Lacunary Interpolation by Fractal Splines with Variable Scaling Parameters

For a prescribed set of lacunary data{(x_(ν),f_(ν),f^(″)_(ν)):ν=0,1,...,N}with equally spaced knot sequence in the unit interval,we show the existence of a fam-ily of fractal splines S^(α)_(b)∈C 3[0,1]satisfying S^(α)_(b)(x_(ν))=f_(ν),(S^(α)_(b))^(2)(x_(ν))=f^(″)_(ν)forν=0,1,...,N and suitable boundary conditions.To this end,the unique quintic spline introduced by A.Meir and A.Sharma[SIAM J.Numer.Anal.10(3)1973,pp.433-442]is generalized by using fractal functions with variable scaling pa-rameters.The presence of scaling parameters that add extra“degrees of freedom”,self-referentiality of the interpolant,and“fractality”of the third derivative of the in-terpolant are additional features in the fractal version,which may be advantageous in applications.If the lacunary data is generated from a functionΦsatisfying certain smoothness condition,then for suitable choices of scaling factors,the corresponding fractal spline S^(α)_(b)satisfies||Φ^(r)−(S^(α)_(b))(r)||∞→0 for 0≤r≤3,as the number of partition points increases.

Considering Process Nonlinearity in Dual-Point Composition Control of a High-Purity Ideal Heat Integrated Distillation Column

Dual-point composition control for a high-purity ideal heat integrated distillation column (HIDiC) is addressed in this work. Three measures are suggested and combined for overcoming process inherent nonlinearities:(1) variable scaling; (2) multi-model representation of process dynamics and (3) feedforward compensation. These strategies can offer the developed control systems with several distinct advantages: (1) capability of dealing with severe disturbances; (2) tight tuning of controller parameters and (3) high robustness with respect to variation of operating conditions. Simulation results demonstrate the effectiveness of the proposed methodology.

GLOBAL CONVERGENCE OF A CLASS OF OPTIMALLY CONDITIONED SSVM METHODS

This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.

On the Variability of Charleston South Carolina Winds, Atmospheric Temperatures, Water Levels, Waves and Precipitation

Atmospheric winds, air temperatures, water levels, precipitation and oceanic waves in the Charleston South Carolina (SC) coastal zone are evaluated for their intrinsic, internal variability over temporal scales ranging from hours to multi-decades. The purpose of this study was to bring together a plethora of atmospheric and coastal ocean state variable data in a specific locale, to assess temporal variabilities and possible relationships between variables. The questions addressed relate to the concepts of weather and climate. Data comprise the basis of this study. The overall distributions of atmospheric and coastal oceanic state variable variability, including wind speed, direction and kinematic distributions and state variable amplitudes over a variety of time scales are assessed. Annual variability is shown to be highly variable from year to year, making arithmetic means mathematically tractable but physically meaningless. Employing empirical and statistical methodologies, data analyses indicate the same number of intrinsic, internal modes of temporal variability in atmospheric temperatures, coastal wind and coastal water level time series, ranging from hours to days to weeks to seasons, sub-seasons, annual, multi-year, decades, and centennial time scales. This finding demonstrates that the atmosphere and coastal ocean in a southeastern U.S. coastal city are characterized by a set of similar frequency and amplitude modulated phenomena. Kinematic hodograph descriptors of atmospheric winds reveal coherent rotating and rectilinear particle motions. A mathematical statistics-based wind to wave-to-wave algorithm is developed and applied to offshore marine buoy data to create an hour-by-hour forecast capability from 1 to 24 hours;with confidence levels put forward. This affects a different approach to the conventional deterministic model forecasting of waves.

Micro-Newton scale variable thrust control technique and its noise problem for drag-free satellite platforms:a review

High-precision detection in fundamental space physics,such as space gravitational wave detection,high-precision earth gravity field measurement,and reference frame drag effect measurement,is the key to achieving important breakthroughs in the scientific study of fundamental space physics.Acquiring high-precision measurements requires high-performance satellite platforms to achieve“drag-free control”in a near“pure gravity”flight environment.The critical technology for drag-free control is variable thrust control at the micro-Newton scale.Thrust noise is the most important technical indicator for achieving drag-free flight.However,there is no literature about the current status and future prospects of variable thrust control based on thrust noise.Therefore,the micro-Newton variable thrust control technology and the thrust noise of the drag-free satellite platform are reviewed in this work.Firstly,the research status of micro-Newton scale variable thrust control technology and its applications to drag-free satellite platforms are introduced.Then,the noise problem is analyzed in detail and its solution is theoretically investigated in three aspects:“cross-basin flow problem,”“control problem,”and“system instability and multiple-coupled problem.”Finally,a systematic overview is presented and the corresponding suggested directions of research are discussed.This work provides detailed understanding and support for realizing low-noise variable thrust control in the next generation of drag-free satellites.

An FPGA-based LDPC decoder with optimized scale factor of NMS decoding algorithm

Considering that the hardware implementation of the normalized minimum sum(NMS)decoding algorithm for low-density parity-check(LDPC)code is difficult due to the uncertainty of scale factor,an NMS decoding algorithm with variable scale factor is proposed for the near-earth space LDPC codes(8177,7154)in the consultative committee for space data systems(CCSDS)standard.The shift characteristics of field programmable gate array(FPGA)is used to optimize the quantization data of check nodes,and finally the function of LDPC decoder is realized.The simulation and experimental results show that the designed FPGA-based LDPC decoder adopts the scaling factor in the NMS decoding algorithm to improve the decoding performance,simplify the hardware structure,accelerate the convergence speed and improve the error correction ability.

Impact of polar lows on synoptic scale variability of Atlantic inflow in the Fram Strait

The Atlantic inflow in the Fram Strait（78°50′N） has synoptic scale variability based on an array of moorings over the period of 1998–2010. The synoptic scale variability of Atlantic inflow, whose significant cycle is 3–16 d, occurs mainly in winter and spring（from January to April） and is related with polar lows in the Barents Sea. On the synoptic scale, the enhancement（weakening） of Atlantic inflow in the Fram Strait is accompanied by less（more）polar lows in the Barents Sea. Wind stress curl induced by polar lows in the Barents Sea causes Ekman-transport,leads to decrease of sea surface height in the Barents Sea, due to geostrophic adjustment, further induces a cyclonic circulation anomaly around the Barents Sea, and causes the weakening of the Atlantic inflow in the Fram Strait. Our results highlight the importance of polar lows in forcing the Atlantic inflow in the Fram Strait and can help us to further understand the effect of Atlantic warm water on the change of the Arctic Ocean.

Seasonal Characteristics and Interannual Variability of Monthly Scale Low-Frequency Oscillation in a Low-Order Global Spectral Model

Analysis is done of five-year low-pass filtered data by a five-layer low-order global spectral model, indicating that although any non-seasonal external forcing is not considered in the model atmosphere,monthly-scale anomaly takes place which is of remarkable seasonality and interannual variability.Analysis also shows that for the same seasonal external forcing the model atmosphere can exhibit two climatic states,similar in the departure pattern but opposite in sign, indicating that the anomaly is but the manifestation of the adverse states, which supports the theory of multi-equilibria proposed by Charney and Devore(1979) once again.Finally, the source for the low-frequency oscillation of the global atmosphere is found to be the convective heat source / sink inside the tropical atmosphere as discussed before in our study.Therefore, the key approach to the exploration of atmospheric steady low-frequency oscillation and the associated climatic effect lies in the examination of the distribution of convective heat sources / sinks and the variation in the tropical atmosphere.

Data Envelopment Analysis in Estimation of Technical Efficiency Change of Regional Agriculture Production EU, 1989-2007

Assessment of production efficiency in economic activity is a major issue focused on by economists since the middle of the 20th century. One of the methods suitable in this respect is data envelopment analysis （DEA） facilitating the estimation of technical efficiency based on results obtained by a specified set of producers. Dynamics of changes in efficiency in agricultural production may be assessed on the basis of time series of several years. In the study, one of the variants of DEA was applied to economic results recorded in the years 1989-2007 by average farms representing selected regions of the European Union. The resulting individual dynamics of technical efficiency changes were divided into four homogeneous groups to facilitate identification of differences in production technology. These differences were then explained by classical analysis of basic factors use in agricultural production.

Variability scaling and capacity planning in Covid-19 pandemic

Capacity planning is a very important global challenge in the face of Covid-19 pandemic.In order to hedge against the fluctuations in the random demand and to take advantage of risk pooling effect,one needs to have a good understanding of the variabilities in the demand of resources.However,Covid-19 predictive models that are widely used in capacity planning typically often predict the mean values of the demands(often through the predictions of the mean values of the confirmed cases and deaths)in both the temporal and spatial dimensions.They seldom provide trustworthy prediction or estimation of demand variabilities,and therefore,are insufficient for proper capacity planning.Motivated by the literature on variability scaling in the areas of physics and biology,we discovered that in the Covid-19 pandemic,both the confirmed cases and deaths exhibit a common variability scaling law between the average of the demand μ and its standard deviationσ,that is,σ ∝ μ^(β),where the scaling parameterμis typically in the range of 0.65 to 1,and the scaling law exists in both the temporal and spatial dimensions.Based on the mechanism of contagious diseases,we further build a stylized network model to explain the variability scaling phenomena.We finally provide simple models that may be used for capacity planning in both temporal and spatial dimensions,with only the predicted mean demand values from typical Covid-19 predictive models and the standard deviations of the demands derived from the variability scaling law.

Fracture characterization and permeability prediction by pore scale variables extracted from X-ray CT images of porous geomaterials

Pore scale variables(e.g.,porosity,grain size)are important indexes to predict the hydraulic properties of porous geomaterials.X-ray images from ten types of intact sandstones and another type of sandstone samples subjected to triaxial compression are used to investigate the permeability and fracture characteristics.A novel double threshold segmentation algorithm is proposed to segment cracks,pores and grains,and pore scale variables are defined and extracted from these X-ray CT images to study the geometric characteristics of microstructures of porous geomaterials.Moreover,novel relations among these pore scale variables for permeability prediction are established,and the evolution process of cracks is investigated.The results indicate that the porescale permeability is prominently improved by cracks.In addition,excellent agreements are found between the measured and the estimated pore scale variables and permeability.The established correlations can be employed to effectively identify the hydraulic properties of porous geomaterials.

Magnetically stabilized bed dust filters—Analysis through variable length scale approach

Magnetically stabilized beds are packed beds subjected to fluid-driven deformation and controlled by magnetically induced interparticle forces. This paper deals with magnetically stabilized beds as deformable porous media and describes their application in dust filtration. The Richardson-Zaki scaling law, U/Ut = ε^n describes the field controlled bed expansion via the exponent n, that yields a porosity-dependent flow length scale dc = dpε^n. The paper addresses two issues： （i） deformation characteristics by assuming homogeneous bed expansion and a definition of bed variable flow length scale; （ii） dust filtration characteristics such as filter coefficient, specific deposit and filtration efficiency expressed in terms of the variable flow length scale and illustrated by experimental data.

THE OPTICAL VARIABILITY ON A SHORT TIME SCALE OF 6 BL LAC OBJECTS

Ⅰ. INTRODUCTION BL Lac objects were the prototype of a new class of astrophysically interested objects with these peculiar characteristies: (ⅰ) Absence of emission lines in the core source;(ⅱ) rapid variability at radio, IR and visual wavelengths; (ⅲ) non-thermal