We study the normalized solutions of the fractional nonlinear Schrödinger equations with combined nonlinearities
(
-
Δ
)
s
u
=
λ
u
+
μ
|
u
|
q
-
2
u
+
|
u
|
p
-
2
u
in
R
N
,
and we look for solutions ...which satisfy prescribed mass
∫
R
N
|
u
|
2
=
a
2
,
where
N
≥
2
,
s
∈
(
0
,
1
)
,
μ
∈
R
and
2
<
q
<
p
<
2
s
∗
=
2
N
/
(
N
-
2
s
)
. Under different assumptions on
q
<
p
,
a
>
0
and
μ
∈
R
, we prove some existence and nonexistence results about the normalized solutions. More specifically, in the purely
L
2
-subcritical case, we overcome the lack of compactness by virtue of the monotonicity of the least energy value and obtain the existence of ground state solution for
μ
>
0
. While for the defocusing situation
μ
<
0
, we prove the nonexistence result by constructing an auxiliary function. We emphasis that the nonexistence result is new even for Laplacian operator. In the purely
L
2
-supercritical case, we introduce a fiber energy functional to obtain the boundedness of the Palais–Smale sequence and get a mountain-pass type solution. In the combined-type cases, we construct different linking structures to obtain the saddle type solutions. Finally, we remark that we prove a uniqueness result for the homogeneous nonlinearity (
μ
=
0
), which is based on the Morse index of ground state solutions.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In this paper, Nickel–Cobalt layered double hydroxide (NiCo-LDH) nanosheets were first in situ synthesized on MXene (Ti3C2) via a simple hydrothermal method, then glucose sensing performance based on ...three-dimensional porous MXene/NiCo-LDH nanocomposite was explored. At a working potential of 0.45 V (vs. SCE), the glucose sensor exhibits a wide linearity range (0.002 mM–4.096 mM), a low limit of detection (0.53 μM) and a rapid response (<3 s). Moreover, good selectivity, reproducibility and stability were also obtained. And the excellent performance can attribute to large area of contact of materials surface with glucose, fast electron transfer rate and easy diffusion of electrolyte provided by the novel 3D porous NiCo-LDH nanosheets on the conductive MXene substrate. Therefore, MXene/NiCo-LDH composites will be a candidate for electrochemical detection of glucose.
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•NiCo-LDH nanosheets with high specific surface area grew on the surface of MXene and formed 3D porous structure.•The oxidation performance towards glucose between MXene/NiCo-LDH and NiCo-LDH was compared.•The MXene/NiCo-LDH/GCE was used for detection of glucose and the limit of detection is 0.53 μM.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Layered double hydroxide (LDH) is potentially excellent supercapacitor (SC) materials, but the low conductivity and easy agglomeration limit the further improvement of their electrochemical ...properties. Therefore, LDHs are requisite to grow on some conductive substrates to produce high-performance SC. In this paper, the conductive two-dimensional (2D) transition metal carbides, nitrides and carbonitrides (called MXene) were explored as the substrate to directly deposit NiFe-LDH nanosheets by a one-step hydrothermal method, then a three-dimensional (3D) porous NiFe-LDH/MXene electrode was obtained. The morphology and electrochemical performance of the composite electrodes were analyzed and investigated. The results show that the NiFe-LDH/MXene electrode has larger specific capacitance (720.2 F/g) than NiFe-LDH (465 F/g), and the capacitance of the composite electrode retained 86% after 1000 cycles (only 24% for NiFe-LDH), showing excellent cycle stability. The improved electrochemical performance of the composites is caused by the stable sheet-like structure of NiFe-LDH during charge-discharge time and the conductive network formed by the MXene, which can accelerates electron transport. In addition, the asymmetric SC based on NiFe-LDH/MXene positive electrode display a power density of 758.27 W/kg at an energy density of 42.4 Wh/Kg. These results indicate the NiFe-LDH/MXene composites can be applied as the novel candidate of high-performance SC electrodes.
•The LDH/MXene synergistic hybrid structure is developed with MXene nanosheets as the substrate.•Prominent electrical performance is attributed to MXene providing a fast charge transfer path for LDH.•The anchoring of LDH on MXene surface provides the material with enhanced cyclic stability.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In this paper, we consider the following Kirchhoff type equation
-
a
+
b
∫
R
3
|
∇
u
|
2
Δ
u
+
V
(
x
)
u
=
f
(
u
)
,
x
∈
R
3
,
where
a
,
b
>
0
and
f
∈
C
(
R
,
R
)
, and the potential
V
∈
C
1
(
R
3
,
...R
)
is positive, bounded and satisfies suitable decay assumptions. By using a perturbation approach together with a new version of global compactness lemma of Kirchhoff type, we prove the existence and multiplicity of bound state solutions for the above problem with a general nonlinearity. We especially point out that neither the Ambrosetti-Rabinowitz condition with
μ
>
4
nor any monotonicity assumption on
f
is required. Moreover, the potential
V
may not be radially symmetry or coercive. As a prototype, the nonlinear term involves the power-type nonlinearity
f
(
u
)
=
|
u
|
p
-
2
u
for
p
∈
(
2
,
6
)
.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Hemorrhage imaging is one of the most common applications of magnetic induction tomography (MIT). Depth and the mass of stroke stimulated (MSS) are the most important issues that need to be solved ...for this application. Transcranial magnetic stimulation (TMS) is a technique belonging to the deep brain stimulation (DBS) field, which aims at overcoming human diseases such as depression. TMS coils, namely, circular, figure-8, and H-coils, play an important role in TMS. Among these, H-coils individually focus on the issues of achieving effective stimulation of deep region. MIT and TMS mechanisms are similar. Herein, for the first time, improved TMS coils, including figure-8 and H-coils, are applied as MIT excitation coils to study the possibility of achieving the mass of stroke stimulated and deep detection through MIT. In addition, the configurations of the detection coils are varied to analyze their influence and determine the optimal coils array. Finally, MIT is used to detect haemorrhagic stroke occurring in humans, and the application of deep MIT to the haemorrhagic stroke problem is computationally explored. Results show that among the various coils, the improved H-coils have MSS and depth characteristics that enable the detection of deep strokes through MIT. Although the detecting depth of the figure-8 coil is weaker, its surface signal is good. The deep MIT technique can be applied to haemorrhagic detection, providing a critical base for deeper research.
We study the existence and orbital stability of normalized solutions of the biharmonic equation with the mixed dispersion and a general nonlinear term
<disp-formula> <tex-math id="FE1"> ...\begin{document}$ \begin{equation*} \gamma\Delta^2u-\beta\Delta u+\lambda u = f(u), \quad x\in\mathbb{R}^N \end{equation*} $\end{document} </tex-math></disp-formula>
with a priori prescribed $ L^2 $-norm constraint $ S_a: = \left\{u\in H^2(\mathbb{R}^N):\int_{\mathbb{R}^N}|u|^2dx = a\right\}, $ where $ a > 0 $, $ \gamma > 0, \beta\in\mathbb{R} $ and the nonlinear term $ f $ satisfies the suitable $ L^2 $-subcritical assumptions. When $ \beta\geq0 $, we prove that there exists a threshold value $ a_0\geq0 $ such that the equation above has a ground state solution which is orbitally stable if $ a > a_0 $ and has no ground state solution if $ a < a_0 $. However, for $ \beta < 0 $, this case is more involved. Under an additional assumption on $ f $, we get the similar results on the existence and orbital stability of ground state. Finally, we consider a specific nonlinearity $ f(u) = |u|^{p-2}u+\mu|u|^{q-2}u, 2 < q < p < 2+8/N, \mu < 0 $ under the case $ \beta < 0 $, which does not satisfy the additional assumption. And we use the example to show that the energy in the case $ \beta < 0 $ exhibits a more complicated nature than that of the case $ \beta\geq0 $.
The supercapacitor (SC) based on nickel cobalt layered double hydroxide (NiCo-LDH) has aroused great interest in the field of energy storage. However, the agglomeration and low electrical ...conductivity are unfavorable for electrochemical performance. Herein, Ag nanowires (Ag NWs) was first dip-coated on nickel foam (NF) to form a conductive substrate, on which the NiCo-LDH nanosheet array in-situ grew to construct an efficient three-dimensional (3D) self-supported hierarchical structure NiCo-LDH/Ag NWs/NF electrode. The presence of Ag NWs inhibits aggregation of LDH nanosheets and accelerates the electron transfer. Electrochemical studies exhibit that NiCo-LDH/Ag/NF hybrid electrode possesses the higher specific capacitance of 2920.6 F g−1 at a current density of 5 A g−1 and excellent cycling stability (89.8% after 2000 cycles) compared with the electrode without Ag NWs. The asymmetric supercapacitor (ASC) with the NiCo-LDH/Ag/NF heterostructure as the positive electrode and active carbon (AC) as the negative electrode displays a high energy density of 42.9 Wh kg−1 at a power density of 800 W kg−1. When two aqueous ASCs were assembled in series and charged for only 1 min, the stored energy was capable of powering two green light-emitting-diodes (LEDs) for more than 3 min, indicating NiCo-LDH/Ag/NF electrode material shows great potential application in supercapacitor.
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•Ag NWs and 3D ultrathin NiCo-LDH nanosheets are successively decorated on Ni foam.•The conductivity and active sites of electrode are enhanced by the addition of Ag NWs.•The specific capacitance of NiCo-LDH/Ag/NF electrode is 2920.6 F g−1 at 5 A g−1.•The assembled asymmetric supercapacitor exhibits high energy and power densities.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The roles of F-box protein 43 (FBXO43) in carcinogenesis have been rarely revealed. The present study investigates the expression, function, and underlying mechanism of FBXO43 in hepatocellular ...carcinoma (HCC). Firstly, the expression and clinical significance of FBXO43 in HCC were investigated bioinformatically and experimentally using online omics data and local tissue samples. The role of N6-methyladenosine modification (m6A) of mRNA in regulating FBXO43 expression and the effects of m6A/FBXO43 axis alteration on cell proliferation and invasion were investigated further. Moreover, the underlying mechanism of the oncogenic FBXO43 was also explored. The results demonstrated that FBXO43 was significantly upregulated in HCC and was positively correlated with advanced progression and poor prognosis in patients. METTL3 and IGF2BP2 expressions were positively correlated with FBXO43 expression and served as the writer and reader of FBXO43 m6A, respectively, which stabilized and upregulated FBXO43 mRNA in HCC. FBXO43 silencing significantly reduced cell proliferation and invasion, and ectopic expression of FBXO43 could significantly restore the inhibitory effects caused by METTL3 and IGF2BP2 depletion in HCC cells. Mechanistically, FBXO43 depletion reduced the expression of UBE2C, a p53 ubiquitin-conjugating enzyme, suppressed proteasomal degradation of p53, and thus inhibited cell proliferation and invasion in HCC. In summary, the present study revealed that METTL3/IGF2BP2 mediated m6A contributed to the upregulation of FBXO43 that promoted the malignant progression of HCC by stimulating p53 degradation in a UBE2C-dependent manner, highlighting the promising application of FBXO43 as a target in HCC treatment.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
•Favorable adsorption configurations of H2S, HS on Mo(100) were characterized.•All possible dissociation pathways of H2S dehydrogenation were distinguished and mapped.•Decomposition of H2S on Mo(100) ...is facile.•The difference of reaction barrier during the second dehydrogenation with and without hydrogen co-adsorption is minor.
Density-functional theory calculations had been used to investigate the adsorption and dissociation of H2S on Mo(100) surface. Adsorption mechanisms of H2S, HS, S and H on the Mo(100) surface were analyzed. H2S was found to be adsorbed at bridge, hollow and top sites with adsorption energies of −1.25, −1.03 and −0.92eV, respectively. HS was strongly chemically absorbed at hollow, bridge and top sites with adsorption energies of −4.51, −4.08 and −3.45eV, respectively, and sulfur and hydrogen preferred to be absorbed at hollow and bridge sites, respectively. In addition, potential energy profiles of H2S dissociation on Mo(100) had been constructed by a climbing image nudged elastic band method. Four possible dissociation pathways of the first H2S dehydrogenation were examined with reaction barriers of 0.28, 0.37, 0.075, and 0.21eV, respectively, while the energy barrier to break the SH bond of HS with or without hydrogen co-adsorption was almost the same low. This work showed that the decomposition of H2S on the molybdenum surface was kinetically and thermodynamically facile. Local densities of electronic states were further used to characterize the interaction between H2S and substrate.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Inserting corrosion inhibitors into a lamellar protective coating is an effective way to improve the corrosion resistance of metal substrates. In this work, two kinds of environmentally friendly ...organic acid anions, aspartic acid (ASP) and lauric acid (La), were explored as corrosion inhibitors to in situ intercalate into the ZnAl-layered double hydroxides (ZnAl-LDHs) on AZ31 magnesium alloys by a facile one-step hydrothermal method. The morphology, composition, structure and the corrosion resistance of these two LDHs coating before and after corrosion experiment were investigated. It is found that both the two kinds of ZnAl-LDHs films consist of uniform and dense layered nanosheets (NSs), and the NSs of ZnAl-ASP-LDHs films grow vertically, but those of ZnAl-La-LDHs films exhibit a staggered tilted structure. The corrosion current density of the two ZnAl-LDHs films are two orders of magnitude lower than that of Mg alloy substrate. After one week's immersion in NaCl solution, the NSs structure of two kind of ZnAl-LDHs films still remains the uniform and densely coverage on Mg alloy. Owing to the larger d(003) spacing, the ZnAl-La-LDHs have better ability to absorb Cl− and release interlayer anions than ZnAl-ASP-LDHs. These results indicate that the ZnAl-LDHs films intercalated with organic anions, specially La anions, can significantly improve the corrosion resistance of Mg alloy.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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