Abstract:In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation laws of the BBM and MBBM equations are presented. Some aspects of their symmetry properties are given too.

In this paper, an extension of Darbo’s fixed point theorem via θ -F-contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

Background & Aim: The key to playing role in the nursing profession is the proper communication and is, in fact, the basic part of nurses' careers in looking after the patients. Recognizing the factors related to communication skills of nursing students, including spiritual intelligence, can be used to increase the quality of care. The purpose of this study was to investigate the correlation between spiritual intelligence and communication skills of nursing students in Kurdistan University of Medical Sciences. Materials & Methods: In this descriptive-correlational study, 286 nursing students were selected by stratified sampling method. Data were collected by King's Spiritual Intelligence Questionnaire and Barton's Communication Skills Questionnaire. Data analysis was done by descriptive and inferential statistics using SPSS 21 software. Results: The mean age of the students was 21.37±2.39 years. Most of the students were male (55%) and studying in the fourth year of the university (30%) (Seventh semester (17.1%)). The mean (standard deviation) of spiritual intelligence was 59.71 (12.04) and communication skills was 51.83 (10.10). Based on Pearson correlation coefficient, the correlation between communication skills with spiritual intelligence and its areas was positive (0.414) and was statistically significant (p<0.05). Conclusion: There was a positive and significant correlation between spiritual intelligence and communication skills. Considering this issue in students, along with physical, mental and social dimensions, can increase the communication skills and increase the quality of nursing care in the future.

The aim of this paper is to generalize the F -contractive condition in the framework of α - ν -complete modular b-metric spaces. Some results in ordered modular b-metric spaces are also presented. Moreover, an illustrative example and some related applications are presented to support the obtained results.

In this paper, we extend Darbo’s fixed point theorem via weak JS-contractions in a Banach space. Our results generalize and extend several well-known comparable results in the literature. The technique of measure of non-compactness is the main tool in carrying out our proof. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.