Computed tomography and magnetic resonance diagnosis of variations in the anatomical location of the major salivary glands in 1680 dogs and 187 cats

During assessment of routine clinical magnetic resonance imaging (MRI) of the heads of dogs, variations in the location of mandibular and zygomatic salivary glands (SGs) were observed incidentally. The aims of this retrospective study were to describe anatomical variations of the major SGs found on MRI and computed tomography (CT) studies of the head in dogs and cats and to investigate possible clinical relevancy. No anatomical variation of the SGs was seen in cats, but in dogs, although variation of the parotid SG was not identified, that of the mandibular SG was found in 33/1680 animals (2%), either unilaterally (6/33 right-sided, 13/33 left-sided) or bilaterally (14/33). The Border terrier breed (19/33, 58%) was over-represented. Each atypically located mandibular SG was positioned medial to the digastric muscle and rostral to the retropharyngeal lymph node. The sublingual glands were difficult to delineate from the mandibular glands. Anatomical variation of one zygomatic gland (3/4 left-sided) was identified in four small-breed dogs (0.2%). Each atypically located zygomatic gland was tilted at the ventrorostral aspect of the masseter muscle underneath the skin surface. MRI and CT characteristics were not different between typically and atypically located SGs. None of the dogs had clinical signs related with SG disease. It was concluded that, with suspected breed predispositions, incidental unilateral or bilateral anatomical variations of mandibular and zygomatic SGs can be encountered in dogs and an awareness of these possible variations may be important in pre-surgical planning

Hybrid computer techniques for solving partial differential equations

Techniques overcome equipment limitations that restrict other computer techniques in solving trivial cases. The use of curve fitting by quadratic interpolation greatly reduces required digital storage space

Electrodynamics with radiation reaction

The self force of electrodynamics is derived from a scalar field. The resulting equation of motion is free of all of the problems that plague the Lorentz Abraham Dirac equation. The age-old problem of a particle in a constant field is solved and the solution has intuitive appeal.Comment: 5 page

SOCIAL COST OF THE DAIRY PRICE SUPPORT PROGRAM

Agricultural and Food Policy,

Moment bounds for the Smoluchowski equation and their consequences

We prove uniform bounds on moments X_a = \sum_{m}{m^a f_m(x,t)} of the Smoluchowski coagulation equations with diffusion, valid in any dimension. If the collision propensities \alpha(n,m) of mass n and mass m particles grow more slowly than (n+m)(d(n) + d(m)), and the diffusion rate d(\cdot) is non-increasing and satisfies m^{-b_1} \leq d(m) \leq m^{-b_2} for some b_1 and b_2 satisfying 0 \leq b_2 < b_1 < \infty, then any weak solution satisfies X_a \in L^{\infty}(\mathbb{R}^d \times [0,T]) \cap L^1(\mathbb{R}^d \times [0,T]) for every a \in \mathbb{N} and T \in (0,\infty), (provided that certain moments of the initial data are finite). As a consequence, we infer that these conditions are sufficient to ensure uniqueness of a weak solution and its conservation of mass.Comment: 30 page

Radiographic measurements of the trachea in domestic short haired and Persian cats

Tracheal diameter can be assessed from a thoracic radiograph, with assessment of tracheal diameter in dogs based on ratios between tracheal diameter and a skeletal measurement – however reference ranges are not available for the cat. Tracheal narrowing may cause significant clinical problems, although tracheal hypoplasia in dogs may be clinically silent, and is rarely reported in cats (both mesati- and brachycephalic). The tracheal diameter and trachea:thoracic inlet and trachea:rib ratios were calculated for populations of Domestic Short Haired (DSH) (n=68) and Persian (n=40) cats. This gave reference ranges for radiographic tracheal measurements in these breeds. It is proposed that the tracheal diameter in a normal DSH cat should be 18% of the diameter of the thoracic inlet, and compared to 20% in Persian cats