Defining relations of a free modular lattice of rank 3

For a 3-generated free modular lattice we obtain a set of 11 defining relations and prove that this set is minimal.     

Finiteness and Infiniteness of 3-Generated Lattices with Distributive Elements Among Generators

Siberian Mathematical Journal - We consider 3-generated lattices whose generators are distributive, dually distributive, right modular, dually right modular elements, or elements possessing a...     

On 3-generated lattices with a completely modular element among generators

We consider a lattice generated by three elements, one of which is completely modular. The free lattice with this property is proved to be finite. It is not modular and contains exactly 39 elements. We have also found a finite set of defining relations for the generating elements of this lattice.     

Lattices with Defining Relations Close to Distributivity

We consider the 3-generated lattices whose generators enjoy the defining relations of the type a∨(b∧c) = (a∨b)∧(a∨c). Moreover, if the lattice is finite then we obtain its diagram; otherwise, we prove that the corresponding lattice is infinite.     

3-Generated Lattice with Left Modular and Separating Generators

Mathematical Notes - We consider a lattice generated by three elements, two of which are a left modular element and a separating element. It is proved that such a lattice is finite and contains at...     

Free 3-Generated Lattices with Two Semi-Normal Generators

We consider a lattice generated by three elements, two of which are semi-normal. We have proved it is infinite and have also found an additional condition for the lattice to be modular. As a result, it is proved that the sublattice generated in the subgroup lattice by two normal subgroups and any subgroup is modular.     

Radiation—measurement complex of the Sirius synchrotron

The radiation-measurement complex associated with the Sirius synchrotron has been operating in the Scientific-Research Institute of Nuclear Physics of the S. M. Kirov Polytechnic Institute in Tomsk since 1985. Research on meson physics, channeling of high-energy electrons in crystals, new types of radiation, and applications of synchrotron radiation is carried out in this complex. The renovation of the synchrotron presently under way will allow these problems to be studied more effectively.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 5–7, June, 1991.