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Background We aimed to evaluate dynamic alterations in cerebral total hemoglobin concentration (HbT) in individuals with orthostatic hypotension (OH) and orthostatic intolerance (OI) symptoms using a portable near-infrared spectroscopy (NIRS) system. Methods Participants comprised 238 individuals (mean age, 47.9 years) without a history of cardiovascular, neurodegenerative, or cerebrovascular diseases, including those with unexplained OI symptoms and healthy volunteers. Participants were categorized by the presence of OH based on the supine-to-stand blood pressure (BP) drop and OI symptoms using on OH questionnaires: classic OH (OH-BP), OH symptoms alone (OH-Sx), and control groups. Random case–control matching sets were constructed, resulting in 16 OH-BP and 69 OH-Sx-control sets. The time-derivative of HbT change in the prefrontal cortex during the squat-to-stand maneuver was measured using a portable NIRS system. Results There were no differences in demographics, baseline BP, and heart rate among matched sets. The peak time of maximum slope variation in HbT change, indicating the recovery rate and speed of cerebral blood volume (CBV) change, was significantly longer in OH-Sx and OH-BP groups than in the control group under transition to a standing position after squatting. In the OH-BP subgrouping, the peak time of maximum slope variation in HbT change was significantly longer only in OH-BP with OI symptoms, but did not differ between OH-BP without OI symptoms and controls. Conclusions Our results suggest that OH and OI symptoms are associated with dynamic alterations in cerebral HbT. Regardless of the severity of the postural BP drop, OI symptoms are associated with prolonged CBV recovery. more...

We show that the energy norm of weak solutions to Vlasov equation coupled with a shear thickening fluid on the whole space has a decay rate the energy norm $E(t) \leq {C}/{(1+t)^{\alpha }}, \forall t \geq 0$ for $\alpha \in (0,3/2)$. more...

We consider the motion of an incompressible shear-thickening power-law-like non-Newtonian fluid in $R^3$ with a variable power-law index. This system of nonlinear partial differential equations arises in mathematical models of electrorheological fluids. The aim of this paper is to investigate the large-time behaviour of the difference $u-\tilde{u}$ where $u$ is a strong solution of the given equations with the initial data $u_0$ and $\tilde{u}$ is the strong solution of the same equations with perturbed initial data $u_0+w_0$. The initial perturbation $w_0$ is not required to be small, but is assumed to satisfy certain decay condition. In particular, we can show that $(1+t)^{-\frac{\gamma}{2}}\lesssim \|u(t)-\tilde{u}(t)\|_2\lesssim(1+t)^{-\frac{\gamma}{2}}$, for sufficiently large $t>0$, where $\gamma\in(2,\frac{5}{2})$. The proof is based on the observation that the solution of the linear heat equation describes the asymptotic behaviour of the solutions of the electrorheological fluids well for sufficiently large time $t>0$, and the generalized Fourier splitting method with an iterative argument. Furthermore, it will also be discussed that the argument used in the present paper can improve the previous results for the generalized Newtonian fluids with a constant power-law index. more...

We investigate the space-time decay properties for strong solutions to the 3D Navier–Stokes equations with power-law type nonlinear viscous fluid. Based on the temporal decay results for this equation, we find that one can obtain decay estimate of the weight for the velocity field u by direct weighted energy estimate. more...

We give some regularity criterion (of a weak $$-L^{p}$$ Serrin type) of a weak solution to the 3D Navier–Stokes equations in a bounded domain $$\Omega \subset \mathbb {R}^3$$ with a smooth boundary. In particular, in case of the half space, we give a regularity condition of a weak solution with respect to a tangential component of the velocity flow vector. more...

Inadequate cerebral perfusion is a risk factor for cerebral ischemia in patients with large artery steno-occlusion. We investigated whether prefrontal oxyhemoglobin oscillation (ΔHbO2, 0.6–2 Hz) was associated with decreased vascular reserve in patients with steno-occlusion in the large anterior circulation arteries. Thirty-six patients with steno-occlusion in the anterior circulation arteries (anterior cerebral artery, middle cerebral artery, and internal carotid artery) were included and compared to thirty-six control subjects. Patients were categorized into two groups (deteriorated vascular reserve vs. preserved vascular reserve) based on the results of Diamox single- photon emission computed tomography imaging. HbO2 data were collected using functional near-infrared spectroscopy. The slope of ΔHbO2 and the ipsilateral/contralateral slope ratio of ΔHbO2 were analyzed. Among the included patients (n = 36), 25 (69.4%) had deteriorated vascular reserve. Patients with deteriorated vascular reserve had a significantly higher average slope of ΔHbO2 on the ipsilateral side (5.01 ± 2.14) and a higher ipsilateral/contralateral ratio (1.44 ± 0.62) compared to those with preserved vascular reserve (3.17 ± 1.36, P = 0.014; 0.93 ± 0.33, P = 0.016, respectively) or the controls (3.82 ± 1.69, P = 0.019; 0.94 ± 0.29, P = 0.001). The ipsilateral/contralateral ΔHbO2 ratio could be used as a surrogate for vascular reserve in patients with severe steno-occlusion in the anterior circulation arteries. more...

We report a novel strategy for the synthesis of Pt@Au nanorings possessing near-field focusing capabilities at the center through which single-particle surface enhanced Raman scattering could be readily observed. We utilized Pt@Au nanorings as a light-absorber; the absorbed light could be focused at the center with the aid of a Au nanoporous structure. We synthesized the Au nanolens structure through a Galvanic exchange process between Au ions and Ag block at the inner domain of the Pt@Au nanoring. For this step, Ag was selectively pre-deposited at the inner domain of the Pt@Au nanorings through electrochemical potential-tuned growth control and different surface energies with regard to the inner and outer boundaries of the nanoring. Then, the central nanoporous architecture was fabricated through the Galvanic exchange of sacrificial Ag with Au ions leading to the resulting Au nanoring with a Au nanoporous structure at the center. We monitored the shape-transformation by observing their corresponding localized surface plasmon resonance (LSPR) profiles. By varying the rim thickness of the starting Pt@Au nanorings, the inner diameter of the nanolens was accordingly tuned to maximize near-field focusing, which enabled us to obtain the reproducible and light-polarization independent measurements of single-particle SERS. Through theoretical simulation, the near-field electromagnetic field focusing capability was visualized and confirmed through single-particle SERS measurement showing an enhancement factor of 1.9 × 108 to 1.0 × 109., We synthesized a Au nanolens with electromagnetic near-field focusing capability by integrating a Au nanoporous structure at the center of the Pt@Au nanoring via synthetic steps of eccentric growth of Ag and nanoscale Galvanic exchange reaction. more...

We investigate the following elliptic equations: $$\left\{ {\matrix{ { - M\left( {\int_{{\mathbb{R}^N}} {\phi ({{\left| {\nabla u} \right|}^2}){\rm{d}}x} } \right){\rm{div(}}\phi \prime ({{\left| {\nabla u} \right|}^2})\nabla u{\rm{) + }}{{\left| u \right|}^{\alpha - 2}}u = \lambda h(x,u),} \hfill \cr {u(x) \to 0,\;\;\;\;\;{\rm{as}}\left| x \right| \to \infty ,} \hfill \cr } } \right.\;\;\;\;\;\;\;\;{\rm{in}}\;\;\;\;{\mathbb{R}^N},$$ where N ≥ 2, 1 < p < q < N, α < q, 1 < α < p*q†/p† with $${p^ * } = {\textstyle{{Np} \over {N - p}}},\;\;\phi (t)$$ behaves like tq/2 for small t and tp/2 for large t, and p′ and q′ are the conjugate exponents of p and q, respectively. We study the existence of nontrivial radially symmetric solutions for the problem above by applying the mountain pass theorem and the fountain theorem. Moreover, taking into account the dual fountain theorem, we show that the problem admits a sequence of small-energy, radially symmetric solutions. more...

We developed a synthetic strategy to form cyclodextrin-based intrananogap particles (CIPs) with a well-defined ∼1 nm interior gap in a high yield (∼97%), and were able to incorporate 10 different Raman dyes inside the gap using the cyclodextrin-based host-guest chemistry, leading to strong, reproducible, and highly multiplexable surface-enhanced Raman scattering (SERS) signals. The average SERS enhancement factor (EF) for CIPs was 3.0 × 109 with a very narrow distribution of the EFs that range from 9.5 × 108 to 9.5 × 109 for ∼95% of the measured particles. Remarkably, 10 different Raman dyes can be loaded within the nanogap of CIPs, and 6 different Raman dye-loaded CIPs with little spectral overlaps were distinctly detected for cancer cell imaging applications with a single excitation source. Our synthetic strategy provides new platforms in precisely forming plasmonic nanogap structures with all key features for widespread use of SERS including strong signal intensity, reliability in quantification of signal and multiplexing capability. more...

In this Letter, a rational and stepwise method for the solution-phase synthesis of asymmetric Au split nanorings by adopting Au nanoprisms as a template has been demonstrated. The selective chemical etching of Au nanoprism tips activated the surface reactivity of edges and led to the selective deposition of Pt at the periphery of Au nanoplates. By controlling the total amount of Pt on the edges, different degrees of split Au@Pt nanorings were obtained; the subsequent Au coating around the Au@Pt scaffold eventually resulted in asymmetric Au hexagonal split nanorings. Their surface plasmonic features as a function of split degrees were investigated, including straight nanorods, bent nanorods, split nanorings, and full nanorings. The electrical field focusing using single-particle surface-enhanced Raman spectroscopy was evaluated under different polarization angles of the incident light for two different structures with the point gap and line gap between two arms. more...

Silver double nanorings with circular intra-nanogaps between two nanorings of different diameters were synthesized without a linker molecule to confine an incident electromagnetic field in a single entity. We used on-demand, rational, and systematic multi-stepwise reactions consisting of (1) selective etching of gold, (2) rim-on deposition of platinum, (3) eccentric growth of gold, and (4) concentric growth of silver. The resulting silver double nanorings exhibited a high degree of homogeneity in both shape and size, with strongly coupled circular hot zones (or "hot halos", referring to the circular intra-nanogaps capable of focusing the near electromagnetic field) resulting from strong surface plasmon coupling between the inner and outer nanorings. Remarkably, these silver double nanorings exhibited strong, stable, and reproducible single-particle surface-enhanced Raman scattering signals without blinking. The signals appeared independently of polarization directions, which is a unique feature of a circular hot halo. The estimated enhancement factor was between 2 × 108 and 7 × 108. The measured limit of detection was 10-7 M in bulk concentration, and the signal appeared 570 s after sample exposure. more...

Herein, plasmonic metal tripod nanoframes with three-fold symmetry were synthesized in a high yield (∼83%), and their electric field distribution and single-particle surface-enhanced Raman scattering (SERS) were studied. We realized such complex frame morphology by synthesizing analogous tripod nanoframes through multiple transformations. The precise control of the Au growth pattern led to uniform tripod nanoframes embedded with circle or line-shaped hot spots. The linear-shaped nanogaps ("Y"-shaped hot-zone) of the frame structures can strongly and efficiently confine the electric field, allowing for strong SERS signals. Coupled with a high synthetic yield of the targeted frame structure, strong and uniform SERS signals were obtained inside the nanoframe gaps. Remarkably, quite reproducible SERS signals were obtained with these structures-the SERS enhancement factors with an average value of 7.9 × 10 more...

The development of a stepwise synthetic strategy for Au ring-in-a-triangle nanoframes with a high degree of structural solidity is essential to the advancement of highly amplified near-field focusing. This strategy leads to the formation of an inscribed nanoring in a triangular metal frame with stability to withstand elevated temperatures and an oxidizing environment, which is critical for successful single-particle surface-enhanced Raman scattering (SERS). The existence of inscribed nanorings plays an important role in enhancing the so-called "lightning rod effect," whereby the electromagnetic near-field enhancement occurs on the highly curved curvature of a metallic interface. We evaluated the corresponding single-particle SERS as a function of the thickness of the rims and then constructed two-dimensional (2D) bulk SERS substrates, wherein an ensemble of hotspots exists. The synergic contribution from both inter- and intrahotspots allowed the outstanding linearity of the calibration curve and the lowest limit of detection, ∼10 more...

The aim of this paper is to examine the existence of at least two distinct nontrivial solutions to a Schrödinger-type problem involving the nonlocal fractional $p(\cdot )$ p ( ⋅ ) -Laplacian with concave–convex nonlinearities when, in general, the nonlinear term does not satisfy the Ambrosetti–Rabinowitz condition. The main tools for obtaining this result are the mountain pass theorem and a modified version of Ekeland’s variational principle for an energy functional with the compactness condition of the Palais–Smale type, namely the Cerami condition. Also we discuss several existence results of a sequence of infinitely many solutions to our problem. To achieve these results, we employ the fountain theorem and the dual fountain theorem as main tools. more...