Characteristic estimation of differential polynomials

In this paper, we give the characteristic estimation of a meromorphic function f with the differential polynomials $f^{l}(f^{(k)})^{n}$ f l ( f ( k ) ) n and obtain that $$\begin{aligned} T(r,f)\leq M\overline{N} \biggl(r,\frac{1}{f^{l}(f^{(k)})^{n}-a} \biggr)+S(r,f) \end{aligned}$$ T ( r , f ) ≤ M N ‾ ( r , 1 f l ( f ( k ) ) n − a ) + S ( r , f ) holds for $M=\min \{\frac{1}{l-2},6\}$ M = min { 1 l − 2 , 6 } , integers $l(\geq 2)$ l ( ≥ 2 ) , $n(\geq 1)$ n ( ≥ 1 ) , $k(\geq 1)$ k ( ≥ 1 ) , and a non-zero constant a. This quantitative estimate is an interesting and complete extension of earlier results. The value distribution of a differential monomial of meromorphic functions is also investigated.

Reading the footprints of the B-meson flavor anomalies

Motivated by the recent LHCb announcement of a 3.1σ violation of lepton- flavor universality in the ratio RK = Γ(B → Kμ+μ−)/Γ(B → Ke+e−), we present an updated, comprehensive analysis of the flavor anomalies seen in both neutral-current (b → sℓ+ℓ−) and charged-current (b → $$ c\tau \overline{\nu} $$ cτ ν ¯ ) decays of B mesons. Our study starts from a model-independent effective field-theory approach and then considers both a simplified model and a UV-complete extension of the Standard Model featuring a vector leptoquark U1 as the main mediator of the anomalies. We show that the new LHCb data corroborate the emerging pattern of a new, predominantly left-handed, semileptonic current-current interaction with a flavor structure respecting a (minimally) broken U(2)5 flavor symmetry. New aspects of our analysis include a combined analysis of the semileptonic operators involving tau leptons, including in particular the important constraint from Bs-$$ {\overline{B}}_s $$ B ¯ s mixing, a systematic study of the effects of right-handed leptoquark couplings and of deviations from minimal flavor-symmetry breaking, a detailed analysis of various rare B-decay modes which would provide smoking-gun signatures of this non-standard framework (LFV decays, di-tau modes, and B → K(*)$$ \nu \overline{\nu} $$ ν ν ¯ ), and finally an updated analysis of collider bounds on the leptoquark mass and couplings.

Brachioradialis Muscle Tendon Transposition in Extensor Pollicis Longus Reconstruction: Anatomical Study and a New Surgical Approach

Background Complete extension of the thumb and activation of the extensor pollicis longus (EPL) tendon are fundamental to ensure maximum function. Many EPL repair techniques are described in the literature. Methods The authors present an alternative technique using the brachioradialis (BR) tendon. Thirty patients with injuries of the EPL tendon in zone 8 were studied. In all cases, neither direct suture repair nor traditional tendon transfer was possible. Results Thumb extension was restored in all patients with satisfactory extension recovery. All patients achieved excellent extension; good functional results were observed in 2 cases, and in 1 case satisfactory results were achieved using the Geldmacher assessment and the Kapandji assessment. The overall results were rated as excellent, good, fair, or poor according to the Quick Disabilities of the Arm, Shoulder, and Hand Scale. Discussion The BR tendon was suitable to treat all cases, in particular injuries occurring near Lister’s tubercle, due to its appropriate length for tenorrhaphy albeit with a short distal head.

Investigation of Knee Arthrokinematic Changes Before and After Reconstruction of Anterior Cruciate Ligament: A Systematic Review

Objective: The aim of this study was to investigation the arthrokinematic changes of the knee before and after the reconstruction of the anterior cruciate ligament and also to examine these changes after a period of rehabilitation exercises. Methods: In this systematic review study search was conducted in online databases of, Ebsco, Scopus, Web of Science, PEDro, Google scholar, PubMed, Science Direct, CINAHL, SPORTDiscus, EMBASE and MEDLINE from 1970 to 2020 . And keywords related to the topic were used to search for articles. Results: According to the search method, 127 articles were found that considering the inclusion criteria, 20 articles (20 English and 0 Persian) were selected. The results showed that the anterior glide in the injured knee increased significantly compared to the healthy knee. However, this arthrokinematic change was more observed in the medial epicondyle than in the lateral epicondyle. Also, among the articles, it is agreed that the highest arthrokinematic difference observed in injured persons compared to healthy individuals occurred between 15 degrees of flexion and complete extension of the knee. And Finally, the findings showed that the arthrokinematics of the knee after reconstruction, were more similar with before the reconstruction it up to a healthy knee. And also the arthrokinematic movements of the reconstructed ligament, even after a rehabilitation period, were more similar to the un reconstructed knee than to the healthy knee. Conclusion: According to the results of previous articles and being more obvious change of anterior glide, medial glide and to some extent external rotation in persons with anterior cruciate ligament rupture as well as no difference arthrokinematic knee before and after reconstruction of the anterior cruciate ligament, it seems important that rehabilitation programs and anterior cruciate ligament reconstruction techniques be planned in order to correct or prevent arthrokinematic changes are mentioned.

Subintermeniscal Ligament Pullout Suture Technique for Anterior Cruciate Ligament Avulsion Fracture Fixation—AIIMS Technique

Many methods have been described, including pullout suture technique, for arthroscopic fixation of displaced tibial eminence fracture. We are describing our technique of pullout suture, which is a modification of previously described techniques. We passed two sutures arthroscopically through anterior cruciate ligament (ACL) just above the avulsed fragment and then pulled them out through medial and lateral bone tunnel in anterior aspect of crater in tibial plateau. The third suture passed through ACL was pulled out anteriorly under the transverse intermeniscal ligament through a submeniscal route. All sutures were tied under tension to a screw post placed on the anterior tibia after reducing the avulsed bone fragment. Our technique provides good reduction and even overreduction of the fragment. It also provides good initial fixation strength to work against displacing forces even in small and comminuted bony fragment. This is helpful for achieving adequate stability of knee, complete extension of knee, early rehabilitation, and quicker recovery.

On topologies related to the extension of the Lebesgue measure

The aim of this paper is the investigation of topologies generated by operators related to a complete extension of the Lebesgue measure over the real line. Some properties of such topologies provide their structure and separation axioms.

Functional Outcomes of Revision Osteosynthesis after Failure of Surgical Treatment of Patellar Fractures

Patellar fractures account for approximately 1% of all skeletal fractures. These fractures are rare; however, because of the crucial function of the patella in the extensor mechanism of the knee, they may lead to serious impairment. New data are revealing functional impairment remains common even with improved surgical techniques. The aim of this study was to assess the functional outcomes of patients after revision surgery in cases of secondary fracture dislocation or persistent articular incongruity. This study included 16 patients with a mean age of 51.8 years (range: 16–85 years) with a mean follow-up of 35.1 months. According to the AO/OTA classification, 15 patients had a C-type fracture, including 10 patients with C3 fracture. Thirteen patients were initially treated with tension band wiring via K-wires or cannulated screws. Revision surgery was performed because of persistent articular incongruity in five patients and secondary fracture dislocation or refracture in 11 patients. We analyzed pain (visual analog scale [0–10]), satisfaction, range of motion (ROM), Böstman's score, Lysholm's score, and knee injury and osteoarthritis outcome score (KOOS) after revision surgery and could extract follow-up data from 15 patients. Mean pain score at rest was 0.57 (range: 0–3.5) and on exertion 2.79 (range: 0–8). The measurement of the ROM of the affected knee compared with that of the opposite knee revealed complete extension. Mean flexion was 123 degrees, in the corresponding knee it was 136 degrees (p = 0.05). The mean postoperative Böstman's and Lysholm's scores were 25.11 (good, maximum: 30) and 78.67 (moderate, maximum: 100), respectively. KOOS was as follows: symptoms, 66.8 points; pain, 77.55 points; activity of daily living (ADL), 75.67 points; and quality of life, 56.25 points. The results of this study suggested that early revision surgery after failure of primary osteosynthesis with secondary anatomic reconstruction and good radiological results leads to satisfactory functional outcomes with persistent functional deficits.

Proposal for Treatment of Severe Dupuytren Disease in 2 Steps: Progressive Distraction With External Fixator and Collagenase - A Preliminary Case Series

Background: We want to describe a treatment for advanced Dupuytren disease using a spanning external fixator (EF) applied dorsally to produce progressive extension, followed by collagenase injection. Methods: Between October 2014 and September 2016, a total of 22 fingers from 18 patients were treated with an EF. The devices were implanted under local anesthesia, and the patients were instructed to gradually extend the hinge to gain a progressive extension. The EF was removed in an outpatient clinic setting after obtaining a complete extension of the treated joint in a mean of 19 days (range 15-22 days), and a collagenase injection was performed in the residual cord after a mean of 20 days (18-24 days), followed by splinting. Results: All patients were evaluated at an average follow-up of 14 months (range 3-23 months): the total average residual flexion deformity was 9.7° (range 0°-19°) with a correction of 107.2° (range 94°-138°), the average flexion deformity of the proximal interphalangeal joint was 7.4° (range 0°-15°) with a correction of 64.4° (range 46°-92°), and the average flexion deformity of the metatarsophalangeal joint was 2.4° (range 0°-9°) with a correction of 42.8° (range 15°-59°). No complications were reported in relation to EF treatment. Two cases of cutaneous laceration after collagenase injection were observed, neither of which required any additional treatment. Conclusions: All patients obtained a regression from 2 to 3 stages in disease severity only with EF. We had no report of complications due to the device. After collagenase injection and splinting, we obtained further finger extension with a mean total residual flexion deformity of 9.7° at 14-month follow-up.

Minimally invasive thread trigger digit release: a preliminary report on 34 digits of the adult hands

The trigger finger release was performed in 34 digits (11 thumbs and 23 fingers) of 24 patients through the thread transecting technique with the tip-to-tip approach, in which a 22-gauge needle inserts into a 18-gauge needle when both needles are inside the hand, guiding the 22-gauge needle to exit the hand at the same access point of 18-gauge needle. We prospectively evaluated the effectiveness and functional recovery of these patients. In all 34 digits, triggering and locking were resolved, and complete extension and flexion occurred immediately following the release. There were no complications, such as incomplete release, neurovascular or flexor tendon or A2 pulley injury, infection, or tendon bow-stringing. Patients did not require prescription pain medications. Most patients used their hands to meet their basic living needs the same day of the procedure. The hand function evaluated with the Quick Disabilities of the Arm, Shoulder and Hand questionnaire, and scored 4 within 3 months. Level of evidence: II

Change in mechanical axis alignment highly correlates with increased limb loading after total knee arthroplasty

Mechanical axis of the lower limb assessed in standing long-leg radiographs was demonstrated to change within the first three postoperative months after total knee arthroplasty (TKA). The underlying mechanism including the influence of limb loading for the change in mechanical axis alignment after TKA has not been evaluated so far. Mechanical axis of the lower limb and limb loading were evaluated in 115 patients 10 days and 12 weeks after TKA. Mechanical axis was measured in standing long-leg radiographs while limb loading was simultaneously assessed using a scale. Absolute and relative limb loading with their correlation to the mechanical axis were calculated. Mechanical axis in patients with postoperative complete extension (n = 100) changed from an initial -0.82° ± 1.9° valgus alignment to a varus axis of +0.6° ± 1.5 (p < 0.01). This change in alignment was accompanied by an increased limb loading from 89.9% 10.7% to 93.0% 7.0% (p < 0.01). The mechanical axis highly/significantly correlated with relative limb loading in both measurements (r = 0.804, p < 0.001 respectively r = 0.562, p < 0.001). These alterations and distinctions were much more pronounced in patients with postoperative incomplete extension. Mechanical axis of the leg significantly changes while limb loading increases within the first three postoperative months after TKA. The postoperative alignment highly correlates with the loading of the lower limb. Therefore, the actual mechanical axis can only be assessed at physiological limb loading in long-leg radiographs at complete extension with full weight bearing.