The security of lattice-based cryptosystems such as NTRU, GGH and Ajtai-Dwork essentially relies upon the intractability of computing a shortest non-zero lattice vector and a closest lattice vector to a given target vector in high dimensions. The best algorithms for these tasks are due to Kannan, and, though remarkably simple, their complexity estimates have not been improved since more than tw...

Recently, José R. Morales and Edixon Rojas [José R. Morales and Edixon Rojas, Cone metric spaces and fixed point theorems of T -Kannan contractive mappings, Int. J. Math. Anal. 4 (4) (2010) 175–184] proved fixed point theorems for T -Kannan and T -Chatterjea contractions in conemetric spaces when the underlying cone is normal. The aim of this paper is to prove this without using the normality c...

Fabrication, Physicochemical Characterization and Evaluation of In vitro Anticancer Efficacy a Novel pH Sensitive Polymeric Nanoparticles for Efficient Delivery Hydrophobic Drug against Colon CancerManikandan Mahalingam, Kannan Krishnamoorthy

We initiate a systematic study of linear sketching over F2. For a given Boolean function f : {0, 1} → {0, 1} a randomized F2-sketch is a distributionM over d×n matrices with elements over F2 such thatMx suffices for computing f(x) with high probability. We study a connection between F2-sketching and a two-player one-way communication game for the corresponding XOR-function. Our results show tha...

In this paper, we continue the study of contractive conditions for mappings in complete partial metric spaces. Concretely, we present fixed point results for weakly contractive and weakly Kannan mappings in such a way that the classical metric counterpart results are retrieved as a particular case. Special attention to the cyclical case is paid. Moreover, the well-posedness of the fixed point p...

Some generalizations of Banach's contraction principle, which is a fixed-point theorem for mapping in metric spaces, have developed rapidly recent years. the things that support development generalization are emergence mappings more general than and spaces spaces. The generalized Kannan type one mappings. Furthermore, some b-metric modular bring concept into theorems Kannan-type on been given. ...

In this paper, we establish some existence of fixed-point results for asymptotically regular multivalued mappings satisfying Kannan-type contractive condition without assuming compactness the underlying metric space or continuity mapping.