• Korean Journal of Mathematics
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• 제30권1호
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• pp.91-107
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• 2022

Controlled frames have been the subject of interest because of their ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the notion of controlled K-frame or controlled operator frame in Hilbert C^*-modules. We establish the equivalent condition for controlled K-frame. We investigate some operator theoretic characterizations of controlled K-frames and controlled Bessel sequences. Moreover, we establish the relationship between the K-frames and controlled K-frames. We also investigate the invariance of a controlled K-frame under a suitable map T. At the end, we prove a perturbation result for controlled K-frame.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1247-1256
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• 2008

Based on two real and invertible $d{\times}d$ matrices Band C such that the norm $||C^T\;B||$ is sufficiently small, we provide a construction of tight Gabor frames $\{E_{Bm}T_{Cn}g\}_{m,n{\in}{\mathbb{Z}^d}$ with explicitly given and compactly supported generators. The generators can be chosen with arbitrary polynomial decay in the frequency domain.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.547-557
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• 2020

In this paper, we introduce the notions of (dual) residuated frames for a fuzzy logic as an extension of residuated frames for classical relational semantics. We investigate the relations between residuated connections and residuated frames on Alexandrov topologies based on [0, ∞]. Moreover, we study their properties and give their examples.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.315-328
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• 2021

A characterization of frame operators of finite Gabor frames is presented here. Regularity aspects of Gabor frames in 𝑙²(ℤ_N) are discussed by introducing associated semi-frame operators. Gabor type frames in finite dimensional Hilbert spaces are also introduced and discussed.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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• pp.321-334
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• 2022

We introduce a special class of structured frames having single generators in finite dimensional Hilbert spaces. We call them as pseudo B-Gabor like frames and present a characterisation of the frame operators associated with these frames. The concept of Gabor semi-frames is also introduced and some significant properties of the associated semi-frame operators are discussed.

• 대한수학회지
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• 제42권2호
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• pp.291-304
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• 2005

We introduce a concept of Cauchy complete Csaszar frames and construct Cauchy completions of Csaszar frames using strict extensions of frames and show that the Cauchy completion gives rise to a coreflection in the categories CsFrm and UCsFrm.

• Korean Journal of Mathematics
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• 제20권1호
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• pp.61-75
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• 2012

We investigate the properties of various frames and connections on partially ordered sets. In particular, we study the relations between various connections and various frames.

• Smart Structures and Systems
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• 제19권6호
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• pp.643-652
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• 2017

Pitched roof frames are widely used in construction of the industrial buildings, gyms, schools and colleges, fire stations, storages, hangars and many other low rise structures. The weight and shape of the gable frames with tapered members, as a familiar group of the pitched roof frames, are highly dependent on the properties of the member cross-sectional. In this work Enhanced Colliding Bodies Optimization (ECBO) is utilized for optimal design of three gable frames with tapered members. In order to optimize the frames, the design is performed using the AISC specifications for stress, displacement and stability constraints. The design constraints and weight of the gable frames are computed from the cross-section of members. These optimum weights are obtained using aforementioned optimization algorithms considering the cross-sections of the members and design constraints as optimization variables and constraints, respectively. A comparative study of the PSO and CBO with ECBO is also performed to illustrate the importance of the enhancement of the utilized optimization algorithm.

• Steel and Composite Structures
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• 제24권5호
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• pp.561-568
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• 2017

Steel frames are widely used in steel structures. Exiting steel structures may be needed to strengthen for various reasons. Carbon Fiber Reinforced Polymers (CFRP) is one of the materials that are used to strengthen steel structures. Most studies on strengthening steel structures have been done on beams and steel columns. No independent study, to the researcher's knowledge, has studied the effect of CFRP strengthening on steel frames. This study explored the use of CFRP composite on retrofitting square hollow section (SHS) steel frames, using numerical investigations. Ten Finite Element (FE) models, which were strengthened with CFRP sheets, were analyzed under different coverage length, number of layers, and location of CFRP composite. One FE model without strengthening was analyzed as a control FE model to determine the increase of the ultimate load in the strengthened steel frames. ANSYS software was used to analyze the SHS steel frames. The results showed that the coverage length and the number of layers of CFRP composite have a significant effect on increasing the ultimate load of the SHS steel frames. The results also showed that the location of CFRP composite had no similar effect on increasing the ultimate load and the amount of mid span deflection of the SHS steel frames.

• Structural Engineering and Mechanics
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• 제23권5호
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• pp.469-486
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• 2006

The main objective of this study was to investigate the seismic behavior of damaged reinforced concrete frames rehabilitated by introducing cast in place reinforced concrete infills. Four bare and five infilled frames were constructed and tested. Each specimen consisted of two (twin) 1/3-scale, one-bay and two-story reinforced concrete frames. Test specimens were tested under reversed-cyclic lateral loading until considerable damage occurred. RC infills were then introduced to the damaged specimens. One bare specimen was infilled without being subjected to any damage. All infilled frames were then tested under reversed-cyclic lateral loading until failure. While some of the test frames were detailed properly according to the current Turkish seismic code, others were built with the common deficiencies observed in existing residential buildings. The variables investigated were the effects of the damage level and deficiencies in the bare frame on the seismic behavior of the infilled frame. The deficiencies in the frame were; low concrete strength, inadequate confinement at member ends, 90 degree hooks in column and beam ties and inadequate length of lapped splices in column longitudinal bars made above the floor levels. Test results revealed that both the lateral strength and lateral stiffness increased significantly with the introduction of reinforced concrete infills even when the frame had the deficiencies mentioned above. The deficiency which affected the behavior of infilled frames most adversely was the presence of lap splices in column longitudinal reinforcement.