We introduce the problem of constructing explicit
variety evasive subspace families
. Given a family
F
of subvarieties of a projective or affine space, a collection
H
of projective or affine
k
...-subspaces is
(
F
,
ϵ
)
-evasive if for every
V
∈
F
, all but at most
ϵ
-fraction of
W
∈
H
intersect every irreducible component of
V
with (at most) the expected dimension. The problem of constructing such an explicit subspace family generalizes both deterministic black-box polynomial identity testing (PIT) and the problem of constructing explicit (weak) lossless rank condensers.
Using Chow forms, we construct explicit
k
-subspace families of polynomial size that are evasive for all varieties of bounded degree in a projective or affine
n
-space. As one application, we obtain a complete derandomization of Noether’s normalization lemma for varieties of low degree in a projective or affine
n
-space. In another application, we obtain a simple polynomial-time black-box PIT algorithm for depth-4 arithmetic circuits with bounded top fan-in and bottom fan-in that are not in the Sylvester–Gallai configuration, improving and simplifying a result of Gupta (ECCC TR 14-130).
As a complement of our explicit construction, we prove a tight lower bound for the size of
k
-subspace families that are evasive for degree-
d
varieties in a projective
n
-space. When
n
-
k
=
n
Ω
(
1
)
, the lower bound is superpolynomial unless
d
is bounded. The proof uses a dimension counting argument on Chow varieties that parametrize projective subvarieties.
Natural gas hydrate is one of the most potential carbon energy resources because of its tremendous reserves. Gas and water permeability of natural gas hydrate-bearing sediments (HBS) directly affects ...gas recovery from hydrate reservoirs and gas production efficiency. In this paper, we review the permeability of HBS with respect to its relevant factors and development in characterization. Hydrate morphology and distribution inherently affect the permeability, and are identified in both coarse- and fine-grained sediments. Measurement and estimation methods of permeability are discussed in four aspects: theoretical analysis and numerical simulation, laboratory experiment, and filed test. Research challenges to this subject are comprehensively discussed, and future prospects of research are addressed. We suggest that future research should focus on understanding hydrate formation and dissociation mechanism and their effect on the permeability in fine-grained sediments, obtaining reliable measurement results of the permeability, bridging the gap of permeability between laboratory samples and natural sediments, and highlighting multi-scale analysis on the permeability with appropriate parameters as well as developing models for safe and economically feasible gas production from HBS eventually.
•A comprehensive review of permeability in natural gas hydrate-bearing sediments is presented.•Hydrate morphology and pore habit as well as their effects on permeability are reviewed.•Research challenges and prospects for permeability of hydrate sediments are discussed.
The performance of attitude stabilization control algorithms for rigid spacecraft can be limited by disturbances. In this paper, the global finite-time attitude stabilization problem with ...disturbances is investigated and handled by constructing a second-order sliding mode controller. Firstly, a virtual controller based on set stabilization idea is constructed to globally finite-time stabilize the system. Then, a relay polynomial second-order sliding mode controller is constructed to guarantee that the tracking error toward the virtual controller will converge to zero in finite-time. Finite-time Lyapunov theory is applied to support the proof and stability analysis. The global finite-time stability holds even with bounded disturbances. The effectiveness and feasibility of the controller are illustrated by the numerical simulations.
•Co3O4/CdO composite nanospheres were firstly synthesized.•They showed a high capacitance of 351 F g−1 at 2 A g−1.•84.9% of the original capacitance was retained from 2 to 10 A g−1.
For the first ...time, Co3O4/CdO composite nanospheres were synthesized using a simple solvothermal method. During electrochemical study, Co3O4/CdO nanospheres showed a high capacitance of 351 F g−1, and 84.9% of the original capacitance was also reached from 2 to 10 A g−1, indicating an excellent rate performance. The asymmetric supercapacitor containing Co3O4/CdO nanospheres exhibited high capacitance of 109.4 F g−1 at 1 A g−1. The fabricated Co3O4/CdO nanospheres were promising alternatives for highly performed supercapacitors.
RIG-I-like receptors (RLRs) are intracellular pattern recognition receptors that detect viral or bacterial infection and induce host innate immune responses. The RLRs family comprises retinoic ...acid-inducible gene 1 (RIG-I), melanoma differentiation-associated gene 5 (MDA5) and laboratory of genetics and physiology 2 (LGP2) that have distinctive features. These receptors not only recognize RNA intermediates from viruses and bacteria, but also interact with endogenous RNA such as the mislocalized mitochondrial RNA, the aberrantly reactivated repetitive or transposable elements in the human genome. Evasion of RLRs-mediated immune response may lead to sustained infection, defective host immunity and carcinogenesis. Therapeutic targeting RLRs may not only provoke anti-infection effects, but also induce anticancer immunity or sensitize "immune-cold" tumors to immune checkpoint blockade. In this review, we summarize the current knowledge of RLRs signaling and discuss the rationale for therapeutic targeting RLRs in cancer. We describe how RLRs can be activated by synthetic RNA, oncolytic viruses, viral mimicry and radio-chemotherapy, and how the RNA agonists of RLRs can be systemically delivered in vivo. The integration of RLRs agonism with RNA interference or CAR-T cells provides new dimensions that complement cancer immunotherapy. Moreover, we update the progress of recent clinical trials for cancer therapy involving RLRs activation and immune modulation. Further studies of the mechanisms underlying RLRs signaling will shed new light on the development of cancer therapeutics. Manipulation of RLRs signaling represents an opportunity for clinically relevant cancer therapy. Addressing the challenges in this field will help develop future generations of cancer immunotherapy.
Most soil-water characteristic curve (SWCC) models contain more than three parameters, but these parameters typically do not have a distinct geometric or physical meaning, or the parameters used are ...inaccurate because of their high reliance on inverse parameter estimation methods. This phenomenon greatly limits the application of SWCC in the study of mechanical and hydraulic properties of unsaturated soils. To explore the nature of SWCC, this paper reexamines the role of the parameters in the two most commonly used SWCC models from the perspective of the relationship between capillary and adsorbed water. A new and flexible SWCC model (named the MVF model) with four parameters is proposed, which can separate the two different regions by physical constraints on the residual saturation Sr and residual suction ψr. Ten published experimental data sets are compiled to evaluate the performance of the MVF model by comparing it with both the existing models and the experimental data. The MVF model shows excellent performance in terms of goodness of fit, and the fitting parameters are provided with a clear geometric meaning, which helps to establish the connection between the basic properties of the soil and the SWCC. This study consolidates the application and reliable determination of SWCC in estimating the mechanical and hydraulic properties of unsaturated soils.
•The relationship of capillary and adsorbed water and the role of the fitting parameters for FX and VG models are reviewed.•A flexible modified SWCC model with four fitting parameters based on FX and VG model is proposed.•The physical constraints from residual suction and residual saturation are employed in this study to reduce the uncertainty of the parameters.•The parameters in the proposed model can better capture the features of the SWCC.•A flexible variation on the mathematical form of the model can be applied to bimodal soils.
Hierarchical MnO
2
@NiCo
2
O
4
core–shell nanostructures are well fabricated via a simple two-step hydrothermal process. The MnO
2
@NiCo
2
O
4
core–shell nanostructures materials electrode presents a ...high capacitance of 684 F g
−1
at 2 A g
−1
current density, 40 times higher than that of the single MnO
2
nanowires electrode. And 87.4% retain is approached even at a high current density of 15 A g
−1
, showing satisfactory rate capability. Furthermore, the theoretical analysis reveals the surface capacitance contribution is predominant in the capacitive contribution. The asymmetric supercapacitor assembled with MnO
2
@NiCo
2
O
4
exhibited a maximum energy density of 35.6 Wh kg
−1
and a maximum power density of 745.1 W kg
−1
. After 7000 charge–discharge cycling at a current density of 4 A g
−1
, it still can maintain 90% of the initial capacitance. These results suggest that MnO
2
@NiCo
2
O
4
is the promising candidate of supercapacitors.
The electrocatalytic carbon dioxide reduction reaction is an effective means of combating the greenhouse effect caused by massive carbon dioxide emissions. Carbon nitride in the graphitic phase ...(g-C3N4) has excellent chemical stability and unique structural properties that allow it to be widely used in energy and materials fields. However, due to its relatively low electrical conductivity, to date, little effort has been made to summarize the application of g-C3N4 in the electrocatalytic reduction of CO2. This review focuses on the synthesis and functionalization of g-C3N4 and the recent advances of its application as a catalyst and a catalyst support in the electrocatalytic reduction of CO2. The modification of g-C3N4-based catalysts for enhanced CO2 reduction is critically reviewed. In addition, opportunities for future research on g-C3N4-based catalysts for electrocatalytic CO2 reduction are discussed.
Suspended solids (SS) have become the main cause of water quality deterioration in aquaculture ponds. The application of ozone to aquaculture water bodies can improve the water quality and facilitate ...the removal of suspended solids. We used different concentrations of ozone to oxidize aquaculture water and then determined the resulting concentration of suspended solids and their particle size distribution, as well as CODMn, UV254, algal density, and nitrogen content. The results showed the following: (i) The decrease in SS was the highest, amounting to 10.47%, after the addition of 2 mg/L of ozone and the completion of the oxidation reaction. Ozone caused the fragmentation of large SS particles and the flocculation of small particles, and these effects became more pronounced as the ozone concentration increased; (ii) After the introduction of ozone, the humus macromolecules naturally present in the water were oxidized, which improved the biochemical degradation of the water pollutants; (iii) Ozone oxidation caused the degradation of algae, resulting in a decrease in phytoplankton biomass and in the eutrophication of the water body; (iv) As the ozone concentration increased, the level of nitrous nitrogen decreased, while the concentrations of nitrate nitrogen and ammonia nitrogen were unchanged. The highest increase in total nitrogen was measured when 0.5 mg/L of ozone was applied. This study provides a theoretical basis for the application of ozone to eliminate eutrophic substances in freshwater ponds.
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