• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1951-1967
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• 2017

We aim to introduce a further extension of a family of the extended Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate several interesting properties of the extended function such as its integral representations which provide extensions of various earlier corresponding results of two and one variables, its summation formula, its Mellin-Barnes type contour integral representations, its computational representation and fractional derivative formulas. A multi-parameter extension of the extended Hurwitz-Lerch Zeta function of two variables is also introduced. Relevant connections of certain special cases of the main results presented here with some known identities are pointed out.

• Interaction and multiscale mechanics
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• v.1 no.1
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• pp.83-101
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• 2008

A derivation is given of two-scale models that are able to describe deformation and flow in a fluid-saturated and progressively fracturing porous medium. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for a fluid-saturated porous medium, which are assumed to hold on the macroscopic scale. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The finite element equations are derived for this two-scale approach and integrated over time. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton-Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.473-484
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• 2018

In this paper, we discuss how the operational calculus can be exploited to the theory of generalized special functions of many variables and many indices. We obtained the generating relations for 3-index, 3-variable and 1-parameter Hermite polynomials. Some mixed type generating relations and bilateral generating relations of many indices and many variable like Lagurre-Hermite and Hermite-Sister Celine's polynomials are also obtained. Further we generalize some results on old symbolic notations using operational identities.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1253-1259
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• 2011

Let R be a prime ring, I a nonzero ideal of R and n a fixed positive integer. If R admits a generalized derivation F associated with a derivation d such that c for all x, $y{\in}I$. Then either R is commutative or n = 1, d = 0 and F is the identity map on R. Moreover in case R is a semiprime ring and $(F([x,\;y]))^n=[x,\;y]$ for all x, $y{\in}R$, then either R is commutative or n = 1, $d(R){\subseteq}Z(R)$, R contains a non-zero central ideal and for all $x{\in}R$.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.19-35
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• 2018

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [30] and the second Appell function [6], we introduce here the incomplete Lauricella functions ${\gamma}^{(n)}_A$ and ${\Gamma}^{(n)}_A$ of n variables. We then systematically investigate several properties of each of these incomplete Lauricella functions including, for example, their various integral representations, finite summation formulas, transformation and derivative formulas, and so on. We provide relevant connections of some of the special cases of the main results presented here with known identities. Several potential areas of application of the incomplete hypergeometric functions in one and more variables are also pointed out.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.129-135
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• 2012

The aim of this paper is to establish the well-known and very useful classical Saalsch$\ddot{u}$tz's theorem for the series $_3F_2$(1) by following a different method. In addition to this, two summation formulas closely related to the Saalsch$\ddot{u}$tz's theorem have also been obtained. The results established in this paper are further utilized to show how one can obtain certain known and useful hypergeometric identities for the series $_3F_2$(1) and $_4F_3(1)$ already available in the literature.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.11
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• pp.4680-4700
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• 2015

Broadcast encryption is an efficient way to distribute confidential information to a set of receivers using broadcast channel. It allows the broadcaster to dynamically choose the receiver set during each encryption. However, most broadcast encryption schemes in the literature haven't taken into consideration the receiver's privacy protection, and the scanty privacy preserving solutions are often less efficient, which are not suitable for practical scenarios. In this paper, we propose an efficient dynamic anonymous broadcast encryption scheme that has the shortest ciphertext length. The scheme is constructed over the composite order bilinear groups, and adopts the Lagrange interpolation polynomial to hide the receivers' identities, which yields efficient decryption algorithm. Security proofs show that, the proposed scheme is both secure and anonymous under the threat of adaptive adversaries in standard model.

• International Journal of High-Rise Buildings
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• v.7 no.1
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• pp.47-64
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• 2018

The last decade has seen great design opportunities for tall building construction around the globe. The best designs represent a new generation of skyscrapers that go beyond willful preconceptions of building form and iconography, trying instead to simultaneously address interrelated issues of program space utility, structural efficiency, and environmentally sustainable systems. The resulting identities of these towers are unique because of their search for the intersection of spaces tuned to people's needs, expressive optimized structures, and high performance, site-responsive systems. This paper, through examples of recent SOM towers, both built and unbuilt, will discuss how a design becomes content-driven, how ideas create value, and how the typology of the tall building is advanced through the integration of architecture design and engineering systems.

• International Journal of Computer Science & Network Security
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• v.23 no.2
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• pp.89-95
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• 2023

Cloud computing today provides huge computational resources, storage capacity, and many kinds of data services. Data sharing in the cloud is the practice of exchanging files between various users via cloud technology. The main difficulty with file sharing in the public cloud is maintaining privacy and integrity through data encryption. To address this issue, this paper proposes an Enhanced RSA encryption schema (ERSA) for data sharing in the public cloud that protects privacy and strengthens data integrity. The data owners store their files in the cloud after encrypting the data using the ERSA which combines the RSA algorithm, XOR operation, and SHA-512. This approach can preserve the confidentiality and integrity of a file in any cloud system while data owners are authorized with their unique identities for data access. Furthermore, analysis and experimental results are presented to verify the efficiency and security of the proposed schema.

• The Pure and Applied Mathematics
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• v.30 no.2
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• pp.131-138
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• 2023

The aim of this note is to provide two new and interesting closed-form evaluations of the generalized hypergeometric function ₅F₄ with argument $\frac{1}{256}$. This is achieved by means of separating a generalized hypergeometric function into even and odd components together with the use of two known sums (one each) involving reciprocals of binomial coefficients obtained earlier by Trif and Sprugnoli. In the end, the results are written in terms of two interesting combinatorial identities.