Hardness Results Research Articles

Algebraic Global Gadgetry for Surjective Constraint Satisfaction

The constraint satisfaction problem (CSP) on a finite relationalstructure B is to decide, given a set of constraints on variableswhere the relations come from B, whether or not there is an assignmentto the variables satisfying all of the constraints; the surjectiveCSP is the variant where one decides the existence of a surjective satisfyingassignment onto the universe of B. We present an algebraicframework for proving hardness results on surjective CSPs; essentially,this framework computes global gadgetry that permits one to presenta reduction from a classical CSP to a surjective CSP. We show how toderive a number of hardness results for surjective CSP in this framework,including the hardness of the disconnected cut problem, of theno-rainbow three-coloring problem, and of the surjective CSP on alltwo-element structures known to be intractable (in this setting). Ourframework thus allows us to unify these hardness results and revealcommon structure among them; we believe that our hardness proof forthe disconnected cut problem is more succinct than the original. Inour view, the framework also makes very transparent a way in whichclassical CSPs can be reduced to surjective CSPs.

Enhanced antioxidant activity in Imidazolium-based protic organic salts: An insight into structure activity relationship via experimental and modelling approaches

Sulfonyl hydroxide functionalized imidazolium based protic ionic liquids (PILs) have been evaluated as a new form of antioxidants. The antioxidant activity was performed using free radical quenching using UV–visible spectroscopy and cyclic voltammetry. The studies confirmed that the investigated ILs with variable anions exhibited substantial radical scavenging activity. In UV–Visible study, Glutamine based-IL ([1MeimPS][Gln]) showed least IC50 value of 95 µM indicating maximum radical quenching activity as an oxidant, while proline based-IL ([1MeimPS]Pro]) exhibited highest IC50 value of 675 µM, demonstrating least anti-oxidant activity. Moreover, cyclic voltammetry results complemented well the UV–visible findings with least IC50 value of 90 µM for [1MeimPS][Gln], showing maximum antioxidant activity, and highest IC50 value of 593 µM for [1MeimPS]Pro], exhibiting the least antioxidant activity. The presence of two primary amines moieties in glutaminate anion may be responsible for enhanced antioxidant activity by providing more active sites for radical quenching. Contrarily, lack of primary amine functionality in prolinate anion may contribute to reduced antioxidant activity of respective IL. The Density Functional Theory (DFT) calculations predicted that the trend of radical scavenging potential was comparable with the experimentally obtained IC50 values. Molecular Electrostatic Potential (MESP) Maps illustrated that [1MeimPS][Pro] has the maximum red zones indicating a poor potential against electron scavenging capacity among all the studied ILs, while blue region in [1MeimPS][Gln], corresponding to low electron density, suggested strong attraction for the incoming electrons. Also, the high electronic distribution of HOMO orbital, appreciable stability, and significant chemical potential to attack on radical species provided by [1MeimPS][Gln] with the maximum radical scavenging potential. Furthermore, the associated LUMO energy for [1MeimPS][Pro] (−1.297 eV) is quite higher than that of [1MeimPS][Gln] (−1.422 eV) which reduced the ability of [1MeimPS][Pro] to attack free radicals of 2,2-diphenyl-1-picrylhydrazyl (DPPH) and thus have higher associated IC50 values. This is also supported by the results of chemical hardness (η) and chemical potential (μ) descriptors values indicating [1MeimPS][Pro] is least stable and reactive than [1MeimPS][Gln]. These findings further explain the least IC50 values observed experimentally and consequent enhanced antioxidant potential of [1MeimPS][Gln].

Artificial Neural Networks and Experimental Analysis of the Resistance Spot Welding Parameters Effect on the Welded Joint Quality of AISI 304.

The automobile industry relies primarily on spot welding operations, particularly resistance spot welding (RSW). The performance and durability of the resistance spot-welded joints are significantly impacted by the welding quality outputs, such as the shear force, nugget diameter, failure mode, and the hardness of the welded joints. In light of this, the present study sought to determine how the aforementioned welding quality outputs of 0.5 and 1 mm thick austenitic stainless steel AISI 304 were affected by RSW parameters, such as welding current, welding time, pressure, holding time, squeezing time, and pulse welding. In order to guarantee precise evaluation and experimental analysis, it is essential that they are supported by a numerical model using an intelligent model. The primary objective of this research is to develop and enhance an intelligent model employing artificial neural network (ANN) models. This model aims to provide deeper knowledge of how the RSW parameters affect the quality of optimum joint behavior. The proposed neural network (NN) models were executed using different ANN structures with various training and transfer functions based on the feedforward backpropagation approach to find the optimal model. The performance of the ANN models was evaluated in accordance with validation metrics, like the mean squared error (MSE) and correlation coefficient (R2). Assessing the experimental findings revealed the maximum shear force and nugget diameter emerged to be 8.6 kN and 5.4 mm for the case of 1-1 mm, 3.298 kN and 4.1 mm for the case of 0.5-0.5 mm, and 4.031 kN and 4.9 mm for the case of 0.5-1 mm. Based on the results of the Pareto charts generated by the Minitab program, the most important parameter for the 1-1 mm case was the welding current; for the 0.5-0.5 mm case, it was pulse welding; and for the 0.5-1 mm case, it was holding time. When looking at the hardness results, it is clear that the nugget zone is much higher than the heat-affected zone (HZ) and base metal (BM) in all three cases. The ANN models showed that the one-output shear force model gave the best prediction, relating to the highest R and the lowest MSE compared to the one-output nugget diameter model and two-output structure. However, the Levenberg-Marquardt backpropagation (Trainlm) training function with the log sigmoid transfer function recorded the best prediction results of both ANN structures.

Recovery of residual polyamide (PA12) from polymer powder bed fusion additive manufacturing process through a binder jetting process

PurposeThis study aims to propose the reuse of PA12 (powder) in another AM process, binder jettiinng, which is less sensitive to the chemical and mechanical degradation of the powder after multiple cycles in the laser system.Design/methodology/approachThe experimental process for evaluating the reuse of SLS powders in a subsequent binder jetting process consists of four phases: powder characterization, bonding analysis, mixture testing and mixture characteristics. Analyses were carried out using techniques such as Fourier Transform Infrared Spectroscopy, scanning electron microscopy, thermogravimetric analysis and stress–strain tests for tension and compression. The surface roughness, color, hardness and density of the new mixture were also determined to find physical characteristics. A Taguchi design L8 was used to search for a mixture with the best mechanical strength.FindingsThe results indicated that the integration of waste powder PA12 with calcium sulfate hemihydrate (CSH) generates appropriate particle distribution with rounded particles of PA12 that improve powder flowability. The micropores observed with less than 60 µm, facilitated binder and infiltrant penetration on 3D parts. The 60/40 (CSH-PA12) mixture with epoxy resin postprocessing was found to be the best-bonded mixture in mechanical testing, rugosity and hardness results. The new CSH-PA12 mixture resulted lighter and stronger than the CSH powder commonly used in binder jetting technology.Originality/valueThis study adds value to the polymer powder bed fusion process by using its waste in a circular process. The novel reuse of PA12 waste in an established process was achieved in an accessible and economical manner.

On the complexity of a maintenance problem for hierarchical systems

We prove that a maintenance problem on frequency-constrained maintenance jobs with a hierarchical structure is integer-factorization hard. This result holds even on simple systems with just two components to maintain. As a corollary, we provide a first hardness result for Levi et al.'s modular maintenance scheduling problem (Levi et al. 2014).

The threshold energy of low temperature Langevin dynamics for pure spherical spin glasses

AbstractWe study the Langevin dynamics for spherical ‐spin models, focusing on the short time regime described by the Cugliandolo–Kurchan equations. Confirming a prediction of Cugliandolo and Kurchan, we show the asymptotic energy achieved is exactly in the low temperature limit. The upper bound uses hardness results for Lipschitz optimization algorithms and applies for all temperatures. For the lower bound, we prove the dynamics reaches and stays above the lowest energy of any approximate local maximum. In fact the latter behavior holds for any Hamiltonian obeying natural smoothness estimates, even with disorder‐dependent initialization and on exponential time‐scales.

Impact of the reduction or replacement of NaCl during production and ripening of raw cured pork and turkey sausages

There are health concerns with regard to the consumption of sodium. Excessive consumption of sodium is suspected to cause high blood pressure, among other things. Therefore, sodium should be reduced or replaced during the production of food. In the present study, in the first part, raw fermented sausages from pork and turkey meat, produced with reduced NaCl concentrations, were investigated. In a second part, the salts, potassium chloride, magnesium chloride, and calcium chloride were added to the sausages, replacing 50% of NaCl. To elucidate, if the reduction or replacement influences the quality of the sausages, physicochemical and microbiological parameters of the products were analyzed. The data show that a reduction of sodium chloride partly influences the hardness and water activity results of raw fermented sausages, made from pork and turkey meat, the redness and nitrite content of the pork sausages, and the ripening losses and total viable counts of the turkey products. Raw fermented sausages with potassium, magnesium, and calcium as partial substitutes for sodium had differing water activity, pH, hardness, and microbiological results using pork and differing pH, hardness, and microbiological results using turkey meat. A bactericidal effect was observed in raw fermented sausages with calcium chloride in inoculation tests with Listeria monocytogenes due to the pH reduction due to calcium. The results indicate that reduction and replacement of NaCl can influence the final products. Therefore, the producers should carefully evaluate before alteration the NaCl content, if this change influences the product acceptability.

Preparation and Characterization of Polyvinyl Alcohol (PVA)/Carbonized Waste Rubber Biocomposite Films.

The technological properties of composite materials (thermal, strength, rheology, electrical and morphology) are very important parameters for high-performance applications. In this study, we aimed to improve the properties of PVA by using carbon materials obtained by the pyrolysis of waste tires, with the aim of recycling them instead of disposing of them. For this purpose, PVA biocomposite films containing carbonized waste rubber at different rates were prepared. The thermal properties of the prepared biocomposite films were examined via thermal gravimetric analysis (TGA) and differential scanning calorimetry (DSC) methods. While rheological measurements were carried out with a rheometer, bulk conductivities were measured with a pico-ammeter. In addition, the morphology of biocomposite films was determined via field emission scanning electron microscopy. The nanomechanical properties of biocomposite film was investigated via XPM analyses. According to the rheological measurements and nanoindentation hardness results, it is understood that as the amount of carbonized waste rubber increases, flexibility decreases and harder and brittle structures are observed in biocomposite films. The electrical measurement results showed that electrical conductivity increased as the amount of carbonized waste rubber increased. When all the results obtained were evaluated, it could be concluded that biocomposite films obtained by increasing the electrical conductivity and hardness of PVA can be used in the electronics industry.

Pengaruh variasi campuran serbuk kayu jati (tectona grandis l.) dan sekam padi pada pembuatan material komposit kampas rem

Brake pad composite materials are made from organic materials and are harmless to the environment. In this study, the brake pad composite material was made using teak wood powder, rice husk and aluminium. Comparison of variations A (23.5 grams of teak wood powder, 18.5 grams of rice husk and 7 grams of aluminium powder) B (27 grams of teak wood powder, 15 grams of rice husk and 7 grams of aluminium powder) C (30.5 grams of teak wood powder, 11.5 grams of rice husk and 7 grams of aluminium powder) and the addition of 21 grams of polyurethane resin then compressed for 30 minutes at 100 0C for 20 minutes. The test results of density, hardness, flexibility and wear were compared with SAE J661. Based on the test results, it was found that samples A, B and C met the SAEJ661 standard only in the flexure test with a value of 490.33 - 529.55 N/cm2. Teak wood powder can increase the value of flexibility while rice husk is used to increase the value of density, hardness and wear due to its silica content.

Effect of copper addition on mechanical properties and microstructures of LM25 cast alloys

The use of aluminum alloys in automobiles is expanding, and the potential for additional increases is significant. Further growth will be determined by improvements in material qualities for existing applications or the discovery of new applications. Alloy A-356 (LM25) is commonly employed for high-quality alloy wheel rims in various motor vehicles, constituting 40% of global car usage. This study introduces 0.2% Cu into the Al–Si–Mg alloy system to enhance the mechanical properties. The alloy blend is cast into a metal mold, subjected to a 4-h cure at 540 °C, quenched with water, and precipitation hardened for 12 h at 1800 °C. Optical and scanning electron microscopes are utilized to analyze the alkali microstructure. The mechanical properties of alloyed and unalloyed castings, including hardness and tensile test results, are examined in untreated and heat-treated states. Fracture surfaces of tensile specimens are scrutinized. Intermetallic compounds formed during solidification are studied using scanning electron microscopy and x-ray diffraction analysis. The tensile strength under unalloyed (LM25) and alloyed (LM25 + 0.2 wt. % Cu) conditions before and after heat treatment [(72, 165.4 and 88.3, 237.1) and (78, 179.6 and 98, 252.9, respectively)] shows a significant increase.

Pengaruh Pemberian Ekstrak Cangkang Telur Bebek (Anas Plaptyrhynchos Domesticus) Konsentrasi 20% Dalam Sediaan Gel Dan Pasta Terhadap Kekerasan Permukaan Email Gigi Tikus Wistar (Rattus Norvegicus) : Studi (In Vivo)

Dental caries is a disease of the hard tissues of the teeth which is characterized by damage to the email and dentin caused by bacterial activity in fermented carbohydrates. One way to overcome and prevent caries is by giving anticariogenic substances that can inhibit caries development and trigger remineralization. As for other alternative materials used for remineralization, one of them is duck egg shell (Anas platyrhynchos domesticus) because it contains calcium carbonate which is in the eggshell can be converted into hydroxyapatite or calcium compounds, so that it can be used as the formation of damaged bones and teeth. In this study, duck egg shell hydroxyapatite extract was made in gel and paste preparations. In gel preparations, it has a high adhesive power so that the absorption on an email surface will be maximized. While in the preparation of pasta also has a great absorption power. This study aimed to determine the effect of hydroxyapatite gel and paste from duck eggshell extract (Anas platyrhynchos domesticus) and Casein Phosphopeptide-Amorphous Calcium Phosphate (CPP-ACP) on the tooth email hardness of wistar rats (Rattus norvegicus). In this study there were 3 treatment groups. Prior to treatment, the tooth sample was etched in the labial section for 20 seconds and rinsed using a brush and water. After etching was applied, in group 1, duck egg shell hydroxyapatite extract gel was applied, in group 2, duck egg shell hydroxyapatite extract paste was applied, and in group 3 as a control group, CPP-ACP was applied to the lower anterior teeth of wistar rats for 30 minutes 2 times a day. for 14 days. On the 15th day, the lower anterior teeth were decapitated by wistar rats and hardness testing was carried out using microvikers hardness in the labial part of the teeth. This research is a true experimental with Post Test Control Group Design. The result of the average hardness of email that has been treated with the highest hardness is CPP-ACP of 332 VHN. The results of the normality test using Shapiro Wilk showed that the duck egg shell extract gel could increase the surface hardness of tooth email. The results of the comparison test using Kruskal Wallis showed that there was a change in hardness between the hydroxyapatite gel of duck eggshell extract, hydroxyapatite paste of duck eggshell extract and CPP-ACP and there were significant differences. From the results of this study, there was an increase in the surface hardness of tooth email after the application of duck egg shell hydroxyapatite gel (Anas platyrhynchos domesticus) compared to paste preparations and as a positive control with CPP-ACP also increased the hardness of tooth email.

An Exercise in Tournament Design: When Some Matches Must Be Scheduled

Single-elimination (SE) tournaments are a popular format used in competitive environments and decision making. Algorithms for SE tournament manipulation have been an active topic of research in recent years. In this paper, we initiate the algorithmic study of a novel variant of SE tournament manipulation that aims to model the fact that certain matchups are highly desired in a sporting context, incentivizing an organizer to manipulate the bracket to make such matchups take place. We obtain both hardness and tractability results. We show that while the problem of computing a bracket enforcing a given set of matches in an SE tournament is NP-hard, there are natural restrictions that lead to polynomial-time solvability. In particular, we show polynomial-time solvability if there is a linear ordering on the ability of players with only a constant number of exceptions where a player with lower ability beats a player with higher ability.

Lost Domain Generalization Is a Natural Consequence of Lack of Training Domains

We show a hardness result for the number of training domains required to achieve a small population error in the test domain. Although many domain generalization algorithms have been developed under various domain-invariance assumptions, there is significant evidence to indicate that out-of-distribution (o.o.d.) test accuracy of state-of-the-art o.o.d. algorithms is on par with empirical risk minimization and random guess on the domain generalization benchmarks such as DomainBed. In this work, we analyze its cause and attribute the lost domain generalization to the lack of training domains. We show that, in a minimax lower bound fashion, any learning algorithm that outputs a classifier with an ε excess error to the Bayes optimal classifier requires at least poly(1/ε) number of training domains, even though the number of training data sampled from each training domain is large. Experiments on the DomainBed benchmark demonstrate that o.o.d. test accuracy is monotonically increasing as the number of training domains increases. Our result sheds light on the intrinsic hardness of domain generalization and suggests benchmarking o.o.d. algorithms by the datasets with a sufficient number of training domains.

Influence of Quenching and Tempering on the Tribological and Corrosion Behavior of Plasma‐Nitrided Society of Automotive Engineers 52100

Society of automotive engineers (SAE) 52100 (100Cr6) steel, used in manufacturing bearings and shafts, deserves attention due to wear and corrosion problems that cause machine losses in the industry. To solve these problems, heat treatments such as quenching and tempering are adopted to reduce wear mechanisms. However, in this work, the effect of these previous heat treatments on the final properties of plasma nitrided steel at three different temperatures (400, 450, and 500 °C) is evaluated. Surface hardness, tribological behavior, and corrosion resistance are evaluated. In the results of Vickers hardness, wear, and electrochemical analysis, it is shown that performing plasma nitriding at 400 and 450 °C on previously heat‐treated SAE 52100 steel provides better mechanical resistance and chemical integrity in a corrosive environment, making the studied steel more comprehensive for important industrial applications.

CHARACTERIZATION OF PERIWINKLE SHELL ASH REINFORCED POLYMER COMPOSITE FOR AUTOMOTIVE APPLICATION

The Periwinkle shell (Tympanotonus fuscatus) is one of the most abundant wastes in the Calabar coastal region of Nigeria and needs to be put into proper use. The great need to shift attention towards waste materials with good mechanical properties to replace some materials used in the Automobile industries for Automobile products is paramount. This research focused on the Mechanical characterization of several composites developed from Periwinkle Shell Powder (PSP) as filler and four selected polymeric materials as the matrix. Recycled high-density polyethylene (rHDPE), Recycled linear low-density polyethylene (rLLDPE), Recycled polystyrene (rPP) and recycled polystyrene (rPS) from waste dumps were selected as the Matrix for the composites. The crushed periwinkle shell (CPSP) was subjected to a calcination (ashing) process. Ashed Periwinkle Shell Powder (APSP) was used to reinforce the rHDPE, rLLDPE, rPP and rPS at 0 to 40% filler loading. Mechanical tests carried out resulted in the 30%PSP and 70%PP composite having better tensile and flexural strengths, good flexural modulus, hardness, impact and moisture absorption results. Results obtained from the mechanical tests were comparable with values obtained from a tested existing vehicle bumper. The APSP-filled recycled polymer composites can serve as a suitable green alternative to existing vehicle bumpers.

Optimization Algorithms for Multi-species Spherical Spin Glasses

This paper develops approximate message passing algorithms to optimize multi-species spherical spin glasses. We first show how to efficiently achieve the algorithmic threshold energy identified in our companion work (Huang and Sellke in arXiv preprint, 2023. arXiv:2303.12172), thus confirming that the Lipschitz hardness result proved therein is tight. Next we give two generalized algorithms which produce multiple outputs and show all of them are approximate critical points. Namely, in an r-species model we construct 2r\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^r$$\\end{document} approximate critical points when the external field is stronger than a “topological trivialization" phase boundary, and exponentially many such points in the complementary regime. We also compute the local behavior of the Hamiltonian around each. These extensions are relevant for another companion work (Huang and Sellke in arXiv preprint, 2023. arXiv:2308.09677) on topological trivialization of the landscape.

Heat-Affected Zone Microstructural Study via Coupled Numerical/Physical Simulation in Welded Superduplex Stainless Steels

Superduplex stainless steels (SDSS) are known for their combination of good mechanical properties and excellent corrosion resistance, enabled by the microstructural balance between austenite and ferrite and an amount of alloying elements. Their application in welded components is, however, limited by the possibility of the precipitation of intermetallic phases and microstructural misbalance, which might hinder their properties, especially in the heat-affected zone (HAZ). This work introduces a methodology that relies simultaneously on physical and numerical simulations to study the HAZ in a UNS S32750 SDSS. Dimensions of the fusion zone and thermal cycles were calibrated for a numerical model using preliminary welding trials. Numerically simulated cycles for each heat input (HI) were physically reproduced in a Gleeble® simulator, and the heat-treated samples were characterized and compared with real specimens welded using the same parameters. Thermal curves resulting from the numerical simulations were successfully replicated by the Gleeble®, indicating adequate application of the desired HI. The hardness and microstructural results from simulated and welded specimens were also found to be quite similar. Therefore, the proposed methodology showed itself adequate not only for the study of duplex stainless steels, but also of materials with similar thermal and mechanical properties, including the extrapolation of welding parameters.

CARBURIZING-QUENCHING HARDNESS MODEL ANALYSIS AND COMPARISON

Unlike the conventional calculation models of the hardness, a carburizing-quenching hardness model considers the influence of the carbon content on the phase transformation and hardness. The volume fraction model (VFM) and Jominy curve model (JCM) for calculating carburizing-quenching hardness of 20CrNi2Mo steel were built in this study, and the models were used to calculate the hardness of Jominy and gear samples. The hardness results of both models were compared, and the simulation results were verified with the corresponding test results. The results show that the hardness values obtained with both models have a certain calculation accuracy. But due to considering the influence of residual austenite (RA) on the hardness, the simulation accuracy of the VFM was better for the low Jominy distance and the hardened case, while the simulation accuracy of the JCM was better for the large Jominy distance and the low-carbon martensite region; the calculation of the latter is more convenient and its accumulated error is small.

On the Parameterized Intractability of Determinant Maximization

In the Determinant Maximization problem, given an n×n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n \ imes n$$\\end{document} positive semi-definite matrix A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf {A}} $$\\end{document} in Qn×n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Q}^{n \ imes n}$$\\end{document} and an integer k, we are required to find a k×k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k \ imes k$$\\end{document} principal submatrix of A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf {A}} $$\\end{document} having the maximum determinant. This problem is known to be NP-hard and further proven to be W[1]-hard with respect to k by Koutis (Inf Process Lett 100:8–13, 2006); i.e., a f(k)nO(1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(k)n^{{{\\,\\mathrm{\\mathcal {O}}\\,}}(1)}$$\\end{document}-time algorithm is unlikely to exist for any computable function f. However, there is still room to explore its parameterized complexity in the restricted case, in the hope of overcoming the general-case parameterized intractability. In this study, we rule out the fixed-parameter tractability of Determinant Maximization even if an input matrix is extremely sparse or low rank, or an approximate solution is acceptable. We first prove that Determinant Maximization is NP-hard and W[1]-hard even if an input matrix is an arrowhead matrix; i.e., the underlying graph formed by nonzero entries is a star, implying that the structural sparsity is not helpful. By contrast, Determinant Maximization is known to be solvable in polynomial time on tridiagonal matrices (Al-Thani and Lee, in: LAGOS, 2021). Thereafter, we demonstrate the W[1]-hardness with respect to the rankr of an input matrix. Our result is stronger than Koutis’ result in the sense that any k×k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k \ imes k$$\\end{document} principal submatrix is singular whenever k>r\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k > r$$\\end{document}. We finally give evidence that it is W[1]-hard to approximate Determinant Maximization parameterized by k within a factor of 2-ck\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^{-c\\sqrt{k}}$$\\end{document} for some universal constant c>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c > 0$$\\end{document}. Our hardness result is conditional on the Parameterized Inapproximability Hypothesis posed by Lokshtanov et al. (in: SODA, 2020), which asserts that a gap version of Binary Constraint Satisfaction Problem is W[1]-hard. To complement this result, we develop an ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-additive approximation algorithm that runs in ε-r2·rO(r3)·nO(1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon ^{-r^2} \\cdot r^{{{\\,\\mathrm{\\mathcal {O}}\\,}}(r^3)} \\cdot n^{{{\\,\\mathrm{\\mathcal {O}}\\,}}(1)}$$\\end{document} time for the rank r of an input matrix, provided that the diagonal entries are bounded.

Explosion Cracking Analysis of Sulfur Resistance Induction Heat Bend Pipe

The explosion cracking reason on induction heat bend pipe was analyzed through macroscopic analysis, chemical composition analysis, mechanical properties testing, metallographic analysis, scanning electron microscopy and XRD. The results showed that the chemical composition, tensile test, Vickers hardness results of the straight section of the bent pipe met the requirements of the technical specifications, and the metallographic structure of the straight section of the bent pipe was pearlite and ferrite. The Charpy impact test in the neutral zone of the bend section had a low shear fracture ratio, and the Vickers hardness test results were on the high side. The metallographic structure was granular bainite. The fracture surface of the failed bent pipe exhibited brittle fracture characteristics on the macro level. The metallographic analysis and hardness test results of the crack source area showed that the fracture surface had typical intergranular propagation characteristics and high hardness values. Energy spectrum analysis of the crack source area revealed the presence of S element. The XRD analysis of the product on the inner wall of the pipe contained sulfides. The comprehensive results indicated that the failed bend pipe undergoes stress corrosion and initiates corrosion cracks on the surface under the combined action of operating pressure, additional bending stress, residual stress, etc. in a sulfide corrosive medium, the cracks continued to propagate along the grain boundaries and ultimately caused the bend pipe to explode.