DUAL FUNCTIONALS OF SAID-BZIER TYPE GENERALIZED BALL BASES OVER TRIANGLE DOMAIN AND THEIR APPLICATION

A family of Said-Bézier type generalized Ball （SBGB） bases and surfaces with a parameter H over triangular domain is introduced,which unifies Bézier surface and Said-Ball surface and includes several intermediate surfaces. To convert different bases and surfaces,the dual functionals of bases are presented. As an application of dual functionals,the subdivision formulas for surfaces are established.

Dual-functional pyrene implemented mesoporous silicon material used for the detection and adsorption of metal ions

A fluorescent active organic–inorganic hybrid material Py N-SBA-15 was synthesized by implementing pyrene derivatives into mesoporous SBA-15 silica.Py N-SBA-15 had detection and removal functionalities toward Al^(3+),Cu^(2+),and Hg^(2+).On the one hand,Py N-SBA-15 was used as a fluorescence sensor and displayed high sensitivity toward Al^(3+),Cu^(2+),and Hg^(2+)cations (limit of detection:8.0×10^(-7),1.1×10^(-7),and 2.9×10^(-6)mol·L^(–1),respectively) among various analytes with“turn-off”response.On the other hand,the adsorption studies for these toxic analytes (Cu^(2+),Hg^(2+),and Al^(3+)) showed that the ion removal capacity could reach up to 45,581,and 85 mg·g^(-1),respectively.Moreover,the Langmuir isotherm models were better fitted with the adsorption data,indicating that the adsorption was mono-layer adsorption.Kinetic analysis revealed that the adsorption process was well described by the pseudo-second-order kinetic model for Cu^(2+)and Hg^(2+)and pseudo-first-order kinetic model for Al^(3+).The prepared silica material could be reused in four recycles without significantly decreasing its adsorption capacity.Therefore,the Py N-SBA-15 material can serve as a promising candidate for the simultaneous rapid detection and efficient adsorption of metal ions.

Standard Dual Quaternion Optimization and Its Applications in Hand-Eye Calibration and SLAM

Several common dual quaternion functions,such as the power function,the magnitude function,the 2-norm function,and the kth largest eigenvalue of a dual quaternion Hermitian matrix,are standard dual quaternion functions,i.e.,the standard parts of their function values depend upon only the standard parts of their dual quaternion variables.Furthermore,the sum,product,minimum,maximum,and composite functions of two standard dual functions,the logarithm and the exponential of standard unit dual quaternion functions,are still standard dual quaternion functions.On the other hand,the dual quaternion optimization problem,where objective and constraint function values are dual numbers but variables are dual quaternions,naturally arises from applications.We show that to solve an equality constrained dual quaternion optimization(EQDQO)problem,we only need to solve two quaternion optimization problems.If the involved dual quaternion functions are all standard,the optimization problem is called a standard dual quaternion optimization problem,and some better results hold.Then,we show that the dual quaternion optimization problems arising from the hand-eye calibration problem and the simultaneous localization and mapping(SLAM)problem are equality constrained standard dual quaternion optimization problems.

Perturbation Theory for Dual Cosine Function（Ⅱ）—Time－dependent Perturbation in the Sun－reflexive Case

In this paper,we proved that the infinitesimal generator of a strongly continuous cosine operator function is preserved under the time-dependent perturbation in the sun-reflexive case,where the perturbed operator is a bounded linear operator from X into a bigger space Xθ(not X),then the corresponding 2-order abstract Cauchy problem is uniformly well-posed.

FURTHER STUDY ON A DUAL ALGORITHM

The dual algorithm for minimax problems is further studied in this paper.The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with changing parameter in the dual algorithm is proportional to the reciprocal of the parameter,which is very important for the efficiency of the dual algorithm.At last,the numerical experiments are reported to validate the analysis results.

Facile wet-chemical fabrication of bi-functional coordination polymer nanosheets for high-performance energy storage and anti-corrosion engineering

Organic materials are of great interest in various applications owing to their intrinsic designability,molecular controllability,ease of synthesis,and ecological sustainability.In this work,a facile and mild wet-chemical strategy was carried out to construct a conjugated Ni-BTA coordination polymer via the π-d hybridization with 1,2,4,5-benzenetetramine(BTA)as π-conjugated ligands and Ni^(2+)as metallic centers,which exhibits a unique two-dimensional nanosheet-like structure with available active sites,sufficient electrochemical activity,and multi-electron redox capability.On the one hand,the as-prepared Ni-BTA coordination polymer as electrode material exhibits a rapid,reversible,and efficient energy storage behavior with a large reversible capacity of 198 mA·h·g^(-1)at 1 A·g^(-1) and a high-rate capability of 150 mA·h·g^(-1) at 20 A·g^(-1) in alkali-ion aqueous electrolyte,which are further demonstrated by the in-situ Raman investigation.On the other hand,the Ni-BTA coordination polymer as anti-corrosion additive was introduced into the epoxy resin to achieve a Ni-BTA epoxy coating,which shows a long-term anticorrosion performance with a low corrosion rate of 4.62×10_(-6) mm·a^(-1) and a high corrosion inhibition efficiency of 99.86%,suggesting its great engineering potential as the bi-functional organic material for high-performance energy storage and corrosion protection.

Enhancement of the CO_(2)adsorption and hydrogenation to CH_(4)capacity of Ru–Na–Ca/γ–Al_(2)O_(3)dual function material by controlling the Ru calcination atmosphere

Integrated CO_(2)capture and utilization(ICCU)technology requires dual functional materials(DFMs)to carry out the process in a single reaction system.The influence of the calcination atmosphere on efficiency of 4%Ru-8%Na_(2)CO_(3)-8%CaO/γ-Al_(2)O_(3)DFM is studied.The adsorbent precursors are first co-impregnated onto alumina and calcined in air.Then,Ru precursor is impregnated and four aliquotes are subjected to different calcination protocols:static air in muffle or under different mixtures(10%H_(2)/N_(2),50%H_(2)/N_(2)and N_(2))streams.Samples are characterized by XRD,N_(2)adsorption-desorption,H_(2)chemisorption,TEM,XPS,H_(2)-TPD,H_(2)-TPR,CO_(2)-TPD and TPSR.The catalytic behavior is evaluated,in cycles of CO_(2)adsorption and hydrogenation to CH_(4),and temporal evolution of reactants and products concentrations is analyzed.The calcination atmosphere influences the physicochemical properties and,ultimately,activity of DFMs.Characterization data and catalytic performance discover the acccomodation of Ru nanoparticles disposition and basic sites is mostly influencing the catalytic activity.DFM calcined under N_(2)flow(RuNaCa-N_(2))shows the highest CH_(4)production(449μmol/g at 370℃),because a well-controlled decomposition of precursors which favors the better accomodation of adsorbent and Ru phases,maximizing the specific surface area,the Ru-basic sites interface and the participation of different basic sites in the CO_(2)methanation reaction.Thus,the calcination in a N_(2)flow is revealed as the optimal calcination protocol to achieve highly efficient DFM for integrated CO_(2)adsorption and hydrogenation applications.

An efficient and reusable bimetallic Ni_3Fe NPs@C catalyst for selective hydrogenation of biomass-derived levulinic acid toγ-valerolactone

Bimetallic nanostructures have attracted great interest as efficient catalyst to enhance activity,selectivity and stability in catalytical conversion.Herein,we report a facile one‐pot carbothermal route to in‐situ controllable synthesize heterogeneous bimetallic Ni3Fe NPs@C nanocatalyst.The X‐ray diffraction,transmission electron microscopy,X‐ray photoelectron spectroscopy and N2 adsorption‐description results reveal that the Ni3Fe alloy nanoparticles are evenly embedded in carbon matrix.The as‐prepared Ni3Fe NPs@C catalyst shows excellent selective hydrogenation catalytic performance toward the conversion of levulinic acid(LA)toγ‐valerolactone(GVL)via both direct hydrogenation(DH)and transfer hydrogenation(TH).In DH of LA,the bimetallic catalyst achieved a 93.8%LA conversion efficiency with a 95.5%GVL selectivity and 38.2 mmol g–1 h–1 GVL productivity(under 130°C,2MPa H2 within 2 h),which are 6 and 40 times in comparison with monometallic Ni NPs@C and Fe NPs@C catalysts,respectively.In addition,the identical catalyst displayed a full conversion of LA with almost 100%GVL selectivity and 167.1 mmol g–1 h–1 GVL productivity at 180°C within 0.5 h in TH of LA.Under optimal reaction conditions,the DH and TH catalytic performance of 500‐Ni3Fe NPs@C(3:1)catalyst for converting LA to GVL is comparable to the state‐of‐the‐art noble‐based catalysts.The demonstrated capability of bimetallic catalyst design approach to introduce dual‐catalytic functionality for DH and TH reactions could be adoptable for other catalysis processes.

Rough law generation and its separation-recognition

By using function S-rough sets（function singular rough sets）, this paper gives rough law generation and the theorem of rough law generation.Based on these results above, the paper proposes rough law separation, the theorem of rough law separation, the compound generation theorem of rough law bands, and the principle of rough law bands.In the end, an application of rough law separation in recognizing the risk law of profit is presented.

■-law collision and system state recognition

Using dual function one direction S-rough sets, this article gives the f-law, the F-law, law distance and the concept of system law collided by the F-law. The characteristics presented by the system law collided by the F-law, the recognition of these characteristics and recognition criterion are also proposed. The dual function one direction S-rough sets is one of the basic forms of function S-rough sets. Its basic theory and application in the study of system law collision are reviewed.

EXISTENCE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS AND HARDY TERMS

This paper deals with the existence of solutions to the elliptic equation-△u-μ/|x|2=λu +|u|2*-2u + f(x,u) in Ω,u = 0 on (?)Ω, where Ω is a bounded domain in RN(N≥3), 0 ∈ Ω 2*=2N/N-2,λ> 0, λ (?) σμ,σμ is the spectrum of the operator -△-μI/|x|2 with zero Dirichlet boundary condition, 0 <μ< μ-,μ-=(N-2)2/4, f(x,u)is an asymmetric lower order perturbation of |u|2* -1 at infinity. Using the dual variational methods, the existence of nontrivial solutions is proved.

EFFICIENT COMPUTATIONAL METHOD FOR TRANSIENT EM RESPONSE OF LARGE-LOOP SOURCE OVER LAYERED EARTH

Calculations of the ElectroMagnetic(EM) response produced by a large horizontal loop placed over layered medium are rather complex because its integral expression contains the product of two Bessel functions and has a divergent term. In this paper, an improved fast Hankel and Gaver-Stehfest transforms are introduced to solve the strong-oscillation and slow-decay properties of the integrand, where one Bessel function in the product is substituted by a carefully chosen polynomial of high accuracy and the other used as the digital filter coefficients in the convolution integral. Comparisons prove the validity and the efficiency of the proposed method.

1,n-Thiosulfonylation using thiosulfonates as dual functional reagents

In recent years,the direct introduction of sulfonyl and sulfenyl groups into unsaturated substrates by using thiosulfonates as unique dual functional reagents has inarguably provided chemists a new platform for the diverse synthesis of important S-containing derivatives.These 1,n-thiosulfonylation reactions usually feature simple procedures,100%atom economy,and high regioselectivity.This review focuses on the recent advancements in the transformations of thiosulfonates through 1,n-thiosulfonylation involving the formation of two distinct C-S bonds under transition-metal-catalyzed or metal-free conditions,where thiosulfonates act as both a sulfonyl and a sulfenyl component.

Bioactive glass sol as a dual function additive for chitosan-alginate hybrid scaffold

Bioactive glass-chitosan-alginate hybrid scaffolds （BG-C-A scaffolds） were fabricated using BG sol as a dual function additive, which behaves as both bioactive inorganic phase to confer the bioactivity and cross-linker to improve the structural stability and mechanical properties. The microstructure, physicochemical and mechanical properties, in vitro bioactivity and cellular biocompatibility of the scaffolds were investigated. The results indicated that BG component was successfully incorporated into the BG-C-A scaffolds through a facile BG sol-immersing method and the original interconnected microstructure could be well preserved. The obtained BG-C-A scaffolds showed improved mechanical properties and structural stability as compared to C-A scaffolds. At the same time, they presented excellent in vitro bioactivity and cellular compatibility. All these results demonstrated that these BG-C-A scaffolds have promising potential for tissue engineering.

Gold-catalyzed ketene dual functionalization and mechanistic insights:divergent synthesis of indenes and benzo[d]oxepines

An unprecedented gold-catalyzed ketene C=O/C=C bifunctionalization method has been developed.Mechanistic studies and density function theory(DFT)calculations indicate that the reaction is initiated by gold-catalyzed Wolff rearrangement of diazoketone to form the ketene intermediate,followed by intermolecular nucleophilic addition and terminated with two divergent cyclization processes via enol intermediates.In the case with alcohols as the nucleophiles,the reaction goes through a C-5-endodig carbocyclization to give the indene products;whereas,O-7-endo-dig cyclization occurs dominantly when indoles/pyrroles are used as the nucleophiles,delivering the 7-membered benzo[d]oxepines.In comparison with the well-documented cycloaddition and nucleophilic addition reactions,this cascade reaction features a novel reaction pattern for the ketene dual functionalization through addition with nucleophile and electrophile in sequence.

Facile fabrication of dolomite-doped biochar/bentonite for effective removal of phosphate from complex wastewaters

The removal of phosphate from wastewater using traditional biological or precipitation methods is a huge challenge.The use of high-performance adsorbents has been shown to address this problem.In this study,a novel composite adsorbent,composed of dolomite-doped biochar and bentonite(DO/BB),was first synthesized via co-pyrolysis.The combination of initial phosphate concentration of 100 mg/L and 1.6 g/L of DO/BB exhibited a high phosphate-adsorption capacity of 62 mg/g with a removal efficiency of 99.8%.It was also stable in complex water environments with various levels of solution pH,coexisting anions,high salinity,and humic acid.With this new composite,the phosphate concentration of the actual domestic sewage decreased from 9 mg/L to less than 1 mg/L,and the total nitrogen and chemical oxygen demand also decreased effectively.Further,the cross-flow treatment using a PVC membrane loaded with DO/BB(PVC-DO/BB),decreased the phosphate concentration from 1 to 0.08 mg/L,suggesting outstanding separation of phosphate pollutants via a combination of adsorption and separation.In addition,the removal of phosphate by the PVC-DO/BB membrane using NaOH solution as an eluent was almost 90%after 5 cycles.The kinetic,isotherm and XPS analysis before and after adsorption suggested that adsorption via a combination of electrostatic interaction,complexation and precipitation contributed to the excellent separation by the as-obtained membranes.

Blue emitting exciplex for yellow and white organic light‑emitting diodes

White organic light-emitting diodes(WOLEDs)have several desirable features,but their commercialization is hindered by the poor stability of blue light emitters and high production costs due to complicated device structures.Herein,we investigate a standard blue emitting hole transporting material(HTM)N,N'-bis(naphthalen-1-yl)-N,N'-bis(phenyl)benzidine(NPB)and its exciplex emission upon combining with a suitable electron transporting material(ETM),3-(biphenyl-4-yl)-5-(4-tert-butylphenyl)-4-phenyl-4H-1,2,4-triazole(TAZ).Blue and yellow OLEDs with simple device structures are developed by using a blend layer,NPB:TAZ,as a blue emitter as well as a host for yellow phosphorescent dopant iridium(III)bis(4-phenylthieno[3,2-c]pyridinato-N,C2')acetylacetonate(PO-01).Strategic device design then exploits the ambipolar charge transport properties of tetracene as a spacer layer to connect these blue and yellow emitting units.The tetracene-linked device demonstrates more promising results compared to those using a conventional charge generation layer(CGL).Judicious choice of the spacer prevents exciton difusion from the blue emitter unit,yet facilitates charge carrier transport to the yellow emitter unit to enable additional exciplex formation.This complementary behavior of the spacer improves the blue emission properties concomitantly yielding reasonable yellow emission.The overall white light emission properties are enhanced,achieving CIE coordinates(0.36,0.39)and color temperature(4643 K)similar to daylight.Employing intermolecular exciplex emission in OLEDs simplifes the device architecture via its dual functionality as a host and as an emitter.

COMPUTE A CELIS-DENNIS-TAPIA STEP

In this paper, we present an algorithm for the CDT subproblem. This problem stems from computing a trust region step of an algorithm, which was first proposed by Celis, Dennis and Tapia for equality constrained optimization. Our algorithm considers general case of the CDT subproblem, convergence of the algorithm is proved. Numerical examples are also provided.

Combining CO_(2) capture and catalytic conversion to methane

Considering the global objective to mitigate climate change,import efforts are made on decreasing the net emission of CO_(2) from gas effluents.On the one hand CO_(2) capture-for example by adsorption onto solid basic materials-allows to withdraw CO_(2) from the waste gas streams emitted by incinerators,cement manufacture plants,combustion plants,power plants,etc.On the second hand,CO_(2) can be converted to useful chemicals-e.g.hydrogenation to methane-using appropriate heterogene-ous catalysts.A relatively innovative strategy consists in combining both technologies by designing materials and processes which can switch between capture and methanation modes cyclically.This allows treating complex waste gas effluents by selectively and reversibly capturing CO_(2),and to perform the catalytic hydrogenation in appropriate reaction conditions.This short review presents the main strategies recently reported in the literature for such combined CO_(2) capture and methanation(CCCM)processes.We discuss the different types of reactor configurations and we present the formulations used in this context as adsorbent,as methanation catalysts,and as“dual functional materials”.