Despite ample research on soft linear spaces, there are many other concepts that can be studied. We introduced in this paper several new concepts related to the soft operators, such as the invertible operator.  We investigated some properties of this kind of operators and defined the spectrum of soft linear operator along with a number of concepts related with this definition; the concepts of eigenvalue, eigenvector, eigenspace are defined. Finally the spectrum of the soft linear operator was divided into three disjoint parts.

Background: White-spot lesion is one of the problems associated with the fixed orthodontic treatment. The aims of this in-vitro study were to investigate enamel damage depth on adhesive removal when the adhesive were surrounded by sound, demineralized or demineralized enamel that had been re-mineralized prior to adhesive removal using 10% Nano-Hydroxy apatite and to determine the effect of three different adhesive removal techniques. Materials and methods: Composite resin adhesive (3M Unitek) was bonded to 60 human upper premolars teeth which were randomly divided in to three groups each containing ten sound teeth and ten teeth with demineralized and re-mineralized lesions adjacent to the adhesive. A window of 2 mm was prepared on the bucca

Background: Oral lichen planus (OLP) is a relatively common chronic inflammatory muco-cutaneous disease classified among the potentially malignant lesions of oral mucosa. The aim of this study is to investigate and compare the expression of p53 and PCNA proteins in oral lichen planus and epithelial dysplasia cases. Materials and methods:Formalin-fixed and paraffin- embedded blocks of 21 lichen planusand 21 oral dysplasia cases were referred to immunohistochemical (IHC) analysis for anti p53 and anti PCNA monoclonal antibodies. Results: The results showed that positive nuclear staining for p53 was found in 11/21 (52.4%) cases of lichen planus and 17/21 (80.9%) cases of dysplasia. Positivity for PCNA was observed in 18/21(85.7%) of oral li

The enhancement of heat exchanger performance was investigated using dimpled tubes tested at different Reynolds numbers, in the present work four types of dimpled tubes with a specified configuration manufactured, tested and then compared performance with the smooth tube and other passive techniques performance. Two dimpled arrangements along the tube were investigated, these are inline and staggered at constant pitch ratio X/d=4, the test results showed that Nusselts number (heat transfer) of the staggered array is higher than the inline array by 13%.  The effect of different depths of the dimple (14.5 mm and 18.5 mm) has been also investigated; a tube with large dimple diameter enhanced the Nusselts number by about 25% for the ran

      This work addressed the assignment problem (AP) based on fuzzy costs, where the objective, in this study, is to minimize the cost. A triangular, or trapezoidal, fuzzy numbers were assigned for each fuzzy cost. In addition, the assignment models were applied on linguistic variables which were initially converted to quantitative fuzzy data by using the Yager’sorankingi method. The paper results have showed that the quantitative date have a considerable effect when considered in fuzzy-mathematic models.

In this research, a mathematical model of tumor treatment by radiotherapy is studied and a new modification for the model is proposed as well as introducing the check for the suggested modification. Also the stability of the modified model is analyzed in the last section.

Superconducting thin films of Bi1.6Pb0.4Sr2Ca2Cu2.2Zn0.8O10 system were prepared by depositing the film onto silicon (111) substrate by pulsed laser deposition. Annealing treatment and superconducting properties were investigated by XRD and four probe resistivity measurement. The analysis reveals the evolution of the minor phase of the films 2212 phase to 2223 phase, when the film was annealed at 820 °C. Also the films have superconducting behavior with transition temperature ≥90K.