Properties Of Solutions Research Articles

A remark on solutions to semilinear equations with Robin boundary conditions

Symmetry properties of solutions to elliptic quasilinear equations have been widely studied in the context of Dirichlet boundary conditions. We show that, in the context of Robin boundary conditions, the symmetry property á la Gidas, Ni, and Nirenberg does not hold in dimension n\geq 2 , even for superharmonic functions, and we provide an explicit example.

Comparative analysis of solution properties and microscopic interactions in [emim][OTf]-[eOHpy][OTf] Mixture and [emim][OTf]-PEA solution

N-hydroxyethylpyridinium trifluoromethanesulfonate ([eOHpy][OTf]) and 2-phenylethyl alcohol (PEA) share similar structural characteristics. This study explored the variations in properties when 1-ethyl-3-methylimidazolium trifluoromethanesulfonate ([emim][OTf]) was dissolved in them. Measurements of excess molar volume and viscosity showed that [emim][OTf]-[eOHpy][OTf] mixture exhibited ideal mixing behavior, whereas [emim][OTf]-PEA solution deviate significantly. 1H NMR spectra revealed a reversed chemical shift of hydroxyl groups in two mixtures, attributed to the presence of different hydrogen bond acceptors. In [emim][OTf]-PEA solution, competition between anions and hydroxyl groups as acceptors led to varying proportions of hydrogen bonds with solution concentrations. Conversely, in [emim][OTf]-[eOHpy][OTf] mixtures, hydrogen bonds mainly occurred between hydroxyl groups and anions, with minimal hydrogen bonds between hydroxyl groups. Molecular dynamics simulations demonstrated negligible changes in the solvation shell structure of ions in [emim][OTf]-[eOHpy][OTf] mixture but significant alterations in [emim][OTf]-PEA solution.

Unravelling molecular interactions in various alcohol-water binary mixtures using femtosecond laser-induced thermal lens spectroscopy

The FTLS (femtosecond laser-induced thermal lens spectroscopy) technique was utilized to explore the photothermal response and heat transfer dynamics in various water-based binary mixtures containing monohydric and polyhydric alcohols. Our results highlight the significant influence of intermolecular hydrogen bonding interactions and the molecular properties of the mixture constituents on the photothermal behavior of both pure solvents and their binary mixtures. Notably, we observed distinct effects of water inclusion on the heat transfer characteristics of monohydric alcohols (such as methanol and ethanol) compared to polyhydric alcohols (such as ethylene glycol (Etg) and glycerol (Gly)). This discrepancy can be attributed to the formation of unique molecular structures via hydrogen bonding interactions, which effectively hinders the natural molecular dynamics of short-chain length alcohols. Conversely, polyhydric alcohols like Etg and Gly exhibit contrasting photothermal characteristics due to their extensive intermolecular hydrogen bonding. Our investigations reveal that molecular attributes, such as chain length and the number of hydroxyl (-OH) groups, play a crucial role in altering the heat transfer mechanisms and thermal lens signal characteristics of the mixtures. These findings emphasize the sensitivity of FTLS as a probe for understanding the effects of intermolecular hydrogen bonding interactions on the molecular dynamics and thermo-optical properties of aqueous-alcoholic solutions.

Investigation of oligosaccharides and allulose as sucrose replacers in low-moisture wire-cut cookies

Non-digestible oligosaccharides (OS) and allulose have beneficial health properties and could reduce the amount of added sugar in baked goods. In this study allulose and various OS [fructo-oligosaccharides (FOS), galacto-oligosaccharides (GOS), lactosucrose (LOS), isomalto-oligosaccharides (IMO), Promitor 70R (P70R), and xylo-oligosaccharides (XOS)] were added to a wire-cut cookie formulation at concentrations determined to have similar effects on the gelatinization temperature (Tgel) of starch relative to sucrose. Different baking performance attributes of the doughs and cookies were assessed, including: appearance, spread, color, texture, and % moisture loss after baking. The results were correlated to: OS solution and solid properties and OS effects on starch thermal events (gelatinization, pasting, and retrogradation). The Tgel-matching formulation protocol was effective in producing reduced-sugar cookies which had similar appearance, color, and spread attributes compared to the sucrose control; however, cookie texture significantly varied. Cookies containing allulose were the least similar to the control, having darker color, reduced spread, and softer cake-like texture. The only OS cookies that matched the texture of the sucrose control contained LOS, while P70R cookies were the hardest. Cookie texture correlated strongly with the % total moisture loss after baking (r = −0.8763) and was best explained by OS solution viscosity: more viscous OS solutions limited moisture release and resulted in harder cookies. The Tgel of starch also correlated with OS solution viscosity (r = 0.7861) and should be accounted for in reduced sugar applications. The OS recommended as sucrose replacers in cookies based on principal component analysis groupings were: XOS > IMO > LOS > and GOS.

Weighted means and an analytic characterization of discs

Weighted means are obtained for solutions of the two-dimensional Helmholtz and modified Helmholtz equations and also for harmonic functions. The presence of a logarithmic weight reduces the coefficient in the last two mean value identities. A new theorem characterizing disks in the Euclidean plane R 2 \mathbb {R}^2 analytically is proved; it is based on the weighted mean value property of solutions to the modified Helmholtz equation.

Soil Solution Properties of Tropical Soils and Brachiaria Growth as Affected by Humic Acid Concentration

The soil solution is the compartment where plants uptake nutrients and this phase is in equilibrium with the soil solid phase. Changes in nutrient content and availability in the soil solution can vary among soil types in response to humic acid concentrations, thereby affecting Brachiaria growth. However, there are no studies demonstrating these effects of humic acid application on different soil types and how they affect Brachiaria growth. Thus, the aim of this study was to evaluate the effects of humic acid concentrations (0, 5, 10, 25, and 60 mg kg−1 carbon-humic acid) on Brachiaria brizantha growth and soil solution properties of contrasting tropical soils. Plants were grown for 35 days in greenhouse conditions in pots containing Sandy Entisol, Clayey (Red Oxisol), and Medium Texture (Red-Yellow Oxisol). Soil solution was assessed for pH, electrical conductivity (EC), carbon, and nutrient content. Shoot and root dry matter, as well as macro and micronutrients accumulation in the shoot, were determined. In a soil type-dependent effect, pH, EC, and concentrations of nutrients in solutions changed in response to carbon-humic acid concentration. In the less-buffered soils, Sandy Entisol and Red-Yellow Oxisol, the addition of 30–40 mg kg−1 carbon-humic acid increased root proliferation by 76–89%, while Brachiaria biomass produced in all soils increased by approximately 30%. Levels of carbon in solution were high (>580 mg L−1) and varied depending on the investigated soil type. Though solution carbon contents did not appear to be a driving factor controlling the positive effects of humic acid concentrations on Brachiaria dry matter, there was a direct relationship between other properties and nutrient content in the soil solution, and Brachiaria dry matter production.

Magnetic properties of Co1-xFexCr2S4 (x = 0–0.4) solid solutions

The magnetic properties of the Co1-xFexCr2S4 solid solutions for compositions adjacent to CoCr2S4 were investigated using various techniques, including magnetization measurements and AC susceptibility. The results revealed that substituting Fe for Co in the CoCr2S4 compound led to changes in the magnetic behavior, such as the presence of ferrimagnetic ordering and the emergence of a cluster spin glass phase. The study found that the temperature of the ferrimagnetic transition (TC) decreased with increasing Fe concentration, indicating the influence of iron on the magnetic properties of the solid solutions. Additionally, the discovery of a cluster spin glass phase for specific compositions (x = 0, 0.1, 0.2, 0.4) suggests complex magnetic behavior in these materials. In summary, the study offers valuable insights into the magnetic properties of Co1-xFexCr2S4 solid solutions and highlights the potential for tuning their magnetic behavior through compositional variations.

Effect of triazolium-based ionic liquid (1, 4-dimethyl- 4H-1, 2, 4-triazolium iodide) on volumetric and ultrasonic properties of binary aqueous solutions of benzamide/benzylamine: experimental and computational study

ABSTRACT In the current investigation, effect of triazolium-based ionic liquid 1, 4-Dimethyl- 4 H-1,2,4-triazolium iodide (DMTI) on volumetric and ultrasonic properties of binary aqueous solutions of benzamide/benzylamine is analysed at four equidistant temperatures and atmospheric pressure. Molecular interactions of DMTI in binary aqueous solutions of benzylamine/benzamide are also interpreted using density (ρ) and speed of sound (u) data along with FT-IR measurements. Different volumetric and ultrasonic parameters were also computed by employing the experimental values of density (ρ) and speed of sound (u), and are further used to elucidate various kinds of interactions in the ternary system. Volumetric and acoustic transfer parameters were further used for the computation of interaction coefficients (pair and triplet). To analyse the outcomes of the estimated parameters, spectroscopic and density-functional theory (DFT) investigations have also been carried out.

On Asymptotic Properties of Solutions for Differential Equations of Neutral Type

On Asymptotic Properties of Solutions for Differential Equations of Neutral Type

Electrokinetic properties of NaCl solution via molecular dynamics simulations with scaled-charge electrolytes.

Scaling ionic charges has become an alternative to polarizable force fields for representing indirect charge transfer effects in molecular simulations. In our work, we apply molecular dynamics simulations to investigate the properties of NaCl aqueous solutions in homogeneous and confined media. We compare classical integer- and scaled-charge force fields for the ions. In the bulk, we validate the force fields by computing equilibrium and transport properties and comparing them with experimental data. Integer-charge ions overestimate dielectric saturation and ionic association. Both force fields present an excess in ion-ion correlation, which leads to a deviation in the ionic conductivity at higher ionic strengths. Negatively charged quartz is used to simulate the confinement effect. Electrostatic interactions dominate counter-ion adsorption. Full-charge ions have stronger and more defined adsorption planes. We obtain the electroosmotic mobility of the solution by combining the shear plane location from non-equilibrium simulations with the ionic distribution from equilibrium simulations. From the Helmholtz-Smoluchowski equation, the zeta potential and the streaming potential coupling coefficient are computed. From an atomic-scale perspective, our molecular dynamics simulations corroborate the hypothesis of maximum packing of the Stern layer, which results in a stable and non-zero zeta potential at high salinity. The scaled-charge model representation of both properties is in excellent qualitative and quantitative agreement with experimental data. With our work, we demonstrate how useful and precise simple scaled-charge models for electrolytes can be to represent complex systems, such as the electrical double layer.

On Vafa–Witten equations over Kähler manifolds

Abstract In this paper, we study the analytic properties of solutions to the Vafa–Witten equation over a compact Kähler manifold. Simple obstructions to the existence of nontrivial solutions are identified. The gauge theoretical compactness for the C ∗ \mathbb{C}^{*} invariant locus of the moduli space is shown to behave similarly to the Hermitian Yang–Mills connections. More generally, this holds for solutions with uniformly bounded spectral covers such as nilpotent solutions. When spectral covers are unbounded, we manage to take limits of the renormalized Higgs fields which are intrinsically characterized by the convergence of the associated spectral covers. This gives a simpler proof for Taubes’ results on rank two solutions over Kähler surfaces together with a new complex geometric interpretation. The moduli space of SU ⁢ ( 2 ) \mathsf{SU}(2) monopoles and some related examples are also discussed in the final section.

Extinction and non-extinction of solutions for nonlocal fractional [formula omitted]-Kirchhoff problem with logarithmic nonlinearity

In this paper, we discuss the extinction and non-extinction properties of solutions for a class of Kirchhoff type parabolic problems involving fractional p-Laplacian and logarithmic nonlinearity. Based on energy estimates, embedding theorems, and certain ordinary differential inequalities, the global existence of solutions, and the extinction and non-extinction properties of global weak solutions are obtained. The results of this paper extend and complement previous research findings on this type of equation.

Qualitative properties of solutions to a nonlinear transmission problem for an elastic Bresse beam

We consider a nonlinear transmission problem for a Bresse beam, which consists of two parts, damped and undamped. The mechanical damping in the damping part is present in the shear angle equation only, and the damped part may be of arbitrary positive length. We prove the well-posedness of the corresponding system in energy space and establish the existence of a regular global attractor under certain conditions on the nonlinearities and coefficients of the damped part only. Besides, we study the singular limits of the problem under consideration when curvature tends to zero, or curvature tends to zero, and simultaneously shear moduli tend to infinity and perform numerical modeling for these processes.

On decay properties for solutions of the Zakharov–Kuznetsov equation

This work mainly focuses on spatial decay properties of solutions to the Zakharov–Kuznetsov equation. For the two- and three-dimensional cases, it was established that if the initial condition u0 verifies 〈σ⋅x〉ru0∈L2(σ⋅x≥κ), for some r∈N, κ∈R, being σ be a suitable non-null vector in the Euclidean space, then the corresponding solution u(t) generated from this initial condition verifies 〈σ⋅x〉ru(t)∈L2σ⋅x>κ−νt, for any ν>0. Additionally, depending on the magnitude of the weight r, it was also deduced some localized gain of regularity. In this regard, we first extend such results to arbitrary dimensions, decay power r>0 not necessarily an integer, and we give a detailed description of the gain of regularity propagated by solutions. The deduction of our results depends on a new class of pseudo-differential operators, which is useful for quantifying decay and smoothness properties on a fractional scale. Secondly, we show that if the initial data u0 has a decay of exponential type on a particular half space, that is, ebσ⋅xu0∈L2(σ⋅x≥κ), then the corresponding solution satisfies ebσ⋅xu(t)∈Hpσ⋅x>κ−t, for all p∈N, and time t≥δ, where δ>0. To our knowledge, this is the first study of such property. As a further consequence, we also obtain well-posedness results in anisotropic weighted Sobolev spaces in arbitrary dimensions.Finally, as a by-product of the techniques considered here, we show that our results are also valid for solutions of the Korteweg–de Vries equation.

Anti-turbulent efficiency of oil-soluble polymer solutions and colloid systems flowing through cylindrical channel

Relevance. The use of anti-turbulent additives for transporting hydrocarbon liquids through main pipelines allows reducing significantly the energy consumption of pumping power stations. Aim. Comparative analysis of the anti-turbulent efficiency of high-molecular polymers and compositions of surfactants. Methods. Laboratory-scale experimentation aimed to study the flow of dilute polymer solutions and dispersed surfactant systems through a cylindrical channel of a turbulent rheometer. Results. The author has carried out the comparative experimental studies of the anti-turbulent efficiency of extremely dilute solutions of polymers and colloidal systems. The results were obtained that suggest a higher anti-turbulent efficiency of high-molecular-weight polymers compared to micellar surfactant systems. Solutions of high molecular weight polybutadiene and aluminum polyhydroxydicarboxylates in gasoline were used as samples for the experimental comparison of hydrodynamic efficiency. The paper describes the laboratory setup, on which the studies were carried out, and introduces the formulas used for quantitative calculations. The structure of polymer solutions and colloidal systems is considered and a theoretical explanation is given for the preferential use in industrial practice of high-molecular polymers in extremely low concentrations in real pipelines. It was found out that the mechanisms of degradation of antiturbulent properties of polymer solutions and dispersed surfactant systems are different. This is due to the difference in the structure of macromolar coils of polymer with an immobilized solvent and that of micelles from low molecular amphiphilic compounds. The paper introduces the arguments that explain the degradation of the antiturbulent properties of polymers not by the destruction of carbon-chain macromolecules, but by decomposition in a turbulent flow of the original large associates, consisting of a large number of chains, into individual and smaller macromolecular coils with an immobilized solvent.

Chemical Composition and Properties of Water-Methanol Solution of Formaldehyde

By reacting paraform with methanol and water at concentrations of 10.8, 11.6 and 22.7 mol/l in the presence of catalytic quantities of monoethanolamine, a method was developed for obtaining a bactericide that, at a concentration of 500 mg/l, completely inhibits the formation of hydrogen sulfide in an accumulative culture of planktonic form of sulfate-reducing bacteria with a quantity of 106 cells/ml. The composition of the resulting bactericide, its effectiveness and corrosion properties were studied. Using scanning electron microscopy using a system for energy-dispersive microanalysis, it was shown that the corrosion products formed during the corrosive action of the bactericide on St-20 steel are iron oxides.

Arbeitsgemeinschaft: QFT and Stochastic PDEs

Quantum field theory (QFT) is a fundamental framework for a wide range of phenomena is physics. The link between QFT and SPDE was first observed by the physicists Parisi and Wu (1981), known as Stochastic Quantisation. The study of solution theories and properties of solutions to these SPDEs derived from the Stochastic Quantisation procedure has stimulated substantial progress of the solution theory of singular SPDE, especially the invention of the theories of regularity structures and paracontrolled distributions in the last decade. Moreover, Stochastic Quantisation allows us to bring in more tools including PDE and stochastic analysis to study QFT.This Arbeitsgemeinschaft starts by covering some background material and then explores some of the advances made in recent years. The focus of this Arbeitsgemeinschaft is QFT models such as the \Phi^{4} , sine-Gordon and Yang–Mills models as examples to discuss stochastic quantisation and SPDE methods and their applications in these models. We introduce the key ideas, results and applications of regularity structure and paracontrolled distributions, construction of solutions of the SPDEs corresponding to these models, and use the PDE method to study some qualitative behaviors of these QFTs, and connections with the corresponding lattice or statistical physical models. We also discuss some other topics of QFT, such as Wilsonian renormalisation group, log-Sobolev inequalities and their implications, and various connections between these topics and SPDEs.

Step-by-step negotiations and the Nash bargaining solution: Efficiency-free characterizations

Real-world bargainings often proceed step-by-step: the agents make intermediate agreements today and continue to negotiate tomorrow to reach a final agreement. We consider two natural properties of the bargaining solutions in such step-by-step negotiations and show that the Nash solution is the only solution that satisfies either of them, a very weak axiom of individual rationality, and Nash’s axioms except for Pareto optimality.

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We consider the stability of the global weak solution of the Quantum Euler system in two space dimensions. More precisely, we establish compactness properties of global finite energy weak solution for large initial data provided that these are axisymmetric. The main novelty is that the initial velocity is not necessary irrotational when the density is not vanishing, our main argument is based on the Madelung transform which enables us to prove new Kato estimates on the irrotational part of the velocity.

Existence and properties of soliton solution for the quasilinear Schrödinger system

Abstract In this article, we consider the following quasilinear Schrödinger system: − ε Δ u + u + k 2 ε [ Δ ∣ u ∣ 2 ] u = 2 α α + β ∣ u ∣ α − 2 u ∣ v ∣ β , x ∈ R N , − ε Δ v + v + k 2 ε [ Δ ∣ v ∣ 2 ] v = 2 β α + β ∣ u ∣ α ∣ v ∣ β − 2 v , x ∈ R N , \left\{\begin{array}{ll}-\varepsilon \Delta u+u+\frac{k}{2}\varepsilon \left[\Delta \hspace{-0.25em}{| u| }^{2}]u=\frac{2\alpha }{\alpha +\beta }{| u| }^{\alpha -2}u{| v| }^{\beta },& x\in {{\mathbb{R}}}^{N},\\ -\varepsilon \Delta v+v+\frac{k}{2}\varepsilon \left[\Delta \hspace{-0.25em}{| v| }^{2}]v=\frac{2\beta }{\alpha +\beta }{| u| }^{\alpha }{| v| }^{\beta -2}v,& x\in {{\mathbb{R}}}^{N},\end{array}\right. where ε > 0 , k < 0 \varepsilon \gt 0,k\lt 0 are real constants, N ≥ 3 N\ge 3 , α , β \alpha ,\beta are integers multiple of constant 2. By using the Mountain Pass Theorem in a suitable Orlicz space proposed by Abbas Moameni [Existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in R N {{\mathbb{R}}}^{N} , J. Differential Equations 229 (2006), 570–587], we proved the existence of soliton solution ( u ε , v ε ) \left({u}_{\varepsilon },{v}_{\varepsilon }) for the above system, and ( u ε ( x ) , v ε ( x ) ) → ( 0 , 0 ) ({u}_{\varepsilon }\left(x),{v}_{\varepsilon }\left(x))\to \left(0,0) as ∣ ε ∣ → 0 | \varepsilon | \to 0 .