Pair Of Solutions Research Articles

Joint Precoder and Beamformer Design for Secure Relay Networks With Finite-Alphabet Inputs and Statistical CSI of Eve

Because of discrepant deteriorations of the intended receiver and the unintended receiver, artificial noise (AN) can be invoked in conjunction with the precoder to wireless transmissions for enhancing the secrecy rate (SR) performance as long as we elaborately frame them. This paper studies a secure transmission strategy by jointly designing the precoder and AN beamformer at the relay network, where a passive eavesdropper and finite-alphabet inputs are taken into account. We propose a pair of solutions for low-order modulation and high-order modulation, respectively. To solve the first optimization problem, we propose a low-complexity algorithm with the aid of the invoked cut-off rate. Interestingly, we find that the phase of an optimum precoder for maximizing the SR has a correlation to both the channels spanning from the transmitter to the relays and spanning from the relays to the legitimate receiver. Furthermore, we reveal that the AN beamformer vector has at most one non-zero component, which only locates at the position corresponding to the minimum element of the channel between the relays and the intended receiver. According to these findings, the SR maximization problem over the two vectors is simplified as one only related to a pair of scalars. As for the high-order modulation, a new solution is further proposed for circumventing the predicament that the computational complexity exponentially increases as the size of the adopted modulation increases, where we not only eliminate two-layer summation over the legitimate symbols but also conceive a concave maximization SR problem. Finally, simulation results demonstrate the efficiency of the proposed algorithms in terms of the SR performance.

Thermo-sensitive self-assembly of poly(ethylene imine)/(phenylthio) acetic acid ion pair in surfactant solutions

Poly(ethylene imine)/(phenylthio) acetic acid (PEI/PTA) ion pairs exhibited an upper critical solution temperature (UCST) behavior in an aqueous solution and the UCST was higher as the PTA content was more. The UCST of the ion pair decreased with increasing Brij S100 (BS 100, a nonionic surfactant) concentration but increased with increasing cetylpridinium chloride (CPC, a cationic surfactant) and sodium lauroylsarcosinate (SLS, an anionic surfactant) concentration. TEM microscopy demonstrated BS 100 markedly reduced the size of PEI/PTA ion pair self-assembly (IPSAM) whereas CPC and SLS had little effect on the size and the integrity of IPSAM. 1H NMR spectroscopy showed the hydrophobic interaction among the phenyl groups of PEI/PTA ion pairs took place. It also demonstrated the hydrophobic interaction between BS 100 and PTA and the electrostatic interaction between CPC and PTA and between SLS and PEI occurred. X-ray photoelectron spectroscopy disclosed the PTA of PEI/PTA IPSAM could be readily oxidized by H2O2 even at a low concentration (e.g. 0.005%). IPSAM released its payload (i.e. nile red) in a temperature and oxidation-responsive manner. The surfactants (i.e. BS 100, CPC, and SLS) suppressed the thermally triggered release in a different way. The effectiveness of the surfactant to suppress the release was in the order of BS 100 > CPC > SLS. IPSAM released its content more extensively as H2O2 (an oxidizing agent) concentration was higher. The ionic surfactants (i.e. CPS and SLS) had little effect on the oxidation-induced release degree but the nonionic surfactant (BS 100) markedly suppressed the release degree.

Square-Wave Electrogravimetry Combined with Voltammetry Reveals Reversible Submonolayer Adsorption of Redox-Active Ions.

Square-wave voltammetry on electrolytes containing reversible redox pairs in solution was complemented by acoustic microgravimetry, where multifrequency lock-in amplification provides for a time resolution of 2.5 ms and a frequency resolution after accumulation of 12 mHz. The instrument operates similar to a quartz crystal microbalance with dissipation monitoring (QCM-D). The use of square-waves rather than linear ramps makes the analysis more transparent because it reduces the contribution of non-Faraday currents. Also, square-wave electrogravimetry determines the rates of mass transfer with much better sensitivity than its counterpart based on linear voltage ramps. The shifts of frequency and bandwidth are in agreement with the Sauerbrey prediction, meaning that the overtone-normalized frequency shifts, Δf/n, are similar on the different overtones and that the shifts in half bandwidth, ΔΓ, are smaller than the shifts in frequency. Small deviations from the Sauerbrey prediction presumably result from the softness of the adsorbed layer. Because the response time of the QCM signals is much longer than the RC time of double layer recharging as determined with electrochemical impedance spectroscopy (EIS), interpretation in terms of adsorption and desorption is more plausible than interpretation in terms of changed viscosity in the diffuse double layer. Ions of methyl viologen (MV) were found to adsorb to the electrode surface more strongly in the state with a single charge than in the fully oxidized state carrying two charges. The difference in apparent thickness between the oxidized and the reduced state was up to 2 nm, depending on concentration. The gravimetric results obtained on flavin adenine dinucleotide (FAD) depended on pH. At neutral pH, adsorption was largest close to the redox potential. Presumably, the adsorbed molecules are semiquinones, that is, are the intermediates of the underlying two-electron process.

Redox-Induced Lipid Vesicle Fusion Onto Electroactive Self-Assembled Monolayers

Supported lipid bilayers (SLBs) are popular model systems to study cell membrane functionalities and various biomolecular interaction forces. A key advantage of SLBs on metallic surfaces, is the application of spectroscopic, electrochemical, and surface plasmon resonance techniques for biomolecular recognition studies. The most common method for forming SLBs is vesicle fusion, which involves the adsorption, deformation, and rupture of small unilamellar vesicles (SUVs) of lipids from aqueous suspension to the substrate surface.1 The formation of continuous single bilayers by vesicle fusion can be problematic due to the many experimental parameters influencing vesicle rupture and bilayer spreading (i.e., lipid and vesicle properties, physicochemical characteristics of the surface, temperature, and solvent environment)1. Vesicle fusion typically works only with smooth hydrophilic surfaces, such as glass, silica, and mica. Although approaches have been developed to form bilayers on technologically relevant surfaces such gold (e.g., surface functionalization with hydrophilic organic films,2 solvent-assisted lipid bilayer formation3 or the addition of a vesicle-destabilizing agent4), there remains a need for active strategies that are fast, versatile, and scalable.We present a redox-induced approach for the formation of single bilayers on gold functionalized with electroactive self-assembled monolayers (SAMs) of ferrocenylalkanethiolates. The electrochemical oxidation of the SAM-bound ferrocene (Fc) to ferrocenium (Fc+) involves coupled electron transfer and ion pairing reactions. Counteranions from solution pair with the ferroceniums to stabilize the oxidized cations and neutralize the excess positive charge at the SAM/aqueous interface. The surface-confined redox reaction triggers the formation of single bilayer membranes from SUVs of anionic or zwitterionic phospholipids onto gold surfaces modified with the electroactive SAM. The ion pairing association of the charged lipid head groups with the electrogenerated ferroceniums drives the assembly of the phospholipids on the SAM surface to produce solid-supported bilayers of high surface coverage (≳ 90%) from gel- or fluid-phase forming phospholipids within minutes at room temperature. The redox-mediated strategy reported in this work is a conceptual advance in the preparation of solid-supported lipid bilayers. It is fast, insensitive to the phase state of the phospholipid in the vesicle precursor, and not limited to hydrophilic surfaces. References Richter, R. P.; Bérat, R.; Brisson, A. R., Formation of Solid-Supported Lipid Bilayers: An Integrated View. Langmuir 2006, 22 (8), 3497-3505.Silin, V. I.; Wider, H.; Woodward, J. T.; Valincius, G.; Offenhausser, A.; Plant, A. L., The Role of Surface Energy on the Formation of Hybrid Bilayer Membranes. J. Am. Chem. Soc. 2002, 124, 14676-14683.Ferhan, A. R.; Yoon, B. K.; Park, S.; Sut, T. N.; Chin, H.; Park, J. H.; Jackman, J. A.; Cho, N.-J., Solvent-Assisted Preparation of Supported Lipid Bilayers. Nat. Protoc. 2019, 14 (7), 2091-2118.Cho, N.-J.; Cho, S.-J.; Cheong, K. H.; Glenn, J. S.; Frank, C. W., Employing an Amphipathic Viral Peptide to Create a Lipid Bilayer on Au and TiO2. J. Am. Chem. Soc. 2007, 129 (33), 10050-10051. Figure 1

Existence and non-existence of solutions to the coboundary equation for measure-preserving systems

AbstractA fundamental question in the field of cohomology of dynamical systems is to determine when there are solutions to the coboundary equation: $$ \begin{align*} f = g - g \circ T. \end{align*} $$ In many cases, T is given to be an ergodic invertible measure-preserving transformation on a standard probability space $(X, {\mathcal B}, \mu )$ and is contained in $L^p$ for $p \geq 0$ . We extend previous results by showing for any measurable f that is non-zero on a set of positive measure, the class of measure-preserving T with a measurable solution g is meager (including the case where $\int _X f\,d\mu = 0$ ). From this fact, a natural question arises: given f, does there always exist a solution pair T and g? In regards to this question, our main results are as follows. Given measurable f, there exist an ergodic invertible measure-preserving transformation T and measurable function g such that $f(x) = g(x) - g(Tx)$ for almost every (a.e.) $x\in X$ , if and only if $\int _{f> 0} f\,d\mu = - \int _{f < 0} f\,d\mu $ (whether finite or $\infty $ ). Given mean-zero $f \in L^p(\mu )$ for $p \geq 1$ , there exist an ergodic invertible measure-preserving T and $g \in L^{p-1}(\mu )$ such that $f(x) = g(x) - g( Tx )$ for a.e. $x \in X$ . In some sense, the previous existence result is the best possible. For $p \geq 1$ , there exists a dense $G_{\delta }$ set of mean-zero $f \in L^p(\mu )$ such that for any ergodic invertible measure-preserving T and any measurable g such that $f(x) = g(x) - g(Tx)$ almost everywhere, then $g \notin L^q(\mu )$ for $q> p - 1$ . Finally, it is shown that we cannot expect finite moments for solutions g, when $f \in L^1(\mu )$ . In particular, given any such that $\lim _{x\to \infty } \phi (x) = \infty $ , there exist mean-zero $f \in L^1(\mu )$ such that for any solutions T and g, the transfer function g satisfies: $$ \begin{align*} \int_{X} \phi ( | g(x) | )\,d\mu = \infty. \end{align*} $$

BMW-TOPSIS: A generalized TOPSIS model based on three-way decision

TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) uses a pair of a positive ideal solution and a negative ideal solution as two reference points to rank a set of decision alternatives. In some situations, a trade-off of the distances to the two extreme reference points may not necessarily be meaningful. Inspired by the theory of three-way decision as thinking in threes (e.g., two opposite poles and a third middle), in this paper we generalize the classical TOPSIS by adding a third middle reference point. We use a common setting for investigating systematically reference-point-based TOPSIS-style multi-criteria decision-making methods. In particular, we examine three classes of approaches: a) a best reference point based model (i.e., B-TOPSIS) and a worst reference point based model (i.e., W-TOPSIS), b) the classical best and worst reference points based model (i.e., BW-TOPSIS), and c) a new best, mean, and worst reference points based model (i.e., BMW-TOPSIS). The three classes are one-way TOPSIS, two-way TOPSIS, and three-way TOPSIS, respectively. Based on one-way and two-way TOPSISs, we give two specific methods of three-way TOPSIS. The experimental results, compared with the existing TOPSIS methods, show that the BMW-TOPSIS model is feasible and effective.

A stabilized difference finite element method for the 3D steady Stokes equations

A stabilized difference finite element (SDFE) method based on the finite element pair ((P1,P1,P1)×P1)×(P1×P0) is presented for the 3D steady Stokes equations. The difference finite element method consists of combining the finite difference discretization based on the P1×P0-element in the z-direction and the finite element discretization based on the (P1,P1,P1)×P1-element in the (x,y)-plane. In this way, the numerical solution of the 3D steady Stokes equations can be transmitted into a series of the finite element solution pair (whk,phk) of the 2D steady Stokes equations and the finite element solution u3hk of the elliptic equation. The core of the stabilized method is to characterize the Ladyzhenskaya-Babusˇka-Brezzi “deficiency” of the unstable finite element pair with an appropriate operator, and the application of the operator in the stabilized mixed variational equations. The rigorous stability analysis and error estimation are developed, showing that the SDFE method is stable and optimally convergent. Several numerical tests are presented, confirming the theoretical predictions and verifying the accuracy of the considered method.

Verification of a fracture model for fiber reinforced concrete beams in bending

Modeling fiber-reinforced concrete at failure by fracture is a challenging task because we need insight into the post-peak behaviour of the model after failure, including crack propagation. In this paper, we present the basic properties of the fiber-reinforced concrete model and its ability to capture the phenomena in three-point bending tests. In this work, we deal with a proof of concept - the verification of the model. The verification of the code includes the selection of the optimal solution algorithm and the selection of the appropriate solution from possible pairs of solutions. Verification of the calculation includes the influence of the number of layers used in the discretisation and, in particular, the influence of the shape of the piecewise defined force–displacement curves of the layers. Only the first stage of verification was performed, i.e. qualitative comparison of the model and experimental results and the influence of the shape of the force–displacement curves. One of the most desirable features of the model is its suitability for subsequent inverse analysis and parameter determination.

Design of saturated boundary control for hyperbolic systems with in-domain disturbances

Boundary feedback control design is studied for 1D hyperbolic systems with an in-domain disturbance and a boundary feedback controller under the effect of actuator saturation. Nonlinear semigroup theory is used to prove well-posedness of mild solution pairs to the closed-loop system. Sufficient conditions in the form of dissipation functional inequalities are derived to establish global stability for the closed-loop system and L2-stability in presence of in-domain disturbances. The control design problem is then recast as an optimization problem over linear matrix inequality constraints. Numerical results are shown to validate the effectiveness of the proposed control design.

Multiple Periodic Solutions for Odd Perturbations of the Discrete Relativistic Operator

We obtain the existence of multiple pairs of periodic solutions for difference equations of type −Δ(Δu(n − 1)1 − |Δu(n − 1)|2)=λg(u(n))(n∈Z), where g:R→R is a continuous odd function with anticoercive primitive, and λ>0 is a real parameter. The approach is variational and relies on the critical point theory for convex, lower semicontinuous perturbations of C1-functionals.

Estimating rate-induced tipping via asymptotic series and a Melnikov-like method* *CK was partly supported by a Lichtenberg Professorship of the VolkswagenStiftung. CK also acknowledges partial support of the EU within the TiPES project funded the European Unions Horizon 2020 research and innovation programme under Grant Agreement No. 820970. IPL was partly supported by MICIIN/FEDER project RTI2018-096523-B-100 and by European Union’s

The paper deals with the study of rate-induced tipping in asymptotically autonomous scalar ordinary differential equations. We prove that, in such a tipping scenario, a solution which limits at a hyperbolic stable equilibrium of the past limit-problem loses uniform asymptotic stability and coincides with a solution which limits at a hyperbolic unstable equilibrium of the future limit-problem. We use asymptotic series to approximate such pairs of solutions and characterize the occurrence of a rate-induced tipping by using only solutions calculable on finite time intervals. Moreover, we show that a Melnikov-inspired method employing the asymptotic series allows to asymptotically approximate the tipping point.

A Probabilistic Method for a Class of Non-Lipschitz BSDEs with Application to Fund Management

The present work is devoted to a study of the solvability of a class of non-Lipschitz and noncanonical backward stochastic differential equations (BSDEs) that naturally arises from an intertemporal mutual fund management problem; to this end, we propose a method of combining the techniques of Malliavin calculus and a discussion on the Jacobian flow of the BSDE. Specifically, based on the intimate relationship between $Y_t$ and $Z_t$ of the BSDE via the Malliavin derivative of the former, namely, $D_tY_t=Z_t$, we construct an iterative Picard converging scheme for approximating the underlying solution pair by first obtaining $Z_t$ from the derived BSDE with respect to the Malliavin derivative and then recovering $Y_t$ from the underlying BSDE. A local unique existence result is first warranted over a short time horizon with carefully examined a priori estimates; indeed, each term in the iterative sequence is related to different Girsanov transforms for change of measure, and comparing them demands a delicate analysis. The use of Jacobian flow further enables us to properly control the lower and upper bounds for a certain product of the forward process and $Z_t$, which enables us to extend the solution globally by an inductive argument. Our proposed method is fundamentally different from other probabilistic methods that also involve estimating or bounding Malliavin traces such as [E. Pardoux and S. Peng, Some Backward SDEs with Non-Lipschitz Coefficients, Technical note, Université de Provence, Aix-en-Provence, France, 1996] and [M. C. Zedouri, Equations Différentielles Stochastiques Rétrogrades avec Générateurs Lipschitiziens Stochastiques, Master's Thesis, Université Mohammed Seddik Ben Yahia-Jijel, Jijel, Algeria, 2010]. We believe that our new approach proposed here can be potentially applied to resolve many other general non-Lipschitz forward-backward stochastic differential equations (FBSDEs) encountered in economics and finance, especially in the presence of generic utility functions.

Collision phenomena among the solitons, periodic and Jacobi elliptic functions to a (3+1)-dimensional Sharma-Tasso-Olver-like model

In this manuscript, we consider a (3+1)-dimensional Sharma-Tasso-Olver-like (STOL) model, which can be used to describe dispersive wave phenomena in optics, plasmas, quantum physics, and others. Based on the simplified Hirota approach, the n-soliton solutions are obtained. We observe that the collisions are non-elastic fusion or fission phenomena where some kink waves disappear due to soliton fusion, or a single kink wave splits into more kink waves due to soliton fusion. We derive kinky-lump breather, combo line kink and kinky-lump breather, and a pair of kinky-lump breather wave solutions that degenerate from two-, three- and four-solitons respectively by choosing complex conjugate values involving free parameters. Moreover, we demonstrate a few new collisions of the Jacobi elliptic sine function with one soliton, and a periodic cosine function which provides kinky-periodic waves and double-periodic waves. All special properties of those collision solutions are illustrated with the 3D, density and contour plots.

Traveling waves for a generalized Beddington–DeAngelis predator–prey model

In this article, we study the traveling waves of a generalized Beddington–DeAngelis predator–prey model which covers the general case of Holling–Tanner model. We also introduce some simulation figures to support the analysis. The main contributions are stated below: (i) We construct a new form of shrinking rectangle, which improves the range of the parameters to ∞, to discuss the asymptotic behavior; (ii) We provide a pair of new upper and lower solutions to deal with the singularity of the predator equation.

Spatial dynamics of a nonlocal predator–prey model with double mutation

In this paper, we are dedicated to studying the global dynamics of a nonlocal predator–prey model with double mutation. First, by defining a pair of upper and lower solutions, we build a new comparison principle. Furthermore, based on the new comparison principle, we get the existence of the solutions by constructing monotone iterative sequences. Finally, using the quasi-fundamental solution, Gronwall’s inequality and auxiliary functions, the uniqueness and uniform boundedness of the solutions are given. It is worth noting that this paper is the first to introduce the double mutation into the system and obtain the well-posedness and the uniform boundedness of the solutions by more detailed analysis and estimation.

Existence and multiplicity of solutions for perturbed fractional p-Laplacian equations with critical nonlinearity in N

In this paper, we consider the existence and multiplicity of solutions for the following perturbed fractional p-Laplacian equation Under some mild conditions on V, A and h, we show that the problem has at least one positive weak solution provided , and for any , it has pairs of solutions if , where and are sufficiently small positive numbers. Moreover, these solutions in as

Study of Mixed Clusters of Water and N,N'-dimethylethyleneurea

Intermolecular interactions between a single water and two N,N'-dimethylethyleneurea (DMEU) molecules have been investigated using local and density-fitting approximations of the standard Møller–Plesset perturbation theory (DF-LMP2) with the aug-cc-pVTZ basis set. Six stable configurations have been found. In the first three, the water molecule intercalates between two DMEU molecules. In the next three configurations, the water molecule is attached to a stacked DMEU dimer, and these structures are more stable than the first three. These results support the viewthat DMEU molecules can form contact pairs in dilute aqueous solutions.

Structural Behavior of Aqueous Solutions Using Time Domain Reflectometry Technique

We have developed and established the TDR technique that provides information about the dielectric permittivity in the frequency range from 10 MHz to 30 GHz. The dielectric permittivity for the aqueous solutions can be explained by using a hydrogen-bond model by assuming the formation of hydrogen bonds between water–water and water–solute pairs. The orientational correlation between neighbouring molecules due to hydrogen bonds is determined in terms of the Kirkwood correlation factor. The number of hydrogen bonds in some aqueous solutions is computed.

Painlevé Test and Exact Solutions for (1 + 1)-Dimensional Generalized Broer–Kaup Equations

In this paper, the Painlevé integrable property of the (1 + 1)-dimensional generalized Broer–Kaup (gBK) equations is first proven. Then, the Bäcklund transformations for the gBK equations are derived by using the Painlevé truncation. Based on a special case of the derived Bäcklund transformations, the gBK equations are linearized into the heat conduction equation. Inspired by the derived Bäcklund transformations, the gBK equations are reduced into the Burgers equation. Starting from the linear heat conduction equation, two forms of N-soliton solutions and rational solutions with a singularity condition of the gBK equations are constructed. In addition, the rational solutions with two singularity conditions of the gBK equation are obtained by considering the non-uniqueness and generality of a resonance function embedded into the Painlevé test. In order to understand the nonlinear dynamic evolution dominated by the gBK equations, some of the obtained exact solutions, including one-soliton solutions, two-soliton solutions, three-soliton solutions, and two pairs of rational solutions, are shown by three-dimensional images. This paper shows that when the Painlevé test deals with the coupled nonlinear equations, the highest negative power of the coupled variables should be comprehensively considered in the leading term analysis rather than the formal balance between the highest-order derivative term and the highest-order nonlinear term.

Porous hetero-structured nickel oxide/nickel phosphide nanosheets as bifunctional electrocatalyst for hydrogen production via urea electrolysis

Urea electrolysis is a promising hydrogen generation and urea-rich wastewaters treatment technology, which requires the development of highly active electrocatalysts. In this study, porous hetero-structured nanosheet electrocatalyst (NiO/Ni2P/NF), composed of crystalline NiO and Ni2P, is prepared via the in-situ acid etching and gas-phase phosphating method, and the obtained NiO/Ni2P/NF material is applied as efficient urea oxidation and hydrogen evolution catalyst for the overall splitting of urea-containing wastewaters. An electrolyzer containing NiO/Ni2P/NF||NiO/Ni2P/NF electrode pair in an alkaline urea aqueous solution requires a potential of just 1.457 V to reach a current density of 10 mA cm−2, lower than that of 1.490 V needed for a Pt/C/NF||RuO2/NF electrolyzer to operate under the same current density. The study demonstrates the synergistic effect between NiO/Ni2P nanosheets as well as their uniform pore structure formed by the Kirkendall effect, resulting in enhanced electrocatalytic performance in hydrogen production by urea electrolysis.