Generation of non-integer high-order harmonics and significant enhancement of harmonic intensity

High-order harmonics from helium atom in the orthogonally two-color(OTC) laser field are investigated by solving the two-dimensional time-dependent Schrodinger equation.Non-integer high-order harmonics are obtained in some ratio of frequencies of two components.Pure odd and even harmonics from atoms could be separated in two components by adjusting the ratio of frequencies in OTC scheme,and the resolution of harmonics is improved at the same time.The physical mechanism is explained by the periodicity of dipole.With the same intensity of the incident laser,the intensity of the high-order harmonics from the OTC field scheme is improved by three orders of magnitude compared to the monochromatic laser field scheme.A theoretical scheme is provided for experimentally achieving improving energy resolution and separation of pure odd and even harmonics in atoms.Also,we provide a means for improving harmonic intensity.

Non-integer Order Control Scheme for Pressurized Water Reactor Core Power

Tracking load changes in a pressurized water reactor(PWR)with the help of an efficient core power control scheme in a nuclear power station is very important.The reason is that it is challenging to maintain a stable core power according to the reference value within an acceptable tolerance for the safety of PWR.To overcome the uncertainties,a non-integer-based fractional order control method is demonstrated to control the core power of PWR.The available dynamic model of the reactor core is used in this analysis.Core power is controlled using a modified state feedback approach with a non-integer integral scheme through two different approximations,CRONE(Commande Robuste d’Ordre Non Entier,meaning Non-integer orderRobust Control)and FOMCON(non-integer order modeling and control).Simulation results are produced using MATLAB■program.Both non-integer results are compared with an integer order PI(Proportional Integral)algorithm to justify the effectiveness of the proposed scheme.Sate-spacemodel Core power control Non-integer control Pressurized water reactor PI controller CRONE FOMCON.

Polynomial Functions Composed of Terms with Non-Integer Powers

Polynomial functions containing terms with non-integer powers are studied to disclose possible approaches for obtaining their roots as well as employing them for curve-fitting purposes. Several special cases representing equations from different categories are investigated for their roots. Curve-fitting applications to physically meaningful data by the use of fractional functions are worked out in detail. Relevance of this rarely worked subject to solutions of fractional differential equations is pointed out and existing potential in related future work is emphasized.

Analysis of Logistic Model with Constant Harvesting in a View of Non-Integer Derivative

The conformable fractional derivative method has been utilized in order to examine the logistic model with constant harvesting.Such method introduces a generalization to the classical analysis of Logistic model,and hence the features of the Logistic model,such as subcritical and supercritical harvesting,have been investigated in a view of fractional calculus.The positive auxiliary parameter,σ,with dimension of time is implemented to maintain the dimensionality of the system.The significant information of such parameter to the population has been discussed.The population expressions,obtained by conformable description,are compared with the expressions of the classical derivative.This comparison shows that the non-integer expressions are in a parallel line with that of the classical one.

Improved rate-distortion optimized video coding using non-integer bit estimation and multiple Lambda search

Many modern video encoders use the Lagrangian rate-distortion optimization （RDO） algorithm for mode deci- sions during the compression procedure. For each encoding stage, this approach involves minimizing a cost, which is a function of rate, distortion and a multiplier called Lambda. This paper proposes to improve the RDO process by applying two modifications. The first modification is to increase the ac- curacy of rate estimation, which is achieved by computing a non-integer number of bits for arithmetic coding of the syntax elements. This leads to a more accurate cost computation and therefore a better mode decision. The second modification is to search and adjust the value of Lambda based on the char- acteristics of each coding stage. For the encoder used, this paper proposes to search multiple values of Lambda for the intra-4x4 mode decision. Moreover, a simple shift in Lambda value is proposed for motion estimation. Each of these modi- fications offers a certain gain in RDO performance, and, when all are combined, an average bit-rate saving of up to 7.0% can be achieved for the H.264/AVC codec while the same concept is applicable to the H.265/HEVC codec as well. The extra added complexity is contained to a certain level, and is also adjustable according to the processing resources available.

Univoque graphs for non-integer base expansions

Unique expansions in non-integer bases have been investigated in many papers during the last thirty years.They are often conveniently generated by labeled directed graphs.We give a precise description of the set of sequences generated by these graphs.This provides a geometric explanation of many former abstract results in this domain.Our results are illustrated by many examples.

One Step Forward, Two Steps Back: Biconvergence of Washed Harmonic Series

We examine variations of the harmonic series by grouping terms into “washings” that alternate sign with the number of terms in a washing growing exponentially with respect to a fixed base. The bases x = 1 and x = ∞ correspond to the alternating harmonic series and the usual harmonic series;we first consider other positive integral bases and further we consider positive real number bases with a unique way to make sense of adding a non-integral number of terms together. In both cases, we prove a remarkable result regarding the difference between the upper and lower convergent values of the series, and give some analysis of this behavior.

The Compound Indexing of Human Self-Similar Behavioural Patterns

Applications of a constitutive framework providing compound complexity analysis and indexing of coarse-grained self-similar time series representing behavioural data are presented. A notion of behavioural entropy and hysteresis is introduced as two different forms of compound measures. These measures provide clinically applicable complexity analysis of behavioural patterns yielding scalar characterisation of time-varying behaviours registered over an extended period of time. The behavioural data are obtained using body attached sensors providing non-invasive readings of heart rate, skin blood perfusion, blood oxygenation, skin temperature, movement and steps frequency. The results using compound measures of behavioural patterns of fifteen healthy individuals are presented. The application of the compound measures is shown to correlate with complexity analysis. The correlation is demonstrated using two healthy subjects compared against a control group. This indicates a possibility to use these measures in place of fractional dimensions to provide a finer characterisation of behavioural patterns observed using sensory data acquired over a long period of time.

A novel co-catalyzed system between persulfate and chlorite by sonolysis for removing triphenylmethane derivative

Triphenylmethane(tpm) derivatives(e.g. tpm CV) have threatened the safety of the aquatic environment due to the potential toxicity and carcinogenicity. In this study, the novel ultrasonic/persulfate/chlorite(US/S_(2)O_(8)^(2-)/ClO_(2)^(-)) oxidation process was developed for the effective removal of tpm CV in wastewater. The apparent non-integer kinetics( n around 1.20) of tpm CV degradation under different factors( R^(2)_(Adj) > 0.990) were investigated, respectively. Inhibiting effects of anions were greater than those of cations(except Fe(Ⅱ/Ⅲ)). The adding of micromolecule organic acids could regulate degradation towards positive direction. The double response surface methodology(RSM) was designed to optimize tpm CV removal process, and the acoustic-piezoelectric interaction was simulated to determine the propagation process of acoustic wave in the reactor. The possible degradation pathway was explored to mainly include carbonylation, carboxylation, and demethylation. The estimated effectivemean temperature at the bubble-water interface was calculated from 721 to 566 K after introducing the ClO_(2)^(-), however, the adsorption or partitioning capacity of tpm CV in the reactive zone was widened from 0.0218 to 0.0982. The proposed co-catalysis of US/S_(2)O_(8)^(2-)/ClO_(2)^(-)was based on the determined active species mainly including ClO_(2), SO_(4)·^(-), and ·OH. Compared with other US-based processes, the operating cost(3.97 $/m^(3)) of US/S_(2)O_(8)^(2-)/ClO_(2)^(-)with the EE/O value(16.8 k Wh/m^(3)) was relatively reduced.

Analysis and Design of an Improved Servo System for Rubidium Atomic Frequency Standard

In this paper, we analyze and design a new type of servo system with noninteger voltage controlled crystal oscillator （VCXO） for rubidium atomic frequency standard （RAFS）, which does not require fractional frequency synthesizer. By the estab- lishment of the loop equations with noises and drifts, we prove that all the components of the loop can affect its performance in- dex, and in which, RAFS long-term frequency stability is mainly determined by frequency multiplier, quantum system, and servo amplifier; the short-term one is mostly decided by VCXO. Owing to the elimination of the frequency synthesizer and its additive mixing unit, we can reduce phase noise and stray of the servo sys- tem, and it is favorable for miniaturizing the RAFS system. In addition, we adopt some targeted optimization measures to im- prove the frequency stability index. The good short-term fre- quency stability index is also validated by the test results.