• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.187-198
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• 2021

This work presents an exposition of both the internal structure of derived category of an abelian category D^*(𝓐) and its contribution in solving problems, particularly in algebraic geometry. Calculation of some morphisms will be presented between objects in D^*(𝓐) as elements in appropriate cohomology groups along with their compositions with the help of Yoneda construction under the assumption that the homological dimension of D^*(𝓐) is greater than or equal to 2. These computational settings will then be considered under sheaf cohomological context with a particular case from projective geometry.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.23-44
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• 2022

In this paper, we consider and introduce some new concepts of the biconvex functions involving an arbitrary bifunction and function. Some new relationships among various concepts of biconvex functions have been established. We have shown that the optimality conditions for the general biconvex functions can be characterized by a class of bivariational-like inequalities. Auxiliary principle technique is used to propose proximal point methods for solving general bivariational-like inequalities. We also discussed the conversance criteria for the suggested methods under pseudo-monotonicity. Our method of proof is very simple compared with methods. Several special cases are discussed as applications of our main concepts and results. It is a challenging problem to explore the applications of the general bivariational-like inequalities in pure and applied sciences.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.369-399
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• 2022

In the last few decades, a lot of generalizations of the Banach contraction principle have been introduced. In this paper, we present the notion of (𝜙, F)-contraction in generalized asymmetric metric spaces and we investigate the existence of fixed points of such mappings. We also provide some illustrative examples to show that our results improve many existing results.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.335-352
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• 2022

In this paper, we give an extended version of fixed point results for 𝜃-contraction and 𝜃-𝜙-contraction and define a new type of contraction, namely, cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction in a complete metric space. Moreover, we prove the existence of best proximity point for cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction. Also, we establish best proximity result in the setting of uniformly convex Banach space.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.855-867
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• 2022

This study finds three different solutions (3-Sol's) for the fourth order nonlinear discrete anisotropic equations (DAE) with real parameter. We use the variational method(VM) and 𝜙_p-Laplacian operator (𝜙_p-LO) to prove the main results. In the following paper, we take the parameters λ, 𝜇 such that λ > 0 and 𝜇 ≥ 0 into consideration.

• The Pure and Applied Mathematics
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• v.30 no.1
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• pp.35-42
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• 2023

In this paper, we find a bound for all the zeros of a polynomial in terms of its coefficients similar to the bound given by Montel (1932) and Kuneyida (1916) as an improvement of Cauchy's classical theorem. In fact, we use a generalized version of Hölder's inequality for obtaining various interesting bounds for all the zeros of a polynomial as function of their coefficients.

• Journal of the Daesoon Academy of Sciences
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• v.16
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• pp.265-304
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• 2003

장례의식은 불교에서 가장 중요한 정기적인 의식들 중에 하나이다. 이러한 의식은 수도자나 죽은 사람들을 위해서 행해지고 있다. 그렇다고 장례의식의 목적이 죽은 사람들만을 위한 것이 아니라 근원적으로는 'saṃsāra'의 윤회로부터 완전한 해방을 구하는 모습을 의미한다. 티벳불교에서의 죽음은 두 가지를 의미를 인식한다. 하나는 열반으로 입적하는 것으로 다섯 가지에 완전히 융해되는 것을 뜻한다. 이러한 죽음은 더 이상의 '태어남'이 없다. 열반의 경지는 카르마 안에서 융해 되거나 평화를 얻은 경지인 것이다. 또 하나의 죽음은 카르마의 법칙에 의해서 통제 되거나 하나의 영혼이 열반 안으로 들어가기 전까지 순환적인 주기 안에서 지속적으로 반복되는 것이다. 카르마는 불교의 관례를 통해서 카르마의 힘은 없어질 수 있다고 할지라도 근본적으로 외부적인 간섭을 수행하지는 않는다. 즉 불교의 이념들은 각자의 노력을 통해 해방을 얻는 것을 가르치고 있다. 하지만 카르마의 경로가 식별하기 어려워 제의식의 효과나 수행의식을 통해 알아 볼 수밖에 없다. 여기서는 티벳불교에서 죽은 후의 몸을 적절히 배치하는 방법을 얻는 제의식이나 축제에 관심을 갖는 것이 아니라 이를 통한 실질적이고 복합적인 힘, 그리고 카르마적 흐름을 바꾸거나 심지어 없애버릴 수 있는 의식에 관심을 갖고자 한다.

• The Pure and Applied Mathematics
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• v.31 no.1
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• pp.49-56
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• 2024

For a Polynomial P(z) = Σⁿ_j=0 a_jz^j with a_j ≥ a_j-1, a₀ > 0 (j = 1, 2, ..., n), a classical result of Enestrom-Kakeya says that all the zeros of P(z) lie in |z| ≤ 1. This result was generalized by A. Joyal et al. [3] where they relaxed the non-negative condition on the coefficents. This result was further generalized by Dewan and Bidkham [9] by relaxing the monotonicity of the coefficients. In this paper, we use some techniques to obtain some more generalizations of the results [3], [8], [9].

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.21-36
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• 2024

In this paper, we study the existence of solutions for hybrid fractional differential equations with p-Laplacian operator involving fractional Caputo derivative of arbitrary order. This work can be seen as an extension of earlier research conducted on hybrid differential equations. Notably, the extension encompasses both the fractional aspect and the inclusion of the p-Laplacian operator. We build our analysis on a hybrid fixed point theorem originally established by Dhage. In addition, an example is provided to demonstrate the effectiveness of the main results.

• Tuberculosis and Respiratory Diseases
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• v.83 no.3
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• pp.211-217
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• 2020

The gold standard method for diagnosis of tuberculosis is the isolation of Mycobacterium tuberculosis through culture, but there is a probability of cross-contamination in simultaneous cultures of samples causing false-positives. This can result in delayed treatment of the underlying disease and drug side effects. In this paper, we reviewed studies on false-positive cultures of M. tuberculosis. Rate of occurrence, effective factors, and extent of false-positives were analyzed. Ways to identify and reduce the false-positives and management of them are critical for all laboratories. In most cases, false-positive is occurring in cases with only one positive culture but negative direct smear. The three most crucial factors in this regard are inappropriate technician function, contamination of reagents, and aerosol production. Thus, to reduce false-positives, good laboratory practice, as well as use of whole-genome sequencing or genotyping of all positive culture samples with a robust, extra pure method and rapid response, are essential for minimizing the rate of false-positives. Indeed, molecular approaches and epidemiological surveillance can provide a valuable tool besides culture to identify possible false positives.