On some degree-and-distance-based graph invariants of trees

Gutman, I.,Furtula, B.,Das, K.Ch. Elsevier [etc.] 2016 Applied Mathematics and Computation Vol.289 No.-

<P>Let G be a connected graph with vertex set V (G). For u, v is an element of V (G), d(v) and d(u, v) denote the degree of the vertex v and the distance between the vertices u and v. A much studied degree-and-distance-based graph invariant is the degree distance, defined as DD = Sigma({u, v}subset of V(G))[d(u) + d(v)] d(u, v). A related such invariant (usually called 'Gutman index') is ZZ = Sigma({u, v}subset of V(G))[d(u) . d(v)] d(u, v). If G is a tree, then both DD and ZZ are linearly related with the Wiener index W = Sigma({u, v}subset of V(G))d(u, v). We examine the difference DD - ZZ for trees and establish a number of regularities. (C) 2016 Elsevier Inc. All rights reserved.</P>

Parameter identification for weakly damped shallow arches

Gutman, S.,Ha, J.,Lee, S. Academic Press 2013 Journal of mathematical analysis and applications Vol.403 No.1

The paper considers shallow arches under weak damping with hinged and clamped boundary conditions. A self-contained presentation of the existence, uniqueness, and regularity of the solutions is provided. The solutions are shown to be continuously dependent on the governing parameters. Furthermore, the solutions are shown to be weakly Gateaux differentiable. The characterization of the weak Gateaux derivative is established by introducing the notion of the weakened solution. Such solutions extend the class of weak solutions utilizing J. Lions' Method of Transposition. The parameter identification problem is stated in terms of the best fit to data objective function. This function is shown to be Frechet differentiable in the interior of the admissible set. The optimal parameters are characterized by a bang-bang control principle.

SHALLOW ARCHES WITH WEAK AND STRONG DAMPING

Gutman, Semion,Ha, Junhong Korean Mathematical Society 2017 대한수학회지 Vol.54 No.3

The paper develops a rigorous mathematical framework for the behavior of arch and membrane like structures. Our main goal is to incorporate moving point loads. Both the weak and the strong damping cases are considered. First, we prove the existence and the uniqueness of the solutions. Then it is shown that the solution in the weak damping case is the limit of the strong damping solutions, as the strong damping vanishes. The theory is applied to a car moving on a bridge.

INVERSE PROBLEM FOR A HEAT EQUATION WITH PIECEWISE-CONSTANT CONDUCTIVITY

Gutman, S.,Ramm, A.G. The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.3

We consider the inverse problem of the identification of a piecewise-constant conductivity in a bar given the extra information of the heat flux through one end of the bar. Our theoretical results show that such an identification is unique. This approach utilizes a "layer peeling" argument. A computational algorithm based on this method is proposed and implemented. The advantage of this algorithm is that it requires only 3D minimizations irrespective of the number of the unknown discontinuities. Its numerical effectiveness is investigated for several conductivities.

IDENTIFIABILITY FOR COMPOSITE STRING VIBRATION PROBLEM

Gutman, Semion,Ha, Jun-Hong Korean Mathematical Society 2010 대한수학회지 Vol.47 No.5

The paper considers the identifiability (i.e., the unique identification) of a composite string in the class of piecewise constant parameters. The 1-D string vibration is measured at finitely many observation points. The observations are processed to obtain the first eigenvalue and a constant multiple of the first eigenfunction at the observation points. It is shown that the identification by the Marching Algorithm is continuous with respect to the mean convergence in the admissible set. The result is based on the continuous dependence of eigenvalues, eigenfunctions, and the solutions on the parameters. A numerical algorithm for the identification in the presence of noise is proposed and implemented.

Extended energy and its dependence on molecular structure

Gutman, Ivan,Furtula, Boris,Das, Kinkar Ch. National Research Council 2017 Canadian journal of chemistry Vol.95 No.5

<P> The extended energy ([Formula: see text]) is a vertex degree based and spectrum-based molecular structure descriptor, shown to be well correlated with a variety of physicochemical molecular properties. We investigate the dependence of [Formula: see text] on molecular structure and establish its basic characteristics. In particular, we show how [Formula: see text] is related with the geometric-arithmetic (GA) topological index. Our main finding is that the difference between [Formula: see text] and the total π-electron energy is linearly proportional to the difference between the number of edges and the GA index. </P>

ESTIMATION ALGORITHM FOR PHYSICAL PARAMETERS IN A SHALLOW ARCH

Gutman, Semion,Ha, Junhong,Shon, Sudeok Korean Mathematical Society 2021 대한수학회지 Vol.58 No.3

Design and maintenance of large span roof structures require an analysis of their static and dynamic behavior depending on the physical parameters defining the structures. Therefore, it is highly desirable to estimate the parameters from observations of the system. In this paper we study the parameter estimation problem for damped shallow arches. We discuss both symmetric and non-symmetric shapes and loads, and provide theoretical and numerical studies of the model behavior. Our study of the behavior of such structures shows that it is greatly affected by the existence of critical parameters. A small change in such parameters causes a significant change in the model behavior. The presence of the critical parameters makes it challenging to obtain good estimation. We overcome this difficulty by presenting the Parameter Estimation Algorithm that identifies the unknown parameters sequentially. It is shown numerically that the algorithm achieves a successful parameter estimation for models defined by arbitrary parameters, including the critical ones.

Dynamic behavior of cracked beams and shallow arches

Semion Gutman,하준홍,손수덕 대한수학회 2022 대한수학회지 Vol.59 No.5

We develop a rigorous mathematical framework for studying dynamic behavior of cracked beams and shallow arches. The governing equations are derived from the first principles, and stated in terms of the subdifferentials of the bending and the axial potential energies. The existence and the uniqueness of the solutions is established under various conditions. The corresponding mathematical tools dealing with vector-valued functions are comprehensively developed. The motion of beams and arches is studied under the assumptions of the weak and strong damping. The presence of cracks forces weaker regularity results for the arch motion, as compared to the beam case.

Hidden and exposed faces of power in Buenos Aires

Margarita Gutman 서울시립대학교 도시과학연구원 2015 도시과학국제저널 Vol.19 No.1

This article presents the expressions of two opposite types of power in the city of Buenos Aires, separated from each other by some 30 years (1976–2010). They are opposites in the way they manifest themselves: one, hidden, subterranean, sinister and silent; the other, extroverted and multitudinous, filling streets and public squares. Their nature, agents and goals are different, but the physical urban sphere in which power is exercised, and the social body on which the latter is imposed, is the same: the capital city and its population, and, by extension, the country as a whole.

EQUATIONS OF MOTION FOR CRACKED BEAMS AND SHALLOW ARCHES

Semion Gutman,Junhong Ha,손수덕 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.2

Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that “absorbs” the boundary conditions at the cracks. Then the equations of motion are derived from the first principles using the Extended Hamilton’s Principle, accounting for non-conservative forces. The variational formulation of the equations is stated in terms of the subdifferentials of the bending and axial potential energies. The equations are given in their abstract (weak), as well as in classical forms.