• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.675-687
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• 2009

We find the multiple nontrivial solutions of the equation of the form $u_{tt}-u_{xx}=b_1[(u+1)^{+}-1]+b_2[(u+2)^{+}-2]$ with Dirichlet boundary condition. Here we reduce this problem into a two-dimensional problem by using variational reduction method and apply the Mountain Pass theorem to find the nontrivial solutions.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1257-1269
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• 2013

Using the three critical points theorem by B. Ricceri [23], we obtain a multiplicity result for a class of nonlocal problems in Orlicz-Sobolev spaces. To our knowledge, this is the first contribution to the study of nonlocal problems in this class of functional spaces.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.737-746
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• 2017

In this paper, we discuss the existence theorem for multiple vortex solutions in the non-Abelian Chern-Simons-Higgs field theory developed by Aharony, Bergman, Jafferis, and Maldacena, on a doubly periodic domain. The governing equations are of the BPS type and derived by Auzzi and Kumar in the mass-deformed framework labeled by a continuous parameter. Our method is based on fixed point method.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.665-732
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• 2015

Existence results for multiple positive solutions of two classes of boundary value problems for bilateral difference systems are established by using a fixed point theorem under convenient assumptions. It is the purpose of this paper to show that the approach to get positive solutions of boundary value problems of finite difference equations by using multi-fixed-point theorems can be extended to treat the bilateral difference systems with one-dimensional Laplacians. As an application, the sufficient conditions are established for finding multiple positive homoclinic solutions of a bilateral difference system. The methods used in this paper may be useful for numerical simulation. An example is presented to illustrate the main theorems. Further studies are proposed at the end of the paper.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.423-436
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• 2011

We obtain a theorem that shows the existence of multiple solutions for the mixed type nonlinear elliptic equation with Dirichlet boundary condition. Here the nonlinear part contain the jumping nonlinearity and the subcritical growth nonlinearity. We first show the existence of a positive solution and next find the second nontrivial solution by applying the variational method and the mountain pass method in the critical point theory. By investigating that the functional I satisfies the mountain pass geometry we show the existence of at least two nontrivial solutions for the equation.

• Journal of Appropriate Technology
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• v.7 no.2
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• pp.172-187
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• 2021

In remote villages without access to modern IT technology, simple devices such as smartcards can be used to carry out business transactions. These devices typically store multiple business applications from multiple vendors. Although devices must prevent malicious or accidental security breaches among the applications, a secure communication channel between two applications from different vendors is often required. In this paper, first, we propose a method of establishing secure communication channels between applications in embedded operating systems that run on multi-applet smart cards. Second, we enforce the high assurance using an intransitive noninterference security policy. Thirdly, we formalize the method through the Z language and create the formal specification of the proposed secure system. Finally, we verify its correctness using Rushby's unwinding theorem.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.213-221
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• 2011

In this paper, we establish a multiple critical points theorem for a one-parameter family of non-smooth functionals. The obtained result is then exploited to prove a multiplicity result for a class of periodic eigenvalue problems driven by the p-Laplacian and with a non-smooth potential. Under suitable assumptions, we locate an open subinterval of the eigenvalue.

• The Korean Journal of Applied Statistics
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• v.3 no.2
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• pp.55-77
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• 1990

In this paper we descuss some E-optimal block designs having unequal block sizes, and give a table of E-optimal designs with 2 different block sizes which can be constructed using the method described in Theorem 3. 2, Theorem 3. 4 and Theorem 3. 5 proved by Lee and Jacroux (1987). All of source designs used are Group Divisible designs which can be found in Clathworthy(1973) or Balanced Incomplete block designs in Raghavarar(1971).

• Journal of Communications and Networks
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• v.11 no.1
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• pp.47-56
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• 2009

We investigate the connectivity of fading wireless ad-hoc networks with a pair of novel connectivity metrics. Our first metric looks at the problem of connectivity relying on the outage capacity of MIMO channels. Our second metric relies on a probabilistic treatment of the symbol error rates for such channels. We relate both capacity and symbol error rates to the characteristics of the underlying communication system such as antenna configuration, modulation, coding, and signal strength measured in terms of signal-to-interference-noise-ratio. For each metric of connectivity, we also provide a simplified treatment in the case of ergodic fading channels. In each case, we assume a pair of nodes are connected if their bi-directional measure of connectivity is better than a given threshold. Our analysis relies on the central limit theorem to approximate the distribution of the combined undesired signal affecting each link of an ad-hoc network as Gaussian. Supported by our simulation results, our analysis shows that (1) a measure of connectivity purely based on signal strength is not capable of accurately capturing the connectivity phenomenon, and (2) employing multiple antenna mobile nodes improves the connectivity of fading ad-hoc networks.

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.501-517
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• 2007

In this paper, we introduce and study a new class containing absolutely summing multilinear mappings and polynomials, which we call multiple weakly summing multilinear mappings and polynomials. We investigate some interesting properties about multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials defined on Banach spaces: In particular, we prove a kind of Dvoretzky-Rogers' Theorem and an ideal property for multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials. We also prove that the Aron-Berner extensions of multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials are also multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing.