We study two decomposition problems in combinatorial geometry. The first part of the thesis deals with the decomposition of multiple coverings of the plane. We say that a planar set is cover-decomposable if there is a constant m such that any m-fold covering of the plane with its translates is decomposable into two disjoint coverings of the whole plane. Pach conjectured that every convex set is...

in this paper, we propose a new method for fuzzy numbers. in this method, we assume that ai= (ai1, ai2, ai3, ai4) is to be a fuzzy number. so, the convex combination of ai1 and ai2 and also the convex combination of ai3 and ai4 are obtained separately. then, mic and mis that are to be the convex combinations and the standard deviation respectively we acquire them from these components. finally,...

Ice streams are distinct, fast-flowing regimes within ice sheets that exhibit fundamentally different characteristics as compared to the slow-moving inner parts of the ice sheets. While alongflow surface profiles of ice sheets are typically convex, some ice streams show linearly sloping or even concave surface profiles. We use observational data of the Siple Coast in Antarctica to inversely cal...

frozen shoulder is a glenohumeral joint disorder that perturbs movement because of adhesion and the existence of fibrosis in the shoulder capsule. platelet-rich plasma can produce collagen and growth factors, which increases stem cells and consequently enhances the healing. to date, there is no evidence regarding the effectiveness of platelet-rich plasma in frozen shoulder. a 45-year-old man wi...

 Abstract A 2.5 year old girl is presented with both hands constriction bands leading to distal amputations and the rare deformity of shoulder duplication in the right side accompanying constriction skin marking over the affected shoulder. The cephalomedial scapula articulated with the clavicle and the caudolateral scapula articulated with humeral head. The most important physical finding which...

Background:  Some studies show that frozen shoulder is due to the pathologic changes in the muscles around the shoulder. Measurement of the ultrasonic thickness of a muscle is a method for measuring the muscle changes. There is no study about the reliability of measurement of the muscle’s ultrasonic thickness around the shoulder in patients with frozen shoulder. The present study aims to invest...