We first introduce 20 weak forms of continuity, which are closely related to 5 known weak forms of continuity. Then we classify them into 9 groups and give 12 decompositions of continuity. 1. Introduction. Continuity is one of the most important concepts in mathematics. In order to find deep properties of continuity, many weak forms of continuity were introduced in the literature. For instance,...

In this work we define generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures recently proposed in the literature. Moreover, we study some properties of the interior, the closure and other concepts in this new context. Mathematics Subject Classification: Primary 54A05, Secondary 54D10

This paper considers a supply chain where a manufacturer sells its product through a retailer. In such a market, a potential entrant can make a substitute product by imitating the incumbent's product and then sells it to the common market with one of three alternative entry modes: (i) selling through the incumbent's retailer, (ii) selling through another independent retailer, or (iii) selling d...

avila and molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α(g),π(g),σ(g) and β(g). this work is a further investigation of generalized weak structures due to avila and molina. further we introduce the structures ro(g) and rc(g) and study the properties of the structur...

in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.

In the title mol-ecule, C17H15ClN4S, the benzene rings form dihedral angles of 16.6 (1) and 77.2 (1)° with the triazole ring. The dihedral angle between the benzene rings is 86.6 (1)°. In the crystal, pairs of N-H⋯S hydrogen bonds form inversion dimers with graph-set notation R 2 (2)(8). Weak C-H⋯S hydrogen bonds link these dimers into layers parallel to (100). Weak intra-molecular C-H⋯S and C-...

Let G=(V(G),E(G)) be a graph.A set of vertices S in a graph G is called to be a Smarandachely dominating k-set, if each vertex of G is dominated by at least k vertices of S. Particularly, if k = 1, such a set is called a dominating set of G. The Smarandachely domination k -number γk(G) of G is the minimum cardinality of a Smarandachely dominating k -set of G. S is called weak domination set if ...

In the title compound, C(20)H(15)N(5)O(4)S, the central benzene ring makes dihedral angles of 59.5 (1) and 51.7 (1)°, respectively, with the terminal phenyl and benzene rings. The mol-ecular structure exhibits weak intra-molecular N-H⋯N and C-H⋯S inter-actions. In the crystal structure, mol-ecules are linked by weak inter-molecular N-H⋯S and C-H⋯O inter-actions, forming a chain along [11].

In the title compound, C(14)H(14)N(2)O(5)S(2)·H(2)O, the six-membered ring fused to the β-lactam unit has a twisted conformation. Weak intra-molecular N-H⋯S and C-H⋯O inter-actions occur. Inter-molecular C-H⋯S, N-H⋯O, C-H⋯O and O-H⋯O hydrogen-bonding inter-actions stabilize the crystal structure, forming a three-dimensional network. Weak C-H⋯π inter-actions are also present.

In this paper we revisit Wiener’s method (IEEE-IT 1990) of continued fraction (CF) to find new weaknesses in RSA. We consider RSA with N = pq, q < p < 2q, public encryption exponent e and private decryption exponent d. Our motivation is to find out when RSA is insecure given d is O(N), where we are mostly interested in the range 0.3 ≤ δ ≤ 0.5. Given ρ (1 ≤ ρ ≤ 2) is known to the attacker, we sh...