Maximum Degree Research Articles

Linearly Polarized Broadband Emission and Multi-Wavelength Lasing in Solution-Processed Quantum Dots.

A miniature laser with linear polarization is a long sought-after component of photonic integrated circuits. In particular, for multi-wavelength polarization lasers, it supports simultaneous access to multiple, widely varying laser wavelengths in a small spatial region, which is of great significance for advancing applications such as optical computing, optical storage, and optical sensing. However, there is a trade-off between the size of small-scale lasers and laser performance, and multi-wavelength co-gain of laser media and multi-cavity micromachining in the process of laser miniaturization remain as significant challenges. Herein, room-temperature linearly polarized multi-wavelength lasers in the visible and near-infrared wavelength ranges are demonstrated, by fabricating random cavities scattered with silica in an Er-doped Cs2Ag0.4Na0.6In0.98Bi0.02Cl6 double-perovskite quantum dots (QDs) gain membrane. By regulating the local symmetry and enabling effective energy transfer in nanocrystals, multi-wavelength lasers with ultra-low thresholds are achieved at room temperature. The maximum degree of polarization reaches 0.89. With their advantages in terms of miniaturization, ultra-low power consumption, and adaptability for integration, these lasers offer a prospective light source for future photonic integrated circuits aimed at high-capacity optical applications. This article is protected by copyright. All rights reserved.

2-Distance coloring of planar graphs with maximum degree 5

A 2-distance coloring of a graph is a proper [Formula: see text]-coloring in which any two vertices with distance at most two get different colors. The 2-distance number is the smallest number [Formula: see text] such that [Formula: see text] has a 2-distance [Formula: see text]-coloring, denoted as [Formula: see text]. In 1977, Wegner conjectured that for each planar graph [Formula: see text] with maximum degree [Formula: see text], [Formula: see text] if [Formula: see text], [Formula: see text] if [Formula: see text], and [Formula: see text] if [Formula: see text]. In 2001, Thomassen supported the conjecture by proving the case [Formula: see text]. The conjecture is still open even for [Formula: see text]. In this paper, we show that [Formula: see text] for the case [Formula: see text] which improves the upper bound 18 recently obtained by Hou et al.

Planar Graphs without Cycles of Length 3, 4, and 6 are (3, 3)-Colorable

For non-negative integers d1 and d2, if V1 and V2 are two partitions of a graph G’s vertex set VG, such that V1 and V2 induce two subgraphs of G, called GV1 with maximum degree at most d1 and GV2 with maximum degree at most d2, respectively, then the graph G is said to be improper d1,d2-colorable, as well as d1,d2-colorable. A class of planar graphs without C3,C4, and C6 is denoted by C. In 2019, Dross and Ochem proved that G is 0,6-colorable, for each graph G in C. Given that d1+d2≥6, this inspires us to investigate whether G is d1,d2-colorable, for each graph G in C. In this paper, we provide a partial solution by showing that G is (3, 3)-colorable, for each graph G in C.

On induced subgraph of Cartesian product of paths

AbstractChung et al. constructed an induced subgraph of the hypercube with vertices and with maximum degree smaller than . Subsequently, Huang proved the Sensitivity Conjecture by demonstrating that the maximum degree of such an induced subgraph of hypercube is at least , and posed the question: Given a graph , let be the minimum of the maximum degree of an induced subgraph of on vertices, what can we say about ? In this paper, we investigate this question for Cartesian product of paths , denoted by . We determine the exact values of when by showing that for and , and give a nontrivial lower bound of when by showing that . In particular, when , we have , which is Huang's result. The lower bounds of and are given by using the spectral method provided by Huang.

Planar Drawings with Few Slopes of Halin Graphs and Nested Pseudotrees

AbstractThe planar slope number$${{\,\textrm{psn}\,}}(G)$$ psn ( G ) of a planar graph G is the minimum number of edge slopes in a planar straight-line drawing of G. It is known that $${{\,\textrm{psn}\,}}(G) \in O(c^{\Delta })$$ psn ( G ) ∈ O ( c Δ ) for every planar graph G of maximum degree $$\Delta $$ Δ . This upper bound has been improved to $$O(\Delta ^5)$$ O ( Δ 5 ) if G has treewidth three, and to $$O(\Delta )$$ O ( Δ ) if G has treewidth two. In this paper we prove $${{\,\textrm{psn}\,}}(G) \le \max \{4,\Delta \}$$ psn ( G ) ≤ max { 4 , Δ } when G is a Halin graph, and thus has treewidth three. Furthermore, we present the first polynomial upper bound on the planar slope number for a family of graphs having treewidth four. Namely we show that $$O(\Delta ^2)$$ O ( Δ 2 ) slopes suffice for nested pseudotrees.

Effect of Geopolymerization Reaction on the Flexural Strength of Kaolin-Based Systems

Geopolymers exhibit broad application prospects, including construction and radiation shielding, which require excellent mechanical performances. However, investigations on the nature of geopolymerization reactions and their consequential impact on mechanical performance are still vague. In this study, the effect of the major factors of Si/Al ratio and curing time on the geopolymerization reaction and flexural strength were studied based on the microstructure evolution and chemical bonding formation analyzed using the SEM, FTIR, peak deconvolution, and XRD methods. The microstructure of geopolymers was transferred from initially layered smooth particles of kaolinite to a 3D network porous structure, corresponding to sodalite. A spectrum exclusive to the geopolymer structure occurred at 973 cm−1, corresponding to the sodium aluminum silicate hydrate (N-A-S-H) links, the integral area of which represents the degree of geopolymerization reaction. Furthermore, a controllable reaction degree was achieved by adjusting the Si/Al ratio and curing time, where the maximum reaction degree of 55% was achieved at a Si/Al ratio of 1.94 when cured for 7 d. The correlation between the flexural strength and reaction degree was found to follow a proportional relationship, achieving a flexural strength of 21.11 MPa with a degree of 45%. This study provides insight into the development of mechanical strength through controlling the reaction process.

Minimum spanning tree analysis of EEG resting-state functional networks in schizophrenia

Schizophrenia is a serious and complex mental disease, known to be associated with various subtle structural and functional deviations in the brain. Recently, increased attention is given to the analysis of brain-wide, global mechanisms, strongly altering the communication of long-distance brain areas in schizophrenia. Data of 32 patients with schizophrenia and 28 matched healthy control subjects were analyzed. Two minutes long 64-channel EEG recordings were registered during resting, eyes closed condition. Average connectivity strength was estimated with Weighted Phase Lag Index (wPLI) in lower frequencies: delta and theta, and Amplitude Envelope Correlation with leakage correction (AEC-c) in higher frequencies: alpha, beta, lower gamma and higher gamma. To analyze functional network topology Minimum Spanning Tree (MST) algorithms were applied. Results show that patients have weaker functional connectivity in delta and alpha frequency bands. Concerning network differences, the result of lower diameter, higher leaf number, and also higher maximum degree and maximum betweenness centrality in patients suggest a star-like, and more random network topology in patients with schizophrenia. Our findings are in accordance with some previous findings based on resting-state EEG (and fMRI) data, suggesting that MST network structure in schizophrenia is biased towards a less optimal, more centralized organization.

Classical multivariate Hermite coordinate interpolation on [formula omitted]-dimensional grids

In this work, we study the Hermite interpolation on n-dimensional non-equally spaced, rectilinear grids over a field k of characteristic zero, given the values of the function at each point of the grid and the partial derivatives up to a maximum degree. Initially, we prove the uniqueness of the interpolating polynomial, followed by deriving a concise closed expression that employs a solitary summation, independent of dimensionality, which is algebraically simpler than the only alternative closed form for the n-dimensional classical Hermite interpolation (Gasca and Sauer, 2000). We also provide the remainder of the interpolation in integral form; we derive the ideal of the interpolation and express the interpolation remainder using only polynomial divisions, in the case of interpolating a polynomial function. Moreover, we prove the continuity of Hermite polynomials defined on adjacent n-dimensional grids, thus establishing spline behavior. Finally, we perform illustrative numerical examples to showcase the applicability and high accuracy of the proposed interpolant, in the simple case of few points, as well as hundreds of points on 3D-grids using a spline-like interpolation, which compares favorably to state-of-the-art spline interpolation methods.

Preparation and characterization of self-aggregating micelles from stearic acid-modified burdock root polysaccharide

In order to obtain amphiphilic polysaccharide self-assembly micelles, the hydrophobic modification by grafting stearic acid (SA) onto the backbone of burdock root polysaccharide (BRP) was carried out and its main physicochemical properties were characterized. The results showed that the optimal esterification conditions were as follows: reaction time of 2 h, reaction temperature of 55 ℃, system pH of 8.0 and the SA addition of 4 mmol, a maximum substitution degree (DS) of the esterification products was obtained as 0.1012. The FTIR analysis verified that the modified polysaccharide successfully introduced the ester carbonyl group. 1H NMR spectra further confirmed that the esterification reaction occurred. The SA-modified BRP micelles were roughly spherical with uniform dispersion and the particle size was in the range of 259–352 nm, which showed a negative correlation with the DS. The solubility of the esterification products also decreased. The smaller critical micelle concentration (CMC) led to easier formation of self-aggregating micelles and stronger solubilization effect. The above results indicated that SA-modified BRP as a novel carrier material possessed potential to deliver hydrophobic active substances.Graphical

A Graph-Theoretic Approach to Ring Analysis: Dominant Metric Dimensions in Zero-Divisor Graphs

This article investigates the concept of dominant metric dimensions in zero divisor graphs (ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as , where nonzero elements and are identified as zero divisors if their product results in zero The set of zero divisors in ring is referred to as . To analyze various algebraic properties of , a graph known as the zero-divisor graph is constructed using This manuscript establishes specific general bounds for the dominant metric dimension (Ddim) concerning the ZD-graph of . To achieve this objective, we examine the zero divisor graphs for specific rings, such as the ring of Gaussian integers modulo , denoted as the ring of integers modulo , denoted as , and some quotient polynomial rings. Our research unveils new insights into the structural similarities and differences among commutative rings sharing identical metric dimensions and dominant metric dimensions. Additionally, we present a general result outlining bounds for the dominant metric dimension expressed in terms of the maximum degree, girth, clique number, and diameter of the associated ZD-graphs. Through this exploration, we aim to provide a comprehensive framework for analyzing commutative rings and their associated zero divisor graphs, thereby advancing both theoretical knowledge and practical applications in diverse domains.

On Conflict-Free Cuts: Algorithms and Complexity

One way to define the Matching Cut problem is: Given a graph G, is there an edge-cut M of G such that M is an independent set in the line graph of G? We propose the more general Conflict-Free Cut problem: Together with the graph G, we are given a so-called conflict graph Gˆ on the edges of G, and we ask for an edge-cutset M of G that is independent in Gˆ. Since conflict-free settings are popular generalizations of classical optimization problems and Conflict-Free Cut was not considered in the literature so far, we start the study of the problem. We show that the problem is NP-complete even when the maximum degree of G is 5 and Gˆ is 1-regular. The same reduction implies an exponential lower bound on the solvability based on the Exponential Time Hypothesis. We also give parameterized complexity results: We show that the problem is fixed-parameter tractable with the vertex cover number of G as a parameter, and we show W[1]-hardness even when G has a feedback vertex set of size one, and the clique cover number of Gˆ is the parameter. Since the clique cover number of Gˆ is an upper bound on the independence number of Gˆ and thus the solution size, this implies W[1]-hardness when parameterized by the cut size. We list polynomial-time solvable cases and interesting open problems. At last, we draw a connection to a symmetric variant of SAT.

Determining rational parameters for the treatment of concentrated wastewater from etching site by using combined systems producing sediments of predefined composition

The object of this study is model solutions, spent sulfuric acid and chloride acid etching solutions, degreasing of metal products at enterprises. The paper reports results of research on the possibility of obtaining sediments of predefined composition and reducing the consumption of chemical reagents in comparison with conventional cleaning schemes. The systematization of the elements of the technological scheme has been shown, which provides for the treatment of concentrated wastewater of the etching area in combined systems with obtaining sediments of predefined composition and is the basis for the implementation of resource-saving technology. Rational parameters were established for the state (рН=3‒4, Eh=+0.3‒+0.33 V, and rH2=16.3–19.38 V) and technological parameters (degree of iron extraction ψ=0.8, reagent consumption from the stoichiometric norm of B=0.8). Such parameters provide the proper conditions for the oxidation of organic compounds and their co-precipitation with insoluble iron hydroxy compounds (the maximum degree of extraction of organic impurities is 86 %). The formed precipitate corresponds to the FeOOH.nH2O composition, contains 2‒3 % of organic impurities, and is subject to burial. As a result of studies on the treatment of concentrated iron-containing wastewater, the obtained sediment is ready for further utilization by processing. The composition of this sediment corresponds to the natural mineral limonite FeOOH (Fe2O3.nH2O) and is formed at pH values from 3.5 to 7.5 with rH2 values from 26 V to 21 V and at technological regeneration parameters of pH=4.0–4.6; rH2 =23.34–32.25 V. As a result of research into the deep purification of wastewater using a magnetic device, a suspension of sediment of ferromagnetic impurities (hydroxo compounds of iron) is obtained, which could be the basis for extraction or production of magnetically favorable dispersed material.

Email Platform: Spam Detection

Abstract: In practically every industry today, from business to education, emails are used. Ham and spam are the two subcategories of emails. Email spam, often known as junk email or unwelcome email, is a kind of email that can be used to hurt any user by sapping their time and computing resources and stealing important data. Spam emailvolume is rising quickly day by day. Today’s email and IoT service providers face huge and massive challenges with spam identification and filtration. Email filteringis one of the most important and well-known methods among all the methods createdfor identifying and preventing spam. SVM, decision trees, and other machine learning and deep learning approaches have all been applied to this problem. Together with the explosive growth in internet users, email spam has increased substantially in recent years. Individuals are using them for illegal and dishonest purposes, such as fraud, phishing, and distributing malicious links through unsolicited email that can harm our systems and attempt to access your systems. By quickly constructing phone-y/fake profiles and email accounts, spammers prey on those who are ignorant of these scams. They use a real name in their spam emails. As a result, it’s critical to identify spam emails that include fraud. This project will accomplish this by utilizing machine learning methods, and this article will examine the machine learning algorithms, put them to use on our data sets, and select the approach that can detect emailspam with the maximum degree of precision and accuracy.

Research on a Classification Method of Goaf Stability Based on CMS Measurement and the Cloud Matter–Element Model

The evaluation and classification of goaf stability are fuzzy and random. To address this problem, a new classification method is proposed. A cavity monitoring system is used to detect the goaf, 3DMine and FLAC3D software are used to conduct the 3D visual modeling of the scanning results, and numerical simulation analysis is performed on the goaf. According to the analysis results, the stability classification standard of the goaf is constructed, and the characteristics of each classification are described. The evaluation indicator system of goaf stability is constructed in accordance with similar engineering experience, and the evaluation indicator is weighted by using the analytic hierarchy process. The cloud–element coupling evaluation model is built, the field measured values of indicators are collected, the cloud correlation degree of goafs belonging to each stability level is calculated, the stability level is evaluated according to the principle of maximum membership degree, and the results are compared with the numerical simulation to analyze the reasons for the differences in the stability evaluation results obtained by the two methods and to improve the accuracy of the evaluation of goaf stability. The pillar stress and surrounding rock deformation are monitored in Room 1# of the inclined mining area of Shirengou Iron Mine. The monitoring results are consistent with the evaluation results, which proves the accuracy of the proposed goaf stability classification method.

Foreground Dust Properties toward the Cluster NGC 7380

Using starlight polarization, we present the properties of foreground dust toward cluster NGC 7380 embedded in H ii region Sh 2-142. Observations of starlight polarization are carried out in four filters using an imaging polarimeter equipped with a 104 cm ARIES telescope. Polarization vectors of stars are aligned along the Galactic magnetic field. Toward the east and southeast regions, the dust structure appears much denser than in other regions (inferred from extinction contours and a color composite image) and is also reflected in polarization distribution. We find that the polarization degree and extinction tend to increase with distance and indication for the presence of a dust layer at a distance of around 1.2 kpc. We have identified eight potential candidates exhibiting intrinsic polarization by employing three distinct criteria to distinguish between stars of intrinsic polarization and interstellar polarized stars. For interstellar polarized stars, we find that the maximum polarization degree increases with the color excess and has a strong scatter, with the mean value of 1.71% ± 0.57%. The peak wavelength spans 0.40–0.88 μm, with a mean value of 0.56 ± 0.07 μm, suggesting similar grain sizes in the region to those in the average diffuse interstellar medium. The polarization efficiency is also found to decrease with visual extinction as Pmax/AV∝AV−0.61 . Our observational results are found to be consistent with the predictions by the radiative torque alignment theory.

Intelligent prediction model of a polymer fracture grouting effect based on a genetic algorithm-optimized back propagation neural network

Polymer grouting can effectively improve the stability of surrounding rock fractures. However, in practical construction, it is difficult to judge the degree of coupling between the slurry and the rock, and the effective grouting range after grouting. Therefore, early prediction of the effect of grouting on the surrounding rock is crucial. In this paper, a new artificial intelligence method is proposed to predict the polymer fracture grouting effect. The genetic algorithm optimized back propagation neural network (GA-BP) is employed to construct an intelligent prediction model. To acquire a substantial dataset for constructing the model, an easily assembled/disassembled test apparatus for polymer fracture grouting is designed. The maximum coupling degree of the fractures and slurry diffusion distance are chosen as the evaluation metrics for the grouting effectiveness. The influences of the fracture characteristic parameters and grouting volume on the grouting effect are investigated. Furthermore, a comprehensive analysis is conducted on the spatiotemporal diffusion characteristics and slurry-rock coupling mechanism of polymer grouting. Compared to traditional BP neural networks, and three other machine learning algorithms (decision trees, random forests and gradient boosting decision trees), the GA-BP model outperforms them in terms of R2 (coefficient of determination), MSE (mean squared error), MBE (mean bias error), MAE (mean absolute error) and RMSE (root mean squared error) in both the test and training sets. The GA algorithm significantly improves the accuracy and robustness of the prediction model. The optimized model demonstrates significant accuracy in predicting grouting results and assessing efficiency, providing a practical reference for grouting construction.

On the parameterized complexity of freezing dynamics

In this paper we establish how alphabet size, treewidth and maximum degree of the underlying graph are key parameters which influence the overall computational complexity of finite freezing automata networks. First, we define a general decision problem, called Specification Checking Problem, that captures many classical decision problems such as prediction, nilpotency, predecessor, asynchronous reachability.Then, we present a fast-parallel algorithm that solves the general model checking problem when the three parameters are bounded, hence showing that the problem is in NC. Moreover, we show that the problem is in XP on the parameters tree-width and maximum degree.Finally, we show that these problems are hard from two different perspectives. First, the general problem is W[2]-hard when taking either treewidth or alphabet as single parameter and fixing the others. Second, the classical problems are hard in their respective classes when restricted to families of graph with sufficiently large treewidth.

The Influence of Various Crosslinking Conditions of EDC/NHS on the Properties of Fish Collagen Film

The process of crosslinking improves the physicochemical properties of biopolymer-based composites, making them valuable for biomedical applications. EDC/NHS-crosslinked collagen materials have a significant potential for tissue engineering applications, due to their enhanced properties and biocompatibility. Chemical crosslinking of samples can be carried out in several ways, which is crucial and has a direct effect on the final properties of the obtained material. In this study, the effect of crosslinking conditions on the properties of collagen films using EDC and NHS was investigated. Studies included FTIR spectroscopy, AFM, swelling and degradation tests, mechanical testing and contact angle measurements. Evaluation of prepared collagen films indicated that both crosslinking agents and crosslinking conditions influenced film properties. Notable alternations were observed in the infrared spectrum of the sample, to which EDC was added directly to the fish collagen solution. The same sample indicated the lowest Young modulus, tensile strength and breaking force parameters and the highest elongation at break. All samples reached the maximum swelling degree two hours after immersion in PBS solution; however, the immersion-crosslinked samples exhibited a significantly lower degree of swelling and were highly durable. The highest roughness was observed for the collagen film crosslinked with EDC, whereas the lowest was observed for the specimen crosslinked with EDC with NHS addition. The crosslinking agents increased the surface roughness of the collagen film, except for the sample modified with the addition of EDC and NHS mixture. All films were characterized by hydrophilic character. The films’ modification resulted in a decrease in their hydrophilicity and wettability. Our research allows for a comparison of proposed EDC/NHS crosslinking conditions and their influence on the physicochemical properties of fish collagen thin films. EDC and NHS are promising crosslinking agents for the modification of fish collagen used in biomedical applications.

Dynamics of entangled Greenberger — Horne — Zeilinger states in three qubits thermal Tavis — Cummings model

In this paper, we investigated the dynamics of systems of two and three identical qubits interacting resonantly with a selected mode of a thermal field of a lossless resonator. We found solutions of the quantum time-dependent Liouville equation for various three- and two-qubit entangled states of qubits. Based on these solutions, we calculated the criterion of the qubit entanglement — fidelity. The results of numerical calculations of the fidelity showed that increasing the average number of photons in a mode leads to a decrease in the maximum degree of entanglement. It is shown that the two-qubit entangled state is more stable with respect to external noise than the three-qubit entangled Greenberger — Horne — Zeilinger states (GHZ). Moreover, a genuine entangled GHZ-state is more stable to noise than a GHZ-like entangled state.

Intelligent Curtain System Based on 51 Microcontroller

In the 21st century, China's overall appearance has undergone a radical change, and people's demand for quality of life level is getting higher and higher. In view of this situation, this project designs an intelligent curtain based on 51 microcontroller control, which is opened remotely by the user, and the corresponding functions are accomplished by collecting environmental data through photosensitive materials and temperature sensors and transmitting the data to the microcontroller for the operation of the motor. The system realizes four modes of light control, temperature control, manual and remote control, and upholds the concept of green, convenient and stable when creating, in order to bring the maximum degree of safety, convenience and comfort to the user experience.