A new Q-matrix in the Eight-Vertex Model

We construct a $Q$-matrix for the eight-vertex model at roots of unity for crossing parameter $\eta=2mK/L$ with odd $L$, a case for which the existing constructions do not work. The new $Q$-matrix \Q depends as usual on the spectral parameter and also on a free parameter $t$. For $t=0$ \Q has the standard properties. For $t\neq 0$, however, it does not commute with the operator $S$ and not with itself for different values of the spectral parameter. We show that the six-vertex limit of \Q(v,t=iK'/2) exists.Comment: 10 pages section on quasiperiodicity added, typo corrected, published versio

The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity η=2mKN\eta = \frac{2m K}{N} for odd N

Following Baxter's method of producing Q_{72}-operator, we construct the Q-operator of the root-of-unity eight-vertex model for the crossing parameter $\eta = \frac{2m K}{N}$ with odd $N$ where Q_{72} does not exist. We use this new Q-operator to study the functional relations in the Fabricius-McCoy comparison between the root-of-unity eight-vertex model and the superintegrable N-state chiral Potts model. By the compatibility of the constructed Q-operator with the structure of Baxter's eight-vertex (solid-on-solid) SOS model, we verify the set of functional relations of the root-of-unity eight-vertex model using the explicit form of the Q-operator and fusion weights of SOS model.Comment: Latex 28 page; Typos corrected, minor changes in presentation, References added and updated-Journal versio

Strawberries for Ice Cream Manufacture

The increasing demand for food products flavored with true fruits and fruit juices is of special interest to the ice cream manufacturer. Many cold packed fruits are available on the market although in numerous cases fruits are sold as cold packed which are actually preserved by the addition of various preservatives such as sodium benzoate

COMPLETE SOLUTION OF THE XXZ-MODEL ON FINITE RINGS. DYNAMICAL STRUCTURE FACTORS AT ZERO TEMPERATURE.

The finite size effects of the dynamical structure factors in the XXZ-model are studied in the euclidean time $(\tau)$-representation. Away from the critical momentum $p=\pi$ finite size effects turn out to be small except for the large $\tau$ limit. The large finite size effects at the critical momentum $p=\pi$ signal the emergence of infrared singularities in the spectral $(\omega)$-representation of the dynamical structure factors.Comment: PostScript file with 12 pages + 11 figures uuencoded compresse

Injunction Against Prosecution of Divorce Actions in Other States

Aims: The formation scenario of extended counter-rotating stellar disks in galaxies is still debated. In this paper, we study the S0 galaxy IC 719 known to host two large-scale counter-rotating stellar disks in order to investigate their formation mechanism. Methods: We exploit the large field of view and wavelength coverage of the Multi Unit Spectroscopic Explorer (MUSE) spectrograph to derive two-dimensional (2D) maps of the various properties of the counter-rotating stellar disks, such as age, metallicity, kinematics, spatial distribution, the kinematical and chemical properties of the ionized gas, and the dust map. Results: Due to the large wavelength range, and in particular to the presence of the Calcium Triplet \u3bb\u3bb8498, 8542, 8662 \uc5 (CaT hereafter), the spectroscopic analysis allows us to separate the two stellar components in great detail. This permits precise measurement of both the velocity and velocity dispersion of the two components as well as their spatial distribution. We derived a 2D map of the age and metallicity of the two stellar components, as well as the star formation rate and gas-phase metallicity from the ionized gas emission maps. Conclusions: The main stellar disk of the galaxy is kinematically hotter, older, thicker and with larger scale-length than the secondary disk. There is no doubt that the latter is strongly linked to the ionized gas component: they have the same kinematics and similar vertical and radial spatial distribution. This result is in favor of a gas accretion scenario over a binary merger scenario to explain the origin of counter-rotation in IC 719. One source of gas that may have contributed to the accretion process is the cloud that surrounds IC 719

The quality of butter made from Vacuum-pasteurized and Vat-pasteurized lots of the same creams

During the past few years a large amount of butter manufactured in the Middle West has been criticised for weedy flavors. This increase in weedy flavors unquestionably has resulted from a number of successive dry years. Some of the most common weed defects in this section are wild onion (Allium cernuum) , ragweed (Ambrosia artemisiifolia L.) and dog fennel (Anthemis cotula L.). The defects resulting from skunk cabbage (Symplocarpus foetidus (L.)), french weed (Thalaspi arvense L.) and peppergrass (Lepidium verginicum L.) (2) are apparently less common. Feed flavors are more important than weed flavors in this section. It has been recognized for some time that silage and alfalfa hay, when fed to dairy herds in fairly large quantities, cause definite milk flavors that are apparent in the butter. Changes in feeding procedures designed to lower fat production costs have, in many cases, increased the problems of the buttermaker. Sweet clover, rye pasture, wheat pasture, soybean hay and cane silage, flavor milk to such an extent that they affect the quality of the resulting butter

XXZ Bethe states as highest weight vectors of the sl2sl_2 loop algebra at roots of unity

We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at roots of unity is a highest weight vector of the $sl_2$ loop algebra, for some restricted sectors with respect to eigenvalues of the total spin operator $S^Z$, and evaluate explicitly the highest weight in terms of the Bethe roots. We also discuss whether a given regular Bethe state in the sectors generates an irreducible representation or not. In fact, we present such a regular Bethe state in the inhomogeneous case that generates a reducible Weyl module. Here, we call a solution of the Bethe ansatz equations which is given by a set of distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}.Comment: 40pages; revised versio

Critical Behavior of an Ising System on the Sierpinski Carpet: A Short-Time Dynamics Study

The short-time dynamic evolution of an Ising model embedded in an infinitely ramified fractal structure with noninteger Hausdorff dimension was studied using Monte Carlo simulations. Completely ordered and disordered spin configurations were used as initial states for the dynamic simulations. In both cases, the evolution of the physical observables follows a power-law behavior. Based on this fact, the complete set of critical exponents characteristic of a second-order phase transition was evaluated. Also, the dynamic exponent $\theta$ of the critical initial increase in magnetization, as well as the critical temperature, were computed. The exponent $\theta$ exhibits a weak dependence on the initial (small) magnetization. On the other hand, the dynamic exponent $z$ shows a systematic decrease when the segmentation step is increased, i.e., when the system size becomes larger. Our results suggest that the effective noninteger dimension for the second-order phase transition is noticeably smaller than the Hausdorff dimension. Even when the behavior of the magnetization (in the case of the ordered initial state) and the autocorrelation (in the case of the disordered initial state) with time are very well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale.Comment: 10 figures, 4 tables and 14 page

Observations on the counting of bacteria in ice cream by the plate method

The development of official or standard methods for various types of laboratory examinations represents a distinct advance from the standpoint of the usefulness of the results obtained. The standard methods for the bacteriological analysis of milk have made it possible to compare, on a satisfactory basis, the results secured in different laboratories and, undoubtedly, have been a factor in extending the use of bacterial counts for the control of milk supplies. The procedure at present required by Standard Methods of Milk Analysis1 for the macroscopic colony count on milk has been developed over a period of years. It is generally recognized that there are other media and incubation conditions which would give higher counts but none of these is at present standard because of the desire to employ a procedure which is easily carried out and comparatively inexpensive