Electroosmotic Flow Hysteresis for Fluids with Dissimilar pH and Ionic Species

Electroosmotic flow (EOF) involving displacement of multiple fluids is employed in micro-/nanofluidic applications. There are existing investigations on EOF hysteresis, i.e., flow direction-dependent behavior. However, none so far have studied the solution pair system of dissimilar ionic species with substantial pH difference. They exhibit complicated hysteretic phenomena. In this study, we investigate the EOF of sodium bicarbonate (NaHCO3, alkaline) and sodium chloride (NaCl, slightly acidic) solution pair via current monitoring technique. A developed slip velocity model with a modified wall condition is implemented with finite element simulations. Quantitative agreements between experimental and simulation results are obtained. Concentration evolutions of NaHCO3–NaCl follow the dissimilar anion species system. When NaCl displaces NaHCO3, EOF reduces due to the displacement of NaHCO3 with high pH (high absolute zeta potential). Consequently, NaCl is not fully displaced into the microchannel. When NaHCO3 displaces NaCl, NaHCO3 cannot displace into the microchannel as NaCl with low pH (low absolute zeta potential) produces slow EOF. These behaviors are independent of the applied electric field. However, complete displacement tends to be achieved by lowering the NaCl concentration, i.e., increasing its zeta potential. In contrast, the NaHCO3 concentration has little impact on the displacement process. These findings enhance the understanding of EOF involving solutions with dissimilar pH and ion species.

Nonexistence of entire positive solutions for conformal Hessian quotient inequalities

<p style='text-indent:20px;'>In this paper, we consider the nonexistence problem for conformal Hessian quotient inequalities in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^n $\end{document}</tex-math></inline-formula>. We prove the nonexistence results of entire positive <inline-formula><tex-math id="M2">\begin{document}$ k $\end{document}</tex-math></inline-formula>-admissible solution to a conformal Hessian quotient inequality, and entire <inline-formula><tex-math id="M3">\begin{document}$ (k, k') $\end{document}</tex-math></inline-formula>-admissible solution pair to a system of Hessian quotient inequalities, respectively. We use the contradiction method combining with the integration by parts, suitable choices of test functions, Taylor's expansion and Maclaurin's inequality for Hessian quotient operators.</p>

Enhancing Challenge Framing in Defence Organisations: Towards Reflexive Methods

This article contributes to problem solving, design, and planning in defence organisations by arguing that a ‘problem’ or a ‘challenge’ is never objective, natural or ready-made. Challenges are contingent to the conditions under which individuals perceive and formulate them. As a result, this article understands ‘challenges’ and ‘approaches’ to address them as co-dependent on one another. This article recommends that officers should attempt to generate the most interesting and, we hope, innovative problem-solution pair or challenge-approach pair in order to integrate this insight into practice when problem solving, designing, or planning. Leaders and their teams can learn to inhabit this mind-set by finding inspiration in three modes observed through practice: initial challenge framing, challenge curation and co-evolution. For each of these modes, the article proposes reflexive methods and tools for enhancing introspection in challenge framing and formulation namely the Five Whys, question-storming, and loyal opposition. The article supports these recommendations and methods through insights gleaned from philosophy of knowledge, design theory, and on design experiences with the North American Aerospace Defence Command (NORAD) in 2019.

Pointwise estimates for Stokes systems with BMO coefficients in Reifenberg domains

Pointwise estimates of weak solution pairs to a stationary Stokes system with small [Formula: see text] semi-norm coefficients are established in Reifenberg flat domains by using the restricted sharp maximal function. These pointwise estimates provide a unified treatment of the Calderón–Zygmund estimates for the solution pair to Stokes systems in [Formula: see text] and [Formula: see text] spaces.

Backward stochastic differential equations with unbounded generators

In this paper, we consider two classes of backward stochastic differential equations (BSDEs). First, under a Lipschitz-type condition on the generator of the equation, which can also be unbounded, we give sufficient conditions for the existence of a unique solution pair. The method of proof is that of Picard iterations and the resulting conditions are new. We also prove a comparison theorem. Second, under the linear growth and continuity assumptions on the possibly unbounded generator, we prove the existence of the solution pair. This class of equations is more general than the existing ones.

MATHEMATICAL PROPERTIES OF AMERICAN CHOOSER OPTIONS

The American chooser option is a relatively new compound option that has the characteristic of offering exceptional risk reduction for highly volatile assets. This has become particularly significant since the start of the global financial crisis. In this paper, we derive mathematical properties of American chooser options. We show that the two optimal stopping boundaries for American chooser options with finite horizon can be characterized as the unique solution pair to a system formed by two nonlinear integral equations, arising from the early exercise premium (EEP) representation. The proof of EEP representation is based on the method of change-of-variable formula with local time on curves. The key mathematical properties of American chooser options are proved, specifically smooth-fit, continuity of value function and continuity of free-boundary among others. We compare the performance of the American chooser option against the American strangle option. We also conduct numerical experiments to illustrate our results.

An iterative algorithm for the best approximate (P, Q)-orthogonal symmetric and skew-symmetric solution pair of coupled matrix equations

This paper deals with developing a robust iterative algorithm to find the least-squares ( P, Q)-orthogonal symmetric and skew-symmetric solution sets of the generalized coupled matrix equations. To this end, first, some properties of these type of matrices are established. Furthermore, an approach is offered to determine the optimal approximate ( P, Q)-orthogonal (skew-)symmetric solution pair corresponding to a given arbitrary matrix pair. Some numerical experiments are reported to confirm the validity of the theoretical results and to illustrate the effectiveness of the proposed algorithm.

SYMMETRY AND EXISTENCE OF SOLUTIONS OF SEMI-LINEAR ELLIPTIC SYSTEMS IN HYPERBOLIC SPACE

Abstract(0.1) \begin{equation}\label{eq:0.1} \left\{ \begin{array}{ll} \displaystyle -\Delta_{\mathbb{H}^{N}}u=|v|^{p-1}v x, \\ \displaystyle -\Delta_{\mathbb{H}^{N}}v=|u|^{q-1}u, \\ \end{array} \right. \end{equation} in the whole Hyperbolic space ℍN. We establish decay estimates and symmetry properties of positive solutions. Unlike the corresponding problem in Euclidean space ℝN, we prove that there is a positive solution pair (u, v) ∈ H1(ℍN) × H1(ℍN) of problem (0.1), moreover a ground state solution is obtained. Furthermore, we also prove that the above problem has a radial positive solution.