Development of Pectin-Based Aerogels with Several Excellent Properties for the Adsorption of Pb2+

Traditional aerogels lack specific functional groups for the adsorption of Pb2+, which results in a low adsorption capacity and limits the application scope. Novel porous pectin-based aerogels (PPEAs) were prepared by incorporating polyethylenimine (PEI) using ethylene glycol diglycidyl ether (EGDE) as a cross-linker for the removal of Pb2+ from water. The cross-linking mechanism, morphology, mechanical strength, thermal stability, adsorption properties, and mechanism of the aerogels were investigated. The aerogels possessed several desirable features, such as a large maximum Pb2+ adsorption capacity (373.7 mg/g, tested at pH 5.0), ultralight (as low as 63.4 mg/cm3), high mechanical strength (stress above 0.24 MPa at 50% strain), and easy recyclability. Meanwhile, the equilibrium adsorption data was well described by the Langmuir–Freundlich (Sips) model and the kinetic adsorption process was well fitted using the pseudo-second-order model. The donor groups, such as -NH2, and oxygen-containing functional groups were responsible for the Pb2+ adsorption, which was confirmed by the FTIR and XPS analysis. The excellent characteristics mean that PPEAs are highly effective adsorbents in the remediation of lead-containing wastewater.

Bayesian analysis of multimessenger M-R data with interpolated hybrid EoS

We introduce a family of equations of state (EoS) for hybrid neutron star (NS) matter that is obtained by a two-zone parabolic interpolation between a soft hadronic EoS at low densities and a set of stiff quark matter EoS at high densities within a finite region of chemical potentials $$\mu _H< \mu < \mu _Q$$ μ H < μ < μ Q . Fixing the hadronic EoS as the APR one and choosing the color-superconducting, nonlocal NJL model with two free parameters for the quark phase, we perform Bayesian analyses with this two-parameter family of hybrid EoS. Using three different sets of observational constraints that include the mass of PSR J0740+6620, the tidal deformability for GW170817, and the mass-radius relation for PSR J0030+0451 from NICER as obligatory (set 1), while set 2 uses the possible upper limit on the maximum mass from GW170817 as an additional constraint and set 3 instead of the possibility that the lighter object in the asymmetric binary merger GW190814 is a neutron star. We confirm that in any case, the quark matter phase has to be color superconducting with the dimensionless diquark coupling approximately fulfilling the Fierz relation $$\eta _D=0.75$$ η D = 0.75 and the most probable solutions exhibiting a proportionality between $$\eta _D$$ η D and $$\eta _V$$ η V , the coupling of the repulsive vector interaction that is required for a sufficiently large maximum mass. We used the Bayesian analysis to investigate with the method of fictitious measurements the consequences of anticipating different radii for the massive $$2~M_\odot $$ 2 M ⊙ PSR J0740+6220 for the most likely equation of state. With the actual outcome of the NICER radius measurement on PSR J0740+6220 we could conclude that for the most likely hybrid star EoS would not support a maximum mass as large as $$2.5~M_\odot $$ 2.5 M ⊙ so that the event GW190814 was a binary black hole merger.

Detection of Microplastics in Water and Ice

It is possible to detect various microplastics (MPs) floating on water or contained in ice due to the unique optical characteristics of plastics of various chemical compositions and structures. When the MPs are measured in the spectral region between 800 and 1000 nm, which has relatively little influence on the temperature change in water, they are frequently perceived as noise or obscured by the surrounding reflection spectra because of the small number and low intensity of the representative peak wavelengths. In this study, we have applied several mathematical methods, including the convex hull, Gaussian deconvolution, and curve fitting to amplify and normalize the reflectance and thereby find the spectral properties of each polymer, namely polypropylene (PP), polyethylene terephthalate (PET), methyl methacrylate (PMMA), and polyethylene (PE). Blunt-shaped spectra with a relatively large maximum of normalized reflectance (NRmax) can be decomposed into several Gaussian peak wavelengths: 889, 910, and 932 nm for the PP and 898 and 931 nm for the PE. Moreover, unique peak wavelengths with the meaningful measure at 868 and 907 nm for the PET and 887 nm for the PMMA were also obtained. Based on the results of the study, one can say that each plastic can be identified with up to 81% precision by compensating based on the spectral properties even when they are hidden in water or ice.

Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences

Automatic sequences are not suitable sequences for cryptographic applications since both their subword complexity and their expansion complexity are small, and their correlation measure of order 2 is large. These sequences are highly predictable despite having a large maximum order complexity. However, recent results show that polynomial subsequences of automatic sequences, such as the Thue–Morse sequence, are better candidates for pseudorandom sequences. A natural generalization of automatic sequences are morphic sequences, given by a fixed point of a prolongeable morphism that is not necessarily uniform. In this paper we prove a lower bound for the maximum order complexity of the sum of digits function in Zeckendorf base which is an example of a morphic sequence. We also prove that the polynomial subsequences of this sequence keep large maximum order complexity, such as the Thue–Morse sequence.

Peg solitaire on graphs with large maximum degree

In 2011, Beeler and Hoilman introduced the peg solitaire on graphs. The peg solitaire on a connected graph is a one-player combinatorial game starting with exactly one hole in a vertex and pegs in all other vertices and removing all pegs but exactly one by a sequence of jumps; for a path [Formula: see text], if there are pegs in [Formula: see text] and [Formula: see text] and exists a hole in [Formula: see text], then [Formula: see text] can jump over [Formula: see text] into [Formula: see text], and after that, the peg in [Formula: see text] is removed. A problem of interest in the game is to characterize solvable (respectively, freely solvable) graphs, where a graph is solvable (respectively, freely solvable) if for some (respectively, any) vertex [Formula: see text], starting with a hole [Formula: see text], a terminal state consisting of a single peg can be obtained from the starting state by a sequence of jumps. In this paper, we consider the peg solitaire on graphs with large maximum degree. In particular, we show the necessary and sufficient condition for a graph with large maximum degree to be solvable in terms of the number of pendant vertices adjacent to a vertex of maximum degree. It is a notable point that this paper deals with a question of Beeler and Walvoort whether a non-solvable condition of trees can be extended to other graphs.

On the Maximum Order Complexity of Thue–Morse and Rudin–Shapiro Sequences along Polynomial Values

Both the Thue–Morse and Rudin–Shapiro sequences are not suitable sequences for cryptography since their expansion complexity is small and their correlation measure of order 2 is large. These facts imply that these sequences are highly predictable despite the fact that they have a large maximum order complexity. Sun and Winterhof (2019) showed that the Thue–Morse sequence along squares keeps a large maximum order complexity. Since, by Christol’s theorem, the expansion complexity of this rarefied sequence is no longer bounded, this provides a potentially better candidate for cryptographic applications. Similar results are known for the Rudin–Shapiro sequence and more general pattern sequences. In this paper we generalize these results to any polynomial subsequence (instead of squares) and thereby answer an open problem of Sun and Winterhof. We conclude this paper by some open problems.

Automated Steering Control System for Reverse Parking Maneuver of Semi-Trailer Vehicles Considering Motion Planning by Simulation of Feedback Control System

With the increase in the demand for road freight transportation, semi-trailers are being increasingly preferedowing to their large maximum load capacity. However, for such vehicles, excellent driving skills are required because unique steering is often necessary during reverse parking. In this paper, the concept of a parking assist system and path tracking controller is proposed. The control system consists of a pure pursuit motion planner for handling the reference path tracking and a feedback controller for stabilizing the hitch angles. We propose a control method to realize the ideal control performance of an actual vehicle subjected to unmeasured disturbance. An actual full-scale vehicle experiment is conducted and the effectiveness of the proposed approach is verified by evaluating the error from the target parking position.

Algorithm for Decreasing the Large Peak to Average Power Ratio in Mimo-Ofdm

Every personal want to use high speed communication system but bandwidth is limited and users are unlimited in that case some of technologies are use for improving speed. One of the best technology called multiple inputs multiple outputs orthogonal frequency division multiplexing. Which provides very fast communication system but drawback of this technique is large maximum to average power ratio, these reduce efficiency of power amplifier. In this article developed new algorithm, for reduction of large maximum to average power ratio and improve bit or symbol error rate in MIMO-OFDM system. Proposed technique, called filter companding selected mapping algorithm technique (FC-SLM) to reduce PAPR using filtering and companding concept. In this techniques, after modulation of input data are converted into serial to parallel steam, phase mapping of all data from 0 to 360 degrees and perform IFFT operation, calculate PAPR and pass through desire range of filter and select minimum PAPR then perform companding and transmitted through an antenna. This scheme is reduce 2.3 dB PAPR and improve bit or symbol error rate. This is one of the most excellent promising techniques for next generation (5-G) communication system.

On minimal Ramsey graphs and Ramsey equivalence in multiple colours

For an integer q ⩾ 2, a graph G is called q-Ramsey for a graph H if every q-colouring of the edges of G contains a monochromatic copy of H. If G is q-Ramsey for H yet no proper subgraph of G has this property, then G is called q-Ramsey-minimal for H. Generalizing a statement by Burr, Nešetřil and Rödl from 1977, we prove that, for q ⩾ 3, if G is a graph that is not q-Ramsey for some graph H, then G is contained as an induced subgraph in an infinite number of q-Ramsey-minimal graphs for H as long as H is 3-connected or isomorphic to the triangle. For such H, the following are some consequences.For 2 ⩽ r < q, every r-Ramsey-minimal graph for H is contained as an induced subgraph in an infinite number of q-Ramsey-minimal graphs for H.For every q ⩾ 3, there are q-Ramsey-minimal graphs for H of arbitrarily large maximum degree, genus and chromatic number.The collection $\{\mathcal M_q(H) \colon H \text{ is 3-connected or } K_3\}$ forms an antichain with respect to the subset relation, where $\mathcal M_q(H)$ denotes the set of all graphs that are q-Ramsey-minimal for H.We also address the question of which pairs of graphs satisfy $\mathcal M_q(H_1)=\mathcal M_q(H_2)$ , in which case H1 and H2 are called q-equivalent. We show that two graphs H1 and H2 are q-equivalent for even q if they are 2-equivalent, and that in general q-equivalence for some q ⩾ 3 does not necessarily imply 2-equivalence. Finally we indicate that for connected graphs this implication may hold: results by Nešetřil and Rödl and by Fox, Grinshpun, Liebenau, Person and Szabó imply that the complete graph is not 2-equivalent to any other connected graph. We prove that this is the case for an arbitrary number of colours.