In this paper a two-dimensional non-oriented guillotine bin packing problem is studied when items have different priorities. Our objective is to maximize the total profit which is total revenues minus costs of used bins and wasted area. A genetic algorithm is developed to solve this problem where a new coding scheme is introduced. To evaluate the performance of the proposed GA, first an upper b...

In this paper we give sharp upper bounds on the Zagreb indices and characterize all trees achieving equality in these bounds. Also, we give lower bound on first Zagreb coindex of trees.

Main result of this paper is the following theorem: given δ, 0 < δ < 1/3 and n ∈ N there exists an (n + 1) × n inner matrix function F ∈ H∞ (n+1)×n such that I ≥ F ∗(z)F (z) ≥ δI ∀z ∈ D, but the norm of any left inverse for F is at least [δ/(1−δ)]−n ≥ (2δ). This gives a lower bound for the solution of the Matrix Corona Problem, which is pretty close to the best known upper b bound C · δ−n−1 log...

The Carnot theorem, one expression of the second law thermodynamics, places a fundamental upper bound on efficiency heat engines operating between two baths. theorem can be stated in more generalized form for with multiple baths, where maximum is achieved reversible quasistatically In this study, we determine irreversible baths linear response regime, i.e., under small temperature differences a...

Our purpose is to show that complements of line graphs (of graphs) enjoy nice coloring properties. We for all in this class the local and usual chromatic numbers are equal. also prove a sufficient condition number be equal natural upper bound. A consequence latter complete characterization induced subgraphs Kneser graph KG ( n , 2 ) have its number, namely − 2. In addition bound, lower bound pr...

Limit analysis studies the asymptotic behavior of elastic-plastic materials and structures. The asymptotic material properties exist for a class of ductile metals and are designed into optimal structural members such as I-beams and composite plates. The analysis automatically ignores the relatively small elastic deformations. Classical lower and upper bound theorems in the form of inequalities ...

We consider a stochastic nonlinear fractional Langevin equation of two orders Dβ(Dα+γ)ψ(t)=λϑ(t,ψ(t))w˙(t),0&lt;t≤1. Given some suitable conditions on the above parameters, we prove existence and uniqueness mild solution to initial value problem for using Banach fixed-point theorem (Contraction mapping theorem). The upper bound estimate second moment is given, which shows exponential growth in ...

For a graph $G = (V, E)$, a partition $pi = {V_1,$ $V_2,$ $ldots,$ $V_k}$ of the vertex set $V$ is an textit{upper domatic partition} if $V_i$ dominates $V_j$ or $V_j$ dominates $V_i$ or both for every $V_i, V_j in pi$, whenever $i neq j$. The textit{upper domatic number} $D(G)$ is the maximum order of an upper domatic partition. We study the properties of upper domatic number and propose an up...