Integrable operators, ∂‾\overline{\partial}-Problems, KP and NLS hierarchy

We develop the theory of integrable operators $\mathcal{K}$ acting on a domain of the complex plane with smooth boundary in analogy with the theory of integrable operators acting on contours of the complex plane. We show how the resolvent operator is obtained from the solution of a $\overline{\partial}$-problem in the complex plane. When such a $\overline{\partial}$-problem depends on auxiliary parameters we define its Malgrange one form in analogy with the theory of isomonodromic problems. We show that the Malgrange one form is closed and coincides with the exterior logarithmic differential of the Hilbert-Carleman determinant of the operator $\mathcal{K}$. With suitable choices of the setup we show that the Hilbert-Carleman determinant is a $\tau$-function of the Kadomtsev-Petviashvili (KP) or nonlinear Schr\"odinger hierarchies.Comment: 24 pages, no figure

Soliton shielding of the focusing nonlinear Schrodinger equation

We consider a gas of $N$ solitons of the Focusing Nonlinear Schr\"odinger (FNLS) equation in the limit $N\to\infty$ with apoint spectrum chosen to interpolate a given spectral soliton density over a domain of the complex spectral plane. We call this class of initial data, deterministic soliton gas. We show that when the domain is a disc and the soliton density is an analytic function, then the corresponding deterministic soliton gas surprisingly yields the one-soliton solution with point spectrum the center of the disc. We call this effect {\it soliton shielding}. When the domain is an ellipse, the soliton shielding reduces the spectral data to the soliton density concentrating between the foci of the ellipse. The physical solution is asymptotically step-like oscillatory, namely, the initial profile is a periodic elliptic function in the negative $x$--direction while it vanishes exponentially fast in the opposite direction.Comment: 5 pages, add references and missprint correction

FRAGILITY FRACTURES OF THE SACRUM: A SILENT EPIDEMIC

Fragility fractures of the sacrum (FFS) are caused by low-energy trauma in the elderly population. Due to the nuanced symptomatology, many FFS remains unrecognized and the prevalence is underestimated. The clinical presentation varies, typically presenting with weightbearing low back pain without even remembering of a previous trauma. Radiographs are usually insufficient for the diagnosis and second level imaging modalities are required. In particular, magnetic resonance demonstrated the highest diagnostic accuracy. Treatment should aim to guarantee early mobilization and weightbearing, efficient pain relief and early discharge from the hospital to a proper facility for rehabilitation. Conservative treatment is reserved to non-displaced fractures with an adequate pain relief within one week allowing early mobilization. Otherwise, surgical treatment must be preferred. Nowadays, minimally invasive techniques, such as ileo-sacral screws or trans-sacral bar osteosynthesis, are safe and effective procedures and have overcome open procedures. In more complex patterns, with complete dissociation between the pelvic ring and the ilio-lumbar spine, spino-pelvic fixation is the procedure of choice

Endosteal plating for the treatment of malunions and nonunions of distal femur fractures

PurposeTo describe the surgical technique and the outcome of a case series of nonunion and malunion of distal femur fractures treated with an endosteal medial plate combined with a lateral locking plate and with autogenous bone grafting. MethodsWe retrospectively analyzed a series of patients with malunion or nonunion of the distal femur treated with a medial endosteal plate in combination with a lateral locking plate, in a period between January 2011 and December 2019, Database from chart review was obtained including all the clinical relevant available baseline data (demographics, type of fracture, mechanism of injury, time from injury to surgery, number of previous surgical procedures, type of bone graft, and type of lateral plate). Time to bone healing, limb alignment at follow-up and complications were documented. ResultsTen patients were included into the study: 7 male and 3 female with mean age of 48.3 years (range 21-67). The mechanism of trauma was in 8 cases a road traffic accident and in 2 cases a fall from height. According to AO/OTA classification 5 fractures were 33 A3, 3 were 33 C1, 1 was 33 C2 and 1 was 33 C3. The average follow up was 13.5 months. In all cases but one bony union was achieved. Bone healing was observed in average 3.3 months after surgery. No intraoperative or postoperative complications were reported. ConclusionA medial endosteal plate is a useful augmentation for lateral plate fixation in nonunion or malunion following distal femur fractures, particularly in cases of medial bone loss, severe comminution, or poor bone quality

Implant retention with serial debridement and use of antibiotic-loaded calcium sulfate beads in acute fracture-related infection (FRI) after pelvic ring or acetabular fractures: A retrospective case series of 7 cases

Background: The development of a pelvic wound infection in the presence of hardware after open reduction and internal fixation presents a clinical dilemma and there is little literature to aid in decision-making. The purpose of this study was to describe the possibility of debridement, antibiotic pearls and retention of the implant (DAPRI) procedure to eradicate the infection. Methods: Tumor-like debridement, antibiotic pearls and retention of the implant (DAPRI) aimed to remove the biofilm allowing a higher and prolonged local antibiotic concentration by using calcium sulfate antibiotic-added beads. Wound status, radiological signs of bone healing, gait and functional activity of the patient were evaluated. Results: Seven patients underwent this technique. The mean follow up time was nine months (range: 6 -16 months). Complete wound healing was achieved in all the patients with no major complications. Average time of bony union was 4.3 months (range: 3-6 months) with no need for implant removal. Conclusion: The DAPRI technique might represent a safe and more conservative treatment for management of early fracture-related infections (FRI) of the pelvis and acetabulum

Integrable operators, dbar-problems, KP and NLS hierarchy

We develop the theory of integrable operators K acting on a domain of the complex plane with smooth boundary in analogy with the theory of integrable operators acting on contours of the complex plane. We show how the resolvent operator is obtained from the solution of adbar-problem in the complex plane. When such adbar-problem depends on auxiliary parameters we define its Malgrange one form in analogy with the theory of isomonodromic problems. We show that the Malgrange one form is closed and coincides with the exterior logarithmic differential of the Hilbert–Carleman determinant of the operator . With suitable choices of the setup we show that the Hilbert–Carleman determinant is a τ-function of the Kadomtsev–Petviashvili (KP) or nonlinear Schrödinger hierarchies

Integrable operators, dbar-problems, KP and NLS hierarchy

We develop the theory of integrable operators K acting on a domain of the complex plane with smooth boundary in analogy with the theory of integrable operators acting on contours of the complex plane. We show how the resolvent operator is obtained from the solution of adbar-problem in the complex plane. When such adbar-problem depends on auxiliary parameters we define its Malgrange one form in analogy with the theory of isomonodromic problems. We show that the Malgrange one form is closed and coincides with the exterior logarithmic differential of the Hilbert–Carleman determinant of the operator . With suitable choices of the setup we show that the Hilbert–Carleman determinant is a τ-function of the Kadomtsev–Petviashvili (KP) or nonlinear Schrödinger hierarchies

Measurement of forces generated during distraction of growing-rods in early onset scoliosis

AIM: To measure the forces applied during distraction of growing-rods in early onset scoliosis (EOS), aimed at developing a motorized elongation device

The clinical relevance of early anti-adalimumab antibodies detection in rheumatoid arthritis, ankylosing spondylitis and psoriatic arthritis: A prospective multicentre study

OBJECTIVES: To evaluate the relevance of anti-adalimumab (anti-ADA) antibodies (Abs) and their relationship with clinical/laboratory features in rheumatoid arthritis (RA), ankylosing spondylitis (AS) and psoriatic arthritis (PsA). METHODS: Fifty-eight patients affected with RA, AS and PsA were prospectively enrolled. Clinical/laboratory characteristics, disease activity, anti-ADA, anti-nuclear (ANA), anti-double strand (ds)DNA, anti-extractable nuclear antigens (anti-ENA) and anti-phospholipid Abs (aPL) were evaluated at baseline, 4, 12 and 24 weeks of adalimumab treatment. RESULTS: Anti-ADA Abs were observed in 11/58 (19%) patients; they were detected within the 4th week of therapy in 90.9% of the positive subjects. Anti-ADA positivity was associated with significantly lower mean adalimumab serum levels (P<0.05). Treatment failure was observed in 20/58 (34.5%) patients and was significantly associated with anti-ADA Abs (P<0.05). Mean adalimumab serum levels were significantly lower in patients with treatment failure than in the responders one, both in the whole cohort (P<0.01) and in the group of anti-ADA positive patients (P<0.01). Adverse events happened more often in anti-ADA positive then in anti-ADA negative patients (27.3% vs 14.9%). CONCLUSIONS: Anti-ADA abs could be considered an early marker associated to a poor clinical response to adalimumab treatment. Routine ANA/anti-ENA/aPL monitoring did not reveal as useful tools to predict the development of anti-ADA abs