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 ）.

The Dual Spaces of Sets of Difference Sequences of Order m and Matrix Transformations

Let p = （pk）k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = （xk）k=0^∞ is any sequence of complex numbers we write Δ（m）x for the sequence of the m th order differences of x and Δu^（m）X = {x=（x）k=0^∞ uΔ（m）x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δμ^（m）X for X=co（p）,c（p）,l∞（p） and characterize some matrix transformations between these spaces Δ^（m）X.

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)).

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.

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.

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.

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.

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.

Configuration Analysis of Metamorphic Mechanisms Based on Extended Adjacency Matrix Operations

The adjacency matrix operations,which connect with configuration transformation correspondingly,can be used for analysis of configuration transformation of metamorphic mechanisms and the corresponding algorithm can easily be simulated by computer.But the adjacency matrix based on monochrome topological graph is not suitable for the topological representation of mechanisms with multiple joints.The method of adjacency matrix operations has its own limitations for analysis of configuration transformation of metamorphic mechanisms because it can only be used in the topological representation of mechanisms with single joints.In order to overcome the drawback of the adjacency matrix,a kind of new matrix named as extended adjacency matrix is proposed to express topological structures of all mechanisms.The extended adjacency matrix is not only suitable for the topological representation of mechanisms with single joints,but also can be used in that of mechanisms with multiple joints.On this basis,a method of matrix operations based on the extended adjacency matrix is proposed to analyze the configuration transformation of metamorphic mechanisms.The method is not only suitable for configuration analysis of metamorphic mechanisms with single joints as well as metamorphic mechanisms with multiple joints.The method is evaluated by calculating two examples representing metamorphic mechanisms with single joint and multiple joints respectively.It can be concluded that the method is effective and correct for analysis of configuration transformation of all metamorphic mechanisms.The proposed method is simple and easy to be achieved by computer programming.It provides a basis for structural synthesis of all metamorphic mechanisms.

A Geometric View on Inner Transformation between the Variables of a Linear Regression Model

In the teaching and researching of linear regression analysis, it is interesting and enlightening to explore how the dependent variable vector can be inner-transformed into regression coefficient estimator vector from a visible geometrical view. As an example, the roadmap of such inner transformation is presented based on a simple multiple linear regression model in this work. By applying the matrix algorithms like singular value decomposition (SVD) and Moore-Penrose generalized matrix inverse, the dependent variable vector lands into the right space of the independent variable matrix and is metamorphosed into regression coefficient estimator vector through the three-step of inner transformation. This work explores the geometrical relationship between the dependent variable vector and regression coefficient estimator vector as well as presents a new approach for vector rotating.

BSTUDY ON Ni25Ti50Cu25 SHAPE MEMORY PARTICLE/Al MATRIX COMPOSITE

Ni_(25)Ti_(50)Cu_(25) shape memory particle/Al matrix composite was prepared by hot pressing and further extrusion.The Ni_(25)Ti_(50)Cu_(25) particles embeded in Al matrix still keep B19 and B19 structure,and have a good thermal-elastic martensitic transition with 6K thermal hysteresis,the phase transition temperatures remaining constant during cycling. The scratching force of Ni_(25)Ti_(50)Cu_(25) particle is two times that of Al matrix,When the scratching force is larger than 4.2N, the Ni_(25)Ti_(50)Cu_(25) particle is separated from Al matrix.

A GROUP REPRESENTATION OF CANONICAL TRANSFORMATION

The mutual relationships between four generating functions F-1(q, Q), F-2(q, P), F-3(p, P), F-4(p, Q) and four kinds of canonical variables q, p, Q, P concerned in Hamilton's canonical transformations, can be got with linear transformations from seven basic formulae. All of them are Legendre's transformation, which are implemented by 32 matrices of 8 x 8 which are homomorphic to D-4 point group of 8 elements with correspondence of 4:1. Transformations and relationships of four state functions G(P, T), H(P, S), U(V, S), F(V, T) and four variables P, V, T, S in thermodynamics, are just the same Lagendre's transformations with the relationships of canonical transformations. The state functions of thermodynamics are summarily founded on experimental results of macroscope measurements, and Hamilton's canonical transformations are theoretical generalization of classical mechanics. Both group represents are the same, and it is to say, their mathematical frames are the same. This generality indicates the thermodynamical transformation is an example of one-dimensional Hamilton's canonical transformation.

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.

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.

SOME TOPOLOGICAL AND GEOMETRICAL PROPERTIES OF THE SEQUENCE SPACE e^r (u, p)

In this paper, we introduce the sequence space e^r（u,p） and investigate its some topological and geometrical properties such as basis, α-,β-, γ- duals and the uniform Opial property.

On a New Summability Result for Operator Matrices

For matrices of quasi-homogeneous operators we establish a summability result which is a useful complement of a recent summability result.

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.