Pair Of Solutions Research Articles

Existence of solutions for a double-phase variable exponent equation without the Ambrosetti-Rabinowitz condition

Abstract The article deals with the existence of a pair of nontrivial nonnegative and nonpositive solutions for a nonlinear weighted quasilinear equation in R N {{\mathbb{R}}}^{N} , which involves a double-phase general variable exponent elliptic operator A {\bf{A}} . More precisely, A {\bf{A}} has behaviors like ∣ ξ ∣ q ( x ) − 2 ξ {| \xi | }^{q\left(x)-2}\xi if ∣ ξ ∣ | \xi | is small and like ∣ ξ ∣ p ( x ) − 2 ξ {| \xi | }^{p\left(x)-2}\xi if ∣ ξ ∣ | \xi | is large. Existence is proved by the Cerami condition instead of the classical Palais-Smale condition, so that the nonlinear term f ( x , u ) f\left(x,u) does not necessarily have to satisfy the Ambrosetti-Rabinowitz condition.

Effect of Microchannel Diameter on Electroosmotic Flow Hysteresis

Electroosmotic flow (EOF) commonly involves inhomogeneous fluids in practical applications. EOF hysteresis, which is defined as direction-dependent flow behavior, has been extensively investigated for dissimilar solution pair systems. Hitherto, there is no investigation being conducted to examine the effect of microchannel diameter on the hysteresis phenomenon. In this investigation, current monitoring experiments and finite element numerical simulations were performed to examine the intensification of the hysteretic behavior with reduction in the microchannel diameter. Three solution pairs were selected for the study, namely KCl–NaCl (dissimilar ionic species with similar concentration), NaCl and KCl (similar ionic species but different concentrations) solution pairs, with microchannels of 5 μm and 100 μm internal diameters. EOF hysteresis augmentation for reduced channel diameter (i.e., 5 μm microchannel) is due to the coupling effect of the resultant wider/tighter interfacial width and the minority pH-governing ion-driven hysteresis, which was earlier discovered to be the origin of EOF hysteresis. This investigation provides an appropriate understanding of the channel dimensional effect on EOF behavior involving multiple fluids, and the outcomes can potentially be implemented on chemical and biological microfluidic systems with adjustable throughput.

Second-Order Symmetric Duality for Multiple Objectives Nonlinear Programming Under Generalizations of Cone-Preinvexity Functions

In this article, we present generalizations of the cone-preinvexity functions and study a pair of second-order symmetric solutions for multiple objective nonlinear programming problems under these generalizations of the cone-preinvexity functions. In addition, we establish and prove the theorems of weak duality, strong duality, strict converse duality, and self-duality by assuming the skew-symmetric functions under these generalizations of the cone-preinvexity functions. Finally, we provide four nontrivial numerical examples to demonstrate that the results of the weak and strong duality theorems are true.

Identification of Ion Pairs in Aqueous NaCl and KCl Solutions in Combination with Raman Spectroscopy, Molecular Dynamics, and Quantum Chemical Calculations

This work summarizes a theoretical analysis of the perturbation on Raman spectra in aqueous NaCl and KCl solutions with the aim to detect ion pairs. The experimental Raman spectra, both polarized and depolarized, are perturbed by these ions to a comparable extent or somewhat less by KCl than NaCl. This result appears to be contrary to the molecular dynamics (MD) simulation showing that the isolated and separated ions of KCl should have a larger perturbation than NaCl, as the solvation shell of K+ is larger than that of Na+. The apparent discrepancy signifies the ion pair formation which is more substantial for KCl than NaCl. The MD simulations and quantum chemical calculations revealed that KCl forms ion pairs more than NaCl and that the ion pair formation reduces the perturbation on the Raman spectra more for KCl. The present analysis shows that the perturbed Raman spectra provide a useful sign to evaluate the ion pair formation in aqueous solutions.

OGLE-2018-BLG-0584 and KMT-2018-BLG-2119: Two microlensing events with two lens masses and two source stars

Aims. We conducted a systematic investigation of the microlensing data collected during the previous observation seasons for the purpose of re-analyzing anomalous lensing events with no suggested plausible models. Methods. We found that two anomalous lensing events, OGLE-2018-BLG-0584 and KMT-2018-BLG-2119, cannot be explained with the usual models based on either a binary-lens single-source (2L1S) or a single-lens binary-source (1L2S) interpretation. We tested the feasibility of explaining the light curves of the events with more sophisticated models by adding either an extra lens (3L1S model) or a source (2L2S model) component to the 2L1S lens system configuration. Results. We find that a 2L2S interpretation explains the light curves of both events well and that for each event there are a pair of solutions resulting from the close and wide degeneracy. For the event OGLE-2018-BLG-0584, the source is a binary composed of two K-type stars and the lens is a binary composed of two M dwarfs. For KMT-2018-BLG-2119, the source is a binary composed of two dwarfs of G and K spectral types and the lens is a binary composed of a low-mass M dwarf and a brown dwarf.

Potential application of hybrid reverse electrodialysis (RED)-forward osmosis (FO) system to fertilizer-producing industrial plant for efficient water reuse

This study presents an experimental investigation and a parametric analysis of the applicability of agricultural fertigation and power generation using a reverse electrodialysis-forward osmosis (RED-FO) hybrid system, with a water stream discharged from a fertilizer-producing plant. The results of this study demonstrated the possibility of achieving high salinity power generation from the RED system utilizing high-salinity brine and low-salinity ammonia solution that simulates reverse osmosis (RO) brine and wastewater streams released by the fertilizer-producing industry. The feasibility of stream dilution for fertigation application is demonstrated when the resulting moderately saline RED effluent is introduced into the FO process as a draw solution. The effect of external load addition, flow velocities variation, and concentration changes of the working solutions on the overall stack internal resistance and, thereby, RED performance was evaluated. As such, the lowest internal resistance converged to a threshold value of 4.03 Ω, giving the highest gross power density of 2.17 W/m2 when a flow velocity of 1.18 cm/s, 10 Ω external load, and 0.015 M (NH4)2SO4/1 M NaCl solution pair were utilized. In addition, the effect of the number of ion exchange membrane pairs and wastewater stream recycling was studied and optimized to amplify the osmotically generated power. As a result, the most consistent power generation was achieved when using 20 pairs of membrane cells in a single-pass flow mode operation. The applicability of the RED effluent to a subsequent FO system as a draw solution (DS) was investigated, showing a dilution rate (17 %) and a conductivity (1–2 mS/cm of DS) suitable for agricultural fertigation applications.

Critical and subcritical fractional Hamiltonian systems of Schrödinger equations with vanishing potentials

We analyze a class of fractional Hamiltonian systems of Schrödinger equations in RN involving vanishing potential with critical and subcritical nonlinearity. We make use of variational methods to prove the existence of at least one pair of positive solutions. Our result in the critical case is new even for the Laplacian operator.

A chiral pentanidium and pyridinyl-sulphonamide ion pair as an enantioselective organocatalyst for Steglich rearrangement.

Enantioselective ion pair catalysis has gained significant attention due to its ability to exert selectivity control in various reactions. Achiral counterions have been found to play crucial roles in modulating reactivity and selectivity. The modular nature of an ion pair catalyst allows rapid alterations of the achiral counterion to achieve optimal outcomes, without the need to modify the more onerous chiral component. In this study, we report the successful development of a stable chiral pentanidium pyridinyl-sulphonamide ion pair as a nucleophilic organocatalyst for asymmetric Steglich rearrangement. The ion pair catalyst demonstrated excellent performance, leading to enantioenriched products with up to 99% ee through simple alterations of the achiral anions. We conducted extensive ROESY experiments and concluded that the reactivity and enantioselectivity were correlated to the formation of a tight ion pair in solution. Further computational analyses provided greater clarity to the structure of the ion pair catalyst in solution. Our findings reveal the critical roles of NMR experiments and computational analyses in the design and optimisation of ion pair catalysts.

Relativistic type systems with parametric odd nonlinearities

We obtain existence of multiple distinct pairs of nontrivial solutions for potential systems involving parametric odd perturbations of the relativistic operator under periodic, Neumann and Dirichlet boundary conditions. The approach relies on critical point theory for convex, lower semicontinuous perturbations of $ C^1 $-functionals. Some illustrative examples concerning nonlinearities of Fisher-Kolmogorov type are provided.

Existence of forced waves for a 2-D lattice differential equation in a time-periodic shifting habitat

This paper is concerned about the existence of forced waves for a 2-D lattice differential equation in a time-periodic shifting habitat. First, we study the corresponding initial value problem and establish the comparison principle. Then we investigate the asymptotic spreading speed $ c_{*} $ and periodic traveling waves for a 2-D lattice differential equation without shifting habitat. Finally, by constructing a pair of upper and lower solutions and using the monotone iteration technique, we establish the existence of periodic forced waves with the speed at which the habitat is shifting.

Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations

We consider the half-linear differential equation \[(|x'|^{\alpha}\mathrm{sgn}\,x')' + q(t)|x|^{\alpha}\mathrm{sgn}\,x = 0, \quad t \geq t_{0},\] under the condition \[\lim_{t\to\infty}t^{\alpha}\int_{t}^{\infty}q(s)ds = \frac{\alpha^{\alpha}}{(\alpha+1)^{\alpha+1}}.\] It is shown that if certain additional conditions are satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as \(t\to\infty\).

Existence of traveling waves by means of fixed point theory for an epidemic model with Hattaf-Yousfi incidence rate and temporary immunity acquired by vaccination

The main aim of this work is to investigate the existence of traveling waves of an epidemic model with temporary immunity acquired by vaccination. The incidence rate of the disease used in the epidemic model is of the form Hattaf-Yousfi that includes many types existing in the literature. By means of Schauder fixed point theorem and construction of a pair of upper and lower solutions, the existence of traveling wave solution that connects the disease-free equilibrium and the endemic equilibrium is obtained and characterized by two parameters that are the basic reproduction number and the minimal wave speed.

Applying Graph Neural Networks to the Decision Version of Graph Combinatorial Optimization Problems

In recent years, there has been a significant increase in the application of graph neural networks on a wide range of different problems. A specially promising direction of research is on graph convolutional neural networks (GCN). This work focuses on the application of GCNs to graph combinatorial optimization problems (GCOPs), specifically on their decision versions. GCNs are applied on the family of GCOPs in which the objective function is directly related to the number of vertices in a graph. The selected problems are the minimum vertex cover, maximum clique, minimum dominating set and graph coloring. In this work, a framework is proposed for solving problems of this type. The performance of this approach is explored for standard multi-layer GCNs using different types of convolutional layers. On top of this, we propose a new structure that is based on graph isomorphism networks. Computational experiments show that this new structure is significantly more efficient than basic structures. To further improve the performance of this method, the use of GCN ensembles is also explored. When using GCNs to generate solution values for GCOPs, they often correspond to non-feasible solutions because they violate the problem boundaries. This issue is addressed by defining an asymmetric loss function that is used during the GCN training. The proposed method is evaluated on a large set of training data consisting of graph solution pairs that can also be accessed online.

Machine Learning Guided Polyamide Membrane with Exceptional Solute-Solute Selectivity and Permeance.

Designing polymeric membranes with high solute-solute selectivity and permeance is important but technically challenging. Existing industrial interfacial polymerization (IP) process to fabricate polyamide-based polymeric membranes is largely empirical, which requires enormous trial-and-error experimentations to identify optimal fabrication conditions from a wide candidate space for separating a given solute pair. Herein, we developed a novel multitask machine learning (ML) model based on an artificial neural network (ANN) with skip connections and selectivity regularization to guide the design of polyamide membranes. We used limited sets of lab-collected data to obtain satisfactory model performance over four iterations by introducing human expert experience in the online learning process. Four membranes under fabrication conditions guided by the model exceeded the present upper bound for mono/divalent ion selectivity and permeance of the polymeric membranes. Moreover, we obtained new mechanistic insights into the membrane design through feature analysis of the model. Our work demonstrates a ML approach that represents a paradigm shift for high-performance polymeric membranes design.

On the generalized Sylvester operator equation AX−Y B = C

In this paper, we study the necessary and sufficient conditions to have a solution pair ( X , Y ) to the generalized Sylvester equation AX−Y B = C where A , B , C ∈ L ( H ) are given. Moreover, we give some connections the generalized Fuglede-Putnam property and the solution pair ( X , Y ) of the operator equation AX−Y B = C. Finally, we consider some properties of the operator equation AX−Y B = C when A and B belong to the special classes of operators.

Solute synergy induced thermal stability of high-strength nanotwinned Al-Co-Zr alloys

Reducing the grain size into the nanoscale regime in metallic materials provides high mechanical strengths, however at the cost of degrading thermal stability, as grain refinement induces a high driving force for grain coarsening. In this study, we present a solute synergy strategy that stabilizes the microstructures of high strength nanotwinned (NT) Al–Co–Zr alloys. Zr solute additions promote microstructural and mechanical stability up to an annealing temperature of 400 °C. In-situ microcompression tests demonstrate concomitant high strengths and deformability in these ternary NT alloys. Density functional theory calculations provide insight into the interplay between Co and Zr solute and how they pin and stabilize incoherent twin boundaries. This work provides a strategy for enhancing both strength and thermal stability of nanocrystalline materials when combining synergistic solute pairs.

Two‐ and Three‐Phase Self‐assembly of Molecular Capsules

AbstractTwo‐ and three‐phase molecular encapsulations of Me4N+ or C7H7+ in the hydrogen‐bonded dimers of resorcin[4]arene tetraphosphates enable ion pair separations, dissolution of solid capsule components, and stabilization of capsule‐separated ion pairs in solution. Self‐assembly of the capsular ion pairs, the exchange of the encapsulated cations and external anions as well as the formation of heterodimeric capsular complexes are slow on hours time scale in heterogeneous systems and instantaneous in solutions. Spectroscopic studies and molecular modeling related the properties of the capsule‐separated ion pairs to the energies of induced conformational changes, hydrogen bonding, host‐guest interactions, ion pair separation, and the relative polarity of the solvent.

An [formula omitted] weak Galerkin mixed finite element method for Sobolev equation

In this paper, we present a new H1 weak Galerkin mixed finite element method for the Sobolev equation which includes the exact solution u and the intermediate solution p. In the H1 weak Galerkin method, we adopt the discontinuous finite elements Pk/Pk for the approximation solution pair (uh,ph) on finite element partitions consisting of arbitrary shape of polygons which are WG shape regular. We give the semi-discrete and full-discrete formulations which are proven to be stable and parameter-free and possess the optimal error estimates. Numerical experiments show the efficiency of our methods.

Modeling of equilibria in an acidified solution of sodium orthotungstate in the presence of barium(II) ions

Interactions in the Ba2+–WO42––H+–H2O system, that was acidified to the molar ratio (acidity) Z=(H+)/(WO42–)=1.00, in the range of Z=0.60–2.00 at 2980.1 K with NaNO3 as the background electrolyte (I=0.1–0.3 mol•l–1), were studied by the methods of pH-potentiometry, mathematical modeling and conductometry. Logarithms of concentration constants of equilibrium were calculated by Newton's method. Previously unknown logarithms of thermodynamic constants and Gibbs energies of formation reactions for some ion pairs (BaOH+,[W12O40(OH)2]10–; Ba2+,[W12O40(OH)2]10–; Ba2+,H2[W12O40(OH)2]8–; Ba2+,H3[W12O40(OH)2]5–; Ba2+,[W12O18(OH)2]6–; and Ba2+,H[W12O18(OH)2]5–) were calculated by Pitzer's method. The formation of particles with a Ba2+:[W12O40(OH)2]10–=1:1 ratio in solutions was established by conductometric titration method. A scheme of interconversions between ion pairs in an aqueous solution was proposed. From acidified to different Z values aqueous solutions of Na2WO4, the normal and double barium(II) paratungstates B Ba5[W12O40(OH)2]30H2O (Z=1.17), Na4Ba2[W12O40(ОН)2]28Н2О (Z=1.25), and Na2Ba4[W12O40(ОН)2]25Н2О (Z=1.33) were synthesized. The data of FTIR spectroscopy showed that the isopoly anion in the salts' composition belongs to the paratungstate B structural type.

Finding preferred solutions under weighted Tchebycheff preference functions for multi-objective integer programs

Many interactive approaches in multi-objective optimization assume the existence of an underlying preference function that represents the preferences of a decision maker (DM). In this paper, we develop the theory and an exact algorithm that guarantees finding the most preferred solution of a DM whose preferences are consistent with a Tchebycheff function for multi-objective integer programs. The algorithm occasionally presents pairs of solutions to the DM and asks which one is preferred. It utilizes the preference information together with the properties of the Tchebycheff function to generate solutions that are candidates to be the most preferred solution. We test the performance of the algorithm on a set of three and four-objective combinatorial optimization problems.