• Korean Journal of Mathematics
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• v.28 no.1
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• pp.75-87
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• 2020

Category F Rel of fuzzy sets and relations does not form a topos. J. Harding, C. Walker and E. Walker [3] showed that FRel has a tensor product and V. Durov [1] introduced basic definitions related to the notion of vectoid endowed with a tensor product. In this paper, we show that FRel forms a quasi topos. Also we show that there are quasi power objects in FRel. And by the use of the concepts of FRel and quasi topos, we get the logic operators of FRel. Moreover, we show that FRel forms a vectoid.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.571-580
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• 2018

The object of the present paper is to prove the non-existence of pseudo projective Ricci symmetric spacetimes $(PW\;RS)_4$ with different types of energy momentum tensor. We also discuss whether a fluid $(PW\;RS)_4$ spacetime with the basic vector field as the velocity vector field of the fluid can admit heat flux. Next we consider perfect fluid and dust fluid $(PW\;RS)_4$ spacetimes respectively. Finally we construct an example of a $(PW\;RS)_4$ spacetime.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.817-827
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• 2021

In this paper, we prove that a diffeomorphism f on a normal almost contact 3-manifold M is a CRL-transformation if and only if M is an α-Sasakian manifold. Moreover, we show that a CR-loxodrome in an α-Sasakian 3-manifold is a pseudo-Hermitian magnetic curve with a strength $q={\tilde{r}}{\eta}({\gamma}^{\prime})=(r+{\alpha}-t){\eta}({\gamma}^{\prime})$ for constant 𝜂(𝛄'). A non-geodesic CR-loxodrome is a non-Legendre slant helix. Next, we prove that let M be an α-Sasakian 3-manifold such that (∇_YS)X = 0 for vector fields Y to be orthogonal to ξ, then the Ricci tensor 𝜌 satisfies 𝜌 = 2α²g. Moreover, using the CRL-transformation $\tilde{\nabla}^t$ we fine the pseudo-Hermitian curvature $\tilde{R}$, the pseudo-Ricci tensor $\tilde{\rho}$ and the torsion tensor field $\tilde{T}^t(\tilde{S}X,Y)$.

• ETRI Journal
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• v.45 no.1
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• pp.138-149
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• 2023

In this study, the problem of blind signal separation for coprime planar arrays is investigated. For coprime planar arrays comprising two uniform rectangular subarrays, we link the signal separation to the tensor-based model called coupled canonical polyadic decomposition (CPD) and propose an improved coupled trilinear decomposition approach. The output data of coprime planar arrays are modeled as a coupled tensor set that can be further interpreted as a coupled CPD model, allowing a signal separation to be achieved using coupled trilinear alternating least squares (TALS). Furthermore, in the procedure of the coupled TALS, a Vandermonde structure enforcing approach is explicitly applied, which is shown to ensure fast convergence. The results of Monto Carlo simulations show that our proposed algorithm has the same separation accuracy as the basic coupled TALS but with a faster convergence speed.

• Geomechanics and Engineering
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• v.19 no.5
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• pp.369-381
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• 2019

The objective of this paper is to study the two dimensional deformation in transversely isotropic thermoelastic medium without energy dissipation due to time harmonic sources using new modified couple stress theory, a continuum theory capable to predict the size effects at micro/nano scale. The couple stress constitutive relationships have been introduced for transversely isotropic thermoelastic medium, in which the curvature tensor is asymmetric and the couple stress moment tensor is symmetric. Fourier transform technique is applied to obtain the solutions of the governing equations. Assuming the deformation to be harmonically time-dependent, the transformed solution is obtained in the frequency domain. The application of a time harmonic concentrated and distributed sources have been considered to show the utility of the solution obtained. The displacement components, stress components, temperature change and couple stress are obtained in the transformed domain. A numerical inversion technique has been used to obtain the solutions in the physical domain. The effects of angular frequency are depicted graphically on the resulted quantities.

• Structural Engineering and Mechanics
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• v.76 no.1
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• pp.17-26
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• 2020

The objective of this paper is to study the deformation in transversely isotropic thermoelastic solid using new modified couple stress theory subjected to ramp-type thermal source and without energy dissipation. This theory contains three material length scale parameters which can determine the size effects. The couple stress constitutive relationships are introduced for transversely isotropic thermoelastic solid, in which the curvature (rotation gradient) tensor is asymmetric and the couple stress moment tensor is symmetric. Laplace and Fourier transform technique is applied to obtain the solutions of the governing equations. The displacement components, stress components, temperature change and couple stress are obtained in the transformed domain. A numerical inversion technique has been used to obtain the solutions in the physical domain. The effects of length scale parameters are depicted graphically on the resulted quantities. Numerical results show that the proposed model can capture the scale effects of microstructures.

• Physical Therapy Rehabilitation Science
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• v.10 no.3
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• pp.304-310
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• 2021

Objective: This study aimed to investigate effective cueing methods for selective muscle activation of gluteus medius muscles. Design: Cross sectional study design. Methods: Using the inclusion criteria for this study, 20 healthy adults, both males and females were selected for the measurement of muscle activation of gluteus maximus, gluteus medius, and tensor fascia latae muscles while performing clamshell exercise, basic movements in leg raise in side-lying, and 3 different cueing methods. Electromyogram was used to measure muscle activation, and both muscle activation and muscle ratio were compared during the basic movements and different cueing methods. Results: Gluteus medius activation was highest using "try not to make your body rotate" (cueing method 2) in both clamshell exercise and leg raise side-lying (F=5.533, p<0.05, F=7.771, p<0.05), and muscle ratio was highest in clamshell exercise using cueing method 2 (p<0.05) and "don't move your tensor fascia late" (cueing method 1) in leg raise side-lying (p<0.05). This study showed that cueing method 1 in leg raise side-lying and cueing method 2 in clamshell exercise were the most effective cueing methods for selective muscle activation of gluteus medius muscle. Conclusions: The results of this study may be used as basic information for future studies on muscle activation and muscle ratio for different cueing methods and different muscles in various exercises.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.601-620
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• 2020

In this paper, firstly we discuss some basic axioms of trans Sasakian manifolds. Later, the trans-Sasakian manifold with quarter symmetric non-metric connection are studied and its curvature tensor and Ricci tensor are calculated. Also, we study the η-Ricci solitons on a Trans-Sasakian Manifolds with quartersymmetric non-metric connection. Indeed, we investigated that the Ricci and η-Ricci solitons with quarter-symmetric non-metric connection satisfying the conditions ${\tilde{R}}.{\tilde{S}}$ = 0. In a particular case, when the potential vector field ξ of the η-Ricci soliton is of gradient type ξ = grad(ψ), we derive, from the η-Ricci soliton equation, a Laplacian equation satisfied by ψ. Finally, we furnish an example for trans-Sasakian manifolds with quarter-symmetric non-metric connection admitting the η-Ricci solitons.

• Communications of the Korean Mathematical Society
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• v.30 no.2
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• pp.131-142
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• 2015

The purpose of this paper is to study real hypersurfaces immersed in a complex hyperbolic space $CH^n$ and especially to investigate certain curvature conditions for such real hypersurfaces to be the model hypersurfaces in classification theorem (said to be Theorem M-R) given by Montiel and Romero ([4]) in Section 3.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.593-602
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• 2013

This paper is devoted to study Ricci semi-symmetric lightlike hypersurfaces of an indefinite cosymplectic space form with structure vector field tangent to hypersurface. The condition for Ricci tensor of lightlike hypersurface of indefinite cosymplectic space form to be semi-symmetric and parallel have been obtained. An example of non-totally geodesic Ricci semi-symmetric lightlike hypersurface in $R^7_2$ have been given.