Small Solutes Research Articles

A note to semilinear de Sitter models in 1d with balanced mass and dissipation

In this paper we consider the Cauchy problem for semilinear de Sitter models in 1d with balanced mass and dissipation. The model of interest is ϕtt−e−2tϕxx+ϕt+14ϕ=|ϕ|p,(ϕ(0,x),ϕt(0,x))=(0,g(x)).We study the global (in time) existence of small data solutions. In particular, we show by applying Schauder’s fixed point theorem that there exists a Sobolev solution for all p>1.

Proteoliposomes reconstituted with human aquaporin-1 reveal novel single-ion-channel properties

Human aquaporin 1 (hAQP1) forms homotetrameric channels that facilitate fluxes of water and small solutes across cell membranes. In addition to water channel activity, hAQP1 displays non-selective monovalent cation-channel activity gated by intracellular cyclic GMP. Dual water and ion-channel activity of hAQP1, thought to regulate cell shape and volume, could offer a target for novel therapeutics relevant to controlling cancer cell invasiveness. This study probed properties of hAQP1 ion channels using proteoliposomes, which, unlike conventional cell-based systems such as Xenopus laevis oocytes, are relatively free of background ion channels. Histidine-tagged recombinant hAQP1 protein was synthesized and purified from the methylotrophic yeast, Pichia pastoris, and reconstituted into proteoliposomes for biophysical analyses. Osmotic water channel activity confirmed correct folding and channel assembly. Ion-channel activity of hAQP1-Myc-His6 was recorded by patch-clamp electrophysiology with excised patches. In symmetrical potassium, the hAQP1-Myc-His6 channels displayed coordinated gating, a single-channel conductance of approximately 75 pS, and multiple subconductance states. Applicability of this method for structure-function analyses was tested using hAQP1-Myc-His6D48A/D185A channels modified by site-directed mutations of charged Asp residues estimated to be adjacent to the central ion-conducting pore of the tetramer. No differences in conductance were detected between mutant and wild-type constructs, suggesting the open-state conformation could differ substantially from expectations based on crystal structures. Nonetheless, the method pioneered here for AQP1 demonstrates feasibility for future work defining structure-function relationships, screening pharmacological inhibitors, and testing other classes in the broad family of aquaporins for previously undiscovered ion-conducting capabilities.

The matrix nonlinear Schrödinger equation with a potential

This paper is devoted to the study of the large-time asymptotics of the small solutions to the matrix nonlinear Schrödinger equation with a potential on the half-line and with general selfadjoint boundary condition, and on the line with a potential and a general point interaction, in the whole supercritical regime. We prove that the small solutions are scattering solutions that asymptotically in time, t→±∞, behave as solutions to the associated linear matrix Schrödinger equation with the potential identically zero. The potential can be either generic or exceptional. Our approach is based on detailed results on the spectral and scattering theory for the associated linear matrix Schrödinger equation with a potential, and in a factorization technique that allows us to control the large-time behavior of the solutions in appropriate norms.

HRM solutions: a framework for small business owners to manage industrial relations while facilitating labour unionisation mitigation

PurposeSmall business owners require objective solutions to deal with threats of labour unionisation. This study aims to centre on a novel exploration for improving the leadership acumen of small business owners to address labour unionisation. Specifically, small business owners need a theoretical framework that uses best practices from human resource management (HRM) and industrial relations to provide solutions.Design/methodology/approachThe design, methodology and approach reflect post-modernist epistemological and ontological perspectives for conducting systematic literature reviews. A systematic literature review revealed the relationship between small business owners’ leadership, positive industrial relations and HRM policies and procedures. To identify relevant studies in the review, the utilisation of several databases (EBSCO Database, including PsycINFO and Psych studies; Web of Science) and a mix of ranked journals from entrepreneurship, human resources, leadership and organisational behaviour.FindingsThe findings and results in this paper reflect the purpose, methodology and literature analysis culminating in 162,132,000 peer-reviewed studies. A total of 142 peer-reviewed studies met criterion for review. For example, the purpose of this review focused on labour unionisation mitigation for small businesses and HRM solutions. In doing so, the methodology allowed for identification of a novel research topic (i.e. how small business owners mitigate labour unionisation) worthy of further investigation. The sparse findings on labour unionisation mitigation represent small business owners' reticence in creating HRM policies and procedures.Originality/valueThis study contributes research implications for theory and practice by offering small business owners a theoretical framework to address labour unionisation. The framework, centring on HRM solutions, is grounded in social exchange theory to address the novel topic of labour unionisation mitigation in small businesses. This study results suggest that HRM solutions for small business owners provide competitive advantages for employee job satisfaction through a holistic industrial relations approach. In future research, examining other issues discussed in this study can influence the understanding of the relationship between small business owners and industrial relations to increase employee job satisfaction.

Rahn Contract Construction as Micro, Small and Medium Enterprises (MSME) Capitalization Solutions in the Halal Industry Sector

Many players in the halal industry do not have access to formal finance. As a result, they do not have access to capital, their business does not develop, and gradually goes out of business. This article aims to develop the concept of financing with the Rahn contract scheme. So far, the Rahn contract is only understood as an agreement in a pawnshop to obtain a certain amount of loans for consumptive purposes. This article uses a type of literature review where data is obtained from a number of publications derived from journals, books, proceedings, review results, magazines or newspapers, and other sources that are considered informative. This article argues that the Rahn contract can be developed as a capitalization solution for halal industry business units in the micro, small, and medium sectors. It further suggests the development of the function of the Rahn contract as a business capitalization contract by issuing shares as Marhun for financing media. The capitalization model with this scheme is intended to develop collateral as a means of investment.

Global smooth solutions of the 4-D quasilinear Klein-Gordon equations on the product space [formula omitted

In this paper, we establish the global existence of small data smooth solution to the 4-D quasilinear Klein-Gordon equation with the initial data posed on the product space R3×T. Our proof relies on the method of the space-time resonance and the energy estimate.

On the edge between organic solvent nanofiltration and ultrafiltration: Characterization of regenerated cellulose membrane with aspect on dendrimer purification and recycling

The performance of commercial cellulose membranes with pore size on the border between ultra- and nanofiltration in selected organic solvents was studied focusing on rejection of small solutes and applicability for dendrimer purification. Organic markers in the MW range 100 – 700 Da and polarity range from nonpolar to polar protic compounds (aliphatics, aromatics, ethers, esters and alcohols) were used for membrane characterization. Transmission experiments in mixtures of methanol and dichloromethane of variable ratio showed the suitability of tested membranes for intended purpose, bringing information on structural factors affecting the rejection. Besides solute molar volume, its polarity type, or affinity, most conveniently expressed by Hansen solubility parameters, was found to be a crucial factor; with increasing size of solute molecule the spatial arrangement becomes also important. Solvent composition influences not only the behavior of solutes, but it also affects the membrane structure: poor solvation of cellulose by less polar solvents causes partial pore collapse, resulting in a decrease of membrane molecular weight cutoff. This effect can be used to improve the retention of a target product, as was shown for the first generation amphiphilic dendron. In addition, a simple mathematical model, allowing to estimate the course of nanofiltration and to optimize its conditions in a semicontinuous dead-end setup, is presented.

On the critical exponent and sharp lifespan estimates for semilinear damped wave equations with data from Sobolev spaces of negative order

We study semilinear damped wave equations with power nonlinearity |u|^p and initial data belonging to Sobolev spaces of negative order dot{H}^{-gamma }. In the present paper, we obtain a new critical exponent p=p_{textrm{crit}}(n,gamma ):=1+frac{4}{n+2gamma } for some gamma in (0,frac{n}{2}) and low dimensions in the framework of Sobolev spaces of negative order. Precisely, global (in time) existence of small data Sobolev solutions of lower regularity is proved for p>p_{textrm{crit}}(n,gamma ), and blow-up of weak solutions in finite time even for small data if 1<p<p_{textrm{crit}}(n,gamma ). Furthermore, in order to more accurately describe the blow-up time, we investigate sharp upper bound and lower bound estimates for the lifespan in the subcritical case.

A mesothelium divides the subarachnoid space into functional compartments

The central nervous system is lined by meninges, classically known as dura, arachnoid, and pia mater. We show the existence of a fourth meningeal layer that compartmentalizes the subarachnoid space in the mouse and human brain, designated the subarachnoid lymphatic-like membrane (SLYM). SLYM is morpho- and immunophenotypically similar to the mesothelial membrane lining of peripheral organs and body cavities, and it encases blood vessels and harbors immune cells. Functionally, the close apposition of SLYM with the endothelial lining of the meningeal venous sinus permits direct exchange of small solutes between cerebrospinal fluid and venous blood, thus representing the mouse equivalent of the arachnoid granulations. The functional characterization of SLYM provides fundamental insights into brain immune barriers and fluid transport.

Decay estimates for Schrödinger systems with time-dependent potentials in 2D

&lt;abstract&gt;&lt;p&gt;We consider the Cauchy problem for systems of nonlinear Schrödinger equations with time-dependent potentials in 2D. Under assumptions about mass resonances and potentials, we prove the global existence of the nonlinear Schrödinger systems with small initial data. In particular, by analyzing the operator $ \Delta $ and time-dependent potentials $ {V_{j}} $ separately, we show that the small global solutions satisfy time decay estimates of order $ O((t\log{t})^{-1}) $ when $ p = 2 $, and the small global solutions satisfy time decay estimates of order $ O({t}^{-1}) $ when $ p &amp;gt; 2 $.&lt;/p&gt;&lt;/abstract&gt;

Small solutions of the Einstein–Boltzmann-scalar field system with Bianchi symmetry

We show that small homogeneous solutions to the Einstein–Boltzmann-scalar field system exist globally toward the future and tend to the de Sitter solution in a suitable sense. More specifically, we assume that the spacetime is of Bianchi type I–VIII, that the matter is described by Israel particles and that there exists a scalar field with a potential which has a positive lower bound. This represents a generalization of the work [H. Lee and E. Nungesser, Classical Quantum Gravity 35, 025001 (2018)], where a cosmological constant was considered, and a generalization of [H. Lee and J. Lee, J. Math. Phys. 63, 031502 (2022)], where a spatially flat FLRW spacetime was considered. We obtain the global existence and asymptotic behavior of classical solutions to the Einstein–Boltzmann-scalar field system for small initial data.

Small data finite-time blow-up solutions for the nonlinear Schrödinger equation in general dimensions

The purpose of this paper is to show the existence of finite-time blow-up solution for the nonlinear Schrödinger equation in general spatial dimension which starts with the initial data as small as we like. We construct a solution of the nonlinear Schrödinger equation defined in negative global time and blows-up at positive finite time. We derive decay estimates for the solutions in the negative time direction by using interpolation inequalities in the weighted Lebesgue spaces.

Invariant tori for the Hamiltonian derivative wave equation with higher order nonlinearity

In this paper, we will study the Hamiltonian derivative wave equation with higher order nonlinearity \begin{document}$ y_{tt}-y_{xx}+my+(Dy)^5 = 0, \quad x\in\mathbb{T}: = \mathbb{R}/2\pi\mathbb{Z}, $\end{document} where $ m&gt;0 $ is a potential and \begin{document}$ D: = \sqrt{-\partial_{xx}+m}. $\end{document} We will prove that, for any integer $ b\geq2 $, the above equation admits many small amplitude quasi-periodic solutions corresponding to $ b $-dimensional invariant tori of an associated infinite dimensional Hamiltonian system. The proof is based on infinite dimensional KAM theory and partial Birkhoff normal form.

Multiple solutions to Kirchhoff-Schrödinger equations involving the $ p(\cdot) $-Laplace-type operator

&lt;abstract&gt;&lt;p&gt;This paper is devoted to deriving several multiplicity results of nontrivial weak solutions to Kirchhoff-Schrödinger equations involving the $ p(\cdot) $-Laplace-type operator. The aims of this paper are stated as follows. First, under some conditions on a nonlinear term, we show that our problem has a sequence of infinitely many large energy solutions. Second, we obtain the existence of a sequence of infinitely many small energy solutions to the problem on a new class of nonlinear term. The primary tools to obtain such multiplicity results are the fountain theorem and the dual fountain theorem, respectively.&lt;/p&gt;&lt;/abstract&gt;

Multiplicity of solutions to non-local problems of Kirchhoff type involving Hardy potential

&lt;abstract&gt;&lt;p&gt;The aim of this paper is to establish the existence of a sequence of infinitely many small energy solutions to nonlocal problems of Kirchhoff type involving Hardy potential. To this end, we used the Dual Fountain Theorem as a key tool. In particular, we describe this multiplicity result on a class of the Kirchhoff coefficient and the nonlinear term which differ from previous related works. To the best of our belief, the present paper is the first attempt to obtain the multiplicity result for nonlocal problems of Kirchhoff type involving Hardy potential by utilizing the Dual Fountain Theorem.&lt;/p&gt;&lt;/abstract&gt;

Weighted estimates and large time behavior of small amplitude solutions to the semilinear heat equation

Weighted estimates and large time behavior of small amplitude solutions to the semilinear heat equation

The lifespan of classical solutions of one dimensional wave equations with semilinear terms of the spatial derivative

&lt;abstract&gt;&lt;p&gt;This paper is devoted to the lifespan estimates of small classical solutions of the initial value problems for one dimensional wave equations with semilinear terms of the spatial derivative of the unknown function. It is natural that the result is same as the one for semilinear terms of the time-derivative. But there are so many differences among their proofs. Moreover, it is meaningful to study this problem in the sense that it may help us to investigate its blow-up boundary in the near future.&lt;/p&gt;&lt;/abstract&gt;

Infrared Small Target Tracking Algorithm via Segmentation Network and Multistrategy Fusion

To solve the problem of infrared (IR) small target tracking loss or error caused by factors such as scale changes, motion blur, occlusion, etc., this paper proposes a multi-strategy fusion tracking algorithm using an IR small target segmentation network as the detection head, which mainly includes six strategies: target pixel clustering, target feature threshold adjustment, large area search, small area tracking, gate tracking, and coordinate solution. First, candidate targets are obtained through the IR small target segmentation network and pixel clustering strategy. Second, the range of candidate targets is further reduced through threshold adjustment strategies. Then, real-time tracking of IR small targets is achieved through large area search, small area tracking, and wave gate tracking strategies. Finally, the longitude, latitude, and altitude of the tracked target are obtained through coordinate calculation strategies. Both qualitative and quantitative experiments based on real IR small target sequences verify that our algorithm can achieve more satisfactory performances in terms of success rate, precision, and robustness compared with other typical visual trackers. In addition, we have deployed tracking algorithms on the Orange Pi 5 embedded platform, and the tracking speed meets the real-time requirements.

On solitary-wave solutions of fifth-order KdV type of model equations for water waves

&lt;p style='text-indent:20px;'&gt;The paper concerns capillary-gravity surface waves propagating on a two-dimensional incompressible and inviscid fluid with or without an obstacle placed at a flat horizontal bottom. Formally second-order correct model equations, analogous to the first-order correct KdV equation, are derived under the classical assumptions of long wavelength and small amplitude of the surface waves. The model equations are a fifth-order KdV type of equations where the obstacle at the bottom introduces forcing terms in the equations. If the forcing is zero, the equation can possess a special Hamiltonian structure after a BBM term is introduced. The existence and set stability of solitary-wave solutions for the fifth-order KdV-BBM type of equations without forcing are studied. If the forcing term is included, only a special case is considered, which is the forced fifth-order KdV type equation (also called forced Kawahara equation) and models the water waves when both the surface tension and wave speed are near their critical values. The existence of small or some large solitary-wave solutions is obtained and the Lyapunov stability of small solitary-wave solutions is proved. Other large amplitude solutions are studied numerically.&lt;/p&gt;

On some quasilinear parabolic equations with non-monotone multivalued terms

In this paper, we study the existence of solutions to the initial-boundary value problem for the following parabolic differential inclusion: \begin{document}$ \begin{equation*} \begin{cases} u_t\left(t, x \right) -\triangle _{p}u\left( t, x \right) \in -\partial \phi \left( u\left( t, x \right) \right) + G\left( t, x, u\left( t, x \right) \right) &amp; (t, x) \in Q_T, \\ u(t, x) = 0 &amp; (t, x) \in \Gamma_T, \\ u(0, x) = u_0(x) &amp; x \in \Omega, \end{cases} \end{equation*} $\end{document} where $ \Omega $ is a bounded open subset of $ \mathbb{R}^{N} $ with smooth boundary $ \partial \Omega, $ $ T&gt;0 $, $ Q_{T}: = [0, T] \times \Omega $, $ \Gamma_T: = [0, T] \times \partial\Omega $, $ u_t = \frac{\partial u}{\partial t} $, $ \triangle_{p} $ is the $ p $-Laplace differential operator, $ \partial \phi $ denotes the subdifferential of a proper lower semicontinuous convex function $ \phi :\mathbb{R}\rightarrow \left[ 0, \infty \right] $, and $ G:Q_{T}\times \mathbb{R}\rightarrow 2^{ \mathbb{R}} \backslash \{\emptyset\} $ is a nonmonotone multivalued mapping.The case where $ \phi \equiv 0 $ and $ G(t, x, u) = |u|^{q-2}u $ gives the prototype of our problem, denoted by (E)$ _p $. The existence of time-local strong solutions for (E)$ _p $ is already studied by several authors. However, these results require a stronger assumption on $ q $ than that for the semi-linear case (E)$ _p $ with $ p = 2 $.More precisely, it has been long conjectured that (E)$ _p $ should admit a time-local strong solution for the Sobolev-subcritical range of $ q $, i.e., for all $ q \in (2, p^\ast) $ with $ p^\ast = \infty $ for $ p \geq N $ and $ p^\ast = \frac{N p}{N-p} $ for $ p&lt;N $, which is the well-known fact for the semi-linear case (E)$ _p $ with $ p = 2 $.The main purpose of the present paper is to show this conjecture holds true and to extend this classical study to the cases where $ u \mapsto G(\cdot, \cdot, u) $ is upper semicontinuous or lower semicontinuous, each one is a generalized notion of the continuity in the theory of multivalued analysis.We also discuss the extension of large or small local solutions along the lines of arguments developed in [28].