Five-dimensional SU(2) AGT conjecture and recursive formula of deformed Gaiotto state

This note deals with the five-dimensional pure SU(2) AGT conjecture proposed by Awata and Yamada. We give a conjecture on a recursive formula for the inner product of the deformed Gaiotto state. We also show that the K-theoretic pure SU(2) Nekrasov partition function satisfies the same recursion relation. Therefore the five-dimensional AGT conjecture is reduced to our conjectural recursive formula.Comment: 16 pages. Typos correcte

On Multiple Zeta Values of Even Arguments

For k <= n, let E(2n,k) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. Of course E(2n,1) is the value of the Riemann zeta function at 2n, and it is well known that E(2n,2) = (3/4)E(2n,1). Recently Z. Shen and T. Cai gave formulas for E(2n,3) and E(2n,4). We give two formulas form E(2n,k), both valid for arbitrary k <=n, one of which generalizes the Shen-Cai results; by comparing the two we obtain a Bernoulli-number identity. We also give explicit generating functions for the numbers E(2n,k) and for the analogous numbers E*(2n,k) defined using multiple zeta-star values of even arguments.Comment: DESY number added; misprints fixed; reference added. Second revision (2016): New result on multiple zeta-star values adde

Integrated comparative validation tests as an aid for building simulation tool users and developers

Published validation tests developed within major research projects have been an invaluable aid to program developers to check on their programs. This paper sets out how selected ASHRAE Standard 140-2004 and European CEN standards validation tests have been incorporated into the ESP-r simulation program so that they can be easily run by users and also discusses some of the issues associated with compliance checking. Embedding the tests within a simulation program allows program developers to check routinely whether updates to the simulation program have led to significant changes in predictions and to run sensitivity tests to check on the impact of alternative algorithms. Importantly, it also allows other users to undertake the tests to check that their installation is correct and to give them, and their clients, confidence in results. This paper also argues that validation tests should characterize some of the significant heat transfer processes (particularly internal surface convection) in greater detail in order to reduce the acceptance bands for program predictions. This approach is preferred to one in which validation tests are overly prescriptive (e.g., specifying fixed internal convection coefficients), as these do not reflect how programs are used in practice

Asymptotically exact trial wave functions for yrast states of rotating Bose gases

We revisit the composite fermion (CF) construction of the lowest angular momentum yrast states of rotating Bose gases with weak short range interaction. For angular momenta at and below the single vortex, $L \leq N$, the overlaps between these trial wave functions and the corresponding exact solutions {\it increase} with increasing system size and appear to approach unity in the thermodynamic limit. In the special case $L=N$, this remarkable behaviour was previously observed numerically. Here we present methods to address this point analytically, and find strongly suggestive evidence in favour of similar behaviour for all $L \leq N$. While not constituting a fully conclusive proof of the converging overlaps, our results do demonstrate a striking similarity between the analytic structure of the exact ground state wave functions at $L \leq N$, and that of their CF counterparts. Results are given for two different projection methods commonly used in the CF approach

Random matrices with external source and KP τ\tau functions

In this paper we prove that the partition function in the random matrix model with external source is a KP $\tau$ function.Comment: 12 pages, title change

Hatching Strategies in Monogenean (Platyhelminth) Parasites that Facilitate Host Infection

In parasites, environmental cues may influence hatching of eggs and enhance the success of infections. The two major endoparasitic groups of parasitic platyhelminths, cestodes (tapeworms) and digeneans (flukes), typically have high fecundity, infect more than one host species, and transmit trophically. Monogeneans are parasitic flatworms that are among the most host specific of all parasites. Most are ectoparasites with relatively low fecundity and direct life cycles tied to water. They infect a single host species, usually a fish, although some are endoparasites of amphibians and aquatic chelonian reptiles. Monogenean eggs have strong shells and mostly release ciliated larvae, which, against all odds, must find, identify, and infect a suitable specific host. Some monogeneans increase their chances of finding a host by greatly extending the hatching period (possible bet-hedging). Others respond to cues for hatching such as shadows, chemicals, mechanical disturbance, and osmotic changes, most of which may be generated by the host. Hatching may be rhythmical, larvae emerging at times when the host is more vulnerable to invasion, and this may be combined with responses to other environmental cues. Different monogenean species that infect the same host species may adopt different strategies of hatching, indicating that tactics may be more complex than first thought. Control of egg assembly and egg-laying, possibly by host hormones, has permitted colonization of frogs and toads by polystomatid monogeneans. Some monogeneans further improve the chances of infection by attaching eggs to the host or by retaining eggs on, or in, the body of the parasite. The latter adaptation has led ultimately to viviparity in gyrodactylid monogeneans

Area products for stationary black hole horizons

Area products for multi-horizon stationary black holes often have intriguing properties, and are often (though not always) independent of the mass of the black hole itself (depending only on various charges, angular momenta, and moduli). Such products are often formulated in terms of the areas of inner (Cauchy) horizons and outer (event) horizons, and sometimes include the effects of unphysical "virtual" horizons. But the conjectured mass-independence sometimes fails. Specifically, for the Schwarzschild-de Sitter [Kottler] black hole in (3+1) dimensions it is shown by explicit exact calculation that the product of event horizon area and cosmological horizon area is not mass independent. (Including the effect of the third "virtual" horizon does not improve the situation.) Similarly, in the Reissner-Nordstrom-anti-de Sitter black hole in (3+1) dimensions the product of inner (Cauchy) horizon area and event horizon area is calculated (perturbatively), and is shown to be not mass independent. That is, the mass-independence of the product of physical horizon areas is not generic. In spherical symmetry, whenever the quasi-local mass m(r) is a Laurent polynomial in aerial radius, r=sqrt{A/4\pi}, there are significantly more complicated mass-independent quantities, the elementary symmetric polynomials built up from the complete set of horizon radii (physical and virtual). Sometimes it is possible to eliminate the unphysical virtual horizons, constructing combinations of physical horizon areas that are mass independent, but they tend to be considerably more complicated than the simple products and related constructions currently being mooted in the literature.Comment: V1: 16 pages; V2: 9 pages (now formatted in PRD style). Minor change in title. Extra introduction, background, discussion. Several additional references; other references updated. Minor typos fixed. This version accepted for publication in PRD; V3: Minor typos fixed. Published versio

Edge State Tunneling in a Split Hall Bar Model

In this paper we introduce and study the correlation functions of a chiral one-dimensional electron model intended to qualitatively represent narrow Hall bars separated into left and right sections by a penetrable barrier. The model has two parameters representing respectively interactions between top and bottom edges of the Hall bar and interactions between the edges on opposite sides of the barrier. We show that the scaling dimensions of tunneling processes depend on the relative strengths of the interactions, with repulsive interactions across the Hall bar tending to make breaks in the barrier irrelevant. The model can be solved analytically and is characterized by a difference between the dynamics of even and odd Fourier components. We address its experimental relevance by comparing its predictions with those of a more geometrically realistic model that must be solved numerically.Comment: 13 pages, including 4 figures,final version as publishe