In this paper, two protocols are presented for private intersection detection of moving objects’ trajectories. Assuming that the movement trajectory an object can be described by a time-dependent polynomial function, problem finding points is simplified to common roots corresponding polynomials. Thereafter, GrObner Basis used design novel secure protocol Another also designed based on distance ...

In this paper we present results of our computer experiments to study effectiveness of involutive criteria for avoiding useless prolongations in construction of polynomial Janet bases. These bases are typical representative of involutive bases. Though involutive bases are usually redundant as Gröbner ones, they can be used as well as the reduced Gröbner bases in whose theory Volker Weispfenning...

The formalising of relations of the theory of relational databases encompasses in the main conventional entity set models and data structures. There is an analytical vehicle and formal definition of knowledge bases. The offered tool of meta-textual relational models of knowledge opens broad capabilities of development of the theory of relational knowledge bases. The basic fields of application:...

One of the main contributions which Volker Weispfenning made to mathematics is related to Gröbner bases theory. In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational field extension (which in particular includes the zero characteristic case). One of the main tools is Gröbner bases theory. Our algorithm also requires computi...

The theory of crystal bases introduced by Kashiwara in [6] to study the category of integrable representations of quantized Kac–Moody Lie algebras has been a major development in the combinatorial approach to representation theory. In particular Kashiwara defined the tensor product of crystal bases and showed that it corresponded to the tensor product of representations. Later, in [7] he define...

The theory of crystal bases introduced by Kashiwara in [4] to study the category of integrable representations of quantized Kac–Moody Lie algebras has been a major development in the combinatorial approach to representation theory. In particular Kashiwara defined the tensor product of crystal bases and showed that it corresponded to the tensor product of representations. Later, in [5] he define...

in the present study, the interactions of three different lithium species li+, li3+ and ch3li with several different sites of the most stable tautomers of dna nucleo-bases are presented. this investigation is based on the results of thermochemical properties, quantum theory of atoms in molecules (qtaim) and natural bond orbital (nbo) analysis, obtained at b3lyp/6-311++g(d,p) level of theory. th...