The Domination Polynomial of a Graph at −1

Let G be a simple graph. The domination polynomial of a graph G of order n is the polynomial ${D(G,x)=\sum_{i=0}^{n} d(G,i) x^{i}}$ , where d(G, i) is the number of dominating sets of G of size i. In this article we investigate the domination polynomial at ?1. We give a construction showing that for each odd number n there is a connected graph G with D(G, ?1) = n.     

An answer to a question on the convolution of functions

Let G be a locally compact group. Recently, G?a¸b and Strobin [2] asked when f*g exists for all \({f, g \in L^p(G)}\) , and also: is the set \({\{(f,g)\in L^p(G) \times L^p(G): f\ast g \in L^p(G)\}}\) σ-c-lower porous (in particular, meager) for \({p\in(1,2]}\) ? In this paper, we answer these questions. In particular, we prove that if 1 <  p <  ∞, 1 ≤  q < ∞, and G is a non-unimodular locally compact group, then the set \({\{(f, g) \in L^p(G) \times L^q(G): f * g}\) is not λ -a.e. finite on G} is a residual set in L ^p (G) ×  L ^q (G).     

Analytical study of mixed electroosmotic-pressure-driven flow in rectangular micro-channels

Operational state of many miniaturized devices deals with flow field in microchannels. Pressure-driven flow (PDF) and electroosmotic flow (EOF) can be recognized as the two most important types of the flow field in such channels. EOF has many advantages in comparison with PDF, such as being vibration free and not requiring any external mechanical pumps or moving parts. However, the disadvantages of this type of flow such as Joule heating, electrophoresis demixing, and not being suitable for mobile devices must be taken into consideration carefully. By using mixed electroosmotic/pressure-driven flow, the role of EOF in producing desired velocity profile will be reduced. In this way, the advantages of EOF can be exploited, and its disadvantages can be prevented. Induced pressure gradient can be utilized in order to control the separation in the system. Furthermore, in many complicated geometries such as T-shape microchannels, turns may induce pressure gradient to the electroosmotic velocity. While analytical formulas are completely essential for analysis and control of any industrial and laboratory microdevices, lack of such formulas in the literature for solving Poisson–Boltzmann equation and predicting electroosmotic velocity field in rectangular domains is evident. In the present study, first a novel method is proposed to solve Poisson–Boltzmann equation (PBE). Subsequently, this solution is utilized to find the electroosmotic and the mixed electroosmotic/pressure-driven velocity profile in a rectangular domain of the microchannels. To demonstrate the accuracy of the presented analytical method in solving PBE and finding electroosmotic velocity, a general nondimensional example is analyzed, and the results are compared with the solution of boundary element method. Additionally, the effects of different nondimensional parameters and also aspect ratio of channels on the electroosmotic part of the flow field will be investigated.     

Introducing the theory of successful settling in order to evaluate and optimize the sedimentation tanks

A rectangular settling tank in full scale is investigated using the Fluent software to increase its efficiency. First, the pure water is simulated in the absence of particles. Then particles are injected into the flow field and tracked by means of the discrete phase model. Three methods are presented to optimize the settling tank: (1) adding a baffle which is mounted in the bottom and is extended up to the near of free surface, (2) adding a baffle which is mounted in the free surface and is extended up to the near of the tank bottom and (3) install a bi-directional baffle which is mounted in the free surface and is extended up to the near of the bottom. These three suggestions are checked using the short-circuiting phenomenon and the successful settling theory. The successful settling theory states that a particle can be accounted as a “trapped” particle if (1) settled particle stays static and stable in the tank bottom and (2) settled particle doesn’t return to purified sewage. Although the second method provided higher efficiency, the third method was selected as the most appropriate method in order to optimize the settling tank.     

New Correlative Models to Improve Prediction of Fracture Permeability and Inertial Resistance Coefficient

Presence of fracture roughness and occurrence of nonlinear flow complicate fluid flow through rock fractures. This paper presents a qualitative and quantitative study on the effects of fracture wall surface roughness on flow behavior using direct flow simulation on artificial fractures. Previous studies have highlighted the importance of roughness on linear and nonlinear flow through rock fractures. Therefore, considering fracture roughness to propose models for the linear and nonlinear flow parameters seems to be necessary. In the current report, lattice Boltzmann method is used to numerically simulate fluid flow through different fracture realizations. Flow simulations are conducted over a wide range of pressure gradients through each fracture. It is observed that creeping flow at lower pressure gradients can be described using Darcy’s law, while transition to inertial flow occurs at higher pressure gradients. By detecting the onset of inertial flow and regression analysis on the simulation results with Forchheimer equation, inertial resistance coefficients are determined for each fracture. Fracture permeability values are also determined from Darcy flow as well. According to simulation results through different fractures, two parametric expressions are proposed for permeability and inertial resistance coefficient. The proposed models are validated using 3D numerical simulations and experimental results. The results obtained from these two proposed models are further compared with those obtained from the conventional models. The calculated average absolute relative errors and correlation coefficients indicate that the proposed models, despite their simplicity, present acceptable outcomes; the models are also more accurate compared to the available methods in the literature.     

Marine Bacterial Dextranases: Fundamentals and Applications

Dextran, a renewable hydrophilic polysaccharide, is nontoxic, highly stable but intrinsically biodegradable. The α-1, 6 glycosidic bonds in dextran are attacked by dextranase (E.C. 3.2.1.11) which is an inducible enzyme. Dextranase finds many applications such as, in sugar industry, in the production of human plasma substitutes, and for the treatment and prevention of dental plaque. Currently, dextranases are obtained from terrestrial fungi which have longer duration for production but not very tolerant to environmental conditions and have safety concerns. Marine bacteria have been proposed as an alternative source of these enzymes and can provide prospects to overcome these issues. Indeed, marine bacterial dextranases are reportedly more effective and suitable for dental caries prevention and treatment. Here, we focused on properties of dextran, properties of dextran—hydrolyzing enzymes, particularly from marine sources and the biochemical features of these enzymes. Lastly the potential use of these marine bacterial dextranase to remove dental plaque has been discussed. The review covers dextranase-producing bacteria isolated from shrimp, fish, algae, sea slit, and sea water, as well as from macro- and micro fungi and other microorganisms. It is common knowledge that dextranase is used in the sugar industry; produced as a result of hydrolysis by dextranase and have prebiotic properties which influence the consistency and texture of food products. In medicine, dextranases are used to make blood substitutes. In addition, dextranase is used to produce low molecular weight dextran and cytotoxic dextran. Furthermore, dextranase is used to enhance antibiotic activity in endocarditis. It has been established that dextranase from marine bacteria is the most preferable for removing plaque, as it has a high enzymatic activity. This study lays the groundwork for the future design and development of different oral care products, based on enzymes derived from marine bacteria.     

Preparation of Polycarbonate-ZnO Nanocomposite Films: Surface Investigation after UV Irradiation

Polycarbonate (PC)-ZnO films with different percentages of ZnO were prepared by a solution stirring technique and subjected to ultraviolet (UV; λ = 254 nm) irradiation. Structural parameters of the samples and the effects of UV irradiation on the surface properties of the PC and PC-ZnO nanocomposites were evaluated by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM), water contact angle (WCA) measurements, and a Vickers microhardness (H_V) tester. The XRD patterns of the nanocomposite films were found to show an increase in crystallinity with the increasing ZnO nanoparticles percentage. The WCA was found to be reduced from 90° to 17° after 15 h of UV irradiation, which could be ascribed to the oxidation of the surface of the samples during the irradiation and exposure of the ZnO nanoparticles, a result that is also supported by the obtained XPS data. The microhardness value of the PC-ZnO films including 30 wt.% ZnO enhanced considerably after UV radiation, which can also be attributed to the exposition of the ZnO nanoparticles after photodegradation of the PC superficial layer of the nanocomposite films.     

Phosphorus Fertilizers from Sewage Sludge Ash and Animal Blood as an Example of Biobased Environment-Friendly Agrochemicals: Findings from Field Experiments

Wastes of biological origin from wastewater treatment systems and slaughterhouses contain substantial amounts of phosphorus (P) with high recovery potential and can contribute to alleviating the global P supply problem. This paper presents the performance of fertilizer (AF) and biofertilizer (BF) from sewage sludge ash and animal blood under field conditions. BF is AF incorporated with lyophilized cells of P-solubilizing bacteria, Bacillus megaterium. In the experiments with spring or winter wheat, the biobased fertilizers were compared to commercial P fertilizer, superphosphate (SP). No P fertilization provided an additional reference. Fertilizer effects on wheat productivity and on selected properties of soil were studied. BF showed the same yield-forming efficiency as SP, and under poorer habitat conditions, performed slightly better than AF in increasing yield and soil available P. Biobased fertilizers applied at the P rate up to 35.2 kg ha^–1 did not affect the soil pH, did not increase As, Cd, Cr, Ni, and Pb content, and did not alter the abundance of heterotrophic bacteria and fungi in the soil. The findings indicate that biobased fertilizers could at least partially replace conventional P fertilizers. Research into strain selection and the proportion of P-solubilizing microorganisms introduced into fertilizers should be continued.