Properties Of Solutions Research Articles

Some asymptotic profiles for the viscous Moore-Gibson-Thompson equation in the Lq framework

This manuscript studies some qualitative properties of solutions to the Cauchy problem for the viscous Moore-Gibson-Thompson (MGT) equation. For one thing, by applying the WKB analysis and diagonalization procedure, we derive some Lp−Lq decay estimates and the large time asymptotic profile for a suitable energy term, which provides a new way to treat higher order MGT-type coupled systems. For another, we obtain the global (in time) singular limits in the Lq framework and the higher order asymptotic profile with respect to small thermal relaxation via the multi-scale analysis and the Fourier analysis. Especially, provided the incompatible initial condition between the viscous MGT equation and the strongly damped wave equation, the formation of initial layer is rigorously justified.

Toward the Establishment of a Harmonized Physicochemical Profiling Platform for Therapeutic Oligonucleotides: A Case Study for Aptamers Where the Higher-Order Structure Influences Physical Properties.

Oligonucleotides are short nucleic acids that serve as one of the most promising classes of drug modality. However, attempts to establish a physicochemical evaluation platform of oligonucleotides for acquiring a comprehensive view of their properties have been limited. As the chemical stability and the efficacy as well as the solution properties at a high concentration should be related to their higher-order structure and intra-/intermolecular interactions, their detailed understanding enables effective formulation development. Here, the higher-order structure and the thermodynamic stability of the thrombin-binding aptamer (TBA) and four modified TBAs, which have similar sequences but were expected to have different higher-order structures, were evaluated using ultraviolet spectroscopy (UV), circular dichroism (CD), differential scanning calorimetry (DSC), and nuclear magnetic resonance (NMR). Then, the relationship between the higher-order structure and the solution properties including solubility, viscosity, and stability was investigated. The impact of the higher-order structure on the antithrombin activity was also confirmed. The higher-order structure and intra-/intermolecular interactions of the oligonucleotides were affected by types of buffers because of different potassium concentrations, which are crucial for the formation of the G-quadruplex structure. Consequently, solution properties, such as solubility and viscosity, chemical stability, and antithrombin activity, were also influenced. Each instrumental analysis had a complemental role in investigating the higher-order structure of TBA and modified TBAs. The utility of each physicochemical characterization method during the preclinical developmental stages is also discussed.

EDOT substitution site effect on fluorenone acceptor units: electrochemical polymerization and electrochromic properties of D-A systems

A series of donor-acceptor-donor type molecules (P(2,7-DEF) and P(3,6-DEF)) based on fluorenone acceptor units and 3,4-ethylenedioxythiophene (EDOT) donor units were successfully obtained by Stille coupling reaction in this work, and then generated their corresponding D-A polymers by electrodeposition method. As prepared P(2,7-DEF) and P(3,6-DEF) were characterized by CV, UV–vis spectroscopy, SEM, spectroelectrochemistry, and kinetic studies. Both of these two monomers revealed bright red/yellow light-emitting property in dilute solution. Since the π-conjugation length is longer, the oxidation potential of 2,7-DEF was reduced to 0.85 V, accompanied with red-shifted electronic spectra and emission spectra. The resulting P(2,7-DEF) demonstrated distinct electrochromic properties under various potentials with two different colors from dark-brown to blue-purple. Due to its more porous structure, P(2,7-DEF) also showed favorable optical contrast (26.3 %), very fast switching time (0.32 s), and decent coloration efficiency (221.25 cm2 C−1). However, P(3,6-DEF) displayed much worse electrochromic performances due to its bad electroactivity. P(2,7-DEF) also displayed better redox stability (remaining 79 % electroactivity after 1000 cycles), good optical stability (6 % reduction in optical contrast after 3200 s), and stable optical memory. From these results, P(2,7-DEF) can be further used as a promising near-infrared electrochromic materials.

Synthesis of benzothioamide derivatives from benzonitriles and H2S-based salts in supercritical CO2

A novel and efficient method has been developed for synthesizing benzothioamide from benzonitrile in supercritical CO2, which could be used to synthesize various benzothioamide derivatives efficiently with yields of up to 98% without the need for organic solvent. Notably, some H2S-based salts were designed and prepared, and they were found to be effective catalysts in promoting the thiolysis of benzonitrile to produce benzothioamide in an excellent yield. Furthermore, the utilization of supercritical CO2 as a solvent has demonstrated a remarkable increase in the yield of the desired product compared to conventional solvents for promoting benzonitrile thiolysis. Additionally, the investigation of the reaction mechanism has revealed that the acid–base properties of the reaction solution played a crucial role in the thiolysis of benzonitrile mediated by the H2S-based salts.

Characterization of the Solution Properties of Sodium Dodecylsulphate Containing Alkaline–Surfactant–Polymer Flooding Media

Alkaline–surfactant–polymer (ASP) flooding by means of which alkali additives, surfactant and polymer are inserted as the same slug is one of the most favourable worldwide focuses of Chemical Enhanced Oil Recovery (cEOR) research and field trials, due to the individual synergy of the three chemical components. To develop efficient oil recovery chemicals, it is essential to fully understand the mechanism behind ASP flooding. Nonetheless, there are hardly any studies reporting a systematic characterization of the ASP process. Thus, the present paper focuses on modelling this process in a laboratory by the use of an anionic surfactant—sodium dodecyl sulphate (SDS) in alkaline–polymer media—which is composed of a commercial water-soluble polymer (Flopaam AN125SH®, SNF Floerger, Andrézieux-Bouthéon, France) and alkali compounds (NaOH and Na2CO3). The samples were characterized using rheometry, dynamic light scattering (DLS), infrared spectroscopy (IR) and measurement of inferfacial tension (IFT) between the samples and rapeseed oil. In accordance with the experimental results, surprisingly lower IFT values were recorded between the alkaline–polymer solutions and rapeseed oil than the samples which contained SDS. Increasing polymer and sodium chloride concentration caused a decrease (from 0.591 mN/m to 0.0486 mN/m) in IFT between the surfactant containing samples and rapeseed oil. The IR measurements confirmed that the surfactant was not detected in the oil phase in the absence of NaOH and Na2CO3. The effects of SDS on the viscosity of the mixtures were also investigated, as viscosity is a considerably important parameter in processes using polymers.

Energetic processes and thermodynamic analysis of the spinning Kiselev black hole with cloud of strings

Here we study the impact of the string clouds, the quintessence dark energy and other spacetime parameters on the center-of-mass energy, Penrose-process and thermodynamic properties of a stationary black hole solution of the Einstein field equations. We observe that the three distinct horizons i.e the Cauchy horizon, the event horizon and the cosmological horizon exist when the spin parameter a of the black hole is less than its extremal value aE. Interestingly we see that the infinite redshift surface of the black hole is not much sensitive to the quintessence parameter γ. It is sensitive to the parameter a and it increases as the parameter a increases. Further, we notice that an increase in the string cloud parameters b, quintessence parameter γ and a make the radius of the ergosphere of the black hole larger. We also notice that a rise in the parameter a makes the innermost stable circular orbits (ISCO) smaller and for an increase in the parameter b and γ the ISCO becomes larger than that for the Kerr spacetime. For the center-of-mass energy of the spinning black hole with quintessence and cloud of strings we observe that it can be arbitrarily high only for the extremal case of the black hole for a specific range of values of the angular momentum of the colliding particles. We notice that the Penrose-process is more efficient for smaller values of the string cloud parameter b and the parameter γ has no significant impact on this process. Moreover we see that an increase in the parameters b, γ and a cause the Helmholtz free energy to increase and opposite is true for the temperature of this type of rotating black hole. We learn that the area and entropy of the black hole are also depend on the parameters b, γ and a, and their effect make the entropy smaller. Interestingly we find a range of the horizon radius for the thermodynamic stability of the black hole. To get more information about the thermodynamic quantities of the rotating black hole with quintessence and cloud of strings, we plot them for different ranges of the spacetime parameters.

Properties of set-valued Young integrals and Young differential inclusions generated by sets of Hölder functions

The present studies concern properties of set-valued Young integrals generated by families of β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-Hölder functions and differential inclusions governed by such a type of integrals. These integrals differ from classical set-valued integrals of set-valued functions constructed in an Aumann’s sense. Integrals and inclusions considered in the manuscript contain as a particular case set-valued integrals and inclusions driven by a fractional Brownian motion. Our study is focused on topological properties of solutions to Young differential inclusions. In particular, we show that the set of all solutions is compact in the space of continuous functions. We also study its dependence on initial conditions as well as properties of reachable sets of solutions. The results obtained in the paper are finally applied to some optimality problems driven by Young differential inclusions. The properties of optimal solutions and their reachable sets are discussed.

Bifurcation, Traveling Wave Solutions and Dynamical Analysis in the (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2+1)$$\\end{document}-Dimensional Extended Vakhnenko–Parkes Equation

This paper is concerned with the bifurcation of the traveling wave solutions, as well as the dynamical behaviors and physical property of the soliton solutions of the (2+1)-dimensional extended Vakhnenko–Parkes (eVP) equation. Firstly, based on the traveling wave transformation, the planar dynamical system corresponding to the (2+1)-dimensional eVP equation is derived, and then the singularity type and trajectory map of this system are obtained and analyzed. Based on the bifurcation of this system, the analytical expression for the periodic wave solution is given and shown graphically. Secondly, the N-soliton solutions are obtained via the bilinear method, and some important physical quantities and asymptotic analysis of one-soliton and two-soliton solutions are discussed. The results obtained in this paper might be useful for understanding the propagation of high-frequency waves.

Greasy Cations Bind to Neutral Macromolecules in Aqueous Solution.

Ions influence the solution properties of macromolecules. Although much is known about anions, cationic effects are considered mostly in terms of weak interactions or exclusion from neutral interfaces. Herein, we have systematically studied the effect of quaternary tetraalkylammonium cations (NH4+, NMe4+, NEt4+, NPr4+, NBu4+) on the phase transition of poly(N-isopropylacrylamide) (PNIPAM) in aqueous solution. Solubility measurements were coupled to 1H NMR and ATR-FTIR spectroscopic measurements. The solubility and NMR measurements revealed a direct binding between the greasiest cations and the isopropyl group of the macromolecule, evidenced from the nonlinear, Langmuir-type chemical shift response only at the isopropyl NMR signals with increasing salt concentrations. The ATR-FTIR measurements focusing on the amide oxygen showed that it is not the main direct-binding site. Additionally, the salting-out effects of the greasier cations correlate with their hydration entropies. These results demonstrate that the most weakly hydrated cations can bind to macromolecules as strongly as the weakly hydrated Hofmeister anions.

Emission Color Tuning of Inverse Type Diarylethene Crystals

AbstractOrganic luminescent solid materials have attracted much attention due to practical applications such as sensor materials and optical waveguides. We have previously reported that inverse type diarylethenes exhibit strong emission in crystal without causing aggregation‐caused quenching. However, the emission color was limited to mainly green. To tune the emission color, in this work, we newly synthesized inverse type diarylethenes having a shortened π‐conjugation length or a polar substituent and investigated their fluorescence properties in solutions and crystals. The crystals exhibited various emission colors from blue, green, yellow to red depending on the molecular structure. The emission color changes of the crystals were induced by the intermolecular interactions such as CH‐π interactions in addition to the shortened π‐conjugation length and the intramolecular charge transfer character.

Kamenev-Type Criteria for Testing the Asymptotic Behavior of Solutions of Third-Order Quasi-Linear Neutral Differential Equations

This paper aims to study the asymptotic properties of nonoscillatory solutions (eventually positive or negative) of a class of third-order canonical neutral differential equations. We use Riccati substitution to reduce the order of the considered equation, and then we use the Philos function class to obtain new criteria of the Kamenev type, which guarantees that all nonoscillatory solutions converge to zero. This approach is characterized by the possibility of applying its conditions to a wider area of equations. This is not the only aspect that distinguishes our results; we also use improved relationships between the solution and the corresponding function, which in turn is reflected in a direct improvement of the criteria. The findings in this article extend and generalize previous findings in the literature and also improve some of these findings.

Algebraic solution and thermodynamic properties for the one- and two-dimensional Dirac oscillator with minimal length uncertainty relations

Abstract We study the quantum characteristics of the Dirac oscillator within the framework of Heisenberg's generalized uncertainty principle. This principle leads to the appearance of a minimal length of the order of the Planck length. Hidden symmetries are identified to solve the model algebraically. The presence of the minimal length leads to a quadratic dependence of the energy spectrum on the quantum number $n$, implying the hard confinement property of the system. Thermodynamic properties are calculated using the canonical partition function. The latter is well determined by the method based on Epstein's zeta function. The results reveal that the minimal length has a significant effect on the thermodynamic properties.

Investigation of the bulk and solution properties for multiblock polyethers

Investigation of the bulk and solution properties for multiblock polyethers

Impacts of substitution of alkali by zinc on thermo-mechanical properties in borosilicate glasses

To decipher the effects of replacing alkali with zinc on thermo-mechanical properties, a series of borosilicate glasses with the molar compositions of 70.65SiO2·21.09B2O3·1.88Al2O3·1Li2O·(5.38-x)R2O·xZnO (x = 0, 0.34, 0.67, 1, 1.34, 2.69, 4.04, and 5.38) were prepared. Upon adding a slight quantity of ZnO, a local extreme point for glass transition temperature (Tg) appears. This behavior is deciphered to be originated from two opposite factors. On one hand, Tg reduces as a characteristic of the colligative properties for a dilute solution; in addition, Tg rises due to the higher field strength, bond energy and covalent characteristic of zinc cations compared to that of alkali ions. Otherwise, based on the evolution of intermediate-range clusters revealed by infrared, Raman and NMR spectra, we elucidate the atomic-scale structural origin, which leads to the nonlinear evolution of elastic moduli and coefficient of thermal expansion with the molar ratio of [ZnO]/([R2O]+[ZnO]).

Physical properties of soft contact lens multipurpose solutions commercially available in Ghana

PurposeTo investigate the physical properties of commercially available multipurpose soft contact lens solutions in Ghana. MethodspH (Kelilong ICL-099 pH meter, China), osmolality (OSMOMAT 3000, GONOTEC, Germany), surface tension (Sigma 700 Tensiometer, Sweden), and viscosity (CFOC-200 Viscometer, Cannon Company, USA) of various soft contact lens multipurpose solutions (MPS) were measured in triplicates at room temperature. Viscosity measurements were also taken at 34 °C ocular surface temperature. The solutions examined were Opti-Free Replenish (OFR), Trufresh (TF), Avizor (AV), Freshlook (FL), and Refresh (RF). ResultsSeveral solutions were largely hypo-osmotic in the range of 108–231 mOsm/kg, the exception being Avizor, which had osmolality values that were closer to human tears (301 ± 0.58 mOsm/kg). The range of pH values of the solutions (6.33–8.24, mean (SD) = 7.53 ± 0.18) fell within the reported tolerable range for the ocular surface (6.20–9.00). Surface tension values ranged from 35.86 to 42.27 mNm with a mean of 38.49 ± 2.32 mNm. The average viscosity of most solutions at room temperature (25 °C) was 1.44 ± 0.49 cP with a range of 1.04–2.15 cP. Significantly lower values ranging from 0.79 to 1.58 cP were obtained at ocular surface temperature (34 °C), p = 0.0001). ConclusionsThe physical properties of many of the solutions used as MPS in Ghana are markedly variable. Nevertheless, pH, surface tension, and viscosity fall within the acceptable limits of ocular physiological tolerance; except for osmolality, which majority were outside the reported tolerable range for the ocular surface. This information may partly explain the reason some patients exhibit strong preferences for certain care systems and should aid clinical decision-making when prescribing eye care systems to patients.

Inverse localization and global approximation for some Schrödinger operators on hyperbolic spaces

We consider the question of whether the high-energy eigenfunctions of certain Schrödinger operators on the d-dimensional hyperbolic space of constant curvature −κ2 are flexible enough to approximate an arbitrary solution of the Helmholtz equation Δh + h = 0 on Rd, over the natural length scale O(λ−1/2) determined by the eigenvalue λ ≫ 1. This problem is motivated by the fact that, by the asymptotics of the local Weyl law, approximate Laplace eigenfunctions do have this approximation property on any compact Riemannian manifold. In this paper we are specifically interested in the Coulomb and harmonic oscillator operators on the hyperbolic spaces Hd(κ). As the dimension of the space of bound states of these operators tends to infinity as κ ↘ 0, one can hope to approximate solutions to the Helmholtz equation by eigenfunctions for some κ > 0 that is not fixed a priori. Our main result shows that this is indeed the case, under suitable hypotheses. We also prove a global approximation theorem with decay for the Helmholtz equation on manifolds that are isometric to the hyperbolic space outside a compact set, and consider an application to the study of the heat equation on Hd(κ). Although global approximation and inverse approximation results are heuristically related in that both theorems explore flexibility properties of solutions to elliptic equations on hyperbolic spaces, we will see that the underlying ideas behind these theorems are very different.

Synthesis of Optimal Control of Spacecraft Angular Momentum for Spatial Turn Taking into Account Energy Costs Using Quaternions

Background: In this paper, we propose solving the specific original problem of control synthesis of spacecraft attitude. Optimization of the control program is made with the use of a new criterion of quality that combines energy costs and duration of reorientation under restrictions on control (the presence of a time factor limits the duration of slew maneuver). Methods: The construction of optimal control for angular momentum change is based on the quaternion method and L.S. Pontryagin maximum principle. An analytical solution to the problem was obtained on the base of a differential equation relating the orientation quaternion and angular momentum of a spacecraft. Results: Key properties of the optimal solution are formulated in analytical form; the features of optimal motion are studied in detail. The control law is formulated in the form of explicit dependence between control and phase variables. In a case when the controlling torque is limited by the given restriction (at the beginning and end of a turn), analytical formulas have been written for the duration of braking and acceleration. Main relations which determine optimal values of parameters of the algorithm for control of angular momentum are given. Examples and results of mathematical modeling of spacecraft motion formed by optimal control were given. This data in addition to the theoretical descriptions illustrates the process of reorientation in evident form and demonstrates the practical feasibility of a designed method for control of angular momentum during spatial turn. Conclusion: The designed optimal algorithm of control of spacecraft motion improves the efficiency of spacecraft attitude system, and originates more economical performance of spacecraft during flight on orbit.

Infinitely degenerate slowly rotating solutions in f(R) gravity

This work tests the no-hair conjecture in f(R) gravity models. No-hair conjecture asserts that all black holes in general relativity coupled to any matter must be Kerr–Newman type. However, the conjecture fails in some cases with non-linear matter sources. Here, we address this by explicitly constructing multiple slow-rotating black hole solutions, up to second order in rotational parameter, for a class of f(R) models ( f(R)=(α0+α1R)p,p>1 ). Such an f(R) includes all higher-powers of R. We analytically show that multiple vacuum solutions satisfy the field equations up to the second order in the rotational parameter. In other words, we show that the multiple vacuum solutions depend on arbitrary constants, which depend on the coupling parameters of the model. Hence, our results indicate that the no-hair theorem for modified gravity theories merits extending to include the coupling constants. The uniqueness of our result stems from the fact that these are obtained directly from metric formalism without conformal transformation. We discuss the kinematical properties of these black hole solutions and compare them with slow-rotating Kerr. Specifically, we show that the circular orbits for the black holes in f(R) are smaller than that of Kerr. This implies that the inner-most stable circular orbit for black holes in f(R) is smaller than Kerr’s; hence, the shadow radius might also be smaller. Finally, we discuss the implications of our results for future observations.

Testing mixing rules for structural and dynamical quantities in multi-component crowded protein solutions.

Crowding effects significantly influence the phase behavior and the structural and dynamic properties of the concentrated protein mixtures present in the cytoplasm of cells or in the blood serum. This poses enormous difficulties for our theoretical understanding and our ability to predict the behavior of these systems. While the use of course grained colloid-inspired models allows us to reproduce the key physical solution properties of concentrated monodisperse solutions of individual proteins, we lack corresponding theories for complex polydisperse mixtures. Here, we test the applicability of simple mixing rules in order to predict solution properties of protein mixtures. We use binary mixtures of the well-characterized bovine eye lens proteins α and γB crystallin as model systems. Combining microrheology with static and dynamic scattering techniques and observations of the phase diagram for liquid-liquid phase separation, we show that reasonably accurate descriptions are possible for macroscopic and mesoscopic signatures, while information on the length scale of the individual protein size requires more information on cross-component interaction.

Gravity-matter sum rules in models with a single extra-dimension

We prove a set of sum rules needed for KK-graviton pair production from matter in orbifolded extra-dimensional models. The sum rules can be found in full generality by considering the properties of solutions to the Sturm-Liouville problem, which describes the wave functions and the masses of the KK-gravitons in four dimensions. They ensure cancellations in the amplitudes of the processes mentioned above which considerably reduce their growth with s in the high-energy limit. This protects extra-dimensional theories from the low-scale unitarity problems that plague other theories with massive spin-2 particles. We argue that such relations are valid for a broader category of models thus generalizing our previous results that were limited to the large μ limit of the Randall-Sundrum model.