THE HAMILTONIAN SYSTEM AND COMPLETENESS OF SYMPLECTIC ORTHOGONAL SYSTEM

In this paper, a new Banach space ZH is defined, and it is proved that there is completeness of eigenfunction system (symplectic orthogonal system) of a class of Hamiltonian system in ZH space. We have also proved the following results: ZH space can be continuously imbedded to L-2[0,1] X L-2[0,1], but ZH not equal L-2[0,1] X L-1[0,1].

Model Order Reduction Methods for Discrete Systems via Discrete Pulse Orthogonal Functions

This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs,and two recurrence formulas for the expansion coefficients of the system’s state variables are obtained.Then,a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices,by which the reduced-order systems are obtained.Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system’s output variables.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed methods.

The formation of orthogonal joint systems and cuboidal blocks:New insights gained from flat-lying limestone beds in the region of Havre-Saint-Pierre(Quebec,Canada)

Vertical orthogonal joints are a common feature in shallow crustal rocks.There are several competing theories for their formation despite the ubiquity.We examined the exceptional exposures of orthogonal joints in flat-lying Ordovician limestone beds from the Havre-Saint-Pierre Region in Quebec,Canada(north shore of Saint-Lawrence River)to test conceptual models of joint formation in a natural setting.In the region,the spacing of cross-joints is consistently larger than the spacing of systematic joints by a factor of 1.5 approximately.The joint-spacing-to-bed-thickness ratios(s/t)are much larger in these beds(s/t=4.3 for systematic joints,and 6.4 for cross-joints)than those in higher strained strata along the south shore of the Saint-Lawrence River(s/t=1),highlighting the effect of tectonic strain in decreasing fracture spacing and block size.The high values of s/t indicate that cross-joint formation was unlikely caused by a switch from compression to tension once a critical s/t ratio for systematic joints was reached(as hypothesized in previous studies).We proposed a new model for the formation of orthogonal joint systems where the principal stress axes locally switch during the formation of systematic fractures.The presence of ladder-shaped orthogonal joints suggests a state of effective stress withσ_(1)^(∗)≫0>σ_(2)^(∗)>σ_(3)^(∗)and whereσ_(2)^(∗)-σ_(3)^(∗)is within the range of fracture strength variability at the time of fracture.This research provides a new mechanical model for the formation of orthogonal joint systems and cuboidal blocks.

Performance Analysis for Orthogonal Time Frequency Space Modulation Systems with Generalized Waveform

Orthogonal time-frequency space(OTFS),which exhibits beneficial advantages in high-mobility scenarios,has been considered as a promising technology in future wireless communication systems.In this paper,a universal model for OTFS systems with generalized waveform has been developed.Furthermore,the average bit error probability(ABEP)upper bounds of the optimal maximum likelihood(ML)detector are first derived for OTFS systems with generalized waveforms.Specifically,for OTFS systems with the ideal waveform,we elicit the ABEP bound by recombining the transmitted signal and the received signal.For OTFS systems with practical waveforms,a universal ABEP upper bound expression is derived using moment-generating function(MGF),which is further extended to MIMO-OTFS systems.Numerical results validate that our theoretical ABEP upper bounds are concur with the simulation performance achieved by ML detectors.

REFINEMENTS OF THE NORM OF TWO ORTHOGONAL PROJECTIONS

In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.

Dynamically enhanced Autler–Townes splitting by orthogonal XUV fields

Based on numerical solutions of the time-dependent Schr ¨odinger equation, we theoretically investigate the photoelectron spectrum of hydrogen atoms ionized by a pair of ultrashort, intense, and orthogonally polarized laser pulses with a relative time delay in a pump–probe configuration. The pump pulse resonantly excites electrons from the 1s and 2p levels,inducing Rabi oscillations. The resulting dynamically enhanced Autler–Townes(AT) splitting is observed in the photoelectron energy spectrum upon interaction with the second probe pulse. In contrast to the previous parallel-polarization scheme, the proposed orthogonal-polarization configuration enables the resolution of dynamically enhanced AT splitting over a considerably wider range of probe photon energies.

Optimization of Center of Gravity Position and Anti-Wave Plate Angle of Amphibious Unmanned Vehicle Based on Orthogonal Experimental Method

When the amphibious vehicle navigates in water,the angle of the anti-wave plate and the position of the center of gravity greatly influence the navigation characteristics.In the relevant research on reducing the navigation resistance of amphibious vehicles by adjusting the angle of the anti-wave plate,there is a lack of scientific selection of parameters and reasonable research of simulation results by using mathematical methods,and the influence of the center of gravity position on navigation characteristics is not considered at the same time.To study the influence of the combinations of the angle of the anti-wave plate and the position of the center of gravity on the resistance reduction characteristics,a numerical calculation model of the amphibious unmanned vehicle was established by using the theory of computational fluid dynamics,and the experimental data verified the correctness of the numerical model.Based on this numerical model,the navigation characteristics of the amphibious unmanned vehicle were studied when the center of gravity was located at different positions,and the orthogonal experimental design method was used to optimize the parameters of the angle of the anti-wave plate and the position of the center of gravity.The results show that through the parameter optimization analysis based on the orthogonal experimental method,the combination of the optimal angle of the anti-wave plate and the position of the center of gravity is obtained.And the numerical simulation result of resistance is consistent with the predicted optimal solution.Compared with the maximum navigational resistance,the parameter optimization reduces the navigational resistance of the amphibious unmanned vehicle by 24%.

Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

In this paper,the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are investigated.Firstly,by means of the orthogonal polynomial approximation(OPA)method,the nonlinear damping and stiffness are expanded into the linear combination of the state variable.The condition for the appearance of the vibro-impact phenomenon is to be transformed based on the calculation of themean value.Afterwards,the stochastic vibro-impact systemcan be turned into an equivalent high-dimensional deterministic non-smooth system.Two different Poincarésections are chosen to analyze the bifurcation properties and the impact numbers are identified for the periodic response.Consequently,the numerical results verify the effectiveness of the approximation method for analyzing the considered nonlinear system.Furthermore,the bifurcation properties of the system with an uncertain parameter are explored through the high-dimensional deterministic system.It can be found that the excitation frequency can induce period-doubling bifurcation and grazing bifurcation.Increasing the randomintensitymay result in a diffusion-based trajectory and the impact with the constraint plane,which induces the topological behavior of the non-smooth system to change drastically.It is also found that grazing bifurcation appears in advance with increasing of the random intensity.The stronger impulse force can result in the appearance of the diffusion phenomenon.

Optimal Design of High-Speed Partial Flow Pumps using Orthogonal Tests and Numerical Simulations

To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second stage impeller guide vanes.Moreover,the impeller blade outlet width,impeller inlet diameter,blade inclination angle,and number of blades were considered for orthogonal tests.Accordingly,nine groups of design solutions were formed,and then used as a basis for the execution of numerical simulations(CFD)aimed at obtaining the efficiency values and heads for each design solution group.The influence of impeller geometric parameters on the efficiency and head was explored,and the“weight”of each factor was obtained via a range analysis.Optimal structural parameters were finally chosen on the basis of the numerical simulation results,and the performances of the optimized model were verified accordingly(yet by means of CFD).Evidence is provided that the increase in the efficiency and head of the optimized model was 12.11%and 23.5 m,respectively,compared with those of the original model.

Turbo Message Passing Based Burst Interference Cancellation for Data Detection in Massive MIMO-OFDM Systems

This paper investigates the fundamental data detection problem with burst interference in massive multiple-input multiple-output orthogonal frequency division multiplexing(MIMO-OFDM) systems. In particular, burst interference may occur only on data symbols but not on pilot symbols, which means that interference information cannot be premeasured. To cancel the burst interference, we first revisit the uplink multi-user system and develop a matrixform system model, where the covariance pattern and the low-rank property of the interference matrix is discussed. Then, we propose a turbo message passing based burst interference cancellation(TMP-BIC) algorithm to solve the data detection problem, where the constellation information of target data is fully exploited to refine its estimate. Furthermore, in the TMP-BIC algorithm, we design one module to cope with the interference matrix by exploiting its lowrank property. Numerical results demonstrate that the proposed algorithm can effectively mitigate the adverse effects of burst interference and approach the interference-free bound.

Manipulating the electron dynamics in the non-sequential double ionization process of Ar atoms by an orthogonal two-color laser field

Electron dynamics during non-sequential double ionization(NSDI) is one of the most attractive areas of research in the field of laser–atom or laser–molecule interaction. Based on the classic two-dimensional model, we study the process of NSDI of argon atoms driven by a few-cycle orthogonal two-color laser field composed of 800 nm and 400 nm laser pulses. By changing the relative phase of the two laser pulses, a localized enhancement of NSDI yield is observed at 0.5πand 1.5π, which could be attributed to a rapid and substantial increase in the number of electrons returning to the parent ion within extremely short time intervals at these specific phases. Through the analysis of the electron–electron momentum correlations within different time windows of NSDI events and the angular distributions of emitted electrons in different channels, we observe a more pronounced electron–electron correlation phenomenon in the recollision-induced ionization(RII) channel. This is attributed to the shorter delay time in the RII channel.

Application of maximum rank distance codes in designing of STBC-OFDM system for next-generation wireless communications

Space-Time Block Coded(STBC)Orthogonal Frequency Division Multiplexing(OFDM)satisfies higher data-rate requirements while maintaining signal quality in a multipath fading channel.However,conventional STBCs,including Orthogonal STBCs(OSTBCs),Non-Orthogonal(NOSTBCs),and Quasi-Orthogonal STBCs(QOSTBCs),do not provide both maximal diversity order and unity code rate simultaneously for more than two transmit antennas.This paper targets this problem and applies Maximum Rank Distance(MRD)codes in designing STBCOFDM systems.By following the direct-matrix construction method,we can construct binary extended finite field MRD-STBCs for any number of transmitting antennas.Work uses MRD-STBCs built over Phase-Shift Keying(PSK)modulation to develop an MRD-based STBC-OFDM system.The MRD-based STBC-OFDM system sacrifices minor error performance compared to traditional OSTBC-OFDM but shows improved results against NOSTBC and QOSTBC-OFDM.It also provides 25%higher data-rates than OSTBC-OFDM in configurations that use more than two transmit antennas.The tradeoffs are minor increases in computational complexity and processing delays.

UAMP-Based Delay-Doppler Channel Estimation for OTFS Systems

Orthogonal time frequency space(OTFS)technique, which modulates data symbols in the delayDoppler(DD) domain, presents a potential solution for supporting reliable information transmission in highmobility vehicular networks. In this paper, we study the issues of DD channel estimation for OTFS in the presence of fractional Doppler. We first propose a channel estimation algorithm with both low complexity and high accuracy based on the unitary approximate message passing(UAMP), which exploits the structured sparsity of the effective DD domain channel using hidden Markov model(HMM). The empirical state evolution(SE) analysis is then leveraged to predict the performance of our proposed algorithm. To refine the hyperparameters in the proposed algorithm,we derive the update criterion for the hyperparameters through the expectation-maximization(EM) algorithm. Finally, Our simulation results demonstrate that our proposed algorithm can achieve a significant gain over various baseline schemes.

Optimization of short-circuit transition parameters of Q235B steel GMAW based on orthogonal gray relational analysis

In gas metal arc welding(GMAW)process,the short-circuit transition was the most typical transition observed in molten metal droplets.This paper used orthogonal tests to explore the coupling effect law of welding process parameters on the quality of weld forming under short-circuit transition,the design of 3 factors and 3 levels of a total of 9 groups of orthogonal tests,welding current,welding voltage,welding speed as input parameters:effective area ratio,humps,actual linear power density,aspect ratio,Vickers hardness as output paramet-ers(response targets).Using range analysis and trend charts,we can visually depict the relationship between input parameters and a single output parameter,ultimately determining the optimal process parameters that impact the single output index.Then combined with gray the-ory to transform the three response targets into a single gray relational grade(GRG)for analysis,the optimal combination of the weld mor-phology parameters as follows:welding current 100 A,welding voltage 25 V,welding speed 30 cm/min.Finally,validation experiments were conducted,and the results showed that the error between the gray relational grade and the predicted value was 2.74%.It was observed that the effective area ratio of the response target significantly improved,validating the reliability of the orthogonal gray relational method.

Optimization of Extraction Process of Fagopyri Dibotryis Rhizoma by Orthogonal Experiment

[Objectives]To optimize the water extraction process of Fagopyri Dibotryis Rhizoma.[Methods]The entropy weight method was used to determine the weight of epicatechin extraction rate and dry extract rate and calculate the comprehensive score.The water extraction process of Fagopyri Dibotryis Rhizoma was optimized by orthogonal design with the comprehensive score as the indicator and the amount of water,extraction time and extraction times as the factors.[Results]The optimum extraction process of Fagopyri Dibotryis Rhizoma was as follows:adding 10 times of water,extracting 3 times,and extracting for 60 min each time.[Conclusions]The optimized extraction process is stable and feasible,and can be used for the extraction of Fagopyri Dibotryis Rhizoma.

Polar codes based OFDM-PLC systems in the presence of impulsive noise

Power line communication(PLC)has the potential to become the preferred technique for providing broadband communication to homes and offices with advantage of eliminating the need for new wiring infrastructure and reducing the cost.But it suffers from the impulsive noise because it introduces significant time variance into the power line channel.In this paper,a polar codes based orthogonal frequency division multiplexing(OFDM)PLC system is proposed to deal with the impulsive noise and thereby improve the transmission performance.Firstly,the impulsive noise is modelled with a multi-damped sine function by analyzing the time behavior of impulse events.Then the polar codes are used to combat the impulsive noise of PLC channel,and a low complexity bit-flipping decoding method based on CRC-aided successive cancellation list(CA-SCL)decoding algorithm is proposed.Simulations evaluate the proposed decoding algorithm and the results validate the suggested polar codes based OFDM-PLC scheme which can improve the BER performance of PLC with impulsive interference.

Steering the energy sharing of electrons in nonsequential double ionization with orthogonally polarized two-color field

Using the semiclassical ensemble model,the dependence of relative amplitude for the recollision dynamics in nonsequential double ionization(NSDI)of neon atom driven by the orthogonally polarized two-color field(OTC)laser field is theoretically studied.And the dynamics in two typical collision pathways,recollision-impact-ionization(RII)and recollisionexcitation with subsequent ionization(RESI),is systematically explored.Our results reveal that the V-shaped structure in the correlated momentum distribution is mainly caused by the RII mechanism when the relative amplitude of the OTC laser field is zero,and the first ionized electrons will quickly skim through the nucleus and share few energy with the second electron.As the relative amplitude increases,the V-shaped structure gradually disappears and electrons are concentrated on the diagonal in the electron correlation spectrum,indicating that the energy sharing after electrons collision is symmetric for OTC laser fields with large relative amplitudes.Our studies show that changing the relative amplitude of the OTC laser field can efficiently control the electron–electron collisions and energy exchange efficiency in the NSDI process.

Optimization and Testing for PCR System of Rice by Orthogonal Design

[Objective] This study was to screen the economic or stable PCR system of rice and detect the generality of the selected system in different molecular markers based on PCR.[Method] With DNA extracted from rice leaves by CTAB method as the template,PCR system was optimized by L16(45)orthogonal design.[Result] Clear bands were amplified from 16 different combinations,but the amplification effects and yields had difference.The most economic and applicable system was as follows:20 ng DNA template,150 μmol/L dNT...

Optimization of SRAP-PCR System of Triticum aestivum——Based on Orthogonal Design

[Objective] The aim was to optimize the technical procedure of SRAP-PCR in Triticum aestivum L. [Method] The orthogonal design L16（45） was used to optimize SRAP-PCR amplification system of wheat Fengyou 68 on five factors （Taq polymerase,Mg2＋,DNA template,dNTPs and primer） at four levels. [Result] Effects of the five factors on SRAP-PCR reaction system were Mg2＋Taq polymerasedNTPsDNA templateprimer. Finally,an optimal SRAP-PCR system was established,that was the total 20 μl reaction system containing 2.0 μl 10×PCR Buffer,2.0 U Taq polymerase,2.0 mmol/L Mg2＋,0.2 mmol/L dNTPs,40 ng DNA template and 0.6 μmol/L primer. [Conclusion] The optimum SRAP-PCR system had provided some technical foundations to conduct SRAP genetic analysis for wheat varieties.

Optimization of RAPD-PCR Reaction System for Glycyrrhiza uralensis Based on Orthogonal Design

[Objective] The aim was to obtain the optimum RAPD-PCR reaction system for Glycyrrhiza uralensis.[Method] Orthogonal design was adopted to screen the suitable concentration of four major factors（dNTPs,primers,Taq polymerase and DNA template） in PCR reaction system.[Result] The optimal reaction system obtained by orthogonal design was 25 μl in total volume,containing 2.5 μl of 10×PCR buffer solution（include MgCl2）,2.5 μl of 10 mmol/L dNTPs,2 μl（100 ng） of DNA template,2 μl of 10 μmol/L primers,0.4 μl（5 U） of Taq polymerase;the optimum annealing temperature was 34 ℃.[Conclusion] Orthogonal design was an effective method for the optimization of RAPD-PCR reaction system for G.uralensis.