Microbiological Shelf Life of Pasteurized Milk in Bottle and Pouch

Shelf life of pasteurized milk in Brazil ranges from 3 to 8 d, mainly due to poor cold chain conditions that prevail throughout the country and subject the product to repeated and/or severe temperature abuse. This study evaluated the influence of storage temperature on the microbiological stability of homogenized whole pasteurized milk (75 degrees C/15 s) packaged in high-density polyethylene (HDPE) bottle and low-density polyethylene (LDPE) pouch, both monolayer materials pigmented with titanium dioxide (TiO(2)). The storage temperatures investigated were 2, 4, 9, 14, and 16 degrees C. Microbiological evaluation was based on mesophilic and psychrotrophic counts with 7 log CFU/mL and 6 log CFU/mL, respectively, set as upper limits of acceptability for maintaining the quality of milk. The microbiological stability for pasteurized milk packaged in HDPE bottle and stored at 2, 4, 9, 14, and 16 degrees C was estimated at 43, 36, 8, 5, and 3 d, respectively. For milk samples packaged in LDPE pouch, shelf life was estimated at 37, 35, 7, 3, and 2 d, respectively. The determination of Q(10) and z values demonstrated that storage temperature has a greater influence on microbiological shelf life of pasteurized milk packaged in LDPE pouch compared to HDPE bottle. Based on the results of this study, HDPE bottle was better for storing pasteurized milk as compared to LDPE pouch.

THE POINCARE-BENDIXSON THEOREM ON THE KLEIN BOTTLE FOR CONTINUOUS VECTOR FIELDS

We present a version of the Poincare-Bendixson Theorem on the Klein bottle K(2) for continuous vector fields. As a consequence, we obtain the fact that K(2) does not admit continuous vector fields having a omega-recurrent injective trajectory.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Coincidence properties for maps from the torus to the Klein bottle

The authors study the coincidence theory for pairs of maps from the Torus to the Klein bottle. Reidemeister classes and the Nielsen number are computed, and it is shown that any given pair of maps satisfies the Wecken property. The 1-parameter Wecken property is studied and a partial negative answer is derived. That is for all pairs of coincidence free maps a countable family of pairs of maps in the homotopy class is constructed such that no two members may be joined by a coincidence free homotopy.