Scope for application of Topological spaces in Data Granulation through a new class of nearly open set Semi* Regular*- Open sets

The purpose of this paper is to define and study a new class of weaker form of regular*-open sets called semi*- regular*- open sets in topological spaces. Finally we conclude with the scope of this new class of open sets in applications of Data granulation.

Algorithmic correspondence and canonicity for possibility semantics

The present paper develops a unified correspondence treatment of the Sahlqvist theory for possibility semantics, extending the results in the work by Yamamoto (2016, Journal of Logic and Computation, 27, 2411–2430) from Sahlqvist formulas to the strictly larger class of inductive formulas and from the full possibility frames to filter-descriptive possibility frames. Specifically, we define the possibility semantics version of the algorithm Ackermann lemma based algorithm (ALBA) and an adapted interpretation of the expanded modal language used in the algorithm. One notable feature of the adaptation of ALBA to possibility frames setting is that the so-called nominal variables, which are interpreted as complete join-irreducibles in the standard setting, are interpreted as regular open closures of ‘singletons’ in the present setting, which is a novelty of the present paper. We prove the soundness of the algorithm with respect to both (the dual algebras of) full possibility frames and (the dual algebras of) filter-descriptive possibility frames, use the algorithm to give an alternative proof to the one in the work by Holliday (2016, Possibility frames and forcing for modal logic. UC Berkeley Working Paper in Logic and the Methodology of Science. URL. http://escholarship.org/uc/item/9v11r0dq) that the inductive formulas are constructively canonical and show that the algorithm succeeds on inductive formulas. We make some comparisons among different semantic settings in the design of the algorithms and fit possibility semantics into this broader picture.

VIDEO-ASSISTED RESECTIONS FOR PULMONARY TUBERCULOSIS WITH THE PRESENCE OF PLEURAL CAVITY OBLITERATION

Pulmonary tuberculosis surgery is characterized by a number of aspects associated with adhesions in the pleural cavity, fibrosis of the lung root, destruction of the parenchyma, which contribute to the development of intra- and postoperative complications such as residual pleural cavity and reactivation of tuberculosis in operated lung due to compensatory tissue distortion. Aim: to improve video-assisted lung resection (VATS) in tuberculosis patients with the presence of pleural cavity obliteration. Materials and methods. The developed method of VATS for tuberculosis patients with pleural cavity obliteration is based on separate intubation of right and left main bronchi for mechanical ventilation of one lung, placement of thoracic port, performing revision of pleural cavity using video-assisted thoracoscopy, performing mini-thoracotomy and resection of lung with separate treatment of anatomical structures in required volume by means of disposable stapler or regular open thoracotomy instruments, pleural cavity draining and layered wound closure. Computed tomography of chest is performed during the operation in order to assess the extent and severity of pleural adhesions and to locate safe position of thoracic ports. Hydraulic needle preparation of parietal pleura is performed in severe adhesions area. Hemorrhage is treated using hemostatic plate Surgicel Fibrillar made of restored cellulose. Phrenicotripsy, pleural cavity drainage and, finally, artificial pneumoperitoneum are performed. The proposed method of video-assisted lung resection was used in 41 patients, 25 patients underwent video-assisted resection according to the prototype method. Results. The proposed method reduced duration of the surgical intervention by 52.7 minutes; the frequency of intraoperative complications by 14.4%; the incidence of postoperative complications by 14.2; the duration of patient�s stay at the hospital by 5.8 days and increased of overall treatment efficiency by 14.5%. The proposed method of VATS for patients with pulmonary tuberculosis and pleural cavity obliteration is safe, effective, simple to implement and can be performed at thoracic surgery departments of various pulmonary hospitals of city and regional level. Key words: pulmo

Family Members of Adults with Intellectual Disability Living in Residential Settings: Roles and Collaboration with Professionals. A Review of the Literature

The aim of this article is to review the literature concerning the role of family members of adults with an intellectual disability living in diverse residential settings and their collaboration with residential staff. Whenever the scarce literature on the subject allowed, the focus was laid on family members of persons with additional challenging behavior. Electronic databases, reference screening, and hand search of selected journals was employed to collate literature using key terms such as family members, intellectual disability, and residential setting. By extracting relevant data of the eighteen articles that fulfilled all inclusion criteria, the following 3 main themes with each subthemes were identified inductively: roles of family members after the transition, the effects of the transition on family members, and the collaboration between the family members and professional care staff. This review presents the different roles family members partake and highlights the importance of regular open two-sided communication for collaboration with professional staff to be successful. Practical implementations are discussed and the need for further research in the field is indicated.

WEAKLY (1,2)$^{\ast}$-$\widetilde{g}$-CLOSED SETS IN BIOTOPOLOGICAL SPACES

The concept of bitopological spaces was first introduced by J.C. Kelly [2] in 1963. Regular open sets have been introduced and investigated by Stone [5]. In this paper, we introduce a new class of generalized closed sets called weakly (1,2)$^{\ast}$-$\widetilde{g}$-closed sets which contains the above mentioned class. Also, we investigate the relationships among the related generalized closed sets.

Regularity in Topological Modules

The framework of Functional Analysis is the theory of topological vector spaces over the real or complex field. The natural generalization of these objects are the topological modules over topological rings. Weakening the classical Functional Analysis results towards the scope of topological modules is a relatively new trend that has enriched the literature of Functional Analysis with deeper classical results as well as with pathological phenomena. Following this trend, it has been recently proved that every real or complex Hausdorff locally convex topological vector space with dimension greater than or equal to 2 has a balanced and absorbing subset with empty interior. Here we propose an extension of this result to topological modules over topological rings. A sufficient condition is provided to accomplish this extension. This sufficient condition is a new property in topological module theory called strong open property. On the other hand, topological regularity of closed balls and open balls in real or complex normed spaces is a trivial fact. Sufficient conditions, related to the strong open property, are provided on seminormed modules over an absolutely semivalued ring for closed balls to be regular closed and open balls to be regular open. These sufficient conditions are in fact characterizations when the seminormed module is the absolutely semivalued ring. These characterizations allow the provision of more examples of closed-unit neighborhoods of zero. Consequently, the closed-unit ball of any unital real Banach algebra is proved to be a closed-unit zero-neighborhood. We finally transport all these results to topological modules over topological rings to obtain nontrivial regular closed and regular open neighborhoods of zero. In particular, if M is a topological R-module and m∗∈M∗ is a continuous linear functional on M which is open as a map between topological spaces, then m∗−1(int(B)) is regular open and m∗−1(B) is regular closed, for B any closed-unit zero-neighborhood in R.

Nearly Soft Menger Spaces

In this paper, we define a weak type of soft Menger spaces, namely, nearly soft Menger spaces. We give their complete description using soft s-regular open covers and prove that they coincide with soft Menger spaces in the class of soft regular⋆ spaces. Also, we study the role of enriched and soft regular spaces in preserving nearly soft Mengerness between soft topological spaces and their parametric topological spaces. Finally, we establish some properties of nearly soft Menger spaces with respect to hereditary and topological properties and product spaces.