Maximum Degree Research Articles

Extraction of gallium from carbon concentrate - Aluminum industry waste

A complex approach to the extraction of gallium from a carbon concentrate (CC), a waste product of the aluminum industry, was considered. Ashing of CC made it possible to remove the main component - carbon and obtain ash, which is an oxide mineral-like compound, from which gallium was leached with solutions of inorganic acids and their mixtures. The maximum degree of leaching (98%) of gallium was achieved with 6 M HCl for ash after ashing the CC at 600 °C. It was shown that Purolite anion exchangers with highly basic tertiary and quaternary ammonium base groups recovered gallium(III) from 2 to 10 M HCl, where the sorption equilibrium was attained after 60 min. The maximum extraction was observed from 6 M HCl. Under optimal conditions, the maximum sorption capacities for gallium(III) were achieved for Purolite A300 (2.7 mmol g−1) and Purolite A500 (2.2 mmol g−1) sorbents. Gallium(III) was quantitatively (99%) eluted from the sorbents with distilled water. Sorption of gallium(III) and its subsequent desorption with water made it possible to separate it from the predominant amounts of transition metal ions: Fe(III), Ni(II), Co(II), Zn(II), V(V) and other cations: Al3+, Ca2+, Mg2+, Na+ and K+. The addition of sodium hydroxide to the concentration of 200 g L−1 resulted in the cementation of gallium on aluminum gallama (liquid gallium‑aluminum alloy).

Large monochromatic components in expansive hypergraphs

AbstractA result of Gyárfás [12] exactly determines the size of a largest monochromatic component in an arbitrary $r$ -colouring of the complete $k$ -uniform hypergraph $K_n^k$ when $k\geq 2$ and $k\in \{r-1,r\}$ . We prove a result which says that if one replaces $K_n^k$ in Gyárfás’ theorem by any ‘expansive’ $k$ -uniform hypergraph on $n$ vertices (that is, a $k$ -uniform hypergraph $G$ on $n$ vertices in which $e(V_1, \ldots, V_k)\gt 0$ for all disjoint sets $V_1, \ldots, V_k\subseteq V(G)$ with $|V_i|\gt \alpha$ for all $i\in [k]$ ), then one gets a largest monochromatic component of essentially the same size (within a small error term depending on $r$ and $\alpha$ ). As corollaries we recover a number of known results about large monochromatic components in random hypergraphs and random Steiner triple systems, often with drastically improved bounds on the error terms.Gyárfás’ result is equivalent to the dual problem of determining the smallest possible maximum degree of an arbitrary $r$ -partite $r$ -uniform hypergraph $H$ with $n$ edges in which every set of $k$ edges has a common intersection. In this language, our result says that if one replaces the condition that every set of $k$ edges has a common intersection with the condition that for every collection of $k$ disjoint sets $E_1, \ldots, E_k\subseteq E(H)$ with $|E_i|\gt \alpha$ , there exists $(e_1, \ldots, e_k)\in E_1\times \cdots \times E_k$ such that $e_1\cap \cdots \cap e_k\neq \emptyset$ , then the smallest possible maximum degree of $H$ is essentially the same (within a small error term depending on $r$ and $\alpha$ ). We prove our results in this dual setting.

Nordhaus–Gaddum-Type Results for the k-Independent Number of Graphs

The concept of [Formula: see text]-independent set, introduced by Fink and Jacobson in 1986, is a natural generalization of classical independence set. A [Formula: see text]-independent set is a set of vertices whose induced subgraph has maximum degree at most [Formula: see text]. The [Formula: see text]-independence number of [Formula: see text], denoted by [Formula: see text], is defined as the maximum cardinality of a [Formula: see text]-independent set of [Formula: see text]. As a natural counterpart of the [Formula: see text]-independence number, we introduced the concept of [Formula: see text]-edge-independence number. An edge set [Formula: see text] in [Formula: see text] is called [Formula: see text]-edge-independent if the maximum degree of the subgraph induced by the edges in [Formula: see text] is less or equal to [Formula: see text]. The [Formula: see text]-edge-independence number, denoted [Formula: see text], is defined as the maximum cardinality of a [Formula: see text]-edge-independent set. In this paper, we study the Nordhaus–Gaddum-type results for the parameter [Formula: see text] and [Formula: see text]. We obtain sharp upper and lower bounds of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] for a graph [Formula: see text] of order [Formula: see text]. Some graph classes attaining these bounds are also given.

Nordhaus–Gaddum-Type Results for the Strong Equitable Vertex k-Arboricity of Graphs

For a graph [Formula: see text] and positive integers [Formula: see text], [Formula: see text], a [Formula: see text]-tree-vertex coloring of [Formula: see text] refers to a [Formula: see text]-vertex coloring of [Formula: see text] satisfying every component of each induced subgraph generated by every set of vertices with the same color forms a tree with maximum degree not larger than [Formula: see text], and it is called equitable if the difference between the cardinalities of every pair of sets of vertices with the same color is at most [Formula: see text]. The strong equitable vertex [Formula: see text]-arboricity of [Formula: see text], denoted by [Formula: see text], is defined as the least positive integer [Formula: see text] satisfying [Formula: see text], which admits an equitable [Formula: see text]-tree-vertex coloring for each integer [Formula: see text] with [Formula: see text]. The strong equitable vertex [Formula: see text]-arboricity of a graph is very useful in graph theory applications such as load balance in parallel memory systems, constructing timetables and scheduling. In this paper, we present the tight upper and lower bounds on [Formula: see text] for an arbitrary graph [Formula: see text] with [Formula: see text] vertices and a given integer [Formula: see text] with [Formula: see text], and we characterize the extremal graphs [Formula: see text] with [Formula: see text], [Formula: see text], [Formula: see text], respectively. Based on the above extremal results, we further obtain the Nordhaus–Gaddum-type results for [Formula: see text] of graphs [Formula: see text] with [Formula: see text] vertices for a given integer [Formula: see text] with [Formula: see text].

Preparation and Characterization of PVA/Chitosan-Based Hydrogels Enriched with Carbon Materials via the Freeze-Thaw Method

The freeze-thaw method successfully prepared polyvinyl alcohol (PVA)/chitosan (CS)-based hydrogels. This study evaluated the hydrogel’s physical and thermal properties with a compositional variation of activated carbon (AC) and reduced graphene oxide (rGO) in PVA/CS (PCS) hydrogel. Incorporating AC into the PCS hydrogel led to pore reduction, yielding a lower swelling degree in PCS/AC hydrogel than in PCS hydrogel. On the other hand, adding rGO had minimal impact on the shape and distribution of pores. However, rGO exhibited effective dispersion on the hydrogel surface, reducing the swelling degree of PCS/rGO hydrogel. The maximum swelling degree only showed an increase in PCS/AC 0.1%, attributed to the porous nature of AC, effectively binding water molecules while maintaining a relatively consistent pore size compared to PCS hydrogel. Incorporating AC and rGO into the PCS hydrogel enhanced thermal stability, which is evident from the increased residue and endothermic peak temperature compared to the hydrogel without AC and rGO. These findings suggest that the modification with AC and rGO can enhance the physical and thermal properties of PCS hydrogel.

Gene Biomarkers in Congenital Hyperinsulinism

Congenital hyperinsulinism (CHI) is a rare type of disease that causes a severe drop in blood sugar in infants. This diseaseprevents reaching enough sugar to the child’s brain and causes lifelong and permanent damage. This study aims to investigate genebiomarkers in congenital hyperinsulinism. In this study, after reviewing the texts and searching for the bioinformatics databases of NCBI,Genecards, Swiss-prot, Diseasome, etc., the genes involved in the disease based on at least one of the methods in-vivo, in-vitro, and insilicohas been extracted as candidate genes. The expression data obtained from each group was standardized compared to the controlgroup to compare the results in case and control groups. Then, the connection network of expression data of candidate genes in patientsand healthy people were drawn separately with the help of MATLAB software (Version 9.1), and the correctness of these networks anddetermined biomarkers were checked using the rectome and diseasome database. All statistical calculations were done using R and Matlabsoftware. In the present study, the essential genes of CHI disease were identified using 5 central criteria, including maximum neighborhoodcomponent, degree, closeness, radiality, and betweeness. Based on the results of the central criteria method, INS-PRKACA-PRKACBPRKACG-AKT1 genes had the most repetitions. According to the identification of the most effective genes related to CHI disease in thepresent study, it is suggested that further studies need to be designed at the in vitro and clinical levels on the identified effective genes asdiagnostic biomarkers of CHI disease.

OPTIMAL CONDITIONS FOR LIME TREATMENT OF MINE WASTEWATER FROM POLYMETALLIC ORE MINES

Mine waters of polymetallic mines are multicomponent systems containing ions of heavy non-ferrous metals, calcium, magnesium, iron, ammonium, as well as chlorides, sulfates, fluorides and other components in a wide range of concentrations. As a rule, water purification of this type is carried out by the lime method, which provides a fairly high degree of extraction of the most toxic pollutants (metals), with relatively small material costs. Taking into account the large volume, complexity and variation of the composition of mine waters, the tasks of optimizing reagent consumption, methods of its supply and effective control of the purification process still do not lose their relevance. The article presents the results of laboratory studies to determine the optimal conditions for processing model solutions that provide the maximum degree of purification for specific conditions of the Irtysh mine (East Kazakhstan). Experimental data obtained on model solutions are confirmed by the results of purification of real mine waste water. The results of experiments with mine water confirmed that the selected pH region of 9.5–10.5 can be accepted as optimal, which will allow achieving a high degree of purification of mine water.

On the total chromatic number of the direct product of cycles and complete graphs

A k-total coloring of a graph G is an assignment of k colors to the elements (vertices and edges) of G so that adjacent or incident elements have different colors. The total chromatic number is the smallest integer k for which G has a k-total coloring. The well known Total Coloring Conjecture states that the total chromatic number of a graph is either Δ(G) + 1 (called Type 1) or Δ(G) + 2 (called Type 2), where Δ(G) is the maximum degree of G. We consider the direct product of complete graphs Km × Kn. It is known that if at least one of the numbers m or n is even, then Km × Kn is Type 1, except for K2 × K2. We prove that the graph Km × Kn is Type 1 when both m and n are odd numbers, by using that the conformable condition is sufficient for the graph Km × Kn to be Type 1 when both m and n are large enough, and by constructing the target total colorings by using Hamiltonian decompositions and a specific color class, called guiding color. We additionally apply our technique to the direct product Cm × Kn of a cycle with a complete graph. Interestingly, we are able to find a Type 2 infinite family Cm × Kn, when m is not a multiple of 3 and n = 2. We provide evidence to conjecture that all other Cm × Kn are Type 1.

Density of identifying codes of hexagonal grids with finite number of rows

In a graph G, a set C ⊆ V (G) is an identifying code if, for all vertices v in G, the sets N[v] ∩ C are all nonempty and pairwise distinct, where N[v] denotes the closed neighbourhood of v. We focus on the minimum density of identifying codes of infinite hexagonal grids Hk with k rows, denoted by d*(Hk), and present optimal solutions for k ≤ 5. Using the discharging method, we also prove a lower bound in terms of maximum degree for the minimum-density identifying codes of well-behaved infinite graphs. We prove that d*(H2) = 9/20, d*(H3) = 6/13 ≈ 0.4615, d*(H4) = 7/16 = 0.4375 and d*(H5) = 11/25 = 0.44. We also prove that H2 has a unique periodic identifying code with minimum density.

Analysis of the thermal properties in short sansevieria cylindrica fibre/PLA composites processed by twin screw extruder followed by hot press molding technique

Abstract Short Sansevieria cylindrica fibre/polylactic acid composites (SCFP) were fabricated using a twin screw extruder followed by the hot press technique, with variations in fibre loadings of 10 wt%, 20 wt%, 30 wt% and 40 wt%. The thermal properties of SCFP were assessed through dynamic mechanical analysis (DMA), thermomechanical analysis (TMA), thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). Notably, the samples loaded with 40 wt% of fibre exhibited an increased storage modulus. In terms of loss modulus, the fibre-loaded samples displayed high values, indicating more heat is released during DMA experiment. Interestingly, the composite trend did not solely rely on increasing fibre loading, highlighting the intricate interplay between reinforcement and matrix crucial for determining viscoelastic properties across various temperatures. The TGA results revealed a decrease in inflection temperature with increasing fibre loadings, accompanied by a proportional rise in residues. The DSC thermograms indicated minimal differences in Tg, Tcc, and Tm values among composites with varying fibre loadings. However, neat PLA showed slightly higher values than the composites. On the other hand, reinforcing SCF into the PLA matrix promoted the crystallization of PLA by 1%–3% with the maximum degree of crystallinity of 25.4% obtained for 30 wt% of SCFP.

Dynamic Correlation between Platelet Aggregation and Inflammatory-like State in Athlete Horses

This study aimed to assess the effect of exercise on serum electrophoretic protein pattern, C-reactive protein (CRP) and platelet aggregation in horses subjected to a jumping exercise. The possible relationship between acute-phase reactions and platelet reactivity in the context of exercise was investigated. Blood samples were collected from 10 jumper horses at rest (TREST), within 5 min from the end of exercise (TPE5), and 30 min (TPE30) and 60 min after exercise (TPE60). The serum values of total proteins; CRP; albumin; α1-, α-2, β1-, β2- and γ-globulins; and the maximum degree of aggregation and the initial velocity of aggregation (slope) were evaluated. According to one-way analysis of variance, CRP and α1-, α-2, β1- and β2-globulins increased after exercise compared with rest condition (p < 0.001), whereas albumin and platelet aggregation showed lower values after exercise than at rest (p < 0.001). CRP and α1-globulin values were negatively correlated with both platelet aggregation indices at TPE5, whereas no significant correlation among these parameters was found at TREST, TPE30 and TPE60. This study provides evidence that an acute-phase response occurred in horses after the jumping exercise and suggests a linkage between the inflammatory status and the platelet responsiveness in horses during exercise.

Minimum collisions assignment in interdependent networked systems via defective colorings

In conjunction with the traffic overload of next-generation wireless communication and computer networks, their resource-constrained nature calls for effective methods to deal with the fundamental resource allocation problem. In this context, the Minimum Collisions Assignment (MCA) problem in an interdependent networked system refers to the assignment of a finite set of resources over the nodes of the network, such that the number of collisions, i.e., the number of interdependent nodes receiving the same resource, is minimized. Given the interdependent networked system's organization in the form of a graph, there already exists a randomized algorithm that converges with high probability to an assignment of resources having zero collisions when the number of resources is larger than the maximum degree of the underlying graph. In this article, differing from the prevailing literature, we investigate the case of a resource-constrained networked system, where the number of resources is less than or equal to the maximum degree of the underlying graph. We introduce two distributed, randomized algorithms that converge in a logarithmic number of rounds to an assignment of resources over the network for which every node has at most a certain number of collisions. The proposed algorithms apply to settings where the available resources at each node are equal to three and two, respectively, while they are executed in a fully-distributed manner without requiring information exchange between the networked nodes.

Impact of Thermal Stress on Biological Parameters of Chrysoperla zastrowi sillemi (Esben Petersen) under Laboratory Conditions

Aphid lions (Chrysoperla zastrowi sillemi, Esben-Petersen) are important predators in integrated pest management for field crops and vegetables (Neuroptera: Chrysopidae). It is found in almost every environment on Earth, except temperate ones. One of the most significant environmental variables influencing an insect species' growth rate is temperature. Five consistent temperatures were observed: 20±1°C, 25±1°C, 30±1°C, 35±1°C, and 40±1°C. The impact of temperature on biological parameters and developmental phases of Aphid lions feeding on rice moth eggs was noted. The development time of C. zastrowi sillemi was found to be 47.26 days at 20°C and 22.18 days at 40°C. The lifespan of adult males and females was more than twice as long at the lower temperature range as it was at the higher one. The temperature of 25°C produced the greatest duration of oviposition (55.12 days), the highest percentage of pupils (91.43%) and adults’ emergence (90.25%), the maximum fecundity (903.33 eggs/female), and the maximum degree of hatchability (90.84%) of eggs, suggesting that this temperature regime was more suited for the C. zastrowi sillemi that originated in Delhi. The results demonstrate significant variations in the developmental cycle of the immature stages at five distinct temperatures, with a negative relation between temperature increase and developmental duration.

Optomechanical squeezing with strong harmonic mechanical driving.

In this paper, we propose an optomechanical scheme for generating mechanical squeezing over the 3 dB limit, with the mechanical mirror being driven by a strong and linear harmonic force. In contrast to parametric mechanical driving, the linearly driven force shakes the mechanical mirror periodically oscillating at twice the mechanical eigenfrequency with large amplitude, where the mechanical mirror can be dissipatively stabilized by the engineered cavity reservoir to a dynamical squeezed steady state with a maximum degree of squeezing over 8 dB. The mechanical squeezing of more than 3 dB can be achieved even for a mechanical thermal temperature larger than 100 mK. The scheme can be implemented in a cascaded optomechanical setup, with potential applications in engineering continuous variable entanglement and quantum sensing.

First assessment of flow phenomena of acute and chronic thrombosis in the jugular veins using new ultrasound vector-flow imaging.

First assessment of flow changes in the jugular veins using high resolution ultrasound vector flow. 15 patients (8 males, 7 females) with an age range of 35 to 82 years (mean age 58.53±12.26 years) were examined by an experienced examiner using high power ultrasound equipment (Resona R9, Mindray) with probe technology (Mindray L9-3U Linear Array transducer, 2.5 to 9.0 MHz). This group was compared with five healthy subjects (mean age 35.4±13.79 years) as a reference. To assess flow changes, the color-coded duplex sonography and the novel vector flow technique were used. The evaluation was performed of vector morphology changes, turbulence, and wall resistance measurements. There were changes after acute and chronic thrombosis in 9 cases, and venous compression in 7 cases. Turbulence was measurable from 0.01 % to 64.44 %, the average turbulence was 19.73±22.06 %. Wall resistance measurement showed values from 0.01 Pa to 3.14 Pa, depending on the age of the thrombosis or compression. The reference veins showed turbulence of 0.94±1.5 % and a mean wall resistance of 0.05±0.05 Pa. There are statistically significant differences between normal and thrombotic or compressed veins in terms of maximum wall stress (p = 0.006) and mean degree of turbulence (p = 0.012), while the difference in mean wall stress is not statistically significant (p = 0.058). Despite still existing technical limitations, the combination of V-flow and wall stress measurements in jugular vein changes suggests a high diagnostic potential.

Pore structure characterization of sandstone under different water invasion cycles using micro-CT

The meso-structural changes of rocks during repeated cycles of water invasion are the fundamental cause of macroscopic physical property damage. In this paper, based on the computed tomography scan images of rock samples under different numbers of water invasion cycles, a three-dimensional pore network model was constructed to analyze the changes in pore structure under the action of water invasion. The damage variable was introduced to quantitatively characterize the parameter damage of each pore and reveal the evolution of rock meso-damage. The results show that 81% of the pore radius is less than 10 μm under 0 water invasion cycles and that 76% of the pore radiuses are less than 10 μm after 10 water invasion cycles. After 10 water invasion cycles, the peak range of the pore radius distribution enlarged from the initial range of 2–4 μm to that of 4–6 μm and the proportion of pore throats with a radius less than 10 μm decreased from an initial 82–72%. With an increase of water invasion cycles, the proportion of large pores increased and the connectivity among pores enhances gradually. The damage variable of each pore parameter changed the most during 2–5 water invasion cycles. After 10 water invasion cycles, the maximum degree of damage that the pore volume reached was up to 41.44% and the minimum degree of damage of the pore coordination number was 5.80%. The test results helped to reveal the pore structure changes and the damage of rock samples during water invasion cycles.

Optimal Operation Model of Ecological Flow of Hydropower Station Based on Genetic Algorithm and Neural Network

In view of the contradiction between the ecological flow regulation of the reservoir River and the power generation flow regulation of the reservoir with the largest power generation, this paper takes the maximum power generation and the maximum average ecological protection degree as the objective function, and uses the genetic algorithm back propagation neural networks (GA-BP) algorithm to establish the reservoir flow regulation model under the constraints of water balance, reservoir capacity, unit output and unit overflow, The optimal solution of the dispatching scheme is carried out, and the Shulehe hydropower station is taken as an example to verify the optimal scheme. The results show that the optimized dispatching model can ensure the demand of ecological flow, increase 32680 kW·h power generation and 23.85% power generation benefit, so as to provide scientific reference for the rational planning, dispatching and utilization of reservoir water resources.

Degree based energy and spectral radius of a graph with self-loops

Let GX be a graph obtained from a simple graph G by attaching a self-loop at each vertex of X ⊆ V ( G ) . The general extended adjacency matrix for the graph GX is defined and the bounds for the degree based energy of the graph GX are obtained. The study extends the notion of degree based energy of simple graphs to graphs with self-loops. For the graph GX of order n and size m with σ self-loops, the adjacency energy, E ( G X ) ≥ 4 mn + 2 σ ( n − σ ) n . The spectral radius ρ ( G X ) of its adjacency matrix is always less than or equal to 1 2 [ − 1 + 1 + 4 ( 2 m + σ + Δ − 1 ) ] , where Δ is the maximum degree in the graph GX and the equality conditions are given for 0 < σ < n . Few more bounds for ρ ( G X ) are also obtained. The study shows that, the spectral radius f max ( G X ) of its extended adjacency matrix satisfies: min i ∼ j F ij ( 2 m + σ ) n ≤ f max ( G X ) ≤ max i ∼ j F ij 2 ( 2 m + σ ) . We conclude the article by computing the extended adjacency spectrum of complete graph and complete bipartite graphs with self-loops.

Submodular Functions and Perfect Graphs

We give a combinatorial polynomial-time algorithm to find a maximum weight independent set in perfect graphs of bounded degree that do not contain a prism or a hole of length four as an induced subgraph. An even pair in a graph is a pair of vertices all induced paths between which are even. An even set is a set of vertices every two of which are an even pair. We show that every perfect graph that does not contain a prism or a hole of length four as an induced subgraph has a balanced separator which is the union of a bounded number of even sets, where the bound depends only on the maximum degree of the graph. This allows us to solve the maximum weight independent set problem using the well-known submodular function minimization algorithm. Funding: This work was supported by the Engineering and Physical Sciences Research Council [Grant EP/V002813/1]; the National Science Foundation [Grants DMS-1763817, DMS-2120644, and DMS-2303251]; and Alexander von Humboldt-Stiftung.

Inclusion chromatic index of random graphs

AbstractErdős and Wilson proved in 1977 that almost all graphs have chromatic index equal to their maximum degree. In 2001 Balister extended this result and proved that the same number of colours is almost always sufficient if we additionally demand the distinctness of the sets of colours incident with any two vertices. We study a stronger condition and show that one more colour is almost always sufficient and necessary if the inclusion of these sets is forbidden for any pair of adjacent vertices. We also settle the value of a more restrictive graph invariant for almost all graphs, where inclusion is forbidden for all pairs of vertices, which necessitates one more colour for graphs of even order.