BANACH SPACES AND INEQUALITIES ASSOCIATED WITH NEW GENERALIZATION OF CESàRO MATRIX

Let the triangle matrix A^(ru)be a generalization of the Cesàro matrix and U∈{c_(0),c,l_(∞)}.In this study,we essentially deal with the space U(A^(ru))defined by the domain of A^(ru)in the space U and give the bases,and determine the Kothe-Toeplitz,generalized K?theToeplitz and bounded-duals of the space U(A^(ru)).We characterize the classes(l_(∞)(A^(ru)):l_(∞)),(l_(∞)(A^(ru)):c),(c(A^(ru)):c),and(U:V(A^(ru)))of infinite matrices,where V denotes any given sequence space.Additionally,we also present a Steinhaus type theorem.As an another result of this study,we investigate the l_(p)-norm of the matrix A^(ru)and as a result obtaining a generalized version of Hardy's inequality,and some inclusion relations.Moreover,we compute the norm of well-known operators on the matrix domain l_(p)(A^(ru)).

Error modeling of 3-RSR parallel robot based on D-H transformation matrix

By selecting any one limb of 3-RSR parallel robot as a research object, the paper establishes a position and orienta- tion relationship matrix between the moving platform and the base by means of Denavit-Hartenberg （D-H） transformation matrix. The error mapping model is derived from original error to the error of the platform by using matrix differential method. This model contains all geometric original errors of the robot. The nonlinear implicit function relation between po- sition and orientation error of the platform and the original geometric errors is simplified as a linear explicit function rela- tion. The results provide a basis for further studying error analysis and error compensation.

CRACK IDENTIFICATION IN STEPPED CANTILEVER BEAM COMBINING WAVELET ANALYSIS WITH TRANSFORM MATRIX

This paper illustrates the crack identification method combining wavelet analysis with transform matrix. Firstly, the fundamental vibration mode was applied to wavelet analysis. The crack location was found by the peaks of the wavelet coefficients. Secondly, based on the identified crack locations, a simple transform matrix method requiring only the first two tested natural frequencies was used to further identify the crack depth. The present method can be used for crack identification in a complex structure. Numerical results of crack identification of a stepped cantilever beam show that the suggested method is feasible.

CHARACTERIZATIONS OF SOME MATRIX CLASSES OF QUASI-HOMOGENEOUS OPERATORS

In this paper, we give a general characterization of a class of matrices of quasi-homogeneous operators between topological vector spaces.

Determination of Transmission Routing of OXC Nodes Based on AWG Multiplexer by Matrix Transformation

The structures of the space switching and the wavelength switching optical cross connect (OXC) nodes which are based on the arrayed waveguide grating (AWG) multiplexer are analyzed.By the matrix transformation relation between the input and output wavelengths of the AWG multiplexer, the wavelength transmission routings of the space switching and wavelength switching OXC nodes are determined.

Matrix transformations of l^q(X) to l^p(Y )

Let X and Y be Banach spaces, 0 〈 q 〈 ＋∞, i ≤ p 〈 ＋∞. In this paper, we characterize matrix transformations of lq （ X ） to lp （ Y ）.

DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B(r,s) ON SOME MADDOX'S SPACES

The domain of generalized difference matrix B（r, s） in the classical spaces L∞, e, and co was recently studied by Kirisci and Basar in [16]. The main goal of this article is to introduce the paranormed sequence spaces L∞（B,p）, c（B,p）, and co（B,p）, which are more general and comprehensive than the corresponding consequences of the matrix domain of B（r, s）, as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces L∞ （B, p）, c（B, p）, and co （B, p） are computed and the bases of the spaces c（B, p） and co （B, p） are constructed. The final section of this article is devoted to the characterization of the classes （λ（B, p）： μ） and （μ：λ（B, p））, where λ ∈ {c, co, L∞ } and μ is any given sequence space. Additionally, the characterization of some other classes which are related to the space of Mmost convergent sequences is obtained by means of a given lemma.

ALMOST CONVERGENCE AND DOUBLE SEQUENTIAL BAND MATRIX

The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80（1948）, 167-190]. Let fo（B） and f（B） be the domain of the double sequential band matrix B（r, s） in the sequence spaces f0 and f. In this article, the β- and γ-duals of the space f（B） are determined. Additionally, we give some inclusion theorems concerning with the spaces f0（B） and f（β）. Moreover, the classes （f（B） ： μ） and （μ： f（B）） of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where μ is an arbitrary sequence space.

Transformation Matrix for Combined Loads Applied to Thin-Walled Structures

This paper transforms combined loads, applied at an arbitrary point of a thin-walled open section beam, to the shear centre of the cross-section of the beam. Therein, a generalized transformation matrix for loads with respect to the shear centre is derived, this accounting for the bimoments that develop due to the way the combined loads are applied. This and the authors’ earlier paper (World Journal of Mechanics 2021, 11, 205-236) provide a full solution to the theory of thin-walled, open-section structures bearing combined loading. The earlier work identified arbitrary loading with the section’s area properties that are necessary to axial and shear stress calculations within the structure’s thin walls. In the previous paper attention is paid to the relevant axes of loading and to the transformations of loading required between axes for stress calculations arising from tension/compression, bending, torsion and shear. The derivation of the general transformation matrix applies to all types of loadings including, axial tensile and compression forces, transverse shear, longitudinal bending. One application, representing all these load cases, is given of a simple channel cantilever with an eccentrically located end load.

Research on the Applications of Probability Model and Matrix Transformation in Data Analysis and Management under the Environment of Information Time

In this paper, we research the probability theory and matrix transformation based technique to manage the data for processing and analysis. Clustering analysis research has a long history, over the decades, the importance and the cross characteristics with other research direction to get the affirmation of the people. The probability theory and linear algebra act as the powerful tool for analyzing and mining data. The experimental result illustrates the effectiveness. In the near future, we plan to conduct more theoretical analysis on the topic.

Orthogonalization of unified and extended Bézier basis and its transformation matrix

UE-Brzier （unified and extended Brzier） basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brzier-like bases, UE-Brzier basis func-tions are not orthogonal. In this paper, a group of orthogonal basis is constructed based on UE-Brzier basis. The transformation matrices between UE-Brzier basis and the proposed orthogonal basis are also solved.

STUDY ON THE COMPENSATION TECHNIQUE OF POSITIONING ERRORS FOR NC MACHINE TOOLS

Through analysis of the basic transformation of a typical body,the error transformations of the position vector and the displacement vector are employed,a general model for positioning errors of NC machine tools by using kinematics of the multi body system is discussed.By means of 8031 single chip system,intelligent error compensation controller has been developed.The results of experiments on XH714 machining center show that the positioning accuracy is enhanced effectively by more than 50%.

DYNAMIC MODELING OF METAMORPHIC MECHANISM

The concept of metamorphic mechanism is put forward according to the changeof configurations from one state to another. Different configurations of metamorphic mechanism aredescribed through the method of Huston lower body arrays. Kinematics analyses for metamorphicmechanism with generalized topological structure, including the velocity, angular velocity,acceleration and angular acceleration, are given. Dynamic equations for an arbitrary configuration,including close-loop constraints, are formed by using Kane's equations. For an arbitrary metamorphicmechanism, the transformation matrix of generalized speeds between configuration zeta and zeta+1 isobtained for the first time. Furthermore, configuration-complete dynamic modeling of metamorphicmechanism including all configurations is completely established.

Fatigue Assessment Method for Composite Wind Turbine Blade

Fatigue strength assessment of a horizontal axis wind turbine(HAWT)composite blade is considered.Fatigue load cases are identified,and loads are calculated by the GH Bladed software which is specified at the IEC61400 international specification and GL(Germanisher Lloyd)regulations for the wind energy conversion system.Stress analysis is performed with a 3-D finite element method(FEM).Considering Saint-Venant′s principle,a uniform cross section FEM model is built at each critical zone.Stress transformation matrixes(STM)are set up by applied six unit load components on the FEM model separately.STM can be used to convert the external load into stresses in the linear elastic range.The main material of composite wind turbine blade is fiber reinforced plastics(FRP).In order to evaluate the degree of fatigue damage of FRP,the stresses of fiber direction are extracted and the well-known strength criterion-Puck theory is used.The total fatigue damage of each laminate on the critical point is counted by the rain-flow counting method and Miner′s damage law based on general S-N curves.Several sections of a 45.3mblade of a 2 MW wind turbine are studied using the fatigue evaluation method.The performance of this method is compared with far more costly business software FOCUS.The results show that the fatigue damage of multi-axis FRP can be assessed conveniently by the FEM-STM method.And the proposed method gives a reliable and efficient method to analyze the fatigue damage of slender composite structure with variable cross-sections.

Adaptive transmit beamspace optimization design based on RD-log-FDA radar

Because of the range-angle dependency in random log frequency diverse array(RD-log-FDA) radar, a method for designing beamspace transformation matrix in angle and range based on the receive signal has been proposed.It is demonstrated that the designed beamspace transformation matrix basically meets the requirements of beam gain.However, there are some problems in the transformation matrix designed, such as unstable beam gain and high sidelobe.Hence, we propose an optimization method by adjusting array element spacing and random number in frequency offset to get the optimum beam gain.Therefore, particle swarm optimization(PSO) is used to find the optimal solution.The beam gain comparison before and after the optimization is obtained by simulation, and the results show that the optimized array after beamspace preprocessing has more stable beam gain, lower sidelobe, and higher resolution in parameter estimation.In conclusion, the RD-log-FDA is capable of forming desired beam gain in angle and distance through beamspace preprocessing, and suppressing interference signals in other areas.

Surface coal mining impacts on land use change and ecological service value:a case study in Shengli coalfield,Inner Mongolia

Coal plays a crucial role in global economic development and remains the most common and widely distributed fossil fuel worldwide.As the world's largest developing country,China's mining and utilization of coal resources have contributed signifcantly to the country’s rapid economic growth.Inner Mongolia is an ecologically fragile arid and semi-arid area of China.The exploitation of opencast mining has seriously hindered the sustainable use of regional land and the residents'well-being.Using ENVI-based remote sensing images from 2000,2005,2010,2015,and 2020,this study employed a random forest algorithm to divide land utilization types into construction land,vegetation,cultivated land,bare land,and water areas and analyzed the characteristics of land use and ecosystem service value changes over the past 20 years.The results were as follows:(1)Construction land in the mining area changed minimally from 2000 to 2020;vegetation and water bodies showed a decreasing trend,whereas bare and cultivated lands showed an increasing trend.Bare land exhibited the largest change in area proportion and water bodies the smallest.(2)The total ecosystem service value of the mining area declined from 10.939 to 9.527 billion Yuan.Vegetation ecosystem service value was the highest,followed by cultivated land and water,with the bare land ecosystem service value the lowest.(3)On a spatial scale,the total ecosystem service value of the Shengli mining area decreased year by year,indicating that land use changes in the mining area do have an impact on ecosystem service value.

Research on Open-circuit Fault Tolerant Control of Six-phase Permanent Magnet Synchronous Machine Based on Fifth Harmonic Current Injection

This paper proposes a novel control approach for fault-tolerant control of dual three-phase permanent magnet synchronous motor(PMSM) under one-phase open-circuit fault.A modified six-phase static coordinate transformation matrix and an extended rotating coordinate transformation matrix are investigated considering the influence of the fifth harmonic space on fault-tolerant control. These mathematical models are further analyzed in the fundamental space and the fifth harmonic space after the fault and to eliminate the coupling between the d-q axis voltage equation in the fundamental wave space and the d-q axis voltage equation in the fifth harmonic space, a secondary rotation coordinate transformation matrix is proposed. To achieve the purpose of reducing torque ripple, the fault-tolerant control method proposed in this paper not only takes the minimum copper loss as the constraint condition, but also injects the fifth harmonic current. The experimental result of current and torque is used to verify the accuracy of fault-tolerant control.

ON SPECTRAL PROPERTIES OF A NEW OPERATOR OVER SEQUENCE SPACES c AND c_0

In this work, we classify and calculate spectra such as point spectrum, continuous spectrum and residual spectrum over sequences spaces？∞, c and c0 according to a new matrix operator W which is obtained by matrix product.

PAPR reduction in mobile WiMAX:A new ZCMT precoded random interleaved OFDMA system

Mobile WiMAX(worldwide interoperability for microwave access) air interface adopts orthogonal frequency division multiple access(OFDMA) as multiple access technique for its uplink(UL) and downlink(DL) to improve the multipath performance.All OFDMA based networks,like mobile WiMAX,experience the problem of high peak-to-average power ratio(PAPR).The high PAPR increases the complexity of analog-to-digital(A/D) and digital-to-analog(D/A) convertors,and also reduces the efficiency of RF high-power-amplifier(HPA).In this work,a new zadoff-chu matrix transform(ZCMT) precoding based random interleaved orthogonal frequency division multiple access(OFDMA) system was proposed for PAPR reduction in mobile WiMAX system.The system is based on precoding the constellation symbols with the ZCMT precoder before subcarrier mapping.The PAPR of proposed system is analyzed with the root-raised-cosine(RRC) pulse shaping to keep out of band radiation low and meet the transmission spectrum mask requirement.Simulation results show that the proposed system has better PAPR gain than the hadamard transform(WHT) precoded random interleaved OFDMA systems and the conventional random interleaved OFDMA systems.Symbol-error-rate(SER) performance of the system is also better than the conventional random interleaved OFDMA systems and the random interleaved OFDMA systems with WHT.The good improvement in PAPR significantly reduces the cost and the complexity of the transmitter.

CHARACTERIZATIONS OF COMPACT OPERATORS ON SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （ m ） ） and e r ∞ （△ （ m ） ） and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.