in this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. we introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some of their important properties.

We prove upper and lower bounds for the leading coefficient of Kolchin dimension polynomial systems partial linear differential equations in case codimension two, quadratic with respect to orders system. A notion typical plays an important role algebra, some its estimations were proved by J. Ritt E. Kolchin; they also advanced several conjectures that later refuted. Our bound generalizes analog...

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

In this paper boundedness and compactness of generalized composition oper-ators from logarithmic Bloch type spaces to Q_K type spaces are investigated.

BACKGROUND The diagnostic process and the surgical procedures in patients with snoring and obstructive sleep apnea syndrome (OSAS) are crucial. The aim of this study was to assess the efficacy of surgical treatment in snoring and OSAS patients. MATERIAL/METHODS A precise laryngological examination and screening polysomnography (Poly-Mesam) were performed in all patients with mild, moderate an...

For any polynomial ideal I, let the minimal triangular set contained in the reduced Buchberger-Gröbner basis of I with respect to the purely lexicographical term order be called the W-characteristic set of I. In this paper, we establish a strong connection between Ritt’s characteristic sets and Buchberger’s Gröbner bases of polynomial ideals by showing that the W-characteristic set C of I is a ...