Classification of full exceptional collections on smooth toric Fano varieties with Picard rank two

In this paper, we give the complete classification of full exceptional collections on smooth toric Fano threefolds and fourfolds with Picard rank two. To be precise, we give a partial answer to the conjecture in \cite{Kuz} and \cite{LYY}: we provide all the exceptional collections of maximal length and prove that they are in fact full exceptional collections.Comment: Comments welcome. Some references adde

Set-valued mapping and Rough Probability

In 1982, the theory of rough sets proposed by Pawlak and in 2013, Luay concerned a rough probability by using the notion of Topology. In this paper, we study the rough probability in the stochastic approximation spaces by using set-valued mapping and obtain results on rough expectation, and rough variance.Comment: 9 page

Generic Lightlike Submanifolds of an Indefinite Cosymplectic Manifold

Lightlike geometry has its applications in general relativity, particularly in black hole theory. Indeed, it is known that lightlike hypersurfaces are examples of physical models of Killing horizons in general relativity (Galloway, 2007). In this paper, we introduce the definition of generic lightlike submanifolds of an indefinite cosymplectic manifold. We investigate new results on a class of generic lightlike submanifolds of an indefinite cosymplectic manifold

A Basic Inequality for the Tanaka-Webster Connection

For submanifolds tangent to the structure vector field in Sasakian space forms, we establish a Chen's basic inequality between the main intrinsic invariants of the submanifold (namely, its pseudosectional curvature and pseudosectional curvature on one side) and the main extrinsic invariant (namely, squared pseudomean curvature on the other side) with respect to the Tanaka-Webster connection. Moreover, involving the pseudo-Ricci curvature and the squared pseudo-mean curvature, we obtain a basic inequality for submanifolds of a Sasakian space form tangent to the structure vector field in terms of the Tanaka-Webster connection

Performance Comparison of CRUD Operations in IoT based Big Data Computing

Nowadays, due to the development of mobile devices, the kinds of data that are generated are becoming diverse, and the amount is becoming huge. The vast amount of data generated in this way is called big data. Big data must be processed in a different way than existing data processing methods. Representative methods of big data processing are RDBMS (Relational Database System) and NoSQL method. We compare NoSQL and RDBMS, which are representative database systems. In this paper, we use MySQL query and MongoDB query to compare RDBMS and NoSQL. We gradually compare the performance of CRUD operations in MySQL and MongoDB by increasing the amount of data. MongoDB sets index and compares it again.  Through result of these operations is to choose a database system that fits the situation.  This makes it possible to design and analyse big data more efficiently.