We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius number. For the case of symmetric semigroups with three generators of Frobenius numbers we found an exact formula, which in a sense is the sum of two Sylvester’s formulaes. We prove that the fraction of the symmetric semigroups is vanishing in the weak limit. 1. Definitions Take n mutually prime numbers a1, a2, ..., an...

OBJECTIVE Aneurysms originating from the proximal segment (A1) of the anterior cerebral artery are rare; however, because of their small size, the risk of injury of perforating arteries, and the location of the aneurysm in the surgical field, they are challenging to treat. We report on 15 patients with A1 aneurysms and review surgical views according to the direction of aneurysms. METHODS Fif...

Quaternionic representations of Coxeter (reflection) groups of ranks 3 and 4, as well as those of E8, have been used extensively in the literature. The present paper analyses such Coxeter groups in the Clifford Geometric Algebra framework, which affords a simple way of performing reflections and rotations whilst exposing more clearly the underlying geometry. The Clifford approach shows that the...

Annexin A1 is a multi functional molecule which is involved in inflammation, innate and adaptive immune systems, tumor progression and metastasis. We have previously showed the impaired tumor growth, metastasis, angiogenesis and wound healing in annexin A1 knockout mice. While tumor is a piece of heterogeneous mass including not only malignant tumor cells but also the stroma, the importance of ...

Heterogeneous ribonucleoprotein A1 (hnRNP A1) is crucial for regulating alternative splicing. Its integrated function within an organism has not, however, been identified. We generated hnRNP A1 knockout mice to study the role of hnRNP A1 in vivo The knockout mice, hnRNP A1-/-, showed embryonic lethality because of muscle developmental defects. The blood pressure and heart rate of the heterozygo...

In this paper, the existence of two A-type cyclins in the mouse is demonstrated. In the adult mouse, the expression of cyclin A1, which has greatest sequence identity with Xenopus cyclin A1, is restricted to germ cells. In contrast cyclin A2, which has greatest sequence identity with human cyclin A and Xenopus cyclin A2, is expressed in all tissues analysed. In order to explore the function of ...