• Geomechanics and Engineering
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• v.20 no.2
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• pp.87-101
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• 2020

The construction of combined pile-raft foundations is considered as the main option in designing foundations in high-rise buildings, especially in soils close to the ground surface which do not have sufficient bearing capacity to withstand building loads. This paper deals with the geotechnical report of the Northern Fereshteh area of Tabriz, Iran, and compares the characteristics of the single pile foundation with the two foundations of pile group and geogrid. Besides, we investigate the effects of five principal parameters including pile diameter and length, the number of geogrid layers, the depth of groundwater level, and pore water pressure on vertical consolidation settlement and pore water pressure changes over a year. This study assessed the mechanism of the failure of the soil under the foundation using numerical analysis as well. Numerical analysis was performed using the two-dimensional finite element PLAXIS software. The results of fifty-four models indicate that the diameter of the pile tip, either as a pile group or as a single pile, did not have a significant effect on the reduction of the consolidation settlement in the soil in the Northern Fereshteh Street region. The optimum length for the pile in the Northern Fereshteh area is 12 meters, which is economically feasible. In addition, the construction of four-layered ten-meter-long geogrids at intervals of 1 meter beneath the deep foundation had a significant preventive impact on the consolidation settlement in clayey soils.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1295-1303
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• 2015

In a mixture experiment, one may be interested in estimating not only main effects but also some interactions. Main effects and interactions may be estimated through appropriate designs such as simplex-centroid designs. However, the estimability problems, implied by the sum to one functional relationship among the factors, have strong consequences on the confounding and identifiability of models for such designs. To handle these problems, we address homogeneous polynomial model based on the computational commutative algebra (CCA) instead of using $Scheff{\acute{e}}s$ canonical model which is typically used. The problem posed here is to give how to choose estimable main effects and also some low-degree interactions. The theory is tested using a fraction of simplex-centroid designs aided by a modern computational algebra package CoCoA.

• Geomechanics and Engineering
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• v.22 no.5
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• pp.397-414
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• 2020

In this paper, practical predictive models for soil shear strength parameters are proposed. As cohesion and internal friction angle are of essential shear strength parameters in any geotechnical studies, we try to predict them via artificial neural network (ANN) and neuro-imperialism approaches. The proposed models was based on the result of a series of consolidated undrained triaxial tests were conducted on reinforced sandy soil. The experimental program surveys the increase in internal friction angle of sandy soil due to addition of polypropylene fibers with different lengths and percentages. According to the result of the experimental study, the most important parameters impact on internal friction angle i.e., fiber percentage, fiber length, deviator stress, and pore water pressure were selected as predictive model inputs. The inputs were used to construct several ANN and neuro-imperialism models and a series of statistical indices were calculated to evaluate the prediction accuracy of the developed models. Both simulation results and the values of computed indices confirm that the newly-proposed neuro-imperialism model performs noticeably better comparing to the proposed ANN model. While neuro-imperialism model has training and test error values of 0.068 and 0.094, respectively, ANN model give error values of 0.083 for training sets and 0.26 for testing sets. Therefore, the neuro-imperialism can provide a new applicable model to effectively predict the internal friction angle of fiber-reinforced sandy soil.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.79-101
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• 2016

Understanding the equal sign is of great significance to the development of algebraic thinking. Given this importance, this study investigated in what ways a total of 695 students from second to sixth graders understand the equal sign. The results showed that students were successful in solving standard problems whereas they were poor at items demanding high relational thinking. It was noticeable that some of the students were based on computational thinking rather than relational understanding of the equal sign. The students had a difficulty both in understanding the structure of equations and in solving equations in non-standard problem contexts. They also had incomplete understanding of the equal sign. This paper is expected to explore the understanding of the equal sign by elementary school students in multiple problem contexts and to provide implications of how to promote students' understanding of the equal sign.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.199-209
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• 2013

In this paper, we study the oscillation problem of the following higher-order neutral differential equation with positive and negative coefficients and mixed arguments $$z^{(n)}(t)+q_1(t)|x(t-{\sigma}_1)|^{\alpha-1}x(t-{\sigma}_1)+q_2(t)|x(t-{\sigma}_2)|^{\beta-1}x(t-{\sigma}_2)=e(t)$$, where $t{\geq}t_0$, $z(t)=x(t)-p(t)x(t-{\tau})$ with $p(t)$ > 0, ${\beta}>1>{\alpha}>0$, ${\tau}$, ${\sigma}_1$ and ${\sigma}_2$ are real numbers. Without imposing any restriction on ${\tau}$, we establish several oscillation criteria for the above equation in two cases: (i) $q_1(t){\leq}0$, $q_2(t)>0$, ${\sigma}_1{\geq}0$ and ${\sigma}_2{\leq}{\tau}$; (ii) $q_1(t){\geq}0$, $q_2(t)<0$, ${\sigma}_1{\geq}{\tau}$ and ${\sigma}_2{\leq}0$. As an interesting application, our results can also be applied to the following higher-order differential equation with positive and negative coefficients and mixed arguments $$x^{(n)}(t)+q_1(t)|x(t-{\sigma}_1)|^{\alpha-1}x(t-{\sigma}_1)+q_2(t)|x(t-{\sigma}_2)|^{\beta-1}x(t-{\sigma}_2)=e(t)$$. Two numerical examples are also given to illustrate the main results.

• Journal of Internet Computing and Services
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• v.17 no.5
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• pp.97-110
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• 2016

Cryptanalysis is very important step for auditing and checking strength of any cryptosystem. Some of these cryptosystem ensures confidentiality and security of large information exchange from source to destination using symmetric key cryptography. The cryptanalyst investigates the strengths and identifies weakness key as well as enciphering algorithm. With increase in key size the time and effort required to guess the correct key increases so trend is increase key size from 8, 16, 24, 32, 56, 64, 128 and 256 bits to strengthen the cryptosystem and thus algorithm continues without compromise on the cost of time and computation. Automatic Variable Key (AVK) approach is an alternative to the approach of fixing up key size and adding security level with key variability adds new dimension in the development of secure cryptosystem. Likewise, whenever any new cryptographic method is invented to replace per-existing vulnerable cryptographic method, its deep analysis from all perspectives (Hacker / Cryptanalyst as well as User) is desirable and proper study and evaluation of its performance is must. This work investigates AVK based cryptic techniques, in future to exploit benefits of advances in computational methods like ANN, GA, SI etc. These techniques for cryptanalysis are changing drastically to reduce cryptographic complexity. In this paper a detailed survey and direction of development work has been conducted. The work compares these new methods with state of art approaches and presents future scope and direction from the cryptic mining perspectives.

• Education of Primary School Mathematics
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• v.19 no.3
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• pp.177-191
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• 2016

Students can calculate the addition and subtraction problem using informal knowledge before receiving the formal instruction. Recently, the value that a computation lesson focus on the understanding and developing the various strategies is highlighted by curriculum developers as well as in reports. Ideally, a educational setting and classroom culture reflected students' learning and problem solving strategies. So, this paper analyzed the similarity and difference with respect to the numeric sentence and word problem in the addition and subtraction. The subjects for the study were 100 third-grade Korean students and 68 third-grade American students. Researcher developed the questionnaire in the addition and subtraction and used it for the survey. The following results have been drawn from this study. The computational ability of Korean students was higher than that of American students in both the numeric sentence and word problem. And it was revealed the differences of the strategies which were used problem solving process. Korean students tended to use algorithms and numbers' characters and relations, but American students tended to use the drawings and algorithms with drawings.

• Education of Primary School Mathematics
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• v.19 no.3
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• pp.223-247
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• 2016

Given the importance of developing algebraic thinking from early grades, this study investigated an overall performance and main characteristics of algebraic thinking from a total of 197 third grade students. The national elementary mathematics curriculum in Korea does not emphasize directly essential elements of algebraic thinking but indicates indirectly some of them. This study compared our students' performance related to algebraic thinking with results of Blanton et al. (2015) which reported considerable progress of algebraic thinking by emphasizing it through a regular curriculum. The results of this study showed that Korean students solved many items correctly as compatible to Blanton et al. (2015). However, our students tended to use 'computational' strategies rather than 'structural' ones in the process of solving items related to equation. When it comes to making algebraic expressions, they tended to assign a particular value to the unknown quantity followed by the equal sign. This paper is expected to explore the algebraic thinking by elementary school students and to provide implications of how to promote students' algebraic thinking.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.257-267
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• 2016

We find examples of Ideals in a tridiagonal algebra ALGL_∞ and study some properties of Ideals in ALGL_∞. We prove the following theorems: Let k and j be fixed natural numbers. Let A be a subalgebra of ALGL_∞ and let A_2,{k} ⊂ A ⊂ {T ∈ ALGL_∞ | T_(2k-1,2k) = 0}. Then A is an ideal of ALGL_∞ if and only if A = A_2,{k} where A_2,{k} = {T ∈ ALGL_∞ | T_(2k-1,2k) = 0, T_(2k-1,2k-1) = T_(2k,2k) = 0}. Let B be a subalgebra of ALGL_∞ such that B_2,{j} ⊂ B ⊂ {T ∈ ALGL_∞ | T_(2j+1,2j) = 0}. Then B is an ideal of ALGL_∞ if and only if B = B_2,{j}, where B_2,{j} = {T ∈ ALGL_∞ | T_(2j+1,2j) = 0, T_(2j,2j) = T_(2j+1,2j+1) = 0}.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.13-30
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• 2010

Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0\;{\in}\;C$ arbitrarily chosen, $x_{n+1}\;=\;{\alpha}_n{\gamma}f(W_nx_n)+{\beta}_nx_n+((1-{\beta}_n)I-{\alpha}_nA)W_nP_C(I-s_nB)x_n$, ${\forall}_n\;{\geq}\;0$, where $\gamma$ > 0, B : C $\rightarrow$ H is a $\beta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $\alpha$ (0 < $\alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${\ldots}$, $T_N$ and {$\lambda_{n,1}$}, {$\lambda_{n,2}$}, ${\ldots}$, {$\lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q\;{\in}\;F$ := $\bigcap^N_{i=1}F(T_i)\;\bigcap\;VI(C,\;B)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)q,\;p\;-\;q{\rangle}\;{\leq}\;0$ for all $p\;{\in}\;F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.