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Connective or muscular tissue crossing the axilla is named axillary arch (of Langer). It is known to complicate axillary surgery and to compress nerves and vessels transiting from the axilla to the arm. Our study aims at systematically researching the frequency, insertions, tissue composition and dimension of axillary arches in a large cohort of individuals with regard to gender and bilaterality. In addition, it aims at evaluating the ability of axillary arches to cause compression of the axillary neurovascular bundle. Four hundred axillae from 200 unembalmed and previously unharmed cadavers were investigated by careful anatomical dissection. Identified axillary arches were examined for tissue composition and insertion. Length, width and thickness were measured. The relation of the axillary arch and the neurovascular axillary bundle was recorded after passive arm movements. Twenty‐seven axillae of 18 cadavers featured axillary arches. Macroscopically, 15 solely comprised muscular tissue, six connective tissue and six both. Their average length was 79.56 mm, width 7.44 mm and thickness 2.30 mm. One to three distinct insertions were observed. After passive abduction and external rotation of the arm, 17 arches (63%) touched the neurovascular axillary bundle. According to our results, 9% of the Central European population feature an axillary arch. Approximately 50% of it bilaterally. A total of 40.74% of the arches have a thickness of 3 mm or more and 63% bear the potential of touching or compressing the neuromuscular axillary bundle upon arm movement. [ABSTRACT FROM AUTHOR]

We study the effects of imposing linear relations within modules of matrices on average sizes of kernels. The relations that we consider can be described combinatorially in terms of partial colourings of grids. The cells of these grids correspond to positions in matrices and each defining relation involves all cells of a given colour. We prove that imposing such relations arising from 'admissible' partial colourings has no effect on average sizes of kernels over finite quotients of discrete valuation rings. This vastly generalises the known fact that average sizes of kernels of general square and traceless matrices of the same size coincide over such rings. As a group‐theoretic application, we explicitly determine zeta functions enumerating conjugacy classes of finite p$p$‐groups derived from free class‐3$\hskip.001pt 3$‐nilpotent groups for p⩾5$p\geqslant 5$. [ABSTRACT FROM AUTHOR]

Introduction/Aims: For cubital tunnel syndrome, the avoidance of predisposing arm positions and the use of elbow splints are common conservative treatment options. The rationale is to prevent excessive stretching and compression of the nerve in the cubital tunnel, as this mechanical stress impedes intraneural perfusion. Data regarding those upper extremity postures to avoid, or whether elbow flexion alone is detrimental, are inconsistent. This study aimed to assess perfusion and size changes of the cubital tunnel during different postures in an experimental cadaver setup. Methods: Axillary arteries in 30 upper extremities of fresh cadavers were injected with ultrasound contrast agent. High‐resolution ultrasound of the cubital tunnel was performed during five different arm postures that gradually increased tension on the ulnar nerve and caused cubital tunnel narrowing. Contrast enhancement within the tunnel was measured to quantify perfusion. Cubital tunnel cross‐sectional area was measured to detect compression. Results: Increasing tension significantly reduced perfusion. When isolated, neither shoulder elevation, elbow flexion, pronation, nor extension of wrist and fingers impaired perfusion. However, combining two or more of these postures led to significant decreases. Significant narrowing of the cubital tunnel was seen in full elbow flexion and shoulder elevation. Discussion: Combinations of some upper extremity joint positions reduce nerve perfusion, but isolated elbow flexion does not have a significant impact. We hypothesize that elbow splints alone may not influence cubital tunnel perfusion but may only prevent direct compression of the ulnar nerve. Advising patients about upper extremity postures that should be avoided may be more effective. [ABSTRACT FROM AUTHOR]

Abstract: Let O be a compact discrete valuation ring of characteristic 0. Given a module M of matrices over O, we study the generating function encoding the average sizes of the kernels of the elements of M over finite quotients of O. We prove rationality and establish fundamental properties of these generating functions and determine them explicitly for various natural families of modules M. Using p‐adic Lie theory, we then show that special cases of these generating functions enumerate orbits and conjugacy classes of suitable linear pro‐ p groups. [ABSTRACT FROM AUTHOR]

We develop techniques for computing zeta functions associated with nilpotent groups, not necessarily associative algebras, and modules, as well as Igusa-type zeta functions. At the heart of our method lies an explicit convex-geometric formula for a class of p-adic integrals under non-degeneracy conditions with respect to associated Newton polytopes. Our techniques prove to be especially useful for the computation of topological zeta functions associated with algebras, resulting in the first systematic investigation of their properties. [ABSTRACT FROM AUTHOR]