In this manuscript, we show that the metric mean dimension of a semigroup action satisfies three variational principles: (a) in our first result, consider local entropy function for free and principle terms such function; (b) second one is about definition Katok’s introduced Carvalho et al. (Ergod, 42, 65–85, 2022); (c) third based on Shapira’s entropy, Shapira (Israel J Math, 158, 225–247, 200...

A molecular descriptor is a mathematical measure that associates graph with some real numbers and predicts the various biological, chemical, structural properties of underlying graph. Wiener (1947) Trinjastic Gutman (1972) used descriptors to find boiling point paraffin total π -electron energy molecules, respectively. F...

We study, in three parts, degree sequences of k-families (or k-uniform hypergraphs) and shifted k-families. • The first part collects for the first time in one place, various implications such as Threshold ⇒ Uniquely Realizable ⇒ Degree-Maximal ⇒ Shifted which are equivalent concepts for 2-families (= simple graphs), but strict implications for kfamilies with k ≥ 3. The implication that uniquel...

In this paper the existence of a quadratic control Lyapunov function for bilinear systems is considered. The existence of a control Lyapunov function ensures the existence of a control law which ensures the global asymptotic stability of the closed loop control system. In this paper we will derive conditions for the existence of a control Lyapunov function for bilinear systems. These conditions...

The matching energy is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph, which is proposed first by Gutman and Wagner [The matching energy of a graph, Discrete Appl. Math. 160 (2012) 2177–2187]. And they gave some properties and asymptotic results of the matching energy. In this paper, we characterize the trees with n vertices whose complements have t...

In this paper, I am raising the issue of missing data treatment in producing continuous spatio-temporal fields of biogeophysical variables from AVHRR and MODIS or MODIS-like sensor data. Climate and numerical forecast models that use surface variables require that input fields be continuous in time and space (e.g. Gutman, 1990). However, quite often the datasets produced for use in the models h...

The matching energy of a graph was introduced by Gutman and Wagner in 2012 and defined as the sum of the absolute values of zeros of its matching polynomial. Let θ(r, s, t) be the graph obtained by fusing two triples of pendant vertices of three paths Pr+2, Ps+2 and Pt+2 to two vertices. The graph obtained by identifying the center of the star Sn−g with the degree 3 vertex u of θ(1, g−3, 1) is ...

Let Ln be the hexagonal chain graph,Fn be the hexacyclic system graph and Mn be the Möbius hexacyclic system graph. Derflinger and Sofer gave the spectra of Ln and Fn by using group theoretical method. Later, Gutman gave the spectra of them using a polynomial result due to Godsil and McKay. In this paper, we give a simple and direct method to determine the characteristic polynomial and spectra ...

We discuss a robust alternative to the ex-post decomposition of a portfolio into the fundamental law co-efficients using statistically estimated breadth. The breadth of a market provides a measure of the number of independent bets available to the investor. We use the Keiser-Gutman stopping criterion to select the integer valued effective dimension eigenvalues greater-than or equal to 1. Such a...

A stable set in a graph G is a set of pairwise non-adjacent vertices and α(G) is the size of a maximum stable set in the graph G. The polynomial I(G; x) = s0 + s1x + s2x + ... + sαx, α = α(G), is called the independence polynomial of G (Gutman and Harary, 1983), where sk is the number of stable sets of cardinality k in G. I(G; x) is partial unimodal if the sequence of its coefficients (sk) is p...