Operative treatment of orthopedic complications in upper limb in children and adults with cerebral palsy

Introduction The benefits of surgical treatment of orthopaedic complications in the upper limb caused by cerebral palsy have been debated by some researchers. Secondary complications developed due to muscle spasticity and retraction are a serious obstacle to a significant improvement in healthrelated quality of life of CP patients. Objective To explore outcomes of CP patients who underwent surgical treatment at the Russian Ilizarov Scientific Centre “Restorative Traumatology and Orthopaedics” between 2014 and 2016. Material and methods Total 23 operative interventions were produced for 21 patients aged from 11 to 36 years (mean age of 16.6 years) using an authors’ technique. We used integral scales of the Gross Motor Function Classification System (GMFCS) and the Manual Ability Classification System (MACS). Classification systems intended for differential evaluation of upper extremity motor and functional impairment included Van Heest’s deformity assessment test, the House upper extremity assessment test and Gshwind and Tonkin classification. Results Spastic diplegia was diagnosed in 6 cases including 4 GMFCS III and 2 GMFCS IV. Manual ability was assessed as MACS IV in 3 cases and MACS V in 3. Fifteen patients with hemiparethic spastic CP underwent surgical treatment of upper limbs. Manual ability was assessed as MACS III in 4 cases, MACS IV in 8 and MACS V in 3. The use of the limb by the House’s scale showed level 1 in 2, level 2 in 5, level 3 in 10 and level 4 in 6 cases. The Gschwind and Tonkin classification for pronated forearm revealed level 1 in1, level 2 in 8, level 3 in 10 and level 4 in 4 cases. There was correlation between an extent of pronation contracture and impaired function of the thumb. Improved functional abilities of the upper limb, the cosmetic appearance and comfort with the use were recorded in all the cases. Conclusion Results of multilevel interventions on upper limbs in CP patients allow us to conclude that differential approach to the choice of technique and extent of surgery to ensure efficacious surgical treatment

Matrix KSGNS construction and a Radon–Nikodym type theorem

In this paper, we introduce the concept of completely positive matrix of linear maps on Hilbert A-modules over locally C∗-algebras and prove an analogue of Stinespring theorem for it. We show that any two minimal Stinespring representations for such matrices are unitarily equivalent. Finally, we prove an analogue of the Radon–Nikodym theorem for this type of completely positive n×n matrices. © 2017 Royal Dutch Mathematical Society (KWG

Matrix KSGNS construction and a Radon–Nikodym type theorem

In this paper, we introduce the concept of completely positive matrix of linear maps on Hilbert A-modules over locally C∗-algebras and prove an analogue of Stinespring theorem for it. We show that any two minimal Stinespring representations for such matrices are unitarily equivalent. Finally, we prove an analogue of the Radon–Nikodym theorem for this type of completely positive n×n matrices. © 2017 Royal Dutch Mathematical Society (KWG