in this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.

The ferrocyanide-based organic redox flow battery (ferrocyanide-based ORFB), based on electrochemistry, has become a potential energy storage technology due to its low price, eco-friendliness, safety, and convenience. However, efficiency poor mass transfer performance hinder the application of ORFB. influence electrode shape (trapezoid, sector, rectangle) are studied numerical model, which is v...

‎in this paper we introduce mixed unitary cayley graph $m_{n}$‎ ‎$(n>1)$ and compute its eigenvalues‎. ‎we also compute the energy of‎ ‎$m_{n}$ for some $n$‎.

A 45-year-old woman presented to the emergency department with left wrist pain following a fall. Physical exam was remarkable for soft tissue swelling of the palmar and dorsal hand, point tenderness at the base of the second metacarpal, and limited active range of motion. Three-view wrist radiographs showed significant soft tissue swelling without evidence of fracture or dislocation. Computed t...

We consider an edge-isoperimetric problem (EIP) on the cartesian powers of graphs. One of our objectives is to extend the list of graphs for whose cartesian powers the lexicographic order provides nested solutions for the EIP. We present several new classes of such graphs that include as special cases all presently known graphs with this property. Our new results are applied to derive best poss...

We introduce nite relational structures called sketches, that represent edge crossings in drawings of nite graphs. We consider the problem of characterizing sketches in Monadic Second-Order logic. We answer positively the question for framed sketches, i.e., for those representing drawings of graphs consisting of a planar connected spanning subgraph (the frame) augmented with additional edges th...

Let c : E(G) → [k] be an edge-coloring of a graph G, not necessarily proper. For each vertex v, let c̄(v) = (a1, . . . , ak), where ai is the number of edges incident to v with color i. Reorder c̄(v) for every v in G in nonincreasing order to obtain c∗(v), the color-blind partition of v. When c∗ induces a proper vertex coloring, that is, c∗(u) 6= c∗(v) for every edge uv in G, we say that c is col...