Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers

This paper is devoted to investigate some characteristic features of complex numbers and functions in terms of non-Newtonian calculus. Following Grossman and Katz, (Non-Newtonian Calculus, Lee Press, Piegon Cove, Massachusetts, 1972), we construct the field ℂ* of *-complex numbers and the concept of *-metric. Also, we give the definitions and the basic important properties of *-boundedness and *-continuity. Later, we define the space C*(Ω) of *-continuous functions and state that it forms a vector space with respect to the non-Newtonian addition and scalar multiplication and we prove that C*(Ω) is a Banach space. Finally, Multiplicative calculus (MC), which is one of the most popular non-Newtonian calculus and created by the famous exp function, is applied to complex numbers and functions to investigate some advance inner product properties and give inclusion relationship between C*(Ω) and the set of C*′(Ω)*-differentiable functions

On the Classical Paranormed Sequence Spaces and Related Duals over the Non-Newtonian Complex Field

The studies on sequence spaces were extended by using the notion of associated multiplier sequences. A multiplier sequence can be used to accelerate the convergence of the sequences in some spaces. In some sense, it can be viewed as a catalyst, which is used to accelerate the process of chemical reaction. Sometimes the associated multiplier sequence delays the rate of convergence of a sequence. In the present paper, the classical paranormed sequence spaces have been introduced and proved that the spaces are ⋆-complete. By using the notion of multiplier sequence, the α-, β-, and γ-duals of certain paranormed spaces have been computed and their basis has been constructed

Comparison of four different reduction methods for anterior dislocation of the shoulder

WOS: 000355166800001PubMed ID: 26016671Background: Shoulder dislocations account for almost 50 % of all major joint dislocations and are mainly anterior. Objective: The aim is a comparative retrospective study of different reduction maneuvers without anesthesia to reduce the dislocated shoulder. Methods: Patients were treated with different reduction maneuvers, including various forms of traction and external rotation, in the emergency departments of four training hospitals between 2009 and 2012. Each of the four hospitals had different treatment protocols for reduction and applying one of four maneuvers: Spaso, Chair, Kocher, and Matsen methods. Thirty-nine patients were treated by the Spaso method, 47 by the Chair reduction method, 40 by the Kocher method, and 27 patients by Matsen's traction-countertraction method. All patients' demographic data were recorded. Dislocation number, reduction time, time interval between dislocation and reduction, and associated complications, pre- and post-reduction period, were recorded prospectively. No anesthetic method was used for the reduction. Results: All of the methods used included traction and some external rotation. The Chair method had the shortest reduction time. All surgeons involved in the study agreed that the Kocher and Matsen methods needed more force for the reduction. Patients could contract their muscles because of the pain in these two methods. The Spaso method includes flexion of the shoulder and blocks muscle contraction somewhat. The Chair method was found to be the easiest because the patients could not contract their muscles while sitting on a chair with the affected arm at their side. Conclusions: We suggest that the Chair method is an effective and fast reduction maneuver that may be an alternative for the treatment of anterior shoulder dislocations. Further prospective studies with larger sample size are needed to compare safety of different reduction techniques

Changes In The Frequencies Of Abdominal Wall Hernias And The Preferences For Their Repair: A Multicenter National Study From Turkey

Abdominal wall hernias are a common problem in the general population. A Western estimate reveals that the lifetime risk of developing a hernia is about 2%.– As a result, hernia repairs likely comprise the most frequent general surgery operations. More than 20 million hernias are estimated to be repaired every year around the world. Numerous repair techniques have been described to date however tension-free mesh repairs are widely used today because of their low hernia recurrence rates. Nevertheless, there are some ongoing debates regarding the ideal approach (open or laparoscopic),, the ideal anesthesia (general, local, or regional),, and the ideal mesh (standard polypropylene or newer meshes).,PubMedWoSScopu