Narrow Results

To solve the problem of a mining triaxial heavy-duty dump’s putting rod ruptures prematurely, When the dump in the bending and twisting conditions, the push rod’s static strength and stiffness was analysed by Hypermesh, and get the modals shapes and modal frequencies and generated a frame MNF file (modal neutral file) from the Ansys, established the rigid - flexible coupling model of the frame in ADAMS, get a load time history of fully loaded front and rear suspension. According to material fatigue properties’ S-N curve of the frame, using of MSC. Fatigue software the frame’s life was analyzed. The result showed the position of minimum fatigue life of frame is consistent to the position of abnormal rupture of putting rod in actual use; in order to improve the design of heavy-duty dump truck provides a reference.

Due to ${\mathrm{ℝ}}_{+}$ not being a group under addition, $L^2({\mathrm{ℝ}}_{+})$ admits no traditional wavelet or Gabor frame. This paper addresses a class of dilation-and-modulation (${ℳ}{𝒟}$) Parseval frames for $L^2({\mathrm{ℝ}}_{+})$. We present a parametric expression of all ${ℳ}{𝒟}$-Parseval frames (frame sequences) and ${ℳ}{𝒟}$-orthonormal bases (systems); and develop an approach to obtain all ${ℳ}{𝒟}$-Parseval frames (frame sequences) and ${ℳ}{𝒟}$-orthonormal bases (systems) starting with one ${ℳ}{𝒟}$-Parseval frame for $L^2({\mathrm{ℝ}}_{+})$.

The theory of Gabor frames has been extensively investigated. This paper addresses partial Gabor systems. We introduce the concepts of partial Gabor system, frame and dual frame. We present some conditions for a partial Gabor system to be a partial Gabor frame, and using these conditions, we characterize partial dual frames. We also give some examples. It is noteworthy that the density theorem does not hold for general partial Gabor systems.

Due to the significance of aquatic robotics and marine engineering, the underwater video enhancement has gained huge attention. Thus, a video enhancement method, namely Manta Ray Foraging Lion Optimization-based fusion Convolutional Neural Network (MRFLO-based fusion CNN) algorithm is developed in this research for enhancing the quality of the underwater videos. The MRFLO is developed by merging the Lion Optimization Algorithm (LOA) and Manta Ray Foraging Optimization (MRFO). The blur in the input video frame is detected and estimated through the Laplacian’s variance method. The fusion CNN classifier is used for deblurring the frame by combining both the input frame and blur matrix. The fusion CNN classifier is tuned by the developed MRFLO algorithm. The pixel of the deblurred frame is enhanced using the Type II Fuzzy system and Cuckoo Search optimization algorithm filter (T2FCS filter). The developed MRFLO-based fusion CNN algorithm uses the metrics, Underwater Image Quality Measure (UIQM), Underwater Color Image Quality Evaluation (UCIQE), Structural Similarity Index Measure (SSIM), Mean Square Error (MSE), and Peak Signal-to-Noise Ratio (PSNR) for the evaluation by varying the blur intensity. The proposed MRFLO-based fusion CNN algorithm acquired a PSNR of 38.9118, SSIM of 0.9593, MSE of 3.2214, UIQM of 3.0041 and UCIQE of 0.7881.

Motivated by frame-vector for a unitary system, we study a class of cyclic operators on a separable Hilbert space which is called frame-cyclic operators. The orbit of such an operator on some vector, namely frame-cyclic vector, is a frame. Some properties of these operators on finite- and infinite-dimensional Hilbert spaces and their relations with cyclic and hypercyclic operators are established. A lower and upper bound for the norm of a self-adjoint frame-cyclic operator is obtained. Also, construction of the set of frame-cyclic vectors is considered. Finally, we deal with Kato’s approximation of frame-cyclic operators and discuss their frame-cyclic properties.

Conventional beam elements ignoring distortion may overestimate the lateral resistance of frames and curved beams made of monosymmetric I-sections. This paper introduces two new distortional modes represented by mechanical couples relative to twisting and shearing of the two flanges that are opposite in directions but unequal in magnitudes. A straight beam element with nine degrees of freedom (DOFs) per node, including the conventional three translations, three rotations, warping and the new two distortions, is newly derived. This allows all the DOFs of the connected elements at a common joint to be easily transformed to the global coordinates for stiffness assembly. As a result, the warping–distortion compatibility problem that occurs in frames and curved beams is resolved. In the numerical examples, the results produced by the present beam element is demonstrated to agree excellently with the shell-element solutions for the lateral-distortional deformation of the angled frame and curved beam. It is observed that the cross-sectional distortion effect becomes extremely significant for angled frames of short unbraced length and for curved beams of high curvature.

The concept of Hilbert–Schmidt frame (HS-frame) was first introduced by Sadeghi and Arefijamaal in 2012. It is more general than $g$-frames, and thus, covers many generalizations of frames. This paper addresses the theory of HS-frames. We present a parametric and algebraic formula for all duals of an arbitrarily given HS-frame; prove that the canonical HS-dual induces a minimal-norm expression of the elements in Hilbert spaces; characterize when an HS-frame is an HS-Riesz basis, and when an HS-Bessel sequence is an HS-Riesz sequence (HS-Riesz basis) in terms of Gram matrices.

Hilbert–Schmidt frame (HS-frame) has interested some mathematicians in recent years, which is more general than g-frame. This paper addresses near Riesz and Besselian properties of HS-operator sequences. We characterize HS-frame and Riesz properties of g-operator sequences using their DSI-sequences; prove that an HS-Riesz basis is an exact HS-frame while the converse is not true, and an arbitrary HS-Riesz frame contains an HS-Riesz basis; and present the connection among near HS-Riesz property, Besselian property and the kernel space dimension of synthesis operator of an HS-operator sequence.

Recently, Gabor analysis on locally compact abelian (LCA) groups has become the focus of an active research. In practice, the time variable cannot be negative. The half real line ${ℝ}_{+}=(0,\infty )$ is an LCA group under multiplication and the usual topology, with the Haar measure $d\mu =\frac{dx}{x}$. This paper addresses Gabor frame multipliers and Parseval duals for $L^2({ℝ}_{+},d\mu )$. We introduce and characterize Gabor frame multipliers and Parseval Gabor frame multipliers based on Zak transform matrices. Our Zak transform matrix is essentially different from the conventional Zibulski–Zeevi matrix. It allows us to define Gabor frame generators by designing suitable matrix-valued functions of finite size. We also prove that an arbitrary Gabor frame ${𝒢}(g,a,b)$ admits a Parseval dual frame/tight dual frame whenever $lna\cdot lnb$ are rational numbers not greater than $\frac{1}{2}$.

Presented herein is a matrix method for buckling analysis of general frames based on the Hencky bar-chain model comprising of rigid segments connected by hinges with elastic rotational springs. Unlike the conventional matrix method of structural analysis based on the Euler–Bernoulli beam theory, the Hencky bar-chain model (HBM) matrix method allows one to readily handle the localized changes in end restraint conditions or localized structural changes (such as local damage or local stiffening) by simply tweaking the spring stiffnesses. The developed HBM matrix method was applied to solve some illustrative example problems to demonstrate its versatility in solving the buckling problem of beams and frames with various boundary conditions and local changes. It is hoped that this easy-to-code HBM matrix method will be useful to engineers in solving frame buckling problems.

Tight frames are extremely useful in applications. A scalable frame was recently introduced as a frame with the property of generating a tight frame by rescaling its frame vectors. In this paper, we consider piecewise scalable frames. We obtain some characterizations for them, and demonstrate that scalability is stable under unitary operators and isomorphisms between two Hilbert spaces. We further obtain a relation between the piecewise scalable frames in Hilbert spaces, and their tensor product

In order to achieve optimally sparse approximations of signals exhibiting anisotropic singularities, the shearlet systems that are systems of functions generated by one generator with dilation, shear transformation and translation operators applied to it were introduced. In this paper, we will construct the shearlet systems that are not only Parseval frames for $L^2({ℝ}^2)$ but they are also obtained from an $AB$-MRA associated with wavelet multiresolution, and by using this approach, we obtain the corresponding filters for these systems. For this purpose, the tensor product of the corresponding wavelet scaling function and a compact support bump function is used to construct the scaling function associated with the shearlet.

Let $L^2(ℝ,ℍ)$ be a space of square integrable quaternionic-valued functions defined on real line. In this paper, for $\mathrm{\Phi }\in L^2(ℝ,ℍ),$$a>1$ and $q>0$, if the sequence of functions $\{a^{m/2}\mathrm{\Phi }(a^{m}x-nq),m,n\in \mathbb{Z}\}$ is a wavelet frame of $L^2(ℝ,ℍ)$, we study the stability of the wavelet frame when the sampling $\{n\}$ or the mother wavelet $\mathrm{\Phi }$ has perturbation by using the theory of wavelet analysis.

This paper addresses the dilation problem on (dual) frames for Krein spaces. We characterize Riesz bases for Krein spaces and equivalence ($(J_1,J_2)$-unitary equivalence) between frames for Krein spaces; prove that every frame (dual frame pair) for a Krein space can be dilated to a Riesz basis (dual Riesz basis pair) for a larger Krein space, and that the corresponding $J$-orthogonal complementary frame ($J$-joint complementary frame) is unique up to equivalence ($(J_1,J_2)$-joint equivalence). Also we illustrate that two equivalent Parseval frames for Krein spaces need not be $(J_1,J_2)$-unitarily equivalent and that not every Parseval frame can be dilated to a $J$-orthonormal basis for a larger Krein space, and derive a result on matrices of finite size as application.

Frames of subspaces for Banach spaces have been introduced and studied. Examples and counter-examples to distinguish various types of frames of subspaces have been given. It has been proved that if a Banach space has a Banach frame, then it also has a frame of subspaces. Also, a necessary and sufficient condition for a sequence of projections, associated with a frame of subspaces, to be unique has been given. Finally, we consider complete frame of subspaces and prove that every weakly compactly generated Banach space has a complete frame of subspaces.

Let ${𝒞}$ be a small well-powered category which has pullbacks. The aim of this paper is to study and characterize two (weak) topologies on presheaf category $\widehat{{𝒞}}$, one of these is constructed by means of a subfunctor of the Yoneda functor which corresponds to an ideal of ${𝒞}$, called (weak) ideal topology, and another constructed by a dominion. Naturally, these (weak) topologies of $\widehat{{𝒞}}$ introduce two (weak) Grothendieck topologies on ${𝒞}$. To find and study their relations, using the induced presheaf $M$ given by the fixed dominion ${ℳ}$ on ${𝒞}$ we construct an action of $M$ on the subobject classifier $\mathrm{\Omega }$ of $\widehat{{𝒞}}$. Then, we investigate which one of (weak) Grothendieck topologies corresponds one-to-one to the ideals of ${𝒞}$ and which one is a sub $M$-set of $\mathrm{\Omega }$. Moreover, among other things, we give some conditions under which the Grothendieck topologies on ${𝒞}$ associated to the double negation topology $\neg \neg$ and two topologies $j_M$ and $j^{{ℐ}}$ (mentioned above) are sub $M$-sets of $\mathrm{\Omega }$.

This paper presents the results of dynamic responses and fire resistance of concrete-filled steel tubular (CFST) frame structures in fire conditions by using the nonlinear finite element method. Both strength and stability criteria are considered in the collapse analysis. The frame structures are constructed with circular CFST columns and steel beams of I-sections. In order to validate the finite element solutions, the numerical results are compared with those from a fire resistance test on CFST columns. The finite element model is then adopted to simulate the behavior of frame structures in fire. The structural responses of the frames, including the critical temperature and fire-resisting limit time, are obtained for the ISO-834 standard fire. Parametric studies are carried out to show their influence on the load capacity of the frame structures in fire. Suggestions and recommendations are presented for possible adoption in future construction and design of similar structures.

A necessary and sufficient condition for the perturbation of a Banach frame by a non-zero functional to be a Banach frame has been obtained. Also a sufficient condition for the perturbation of a Banach frame by a sequence in E* to be a Banach frame has been given. Finally, a necessary condition for the perturbation of a Banach frame by a finite linear combination of linearly independent functionals in E* to be a Banach frame has been given.

In this paper, we introduce and characterize controlled dual frames in Hilbert spaces. We also investigate the relation between bounds of controlled frames and their related frames. Then, we define the concept of approximate duality for controlled frames in Hilbert spaces. Next, we introduce multiplier operators of controlled frames in Hilbert spaces and investigate some of their properties. Finally, we show that the inverse of a controlled multiplier operator is also a controlled multiplier operator under some mild conditions.

Since the introduction of R-duals by Casazza, Kutyniok and Lammers with the motivation to obtain a general version of duality principle in Gabor analysis, various R-duals and some relaxations of the R-dual setup have been introduced and studied by some mathematicians. They provide a powerful tool in the analysis of duality relations in general frame theory, and are far beyond the duality principle in Gabor analysis. In this paper, we introduce the concept of generalized weak R-dual based on a pair of frames which is a relaxation of the R-dual setup. Using generalized weak R-duals, we characterize the frame properties of a sequence and the equivalence between two frames, prove that the generalized weak R-duals of frames (Riesz bases) are frame sequences (frames), and present a coefficient expression corresponding to the canonical duals of generalized weak R-duals. Some examples are provided to illustrate the generality of the theory.