A graph $G$ is a minimal claw-free graph (m.c.f. graph) if it contains no $K_{1,3}$ (claw) as an induced subgraph and if, for each edge $e$ of $G$, $G-e$ contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices, and characterize graphs which have m.c.f. line graphs.
Formulation of many real-life problems evolves as the problem is being solved. These changes are typically initiated by a user intervention or by changes in the environment. In this paper, we propose a formal description of a so called minimal perturbation problem that allows an “automated” modification of the (partial) solution when the problém formulation changes. Our model is defined for constraint satisfaction i)roblenis with emphasis put on finding a solution anytime even for over-constrained problems.
Let $R$ be a ring. We recall that $R$ is called a near pseudo-valuation ring if every minimal prime ideal of $R$ is strongly prime. Let now $\sigma $ be an automorphism of $R$ and $\delta $ a $\sigma $-derivation of $R$. Then $R$ is said to be an almost $\delta $-divided ring if every minimal prime ideal of $R$ is $\delta $-divided. Let $R$ be a Noetherian ring which is also an algebra over $\mathbb {Q}$ ($\mathbb {Q}$ is the field of rational numbers). Let $\sigma $ be an automorphism of $R$ such that $R$ is a $\sigma (*)$-ring and $\delta $ a $\sigma $-derivation of $R$ such that $\sigma (\delta (a)) = \delta (\sigma (a))$ for all $a \in R$. Further, if for any strongly prime ideal $U$ of $R$ with $\sigma (U) = U$ and $\delta (U)\subseteq \delta $, $U[x; \sigma , \delta ]$ is a strongly prime ideal of $R[x; \sigma , \delta ]$, then we prove the following: (1) $R$ is a near pseudo valuation ring if and only if the Ore extension $R[x; \sigma ,\delta ]$ is a near pseudo valuation ring. (2) $R$ is an almost $\delta $-divided ring if and only if $R[x;\sigma ,\delta ]$ is an almost $\delta $-divided ring.
A necessary and sufficient condition for the Reeb vector field of a three dimensional non-Kenmotsu almost Kenmotsu manifold to be minimal is obtained. Using this result, we obtain some classifications of some types of (k, μ, v)-almost Kenmotsu manifolds. Also, we give some characterizations of the minimality of the Reeb vector fields of (k, μ, v)-almost Kenmotsu manifolds. In addition, we prove that the Reeb vector field of an almost Kenmotsu manifold with conformal Reeb foliation is minimal., Yaning Wang., and Obsahuje bibliografii
In this paper we obtain all invariant, anti-invariant and $CR$ submanifolds in $({\mathbb{R}}^4,g,J)$ endowed with a globally conformal Kähler structure which are minimal and tangent or normal to the Lee vector field of the g.c.K. structure.
Photoinactivation of photosystem 2 (PS2) results from absorption of so-called "excessive" photon energy. Chlorophyll a fluorescence can be applied to quantitatively estimate the portion of excessive photons by means of the parameter E = (F - F0')/Fm', which reflects the share of the absorbed photon energy that reaches the reaction centers (RCs) of PS2 complexes with QA in the reduced state ('closed' RCs). Data obtained for cotton (Gossypium hirsutum), bean (Phaseolus vulgaris), and arabidopsis (Arabidopsis thaliana) suggest a linear relationship between the total amount of the photon energy absorbed in excess (excessive irradiation) and the decline in PS2 activity, though the slope may differ depending on the species. This relationship was sensitive not only to the leaf temperature but also to treatment with methyl viologen. Such observations imply that the intensity of the oxidative stress as well as the plant's ability to detoxify active oxygen species may interact to determine the damaging potential of the excessive photons absorbed by PS2 antennae. Energy partitioning in PS2 complexes was adjusted during adaptation to irradiation and in response to a decrease in leaf temperature to minimize the excitation energy that is trapped by 'closed' PS2 RCs. The same amount of the excessive photons absorbed by PS2 antennae led to a greater decrease in PS2 activity at warmer temperatures, however, the delay in the development of non-photochemical and photochemical energy quenching under lower temperature resulted in faster accumulation of excessive photons during induction. Irradiance response curves of EF suggest that, at high irradiance (above 700 μmol m-2 s-1), steady-state levels of this parameter tend to be similar regardless of the leaf temperature. and D. Kornyeyev, A. S. Holaday, B. A. Logan.
This paper provides an extension of results connected with the problem of the optimization of a linear objective function subject to max−∗ fuzzy relational equations and an inequality constraint, where ∗ is an operation. This research is important because the knowledge and the algorithms presented in the paper can be used in various optimization processes. Previous articles describe an important problem of minimizing a linear objective function under a fuzzy max−∗ relational equation and an inequality constraint, where ∗ is the t-norm or mean. The authors present results that generalize this outcome, so the linear optimization problem can be used with any continuous increasing operation with a zero element where ∗ includes in particular the previously studied operations. Moreover, operation ∗ does not need to be a t-norm nor a pseudo-t-norm. Due to the fact that optimal solutions are constructed from the greatest and minimal solutions of a max−∗ relational equation or inequalities, this article presents a method to compute them. We note that the linear optimization problem is valid for both minimization and maximization problems. Therefore, for the optimization problem, we present results to find the largest and the smallest value of the objective function. To illustrate this problem a numerical example is provided.
In this paper we consider the following problem: Over the class of all simple connected unicyclic graphs on $n$ vertices with girth $g$ ($n$, $g$ being fixed), which graph minimizes the Laplacian spectral radius? Let $U_{n,g}$ be the lollipop graph obtained by appending a pendent vertex of a path on $n-g$ $(n> g)$ vertices to a vertex of a cycle on $g\geq 3$ vertices. We prove that the graph $U_{n,g}$ uniquely minimizes the Laplacian spectral radius for $n\geq 2g-1$ when $g$ is even and for $n\geq 3g-1$ when $g$ is odd.
We are considering a two-stage optimal scheduling problem, which involves two similar projects with the same starting times for workers and the same deadlines for tasks. It is required that the starting times for workers and deadlines for tasks should be optimal for the first-stage project and, under this condition, also for the second-stage project. Optimality is measured with respect to the maximal lateness (or maximal delay) of tasks, which has to be minimized. We represent this problem as a problem of tropical pseudoquadratic optimization and show how the existing methods of tropical optimization and tropical linear algebra yield a full and explicit solution for this problem.
Let $G$ be a finite connected graph with minimum degree $\delta $. The leaf number $L(G)$ of $G$ is defined as the maximum number of leaf vertices contained in a spanning tree of $G$. We prove that if $\delta \ge \frac {1}{2}(L(G)+1)$, then $G$ is 2-connected. Further, we deduce, for graphs of girth greater than 4, that if $\delta \ge \smash {\frac {1}{2}}(L(G)+1)$, then $G$ contains a spanning path. This provides a partial solution to a conjecture of the computer program Graffiti.pc [DeLaVi na and Waller, Spanning trees with many leaves and average distance, Electron. J. Combin. 15 (2008), 1–16]. For $G$ claw-free, we show that if $\delta \ge \frac {1}{2}(L(G)+1)$, then $G$ is Hamiltonian. This again confirms, and even improves, the conjecture of Graffiti.pc for this class of graphs.