. These include the stabilizer types of the Werner states, the GHZ state and its generalizations, and Dicke states. For all but the zero algebra, we classify entanglement types (local unitary equivalence classes) of symmetric mixed states that have those stabilizers. We make use of the identification of symmetric density matrices with polynomials in three variables with real coefficients and apply the representation theory of SO(3) on this space of polynomials.Comment: 10 pages, 1 table, title change and minor clarifications for published versio

From the Editors: Assessing the International Journal of Exercise Science after One Year

Western Kentucky University (WKU) strives to be a “leading American university with international reach.” In an effort to contribute to that mission, Drs. Scott Lyons and James Navalta of the Exercise Science program endeavored in 2007 to start a student-focused, on-line journal. Working closely with Berkeley Press, the platform for the International Journal of Exercise Science (IJES) was established during the summer of 2007 and it went “live” in January 2008. The journal has now been on-line for over one year and has enjoyed great success, with quality research submitted from graduate and undergraduate students, as well as professionals. We at IJES look forward to continued success in 2009

A Difference Equation with Anti-Periodic Boundary Conditions

In this paper, we apply an extension of the Leggett-Williams fixed point theorem to the second order difference equation ∆2u(k)+f(u(k+1)) = 0, k ∈ {0, 1, . . . , N}, satisfying the anti-periodic boundary conditions u(0) + u(N + 2) = 0, ∆u(0) + ∆u(N +1) = 0. Two important results of this paper involve providing the Green’s function for −∆2u(k) = 0 satisfying u(0) + u(N + 2) = 0, ∆u(0) + ∆u(N + 1) = 0 and showing this Green’s function satisfies a concavity like property. An example is also given

Existence of an antisymmetric solution of a boundary value problem with antiperiodic boundary conditions

In this work, an application is made of a recent extension of the Leggett-Williams fixed point theorem, commonly referred to as an Avery type fixed point theorem, to a second order boundary value problem with antiperiodic boundary conditions. Under certain conditions and with the use of concavity, an antisymmetric solution to the boundary value problem is shown to exist. In conclusion, a non-trivial example is provided

Positive solutions of a singular fractional boundary value problem with a fractional boundary condition

For $\alpha\in(1,2]$, the singular fractional boundary value problem $$D^{\alpha}_{0^+}x+f\left(t,x,D^{\mu}_{0^+}x\right)=0,\quad 0\lt t\lt 1,$$ satisfying the boundary conditions $x(0)=D^{\beta}_{0^+}x(1)=0$, where $\beta\in(0,\alpha-1]$, $\mu\in(0,\alpha-1]$, and $D^{\alpha}_{0^+}$, $D^{\beta}_{0^+}$ and $D^{\mu}_{0^+}$ are Riemann-Liouville derivatives of order $\alpha$, $\beta$ and $\mu$ respectively, is considered. Here $f$ satisfies a local Carathéodory condition, and $f(t,x,y)$ may be singular at the value 0 in its space variable $x$. Using regularization and sequential techniques and Krasnosel\u27skii\u27s fixed point theorem, it is shown this boundary value problem has a positive solution. An example is given

Student Reflections on a Study Abroad Course to the 2008 Summer Olympics in Beijing

The authors lead a study abroad trip to Beijing, China during the 2008 Summer Olympic Games. Included are reflections from the students who participated. Throughout the visit, students had the opportunity to complete learning outside of the traditional classroom setting. In addition, various challenges were faced and overcome which also constituted a learning experience and was the cause of reflection. The country of China and all of its historical landmarks had a great impression on these students, especially the day that was spent at the Great Wall. Finally, being able to be at the Olympic Games was a life-changing experience, from the Opening Ceremony to the events that were attended. In all, it was a thoroughly worthwhile adventure and one that we hope to replicate every two years

The International Journal of Exercise Science: 2011 Year in Review

The International Journal of Exercise Science: 2011 Year in Revie