A New Spectrum for Nonlinear Operators in Banach Spaces

Given any continuous self-map f of a Banach space E over K (where K is R or C) and given any point p of E, we define a subset sigma(f,p) of K, called spectrum of f at p, which coincides with the usual spectrum sigma(f) of f in the linear case. More generally, we show that sigma(f,p) is always closed and, when f is C^1, coincides with the spectrum sigma(f'(p)) of the Frechet derivative of f at p. Some applications to bifurcation theory are given and some peculiar examples of spectra are provided.Comment: 23 pages, 3 figure

Bollito misto non-bollito

AbstractAn improvement in nutritional and tenderness values, among others, was achieved in a traditional northern Italian recipe, the so-called bollito misto (a mixture of boiled meat) by integrating low temperature cooking. This technique can be used within the traditional recipe and therefore considerably enhance the sensory and the nutritional properties of the dish. This process would get a much tastier meat, preserving meat quality and keeping sauce flavors. This recipe update clearly gives a step forward from a traditional formula to an improved version. These “new traditions” should give new hints to the normal food that people usually consume

Computed tomographic findings in three Pinschers affected by incomplete ossification of the humeral condyle

Incomplete ossification of the humeral condyle is a cause of forelimb lameness in dogs. Affected dogs are predisposed to humeral condylar fractures. Incomplete ossification of the humeral condyle has been reported in breeds such as Spaniel, Rottweiler, Labrador and Pug. Diagnosis is made by a radiographic or computed tomographic study of the elbow, while treatment includes the placement of a bone screw across the humeral condyle. This paper discusses the computed tomography findings of incomplete ossification of the humeral condyle in three Pinschers

Vertebral Formulae and Congenital Vertebral Anomalies in Guinea Pigs: A Retrospective Radiographic Study

The objectives of this retrospective study of 240 guinea pigs (148 females and 92 males) were to determine the prevalence of different vertebral formulae and the type and anatomical localization of congenital vertebral anomalies (CVA). Radiographs of the cervical (C), thoracic (Th), lumbar (L), sacral (S), and caudal (Cd) part of the vertebral column were reviewed. Morphology and number of vertebrae in each segment of the vertebral column and type and localization of CVA were recorded. In 210/240 guinea pigs (87.50%) with normal vertebral morphology, nine vertebral formulae were found with constant number of C but variable number of Th, L, and S vertebrae: C7/Th13/L6/S4/Cd5-7 (75%), C7/Th13/L6/S3/Cd6-7 (4.17%), C7/Th13/L5/S4/Cd6-7 (2.50%), C7/Th13/L6/S5/Cd5-6 (1.67%), C7/Th12/L6/S4/Cd6 (1.25%), C7/Th13/L7/S4/Cd6 (1.25%), C7/Th13/L7/S3/Cd6-7 (0.83%), C7/Th12/L7/S4/Cd5 (0.42%), C7/Th13/L5/S5/Cd7 (0.42%). CVA were found in 30/240 (12.5%) of guinea pigs, mostly as a transitional vertebra (28/30), which represents 100% of single CVA localised in cervicothoracic (n = 1), thoracolumbar (n = 22) and lumbosacral segments (n = 5). Five morphological variants of thoracolumbar transitional vertebrae (TTV) were identified. Two (2/30) guinea pigs had a combination of CVA: cervical block vertebra and TTV (n = 1) and TTV and lumbosacral transitional vertebra (LTV) (n = 1). These findings suggest that guinea pigs’ vertebral column displays more morphological variants with occasional CVA predominantly transitional vertebrae

Computed Tomography Evaluation of Normal Canine Abdominal Lymph Nodes: Retrospective Study of Size and Morphology According to Body Weight and Age in 45 Dogs

The morphological characteristics of the largest lymphatic vessels and lymph nodes of the body have been described through ultrasonography, although food and gas in the gastrointestinal tract can often have negative effects on the response of small abdominal structures. The aim of the study was to describe the size of normal abdominal lymph nodes (ALs) in dogs affected by disease, not including lymphadenomegaly or lymphadenopathy, and divided according to body weight and age. The ALs studied included the jejunal, medial iliac, portal, gastric, splenic, and pancreaticoduodenal lymph nodes. Statistical correlation considering body weight and age as continuous variables showed that all measurements of the ALs increased according to body weight changes (p p p < 0.05). Other characteristics (shape, attenuation, and enhancement) are subsequently reported. The resulting data can be used to categorize CT measurements of normal ALs displayed based on the body weight and age of the subjects. This study aimed to propose a new parameter of normalcy that may serve as a reference for the evaluation of infectious or neoplastic events