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A proper orientation of a graph G=(V,E) is an orientation D of E(G) such that for every two adjacent vertices v and u, dD -(v) ≠ dD -(u) where dD -(v) is the number of edges with head v in D. The proper orientation number of G is defined as χ→(G)=minD∈Γmaxv∈V(G)d D -(v) where Γ is the set of proper orientations of G. We have χ(G)-1≤χ→(G)≤Δ(G), where χ(G) and Δ(G) denote the chromatic number and the maximum degree of G, respectively. We show that, it is NP-complete to decide whether χ→(G)=2, for a given planar graph G. Also, we prove that there is a polynomial time algorithm for determining the proper orientation number of 3-regular graphs. In sharp contrast, we will prove that this problem... 

A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation (Formula presented.) of G for every two adjacent vertices v and u, the sum of incoming edges of v and u in the oriented graph are different from each other. The universal labeling number of a graph G is the minimum number k such that G has universal labeling from (Formula presented.) denoted it by (Formula presented.). We have (Formula presented.), where (Formula presented.) denotes the maximum degree of G. In this work, we offer a provocative question that is: “Is there any polynomial function f such that for every graph G, (Formula presented.)?”. Towards this question, we introduce some... 

An additive labeling of a graph G is a function H: V(G)→ N, such that for every two adjacent vertices v and u of G, Σw∼v l(w) = Σw∼vl(w) (x ∼ y means that x is joined to y). The additive number of G, denoted by η(G), is the minimum number k such that G has a additive labeling l: V(G)→ Nk. The additive choosability of a graph G, denoted by ηl(G), is the smallest number k such that G has an additive labeling for any assignment of lists of size k to the vertices of G, such that the label of each vertex belongs to its own list. Seamone in his PhD thesis conjectured that for every graph G, η(G) = ηe(G). We give a negative answer to this conjecture and we show that for every k there is a graph G... 

A graph G is weakly semiregular if there are two numbers a,b, such that the degree of every vertex is a or b. The weakly semiregular number of a graph G, denoted by wr(G), is the minimum number of subsets into which the edge set of G can be partitioned so that the subgraph induced by each subset is a weakly semiregular graph. We present a polynomial time algorithm to determine whether the weakly semiregular number of a given tree is two. On the other hand, we show that determining whether wr(G)=2 for a given bipartite graph G with at most three numbers in its degree set is NP-complete. Among other results, for every tree T, we show that wr(T)≤2log2 δ(T)+O(1), where δ(T) denotes the maximum... 

A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation ℓ of G for every two adjacent vertices v and u, the sum of incoming edges of v and u in the oriented graph are different from each other. The universal labeling number of a graph G is the minimum number k such that G has universal labeling from { 1 , 2 , … , k} denoted it by χu→ (G). We have 2 Δ (G) - 2 ≤ χu→ (G) ≤ 2 Δ ( G ), where Δ (G) denotes the maximum degree of G. In this work, we offer a provocative question that is: “Is there any polynomial function f such that for every graph G, χu→ (G) ≤ f(Δ (G)) ?”. Towards this question, we introduce some lower and upper bounds on their parameter... 

A graph G is weakly semiregular if there are two numbers a,b, such that the degree of every vertex is a or b. The weakly semiregular number of a graph G, denoted by wr(G), is the minimum number of subsets into which the edge set of G can be partitioned so that the subgraph induced by each subset is a weakly semiregular graph. We present a polynomial time algorithm to determine whether the weakly semiregular number of a given tree is two. On the other hand, we show that determining whether wr(G)=2 for a given bipartite graph G with at most three numbers in its degree set is NP-complete. Among other results, for every tree T, we show that wr(T)≤2log2⁡Δ(T)+O(1), where Δ(T) denotes the maximum... 

Optimization of the placement and operational conditions of oil wells plays an important role in the development of the oilfields. Several automatic optimization algorithms have been used by different authors in recent years. However, different optimizers give different results depending on the nature of the problem. In the current study, a comparison between the genetic algorithm and particle swarm optimization algorithms was made to optimize the operational conditions of the injection and production wells and also to optimize the location of the injection wells in a southern Iranian oilfield. The current study was carried out with the principal purpose of evaluating and comparing the... 

The construction of a facies model could be employed as a conditional data for any property simulation that results in a more reliable reservoir characterization in further steps. In this study, an Iranian gas reservoir with six wells was studied to determine the 3D reservoir facies model. Fifteen reservoir facies were first detected along one of the wells with detailed core and thin section descriptions. Due to the significant difference between the core and log data resolution, facies were clustered into four major groups regarding the digenetic processes and petrophysical lithofacies properties (permeability and porosity). The lithofacies specification effect on petrophysical properties... 

A proper vertex k-coloring of a graph G is called dynamic, if there is no vertex v∈V(G) with d(v)<2 and all of its neighbors have the same color. The smallest integer k such that G has a k-dynamic coloring is called the dynamic chromatic number of G and denoted by χ2(G). We say that v∈V(G) in a proper vertex coloring of G is a bad vertex if d(v)<2 and only one color appears in the neighbors of v. In this paper, we show that if G is a graph with the chromatic number at least 6, then there exists a proper vertex χ(G)-coloring of G such that the set of bad vertices of G is an independent set. Also, we provide some upper bounds for χ2(G)- χ(G) in terms of some parameters of the graph G  

A lucky labeling of a graph G is a function l:V(G)→N, such that for every two adjacent vertices v and u of G, σ w∼vl(w)≠ σ w∼ul(w) (x∼y means that x is joined to y). A lucky number of G, denoted by η(G), is the minimum number k such that G has a lucky labeling l:V(G)→{1,⋯,k}. We prove that for a given planar 3-colorable graph G determining whether η(G)=2 is NP-complete. Also for every k≥2, it is NP-complete to decide whether η(G)=k for a given graph G  

Enhanced oil recovery (EOR) methods assisted by gravity drainage mechanism and application of sophisticated horizontal wells bring new hope for heavy oil extraction. Variety of thermal and non-thermal EOR techniques inject an external source of energy and materials such as steam, solvent vapor, or gas through a horizontal well at the top of the reservoir to reduce in-situ heavy oil viscosity. So, the diluted oil becomes mobile and flows downwards by gravity drainage to a horizontal producer located at the bottom of the reservoir. In this paper, a sector model of an Iranian fractured carbonate heavy oil reservoir was provided to simulate and evaluate capability of some EOR techniques such as... 

In this work, a series of solvent- and water-injection scenarios were conducted on horizontal five-spot glass micromodels that were saturated initially with heavy oil. Sandstone and limestone rock look-alike and network patterns with different pore structures were used in the experiments. The results show that the ultimate oil recovery of a water-alternating-solvent (WAS) scheme was greater than that of a simultaneously water-alternating-solvent (SWAS) scheme, and the efficiency of a solvent-soak scheme also offers a greater recovery. Likewise, the WAS scheme resulted in greater oil recovery when compared with continuous solvent injection (CSI), with the same amount of solvent consumption.... 

This work is concerned with the role of geometrical properties of fractures on oil displacement efficiency during solvent injection to heavy oil. Here, a series of solvent injection processes were conducted on one-quarter five-spot fractured micromodels that were initially saturated with the heavy oil, at a fixed flow rate condition. The oil recovery was measured using image analysis of the continuously provided pictures. The results show that for the range of experiments performed here, the maximum oil recovery happens at a fracture orientation angle of 45 degrees. Also, increasing the number of fractures leads to a higher oil recovery factor by solvent in 45 degrees, while it does not... 

Background and Objective: Probiotics are dietary supplements with potential health benefits for humans when consumed regularly at appropriate quantities. The latest evidence shows possible beneficial effects of probiotics in COVID-19 treatment. Interests in probiotic consumption have led to provide products such as probiotic juices with vitamins, minerals, prebiotics and appropriate levels of probiotics to the market in free and encapsulated forms, which are not fully addressed in scientific literatures. The objective of this review was to investigate effects of probiotics for the management of human health. Other objectives included study on effects of free and encapsulated forms of... 

Background and Objective: Probiotics are dietary supplements with potential health benefits for humans when consumed regularly at appropriate quantities. The latest evidence shows possible beneficial effects of probiotics in COVID-19 treatment. Interests in probiotic consumption have led to provide products such as probiotic juices with vitamins, minerals, prebiotics and appropriate levels of probiotics to the market in free and encapsulated forms, which are not fully addressed in scientific literatures. The objective of this review was to investigate effects of probiotics for the management of human health. Other objectives included study on effects of free and encapsulated forms of... 

We introduce highly antifouling Polymer-Nanoparticle-Nanoparticle/Polymer (PNNP) hybrid membranes as multi-functional materials for versatile purification of wastewater. Nitrogen-rich polyethylenimine (PEI)-functionalized halloysite nanotube (HNT-SiO2-PEI) nanoparticles were developed and embedded in polyvinyl chloride (PVC) membranes for protein and dye filtration. Bulk and surface characteristics of the resulting HNT-SiO2-PEI nanocomposites were determined using Fourier-transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), transmission electron microscopy (TEM), and thermogravimetric analysis (TGA). Moreover, microstructure and...