EXPLICIT VORONOVSKAJA-TYPE RESULTS FOR LINEAR COMBINATIONS OF BDT-OPERATORS

In this paper me prove an explicit Vcionovskvja-type result for linear combmations of the so-called BDT -operators.

Firey linear combinations of convex bodies

For convex bodies, the Firey linear combinations were introduced and studied in several papers. In this paper the mean width of the Firey linear combinations of convex bodies is studied, and the lower bound of the mean width of the Firey linear combinations of convex body and its polar body is given.

Linear Combinations of Composition Operators on Weighted Dirichlet Spaces

In this paper, linear combinations of composition operators acting on weighted Dirichlet spaces are studied. By using the first derivative of the kernel function, we obtain a lower estimate for the essential norms of these operators acting on the Dirichlet space D and S2. For general weighted Dirichlet space, by using complex interpolation methods, we characterize the compactness of these operators induced by linear fractional self-maps of the disk.

Combinations of Right Half-Plane Mappings and Vertical Strip Mappings Convex in the Vertical Direction

In this paper, we explore the linear combinations of right half-plane mappings and vertical strip mappings. We demonstrate that the combinations of these harmonic mappings are convex in the vertical direction provided they are locally univalent and sense-preserving. Furthermore, we extend this analysis to a more general case by setting specific conditions. Additionally, we take some common parameters such as as the dilatation of these harmonic mappings, and prove the sufficient conditions that their combinations are locally univalent and convex in the vertical direction. Several examples are constructed by the Mathematica software to demonstrate our main results.

Revisiting ENSO impacts on the Indian Ocean SST based on a combined linear regression method

The El Nino-Southern Oscillation(ENSO)has great impacts on the Indian Ocean sea surface temperature(SST).In fact,two major modes of the Indian Ocean SST namely the Indian Ocean Basin(IOB)and the Indian Ocean Dipole(IOD)modes,exerting strong influences on the Indian Ocean rim countries,are both influenced by the ENSO.Based on a combined linear regression method,this study quantifies the ENSO impacts on the IOB and the IOD during ENSO concurrent,developing,and decaying stages.After removing the ENSO impacts,the spring peak of the IOB disappears along with significant decrease in number of events,while the number of events is only slightly reduced and the autumn peak remains for the IOD.By isolating the ENSO impacts during each stage,this study reveals that the leading impacts of ENSO contribute to the IOD development,while the delayed impacts facilitate the IOD phase switch and prompt the IOB development.Besides,the decadal variations of ENSO impacts are various during each stage and over different regions.These imply that merely removing the concurrent ENSO impacts would not be sufficient to investigate intrinsic climate variability of the Indian Ocean,and the present method may be useful to study climate variabilities independent of ENSO.

A Linear Combination of Superderivations on Prime Superalgebras

In the paper, we give some results about a linear combination of superderivations on prime superalgebras and generalize a result of Niu Feng-wen.

Quantitative analysis of glutamate compounds in the swine brain following central analgesics nasal spray using proton magnetic resonance spectroscopy and linear combination model

BACKGROUND： In localized brain proton magnetic resonance spectroscopy （^1H-MRS）, metabolite levels are often expressed as ratios, rather than absolute concentrations. Frequently, the denominator is creatine, which is assumed to be stable in normal, as well as many pathological, states. However, in vivo creatine levels do not remain constant. Therefore, absolute metabolite measurements, which provide the precise concentrations of certain chemical compounds, are superior to metabolite ratios for determining pathological and evolutional changes. OBJECTIVE： To investigate the feasibility of quantification analysis of brain metabolite changes caused by central analgesics nasal spray using the ^1H-MRS and linear combination model （LCModel） methods. DESIGN, TIME AND SETTING： This neuroimaging, observational, animal study was performed at the Laboratory of the Department of Medical Imaging, Second Affiliated Hospital, Medical College, Shantou University, China from July to December 2007. MATERIALS： Butorphanol tartrate nasal spray, as a mixed agonist-antagonist opioid analgesic, was purchased from Shanghai Hengrui Pharmacy, China. A General Electric Signa 1.5T System （General Electric Medical Systems, Milwaukee, WI, USA） and LCModel software （Stephen Provencher, Oakville, Ontario, Canada） were used in this study. METHODS： MRS images were acquired in ten healthy swine aged 2 weeks using single-voxel point-resolved spectroscopic sequence. A region of interest （2 cm × 2 cm × 2 cm） was placed in the image centers of maximum brain parenchyma. Repeated MRS scanning was performed 15-20 minutes after intranasal administration of 1 mg of butorphanol tartrate. Three settings of repetition time/echo time were selected before and after nasal spray administration 3 000 ms/30 ms,1 500 ms/30 ms, and 3 000 ms/50 ms. Metabolite concentrations were estimated by LCModel software. MAIN OUTCOME MEASURES： ^1H-MRS spectra was obtained using various repetition time/echo time settings. Concentrations of glutamate compounds （glutamate ＋ glutamine）, N-acetyl aspartate, and choline were detected in swine brain prior to and following nasal spray treatment. RESULTS： The glutamate compounds curve was consistent with original spectra, when a repetition time/echo time of 3 000 ms/30 ms was adopted. Concentrations of glutamate compounds, N-acetyl aspartate, and choline decreased following administration. The most significant reduction was observed in glutamate compound concentrations from （9.28 ± 0.54） mmol/kg to （7.28 ± 0.54） mmol/kg （P 〈 0.05）. CONCLUSION： ^1H-MRS and LCModel software were effectively utilized to quantitatively analyze and measure brain metabolites. Glutamate compounds might be an important neurotransmitter in central analgesia.

Determination of Light Rare Earths by a Spectrophoto-metry Based on the Linear Combination of Multiwavelength Data

The present paper proposes a new method of spectrophotometry based on linear combination of multiwavelength data by means of selecting a set of properly weighted coefficients and combination methods. It is clear that the weighted combination absorbance attained is only in direct proportion to the concentration of the analysed component and independent of coexisting interferents.The accuracy of the analytical results is improved greatly for the analysis of light rare earths with the coexistence of heavy rare earths.The analyti- cal error from the reagent blank and co-coloration of light and heavy rare earths have also been overcome. The greatly improved linearity and additivity of absorbance are obtained.

Generation of Linear Isolated Sub-60 Attosecond Pulses by Combining a Circularly Polarized Pulse with an Elliptically Polarized Pulse

The two-color circularly polarized pulses scheme was proposed to generate isolated attosecond pulses in our previous work [Phys. Rev. A 87 （2013） 043406], while the polarization of the attosecond pulse was not investigated. We show a supplementary explanation of this scheme and present another scheme to generate linear isolated attosecond pulses by combining a circularly polarized pulse with an elliptically polarized pulse. High-order harmonic generation and quantum path control are investigated to compare these two schemes. Both schemes can obtain supercontinuum spectra plateau from about 200eV to 550eV, which belong to the water window region. It is found that the latter scheme can clearly eliminate the short quantum path and extend the harmonic plateau. A linear isolated attosecond pulse with a duration of sub-6Oas can be generated by superposing a bandwidth of 70eV.

Bound Polaron in a Quantum Well Under an Electric Field

We conduct a theoretical study on the properties of a bound polaron in a quantum well under an electric field using linear combination operator and unitary transformation methods, which are valid in the whole range of electron-LO phonon coupling. The changing relations between the ground-state energy of the bound polaron in the quantum well and the Coulomb bound potential, the electric field strength, and the well width are derived. The numerical results show that the ground-state energy increases with the increase of the electric field strength and the Coulomb bound potential and decreases as the well width increases.

Influence of the Electric Field on the Properties of the Bound Magnetopolaron in GaAs Semiconductor Quantum Wells

The influence of the electric field on the properties of the bound magnetopolaron in an infinite-depth GaAs semiconductor quantum well is investigated using the linear-combination operator and the unitary transformation method. The relationships between the polaron＇s ground state energy and the Coulomb bound potential, electric field, magnetic field, and well-width are derived and discussed. Our numerical results show that the absolute value of the polaron＇s ground state energy increases as the electric field and the Coulomb bound potential increase, and decreases as the well-width and the magnetic field strength increase. When the well-width is small,the quantum size effect is significant.

Kinematic Calibration and Forecast Error Compensation of a 2-DOF Planar Parallel Manipulator

Due to large workspace,heavy-duty and over-constrained mechanism,a small deformation is caused and the precision of the 2-DOF planar parallel manipulator is affected.The kinematic calibration cannot compensate the end-effector errors caused by the small deformation.This paper presents a method combined step kinematic calibration and linear forecast real-time error compensation in order to enhance the precision of a two degree-of-freedom(DOF) planar parallel manipulator of a hybrid machine tool.In the step kinematic calibration phase of the method,the end-effector errors caused by the errors of major constant geometrical parameters is compensated.The step kinematic calibration is based on the minimal linear combinations(MLCs) of the error parameters.All simple and feasible measurements in practice are given,and identification analysis of the set of the MLCs for each measurement is carried out.According to identification analysis results,both measurement costs and observability are considered,and a step calibration including step measurement,step identification and step error compensation is determined.The linear forecast real-time error compensation is used to compensate the end-effector errors caused by other parameters after the step kinematic calibration.Taking the advantages of the step kinematic calibration and the linear forecast real-time error compensation,a method for improving the precision of the 2-DOF planar parallel manipulator is developed.Experiment results show that the proposed method is robust and effective,so that the position errors are kept to the same order of the measurement noise.The presented method is attractive for the 2-DOF planar parallel manipulator and can be also applied to other parallel manipulators with fewer than six DOFs.

Landslides susceptibility mapping in Guizhou province based on fuzzy theory

The purpose of this study was to assess the susceptibility of landslides around the area of Guizhou province based on fuzzy theory.In first instance, slope, elevation, lithology, proximity to tectonic lines, proximity to drainage and annual precipitation were taken as independent, causal factors in this study.A landslide hazard evaluation factor system was established by classifying these factors into more subclasses according to some rules.Secondly, a trapezoidal fuzzy number weighting(TFNW) approach was used to assess the importance of six causal factors to landslides in an ArcGIS environment.Thirdly, a landslide susceptibility map was created based on a weighted linear combination model.According to this susceptibility map, the study area was classified into four categories of landslide susceptibility:low, moderate, high and very high.Finally, in order to verify the results obtained, the susceptibility map and the landslide inventory map were combined in the GIS.In addition, the weighting procedure showed that TFNW is an efficient method for weighting causal landslide factors.

Land use suitability analysis for town development planning in Nanjing hilly areas: A case study of Tangshan new town, China

Land use suitability analysis plays an important role in sustainable land use and solving environmental problems caused by rapid urban development.A land use suitability mapping approach for town development planning in hilly areas was constructed based on two multi-criteria evaluation methods:Weighted Linear Combination(WLC)and Ordered Weighted Averaging(OWA),to comparatively evaluate and map land use suitability of Tangshan new town in Nanjing,China.Fourteen evaluation factors related to topographic,environmental,socio-economics and historical sites data were used as suitability criteria.The analytic hierarchy process(AHP)method and GIS techniques were integrated into the evaluation models to create the land use suitability map for town development planning.The results of WLC approach showed that 11.4%of the total area is highly suitable while the 48.6%is unsuitable.The results of WLC and OWA approach showed the distribution of degree of land use suitability is almost the same.The areas located at the southern and eastern flat regions are highly suitable for land use,whereas the areas close to the mountain forests,steep slopes,waters,and hot springs,have lower suitability for land use.Sensitivity analysis indicated that the suitability results of the two proposed methods are robust.Indirect validation was achieved by mutual comparison of suitability maps derived from the WLC and OWA methods.It demonstrated that the overall agreement is 90.81%and kappa coefficient is 0.81,indicating that both methods provide very similar spatial suitability distributions.By overlaying the resultant map with the previous master plan map of Tangshan new town,the overlay map once again indicated a satisfactory ecological fit between the two maps.At last,several recommendations are proposed aiming at improving the long-term town development plan for Tangshan new town.

THE DUAL BRUNN-MINKOWSKI INEQUALITIES FOR STAR DUAL OF MIXED INTERSECTION BODIES

In this article, some dual Brunn-Minkowski inequalities are established for star dual of mixed intersection bodies with respect to the harmonic p-combination and p-radial linear combination.

Vibrational frequency of a strong-coupling polaron in a quantum rod at finite temperatures

The Hamiltonian of a quantum rod with a boundary is presented after a coordinate transformation that changes the original ellipsoidal boundary into a spherical one. We then study the effect of temperature on the vibrational frequency and the ground state binding energy of the strong-coupling polaron in the rod. The two quantities are expressed as functions of the aspect ratio of the ellipsoid, the transverse and the longitudinal effective confinement lengths, the temperature and the electron-phonon coupling strength by linear combination operator and unitary transformation methods. It is found that the vibrational frequency and the ground state binding energy will increase rapidly with decreasing transverse and longitudinal effective confinement lengths. They are increasing functions of the electron- phonon coupling strength but become decreasing ones of the temperature and the aspect ratio.

ON THE INVERTIBILITY OF HILBERT SPACE IDEMPOTENTS

This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.

Landfill Siting Using GIS and AHP （Analytical Hierarchy Process）： A Case Study AI-Qasim Qadhaa, Babylon, Iraq

The selection of a landfill site is considered as a complicated task because this process is based on many factors and restrictions. For Al-Qasim Qadhaa, which is situated in the southern part of the Babylon Governorate, Iraq, there is no landfill site in that area that conforms to the scientific criteria for selecting sites for landfill. For this reason, 15 criteria were adopted in this study （groundwater depth, rivers, soil types, agriculture lands use, land use, elevation, slope, gas pipelines, oil pipelines, power lines, roads, railways, urban centers, villages and archaeological sites） using GIS （geographic information system）, which has a large ability to manage input data. In addition, the AHP （analytical hierarchy process） method was used to derive the relative weightings for each criterion using pair-wise comparison. To obtain the suitability index for candidate landfill sites, a weighted linear combination method was used. After combining these methods, two suitable candidate landfill sites, with areas of 2.766 km2 and 2.055 km2, respectively, were found to satisfy the scientific and environmental requirements. The area of these sites can accommodate solid waste from 2020 until 2030 based on the required area, which was 0.702 km2.

Quantum simulation of τ-anti-pseudo-Hermitian two-level systems

Different from the Hermitian case, non-Hermitian(NH) systems have novel properties and strongly relate to open and dissipative quantum systems. In this work, we investigate how to simulate τ-anti-pseudo-Hermitian systems in a Hermitian quantum device using linear combinations of unitaries and duality quantum algorithm. Specifying the τ to time-reversal(T) and parity-time-reversal(PT) operators, we construct the two NH two-level systems, design quantum circuits including three qubits, and decide the quantum gates explicitly in detail. We also calculate the success probabilities of the simulation.Experimental implementation can be expected in small quantum simulator.

Quantum confinement effects and source-to-drain tunneling in ultra-scaled double-gate silicon n-MOSFETs

By using the linear combination of bulk band （LCBB） method incorporated with the top of the barrier splitting （TBS） model, we present a comprehensive study on the quantum confinement effects and the source-to-drain tunneling in the ultra-scaled double-gate （DG） metal-oxide semiconductor field-effect transistors （MOSFETs）. A critical body thickness value of 5 nm is found, below which severe valley splittings among different X valleys for the occupied charge density and the current contributions occur in ultra-thin silicon body structures. It is also found that the tunneling current could be nearly 100% with an ultra-scaled channel length. Different from the previous simulation results, it is found that the source-to-drain tunneling could be effectively suppressed in the ultra-thin body thickness （2.0 nm and below） by the quantum confinement and the tunneling could be suppressed down to below 5% when the channel length approaches 16 nm regardless of the body thickness.