안내3 - 표준화를 통한 어항 내 안전시설물 설치확대 촉진

정영복,Jeong, Yeong-Bok 한국어촌어항협회 2014 어항어장 Vol.106 No.-

가토 반월상연골 손상후 치유과정의 조직학적 관찰

정영복,이은우 중앙대부설한국의과학연구소 1982 한국의과학 Vol.14 No.2

An extremal problem of holomorphic functions in the complex plane

정영복,박병일 호남수학회 2013 호남수학학술지 Vol.35 No.4

In this paper, we study on a higher order extremal problem relating the Ahlfors map associated to the pair of a finitely connected domain in the complex plane and a point there. We show the power of the Ahlfors map with some error term which is conformally equivalent maximizes any higher order derivative of holomorphic functions at the given point in the domain.

THE GREEN FUNCTION AND THE SZEGO KERNEL FUNCTION

정영복 호남수학회 2014 호남수학학술지 Vol.36 No.3

In this paper, we express the Green function in terms of the classical kernel functions in potential theory. In particular, we obtain a formula relating the Green function and the Szegő kernel function which consists of only the Szegő kernel function in a C∞ smoothly bounded finitely connected domain in the complex plane.

Toeplitz Operators on Hardy and Bergman spaces over bounded domains in the plane

정영복,나희경 호남수학회 2017 호남수학학술지 Vol.39 No.2

In this paper, we show that algebraic properties of Toeplitz operators on both Bergman spaces and Hardy spaces on the unit disc essentially generalizes on arbitrary bounded domains in the plane. In particular, we obtain results for the uniqueness property and commuting problems of the Toeplitz operators on the Hardy and the Bergman spaces associated to bounded domains.

Special orthonormal basis for L2 functions on the unit circle

정영복 대한수학회 2017 대한수학회보 Vol.54 No.6

We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials.

ORTHONORMAL BASIS FOR THE BERGMAN SPACE

정영복,나희정 호남수학회 2014 호남수학학술지 Vol.36 No.4

We construct an orthonormal basis for the Bergman space associated to a simply connected domain. We use the orthonormal basis for the Hardy space consisting of the Szeg\H o kernel and the Riemann mapping function and rewrite their area integrals in terms of arc length integrals using the complex Green's identity. And we make a note about the matrix of a Toeplitz operator with respect to the orthonormal basis constructed in the paper.

UNIQUENESS OF TOEPLITZ OPERATOR IN THE COMPLEX PLANE

정영복 호남수학회 2009 호남수학학술지 Vol.31 No.4

We prove using the Szego kernel and the Garabedian kernel that a Toeplitz operator on the boundary of C∞ smoothly bounded domain associated to a smooth symbol vanishes only when the symbol vanishes identically. This gives a generalization of previous results on the unit disk to more general domains in the plane.

만성 전방십자인대 손상의 치료

정영복 대한슬관절학회 1989 대한슬관절학회지 Vol.1 No.1

A complete tear of the anterior cruciate ligament represent the indication of a clinical syndrome characterized by a continum of functional disability. There is debate about the indications for non-operative treatment or reconstruction of chronic A.C.L. deficient knee. And also, there is controversy about intra-articular reconstruction and extra-articular reconstruction or combine of these two methods. The indication of intra-articular reconstructive surgery for the chronic A.C.L. deficient knee are; 1st, patients who have functional disability and who are unwilling to alter their athletic lifestyle. 2nd, group of patients includes those who are having symptoms even with routine activities of daily living. If the articular cartilage is already worn in areas to subchondral bone (grade IV), we have to advise him to limit all activities. We believe there is little benefit to be gained from intraarticular ligament reconstruction at this point. A more simplified lateral extraarticular substitution procedure that has less morbidity is still warranted if symptoms of giving way occur with daily activities. The patients who have over 40 years of age, and relatively less activity, in this case, more simple extra-articular A.C.L. substitute will be done. Intra-articular reconstructian is contraindicated if there are already moderate arthritic changes present. The substitute of A.C.L. will function more as a $quot;check-rein$quot; for excessive joint displacement than in fine $quot;tunning$quot; the type of joint motion. The substitute of A.C.L. must be high strength graft, good durability and elasticity. The placement of A.C.L. graft create more $quot;isometric loading$quot; over a greater range of knee motion and the necessity for a staged protective rehabilitation program after replacement. Therefore the substitute of A.C.L. has to be placed isometrically placed as mentioned by Ben Graft. If also has to be rigid fixation for early protective rnotion of the knee. The A.C.L. ligament reconstruction procedures must be selected and designed to withstand minimal force levels (22.7-75.0 kg) to allow early motion and all of its attributes including the prevention of joint stiffness. The immediate post-operative early motion, using C.P.M, could minimize the stiffness of the knee and get good results by Noyes and others. The good rehabilitation program could save poor surgery but incorrect rehabilitation could compromise the good surgery. Therefore there is no cook book for the rehabilitation program. It must be indivisualized according to the situation.

만성 후방십자인대의 치료

정영복 대한슬관절학회 1990 대한슬관절학회지 Vol.2 No.1

Posterior cruciate ligament (PCL) is the msot important of the knee ligament because of its cross section area, tensiie strenth and location in the central axis of the knee joint (Hugston et al. 1976, Kennedy & Gringer 1967) Butler el al. (1980) demonstrated that it provides 95 % of the total restraint to posterior displacement of the tibia. Chronic disabling PCL instability has not been demonstrated to have a satisfactory solution. There are many reconstructive procedures since Hey-Groves reported in 1917. Surgical reconstruction of the PCL has a low success rate for several reasons. First, the PCL is more commonly damaged by severe trauma resulting in extensive damage to other structures including nerves, vessels, ligaments, and cartilage surfaces. Secondly, the PCL has few secondary restraints in which to help prevent posterior tibial sag. Therefore, tissues selected for reconstruction of the PCL must maintain exceptional strength during and after healing. Third, posterior drawer forces occur constantly during daily living activities resulting in cyclic loading of the reconstruction. Fourth, because of posterior tibial sag, a $quot;functional$quot; Patella Baja is created which leads to progressive patellofemoral arthrosis. For these reasons and more, a knee which demonstrates posterior cruciate insufficiency presents a formidable challenge. Imperative to the successful outcome of any PCL reconstruction, is the selection of a replacement which has proper biomechanica1 properties with secure fixation to bone at accurate, isometric attachment sites. There are no controversy in operative treatment of the combined injury of the PCL but stilll controversy in surgical treatment of the isolated PCL injury, Because of PCL instability alone is infrequently disabling and rarely requires reconstruction. Dandy and Pusey (1982) recommended non-operative treatment in isolated PCL injury. Torg et al.(1988) reported that unidirectional instability due to PCL deficiency do not require repair or reconstruction. However, in view of the much less favorable prognosis for PCL-deficient knees with multidirectional instability, consideration should be given to surgical stabilization. In contrast to the findings of Dandy and Pusey, Kennedy et al. (1867) reported that in twenty-five of fifty-seven knecs with untreated insufficiency of thc posterior cruciate ligament significant degenerateive changes developed within an average of sixty-one months. Clancy et al. (1983) reported that moderate to severe articular injury of the medial femoral condyle was found at operation in 48 percent of the patients with chronic injury of the PCL. Seventy-one percent of the patients for whom the interval between injury and ligament reconstruction was two to four years, and 90 percent of those for whom the interval was more than four years, showed articular injury of the medial femoral condyle. From the data contained in these reports, it appears that in at least some individuals with isolated insufficiency of the PCL functional disability will develop. To repair or reconstruction a torn PCL successfully, the surgeon must fully appreciate its anatomie structure and its function. The angle between the ligament and the long femoral axis in extension was 43 ± 3 degree. The distance between the central points of the ligament insertion area (ligament length) was 38 ± 4 mm. The thickness was 6 ± 1 mm and the width 14 ± 2 mm measured in the middle third of the ligament. When surgeon try to reconstruction of PCL to make sure that the distance between the insertion points is isometric during flexion and extension of the knee (Odensten & Gillquist 1988). When correctly placed and held that the graft will not allow posterior sag af the tibia and the knee can be flexed to 90 degree and the knee extended to 20 degree of flexion without in-out movement of the graft by Hugston. The new replacement should be seen to tighten sligtly as the knee proceeds from 20 degrees to 100 degrees of flexion within 3 mm excursion on the isometer. Isometric placement of the graft is present if ligament tension is maintained through the range of motion. And also flexion and extension is not impeded. If the femoral attachment site has been placed too distal, the new ligament will tighten and impede motion as the knee is taken into flexion. If the femoral attachment site is too proximal, then the substitute will tighten excessively as the knee is extended. There should be no impingement of the medial femoral notch, and there should be minimal crimping of the ligament fibers over the pasterior edge of the femoral tunnel. At moment the isometric point of the PCL is near the center of posteromedial part of the ligament where is the most favorable site. It should be noted that obtaining an isometric PCL replacement is very difficult and variability from patient to patient is much greater than with isometric anterior cruciate replacements. The use of a guide wire and isometric positioner is encourage. The major indication for surgical reconstruction is unpredictable instability that occurs during the course of everyday activity and dose not improve with adequate program of rehabilitation exercise. Bracing is inapporopriate for these patients, as the brace whould have to be worn continuously. Insall and Hood (1982) estimate that about one-third of their patients who were diagnoged as having posterior cruciate insufficiency have required reconstruction. Over 10 mm laxity in posterior drawer test of the PCL insufficiency should be surgical reconstruction by Tricky (1980). I recommend that surgical reconstruction is over 10 ∼ 15 mm laxity in poIterior drawer test and 2 ∼ 3 degree of the laxity in reverse pivotshift test and reverse Lachman test of the young patients who has discomfort and some symptoms in daily life. Otherwise non-operative treatment should be considered, To have good functional posterior cruciate stability, the greatest possible power and function in the extensor mechanism is necessary. In surgical reconstructed or non-operated cases of the PCL insufficiency, good quadriceps power is very important for normal function of the knee. Quadriceps rehabilitation is a quite worthwhile goal and is associated with good results. Good rehabilitation save bad sugery, bad rehabilitation compromise good surgery. The rehabilitation must be indivisualized acording to patients circumstance. As soon as apossible early mobilization of the knee is very important of the PCL insufficiency. We must remember that the worst knee is the result of poor sugically treated case (Hughston).