Search results for: V. M. Bondarenko

Items from 1 to 9 out of 9 results

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Indecomposable and Isomorphic Objects in the Category of Monomial Matrices Over a Local Ring

V. M. Bondarenko, M. Yu. Bortosh

Ukrainian Mathematical Journal > 2017 > 69 > 7 > 1034-1050

We study the indecomposability and isomorphism of objects from the category of monomial matrices Mmat(K) over a commutative local principal ideal ring K (whose objects are square monomial matrices and the morphisms from X to Y are matrices C such that XC = CY). We also study the subcategory Mmat₀(K) of the category Mmat(K) with the same objects and solely with morphisms that are monomial matrices.

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Local deformations of positive-definite quadratic forms

V. M. Bondarenko, V. V. Bondarenko, Yu. N. Pereguda

Ukrainian Mathematical Journal > 2012 > 64 > 7 > 1019-1035

We give a complete description of real numbers that are P-limit numbers for integer-valued positive-definite quadratic forms with unit coefficients of the squares. It is shown that each of these P-limit numbers is realized in the Tits quadratic form of a certain Dynkin diagram.

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Representations of primitive posets

V. M. Bondarenko, N. M. Gubareni, M. A. Dokuchaev, V. V. Kirichenko, more

Journal of Mathematical Sciences > 2010 > 164 > 1 > 26-48

We give a new proof of the Kleiner theorem for the case of primitive posets.

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Description of posets critical with respect to the nonnegativity of the quadratic Tits form

V. M. Bondarenko, M. V. Stepochkina

Ukrainian Mathematical Journal > 2009 > 61 > 5 > 734-746

We present the complete description of finite posets whose Tits form is not nonnegative but all proper subsets of which have nonnegative Tits forms. A similar result for positive forms was obtained by the authors earlier.

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(Min, max)-equivalence of posets and nonnegative Tits forms

V. M. Bondarenko, M. V. Stepochkina

Ukrainian Mathematical Journal > 2008 > 60 > 9 > 1349-1359

We study the relationship between the (min, max)-equivalence of posets and properties of their quadratic Tits form related to nonnegative definiteness. In particular, we prove that the Tits form of a poset S is nonnegative definite if and only if the Tits form of any poset (min, max)-equivalent to S is weakly nonnegative.

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THE STRUCTURING OF VIABLE DEVELOPMENT: ANALYSIS OF APPROACHES AND DEFINITIONS

S. S. Slava, V. M. Bondarenko

Rehionalna ekonomika (Regional Economy) > 2008 > 4(50) > 208-214

This study involved a theoretical analysis of definitions of sustainable development to identify the weights of different components, to assess what meanings are included in the term by different authors and communities, and to understand the role of managerial approaches in sustainable development. A principled managerial model of sustainable development is presented in which common purposes and...

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On serial posets with positive-definite quadratic Tits form

V. M. Bondarenko, M. V. Stepochkina

Nonlinear Oscillations > 2006 > 9 > 3 > 312-316

We describe all serial posets with positive-definite quadratic Tits form and prove that any poset of order greater than 7 with positive-definite Tits form is serial.