Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure

Cystadenocarcinoma simulating hemangiosarcoma of the salivary gland in dog: case report

Cystadenocarcinoma is regarded as a rare adenocarcinoma variant in animals. This work reports the case of an 8-year-old female Poodle dog with salivary gland cystadenocarcinoma with morphological characteristics similar to a hemangiosarcoma. Histopathological analysis showed a tumor mass with cystic formations containing a large amount of red blood cells. In order to distinguish these two entities, periodic acid Schiff (PAS) staining and immunohistochemical analysis were carried out with the use of cytokeratin AE1/AE3 (CK) and CD31-specific antibodies. Neoplastic cells were PAS-negative, CK-positive and CD31-negative confirming their epithelial origin. Based on the findings, the diagnosis of high grade cystadenocarcinoma was established

Glycogen-rich clear cell carcinoma of the feline mammary gland: case report

ABSTRACT The aim of this report is to describe the first histopathological, immunohistochemical, and clinical characteristics of a feline glycogen-rich clear cell carcinoma (GRCCC). A Persian queen was admitted with mammary gland tumors and underwent radical unilateral mastectomy. Overall survival was considered 33 days and death was due to clinical evolution of the disease. Microscopic evaluation demonstrated epithelial cells arranged in a predominantly solid pattern, tumor cells presented an ample, granular, and foamy clear cytoplasm, and moderate cellular pleomorfism. The presence of cytoplasmatic glycogen was confirmed through diastase digestion followed by PAS staining. Histopathological and histochemical findings lead to the diagnosis of GRCCC with regional metastases