Edge Length Research Articles

Evaluation of Shortest Path by using Breadth-First Algorithm under Neutrosophic Environment

This paper recommends and designs concepts for evaluating the shortest path (SP) for a connected network using a modified breadth-first search algorithm in an uncertain environment. Evaluating the SPs of a network is an essential and extensively encountered optimization problem. Here we develop a new method for determining the SP in a neutrosophic environment in which the arc lengths are uncertain. Here, we use the parameters as neutrosophic numbers, and the new methodology, i.e., canonical representation of neutrosophic numbers in a neutrosophic environment, is used to convert neutrosophic edge lengths to crisp edge lengths and enhance the traditional breadth-first search algorithm. We employ this concept to accommodate the ambiguities in subjective decisions and address these issues. Here we demonstrate that the proposed algorithm has good stability and high efficiency for evaluating the SP. Finally, a numerical example is provided to explain the suggested algorithm.

On the complexity of the upgrading version of the maximal covering location problem

AbstractIn this article, we study the complexity of the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem is NP‐hard on general networks. However, in some particular cases, we prove that this problem is solvable in polynomial time. The cases of star and path networks combined with different assumptions for the model parameters are analysed. In particular, we obtain that the problem on star networks is solvable in time for uniform weights and NP‐hard for non‐uniform weights. On paths, the single facility problem is solvable in time, while the ‐facility problem is NP‐hard even with uniform costs and upper bounds (maximal upgrading per edge), as well as, integer parameter values. Furthermore, a pseudo‐polynomial algorithm is developed for the single facility problem on trees with integer parameters.

Determine the exact length of the veneers through programming the condylar inclination of the semi-adjustable articulator

Purpose: Various aspects of veneers have been described in literature, such as preparation, material, manufacturing method, bonding technique, remaining dental structure color, among others. The length of veneers incisal edge, that has been determined through photos or videos doing a functional evaluation, creating an anterior guide by mockup in addition to the diagnostic elements mentioned above, the veneers were exactly length based on the condyle inclination. Materials and methods: The technique shown in the following clinical case report, aims to customize the length of the veneers by programming the condylar inclination and the incisal plate of the semi-adjustable articulator. Results: The veneers made with the present technique was accurately. Conclusion: Customize the length of the veneers demonstrated avoid wear, fracture or breakdown of the bond.

Simulation-based design of bicuspidization of the aortic valve

ObjectiveSevere congenital aortic valve pathology in the growing patient remains a challenging clinical scenario. Bicuspidization of the diseased aortic valve has proven to be a promising repair technique with acceptable durability. However, most understanding of the procedure is empirical and retrospective. This work seeks to design the optimal gross morphology associated with surgical bicuspidization with simulations based on the hypothesis that modifications to the free edge length cause or relieve stenosis. MethodsModel bicuspid valves were constructed with varying free edge lengths and gross morphology. Fluid-structure interaction simulations were conducted in a single patient-specific model geometry. The models were evaluated for primary targets of stenosis and regurgitation. Secondary targets were assessed and included qualitative hemodynamics, geometric height, effective height, orifice area, and billow. ResultsStenosis decreased with increasing free edge length and was pronounced with free edge length less than or equal to 1.3 times the annular diameter d. With free edge length 1.5d or greater, no stenosis occurred. All models were free of regurgitation. Substantial billow occurred with free edge length 1.7d or greater. ConclusionsFree edge length 1.5d or greater was required to avoid aortic stenosis in simulations. Cases with free edge length 1.7d or greater showed excessive billow and other changes in gross morphology. Cases with free edge length 1.5d to 1.6d have a total free edge length approximately equal to the annular circumference and appeared optimal. These effects should be studied in vitro and in animal studies.

Development of silver nanocubes created by pulsed laser ablation in liquid

This paper describes a simple approach for creating silver (Ag) nanocubes using pulsed laser ablation in a liquid medium. The development of nanocubical formations of Ag obtained by laser ablation using Nd: YAG laser was conducted for 5, 10, 15, and 20[Formula: see text]min. The surface morphological analysis was performed using field-emission scanning electron microscopy (FESEM) to show the formation of silver nanocubes with edge lengths ranging from 150[Formula: see text]nm to 250[Formula: see text]nm. The UV-visible spectroscopy demonstrates that the concentration of Ag nanostructures, evidenced by the characteristic localized surface plasmon resonance band near 400[Formula: see text]nm in the colloidal solution containing Ag nanoparticles, increased with the increasing laser ablation duration from 5[Formula: see text]min to 20[Formula: see text]min. The growth mechanism for Ag nanocubes can be easily understood with the change in laser ablation time from 5 to 10, 15, and then 20[Formula: see text]min. The Ag sheets with no specific shape start to develop after 5 min of laser ablation, and after 10[Formula: see text]min, larger particles form. Then, after 15[Formula: see text]min, a small number of cube-like nanostructures with rough and uneven edges was obtained. At the end of 20[Formula: see text]min, a complete cubic formed with fine and distinct edges and a very large amount of nanocubes. The elemental silver signal was present in Ag nanocubes, as revealed by the energy-dispersive X-ray spectroscopy (EDS) spectra. The produced Ag nanocubes may be used to construct two-dimensional nanocomposites with practical applications in the electrical, optoelectronic, electrochemical, and biological areas.

Adjoint twisted Reidemeister torsion and Gram matrices

We compute the adjoint twisted Reidemeister torsion for closed oriented hyperbolic 3-manifolds and for hyperbolic 3-manifolds with toroidal boundary. In our formula, we consider the manifold as obtained by doing a Dehn-filling along suitable boundary components of a fundamental shadow link complement, and the formula is in terms of the logarithmic holonomy of the meridians of the boundary components. As an important special case, we also write down a formula of the adjoint twisted Reidemeister torsion for the double of a hyperbolic 3-manifold with totally geodesic boundary in terms of the edge lengths of a geometric ideal triangulation of the manifold. These unexpected formulas were inspired by, and played an important role in, the study of the asymptotic expansion of quantum invariants [25].

Контекстный анализ связности двухполюсных структур

The paper discusses an original approach to the analysis of network structures of various natures, which are represented in the form of graphs. It is assumed that the probability of connectivity of individual edges functionally depends on their physical characteristics (edge length) and tends to zero. The issue of increasing the connectivity probability of the entire graph is being addressed, which is defined as the probability of the existence of a sequential set of edges connecting the selected start and end vertices. A distinctive feature of the proposed method is the move away from the traditional reservation of obviously weak connection points towards a functional impact on individual connections of the structure, changing their physical characteristics. Based on the theory of systems functioning and the theory of dominants, contextual approach is being developed aimed at identifying the dominant connections of the graph, reflecting the functional and meaningful meaning of the connections between the vertices of the original modeled object. As a result, a set of dominants S is identified, consisting of edges whose parameters meet the given criteria. The selection criterion is the length of the edge included in the asymptotic relation, which characterizes the connectivity probability of the entire graph. It has been proven that changing the length of edges from a given set by ε > 0 increases the probability of connectedness of the original graph in the maximum case in h-ε or h-εβ times, where h → 0 and β is a parameter depending on the number of graph paths passing through this edge. Various methods have been proposed to increase the connectivity probability of the graph under consideration: from the point of view of the point effect, by reducing the length of a single edge from the set S; from the position of influencing the maximum set of edges from S, allowing to obtain the overall maximum effect. A comparative analysis of the proposed ways to increase the probability of graph connectivity has been carried out, and the appropriate conditions have been identified to achieve the maximum effect from the selected methods of influence.

Structural, optical, magnetic properties and energy-band structure of MFe2O4 (M = Co, Fe, Mn) nanoferrites prepared by co-precipitation technique.

MFe2O4 (M = Co, Fe, Mn) nanoparticles were successfully formed through the chemical co-precipitation technique. X-ray diffraction, scanning electron microscopy, and energy-dispersive X-ray analysis were used to investigate samples' structural properties. The investigated structural properties included phases formed, crystallite size, cation distribution, hopping length, bond length, bond angle, edge length, and shared and unshared octahedral edge length. Scanning electron micrographs of the prepared samples demonstrated well-defined crystalline nanoparticles. The grain diameter was 15, 9, and 34 nm for CoFe2O4, Fe3O4, and MnFe2O4, respectively. The energy-dispersive X-ray analysis confirmed the existence of every element (Co, Fe, and O) and no discernible impurities in the samples. The optical properties were studied in detail through photoluminescence (PL) spectroscopy and Raman spectroscopy. The presence of active modes in Raman spectra confirmed the spinel structure of the MFe2O4 nanoparticles. The direct bandgap energy estimated through UV-visible spectroscopy was about 2.59-2.64 eV, corresponding with the energy-band structures of the octahedral site (1.70 eV) and the tetrahedral site (0.9 eV). This result was further confirmed by PL emission spectra. Based on Mie theory and UV-visible and PL spectral data, the mechanism of photothermal characterization for MFe2O4 nanoparticles was determined. Investigating the changes in temperature of magnetic parameters including coercivity, squareness ratio, and saturation magnetization for MFe2O4 samples showed the dominant influence of ion distribution and A-A, A-B, and B-B exchange interactions. This study also showed that strong anisotropy and weak dipolar interaction tended to increase the coercivity and squareness ratio of CoFe2O4. Conversely, weaker anisotropy and stronger dipolar interaction corresponded with the small coercivity and squareness ratio of Fe3O4 and MnFe2O4 samples.

Research on the environmental stability performance of chromite ore processing residue solidified products.

Chromite ore processing residue (COPR) is a hazardous waste because of leachable chromium, especially Cr(vi). Therefore, ascorbic acid (AA) and blast furnace slag (BFS) have been used to detoxify and solidify COPR. On this basis, environmental stability experiments with high temperature and freeze-thaw cycles were carried out to explore the stability performance of a solidified body with 40% COPR. The environmental stability performance was analyzed through changes in edge length, mass loss, compressive strength development, and leaching concentration of Cr(vi). The result indicated that the high-temperature environment had much more effect on the solidified body than the freeze-thaw cycle environment in these four aspects: after being maintained at 900 °C for 2 h, the compressive strength of the solidified bodies reached its minimum value (35.76 MPa). However, in the freeze-thaw cycle experiments, the compressive strength of the solidified bodies consistently remained above 80 MPa, and the leaching of hexavalent chromium was below the limit (5 mg L-1). In addition, X-ray diffraction (XRD) and Fourier transform infrared spectrometry (FTIR) analysis verified that COPR was effectively solidified through physical and chemical means. Moreover, high temperature changes the molecular structure of the solidified body, thus reducing the compressive strength and curing ability of the solidified body, while the freeze-thaw cycle experiment has little effect on it.

Numerical simulation study on combustion characteristics of square hollow oil pool fire in ship cabins

To study the combustion phenomenon of square hollow fire sources in ship cabins, PyroSim software was used to establish numerical models of different inner and outer edge lengths of the same fire source area. FDS software was used to numerically simulate fire temperature and smoke spread, observe and record the flame and smoke spread characteristics in cabins under different working conditions, and analyze the temperature distribution of flame plumes and the temperature field characteristics inside the cabin. The results indicate that: During the combustion process of a square hollow fire source in a ship’s cabin, a typical flame convergence phenomenon occurs, and the flame temperature of the fire source combustion first increases significantly and then gradually stabilizes. The smaller the inner edge length of a square hollow, the higher the combustion temperature of the fire source, the faster the heating rate, the more obvious the phenomenon of fire convergence, and the more intense the flame combustion. As the inner edge length increases, the influence of flame combustion at the center of the square decreases, and the peak temperature of the flame decreases with a smaller amplitude and tends to concentrate.

Elevated evolutionary rates of biting biomechanics reveal patterns of extraordinary craniodental adaptations in some herbivorous dinosaurs

AbstractAdaptation to specialist ecological niches is a key innovation that has contributed to the evolutionary success of many vertebrate clades, underpinning the acquisition of diverse skull morphologies. Dinosaurs, which dominated Mesozoic terrestrial faunas, acquired herbivory multiple times, and evolution of these herbivorous adaptations is linked to drastic changes in dental and craniomandibular functional morphology, yet whether changes in functionally relevant phenotypic traits occurred more rapidly in herbivorous lineages compared to in carnivorous lineages remains largely untested in a statistical phylogenetic framework. Here, we infer rates of phenotypic evolution using phylogenetic variable‐rate models on relative biting edge (tooth row) lengths of 107 dinosaur taxa to test the hypothesis that the acquisition of herbivory is associated with rapid changes in mandibular biomechanics. We find elevated rates of biomechanical evolution in theropods with foreshortened and beaked skulls (Oviraptorosauria, Limusaurus), as well as in ceratopsians and Diplodocus. The presence and position of a reduced tooth row and increased jaw efficiency unite these high‐rate lineages, indicating selection for greater efficiency in biting biomechanics. Large departures from the isometric scaling of these mandibular characteristics helps explain the differences in evolutionary rates in these clades and those of other herbivorous theropods (Therizinosauria, Ornithomimosauria). Additionally, we hypothesize that extreme ontogenetic changes within species lifetimes may be behind some instances of branch‐wise elevated rates. Thus, we show how exceptional rates of biomechanical evolution can reveal signatures of ecological adaptations within dinosaur lineages as well as within‐species ontogenetic sequences.

Surface treatment of additively manufactured stainless steel 316L lattice structures by plasma electrolytic polishing

Additive manufacturing facilitates the production of lattice structures for lightweight and biomedical applications. Typically, as-built structures exhibit rough surfaces, necessitating post-processing to meet functional requirements. Plasma electrolytic polishing (PEP) offers an approach for smoothing surfaces on complex and filigree parts in an environmentally friendly manner. Nonetheless, achieving uniform treatment depends on PEP process parameters and geometric properties of the workpiece.This study investigates capabilities of PEP for treating lattice structures made from 316L stainless steel. Test specimens consisting of face-centered cubic unit cells with an edge length of 3 mm were manufactured by laser-based powder bed fusion.The findings highlight the influence of developed PEP parameters on roughness and dimensional accuracy based on computed tomography scans. Pre-and-post-treatment-comparisons show that smooth, specular outer surfaces can be obtained.Moreover, smoothing of interior surfaces was demonstrated for a relative cell density of 11%. Increasing the cell density to 35% reduces the smoothing effect.

The Ceresa class and tropical curves of hyperelliptic type

Abstract We define a new algebraic invariant of a graph G called the Ceresa–Zharkov class and show that it is trivial if and only if G is of hyperelliptic type, equivalently, G does not have as a minor the complete graph on four vertices or the loop of three loops. After choosing edge lengths, this class specializes to an algebraic invariant of a tropical curve with underlying graph G that is closely related to the Ceresa cycle for an algebraic curve defined over $\mathbb {C}(\!(t)\!)$ .

Research on the application of multi-feature fusion in ceramic art design

Abstract In this paper, median filtering and linear stretching are used to preprocess the classified ceramic images, respectively, and the LoG operator is utilized to detect the edges of ceramic photos. Combining the Hough transform and TMOAA algorithm to measure the edge length, thickness, and diagonal dimension of ceramics to obtain the basic elements of ceramic art design. The FAST algorithm is used to make up for the shortcomings of the SIFT algorithm in real-time, to extract the features of the overall image of ceramics and the vessel image, and then combined with the thinking framework of ceramic art design to generate the best conceptual model of ceramic art design. Extract and detect the ceramic vessel image and carry out similarity rate calculation, quantify the enamel color characteristics to generate a color design scheme, calculate the color difference value, and evaluate the aesthetic value of ceramic art design works from the perspective of ceramic art design aesthetics. Porcelain enamel color difference ΔE = 2.0369, ΔE ≤ 5.00~6.00, in line with the color quality standards, indicating that the color design scheme generated based on the color semantic elements has a certain applicability. Evaluating the best conceptual model of ceramic art design by aesthetic standards, the works generated based on the seven ceramic patterns have different aesthetic values and different forms, which meet the various demands for ceramic artworks nowadays.

Analyzing blank cutting edge efficiency associated with the adoption of microblade technology: A case study from Tolbor-17, Mongolia.

The phenomenon of lithic miniaturization during the Late Pleistocene at times coincided with increased artifact standardization and cutting edge efficiency-likely reflecting the use of small, sharp artifacts as interchangeable inserts for composite cutting tools and hunting weapons. During Marine Isotope Stage 2, Upper Paleolithic toolmakers in northern East Asia specifically used pressure techniques to make small, highly standardized lithic artifacts called microblades. However, little is currently known about how microblades affected the cutting edge efficiency of the toolkits they were a part of. We applied three methods of analyzing cutting edge efficiency to two Upper Paleolithic assemblages recently excavated from Tolbor-17, Mongolia, that document the periods before and after the introduction of microblade technology to the Tolbor Valley. A model incorporating allometric relationships between blank cutting edge length and mass suggests no difference in efficiency between the two periods, while two more conventional approaches both indicate a significant increase. The potential for improved cutting edge efficiency is only observed when the microblade sample is artificially inflated via simulation. Our results highlight challenges related to detecting and interpreting archaeological differences in cutting edge efficiency at the assemblage level.

Two conjectures on 3D Voronoi structures: a toolkit with biomedical case studies.

3D Voronoi scaffolds are widely applied in the field of additive manufacturing as they are known for their light weight structural resilience and share many topological similarities to various natural (bone, tumours, lymph node) and synthetic environments (foam, functionally gradient porous materials). Unfortunately, the structural design features that promote these topological similarities (such as the number of vertices) are often unpredictable and require the trial and error of varying design features to achieve the desired 3D Voronoi structure. This article provides a toolkit, consisting of equations, based on over 12 000 3D Voronoi structures. These equations allow design features, such as the number of generating points (G), to be efficiently and accurately predicted based on the desired structural parameters (within ±3G). Based on these equations we are proposing, to the best of our knowledge, two new mathematical conjectures that relate the number of vertices or edges, and the average edge length to G in Voronoi structures. These equations have been validated for a wide range of parameter values and Voronoi network sizes. A design code is provided allowing any of over 12 000 structures to be selected, easily adjusted based on user requirements, and 3D printed. Biomedical case studies relevant to T-cell culturing, bone scaffolds and kidney tumours are presented to illustrate the design code.

ПОВЫШЕНИЕ ПРОИЗВОДИТЕЛЬНОСТИ КУТТЕРА ПУТЁМ ИСПОЛЬЗОВАНИЯ КУТТЕРНОГО НОЖА С ДОПОЛНИТЕЛЬНОЙ РЕЖУЩЕЙ КРОМКОЙ

The article presents a technical solution to the issue of improving the meat cutter machine productivity by enhancing the total length of the chopper knife cutting edges. A chopper knife with an additional cutting edge was proposed. A mathematical model was developed to determine the productivity of the meat cutter machine. The calculations have shown that at the main cutting edge length of l1 = 0,25 m and at the additional cutting edge length of 0.125 m, the cutter machine productivity will improve by 38 %. The results confirm the advisability of using chopper knives with an additional cutting edge.

Investigating the Impact of Network Structure on Road Traffic Crashes: A Macro-level Analysis

Road traffic crashes (RTCs) are one of the significant externalities associated with transportation that pose a serious public health risk. While addressing the safety concerns of road transport, road network structure is often overlooked. Among the high-risk locations within a road network, intersections pose a particular concern due to the intricate and conflicting traffic movements. Intersection skewness (the angle at which an intersection deviates from 90 degrees) and intersecting road categories are considered to influence intersection safety significantly. While previous research has extensively explored the impact of skew angles and intersecting road categories at the intersection level, there is a lack of investigation at the ward/zonal level. This study aims (a) to estimate the skewness and heterogeneity of intersecting leg categories at the ward level and (b) to model the RTCs and the street network characteristics such as skewness, hierarchy, connectivity, and centrality along with covariates like ward-level population density and economic status. Utilizing data from OpenStreetMap, this study conducted the ward-level analysis for Delhi, India. This study, along with the proposed metrics, also quantified various network structure metrics that are commonly used in safety analysis, such as betweenness centrality, meshedness coefficient, average edge length, node density, and average circuity. Using three years of crash data from 2017-19, this study modelled the crash rate at the ward level for Delhi (289 wards) by developing a negative binomial regression model. The explanatory variables include the network structure metrics, nightlight intensity (indicative of economic status), and population density. It was observed that wards with a higher deviation from the conventional right-angle intersection experienced a higher rate of crashes. Moreover, the wards with more heterogeneous intersections had more crash rates. However, wards with more central (higher betweenness) road network structure had fewer crashes. Furthermore, wards with more circuitous roads (more network distance to travel from one point to another) had more crash rates. However, a negative association was found between the RTCs and ward economic status, indicating that people who are economically disadvantaged continue to be the most at risk for fatal crashes.

Nanoprisms in plasmonic sensing: A comprehensive analysis of geometric effects

The highly sensitive and versatile technique of plasmonic sensing has been widely employed in detecting and analyzing chemical or biological substances. This work employs classical electrodynamics methods to investigate the sensing performance of nanoprisms systematically. By varying heights, base edge lengths, and rounding radii of base corners of triangular nanoprism, we explore their influence on sensitivity and the figure of merit (FOM) in both transverse and longitudinal polarization cases. Our findings indicate that enlarged triangular prisms exhibit enhanced sensitivity, but a decrease in FOM counterbalances this improvement. Conversely, reducing the rounding radius of the base corners of the triangular prism leads to simultaneous improvements in sensitivity and FOM. We suggest prioritizing triangular or tetrahedral prisms in fabricating nanosensors for higher FOM or sensitivity, respectively. These insights provide valuable directions for designing and optimizing plasmonic sensors in practical usage.

Quaternary nanorods: promising versatile agents for cancer therapy, antimicrobial strategies and free radical neutralization

Cu2XSnS4 (CXTS; X: Zn, Mn or Co) nanorods (NRs) were prepared by a simple hot-injection method and their cytotoxic activities on human breast adenocarcinoma (MCF-7), metastatic melanoma (451Lu) and embryonic kidney (HEK-293) cell lines were investigated for the first time. The antibacterial activities of these nanoparticles on both gram-positive (S. aureus) and gram-negative (E. coli) pathogenic bacteria as well as their DPPH (2,2-diphenyl-1- picrylhydrazyl) scavenging activities were evaluated. The structural characterizations show that the obtained nanoparticles have the same crystal structure and are shaped as nanorods with an average 10–40 nm edge length. The data obtained in cytotoxicity studies revealed that the synthesized CXTS NRs have a significant inhibition effect, especially on cancer cell lines (MCF-7 and 451Lu), in a dose-dependent manner over a period of 24 h, demonstrating their potential for use as anticancer agents. In addition, the findings indicate that the synthesized nanorods possess strong antibacterial properties against the pathogenic microorganisms tested and display a marked antioxidant effect through efficient elimination of DPPH activity. This comprehensive study sheds light on the creation and development of CXTS NRs as promising versatile agents in various biomedical and environmental applications such as cancer therapy, antimicrobial strategies and the neutralization of free radicals.