Counting Quiver Representations over Finite Fields Via Graph Enumeration

Let $\Gamma$ be a quiver on n vertices $v_1, v_2, ..., v_n$ with $g_{ij}$ edges between $v_i$ and $v_j$, and let $\alpha \in \N^n$. Hua gave a formula for $A_{\Gamma}(\alpha, q)$, the number of isomorphism classes of absolutely indecomposable representations of $\Gamma$ over the finite field \F_q with dimension vector $\alpha$. Kac showed that $A_{\Gamma}(\bm{\alpha}, q)$ is a polynomial in q with integer coefficients. Using Hua's formula, we show that for each non-negative integer s, the s-th derivative of $A_{\Gamma}(\alpha,q)$ with respect to q, when evaluated at q = 1, is a polynomial in the variables $g_{ij}$, and we compute the highest degree terms in this polynomial. Our formulas for these coefficients depend on the enumeration of certain families of connected graphs.Comment: 16 page

Preliminary studies on growth and survival of Penaeus japonicus postlarvae fed with Tapes and commercial formula feeds

Growth and survival of P. japonicus postlarvae was studied using Tapes philippinarum and commercial formula feeds. After a 28-day feeding period, the highest survival rate of 100% was obtained in prawns receiving Diet-B, followed by those on Tapes Kyowa Hakko shrimp meal with survival rates of 80 and 76.7%, respectively. The lowest survival rate of 48.3% was obtained among postlarvae fed with squid meal. In this batch cannibalism was observed which resulted in low survival. Growth was highest in the postlarvae fed with Kyowa Hakko and mysid feeds. Diet-B gave a slightly lower weight increase but gave similar gain in length. The composition of the artificial diet, Diet-B, and growth and survival rates are tabulated

Survival rate of Penaeus monodon Fabricius larvae fed Chaetoceros sp. and bread yeast

An evaluation was made of the effects of Chaetoceros species, bread yeast and their combination on the survival of Penaeus monodon larvae. In general it was found that feeding with a combination of the 2 resulted in higher larval survival rates

Mixed-mode impedance and reflection coefficient of two-port devices

From the point of view of mixed-mode scattering parameters, Smm, a two-port device can be excited using different driving conditions. Each condition leads to a particular set of input reflection and input impedance coefficient definitions that should be carefully applied depending on the type of excitation and symmetry of the two-port device. Therefore, the aim of this paper is to explain the general analytic procedure for the evaluation of such reflection and impedance coefficients in terms of mixed-mode scattering parameters. Moreover, the driving of a two-port device as a one-port device is explained as a particular case of a two-port mixed-mode excitation using a given set of mixed-mode loads. The theory is applied to the evaluation of the quality factor, Q, of symmetrical and non- symmetrical inductors.Ministerio de Innovación y Ciencia TEC2010-14825/MIC, TEC2010-21484Junta de Andalucía TIC-253

Polyculture of milkfish (Chanos chanos) and tiger prawn (Penaeus monodon Fab.) with and without supplemental feeding

Twelve 1,000 m2 earthen ponds were used to compare the growth rates, survival and production of milkfish (Chanos chanos) and prawn (Penaeus monodon) in monoculture and polyculture systems in shallow brackishwater ponds and without supplemental feeding. The low production and survival rates obtained were attributed to the lack of natural food; the high salinity during the first month of culture could be one of the causes of the high mortality of prawn observed in both mono and polyculture systems. Although the results of the trial were not ecouraging, it is possible that high yields may be obtained from the combination of the 2 species given enough natural food and favourable water conditions

Observation of fractional quantum Hall effect in an InAs quantum well

The two-dimensional electron system in an InAs quantum well has emerged as a prime candidate for hosting exotic quasi-particles with non-Abelian statistics such as Majorana fermions and parafermions. To attain its full promise, however, the electron system has to be clean enough to exhibit electron-electron interaction phenomena. Here we report the observation of fractional quantum Hall effect in a very low disorder InAs quantum well with a well-width of 24 nm, containing a two-dimensional electron system with a density $n=7.8 \times 10^{11}$ cm$^{-2}$ and low-temperature mobility $1.8 \times 10^6$ cm$^2$/Vs. At a temperature of $\simeq35$ mK and $B\simeq24$ T, we observe a deep minimum in the longitudinal resistance, accompanied by a nearly quantized Hall plateau at Landau level filling factor $\nu=4/3$

Arithmetic harmonic analysis on character and quiver varieties

We present a conjecture generalizing the Cauchy formula for Macdonald polynomials. This conjecture encodes the mixed Hodge polynomials of the character varieties of representations of the fundamental group of a Riemann surface of genus g to GL_n(C) with fixed generic semi-simple conjugacy classes at k punctures. Using the character table of GL_n(F_q) we calculate the E-polynomial of these character varieties and confirm that it is as predicted by our main conjecture. Then, using the character table of gl_n(F_q), we calculate the E-polynomial of certain associated comet-shaped quiver varieties, the additive analogues of our character variety, and find that it is the pure part of our conjectured mixed Hodge polynomial. Finally, we observe that the pure part of our conjectured mixed Hodge polynomial also equals certain multiplicities in the tensor product of irreducible representations of GL_n(F_q). This implies a curious connection between the representation theory of GL_n(F_q) and Kac-Moody algebras associated with comet-shaped, typically wild, quivers.Comment: To appear in Duke Math. Journal + a section with examples is adde