• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.761-768
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• 2021

Let I be a nonzero ideal of a prime ring R and m, n are positive integers. If R admits a generalized derivation F satisfying F(x)ⁿF(y)^m - xⁿy^m = 0 for any y, x ∈ I, then F(x) = ax for any x ∈ R and a^m+n = 1, where a ∈ C, the extended centroid of R.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.15 no.4
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• pp.301-314
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• 1990

This paper is an attempt to use vision-pattern recognition technique to analyzation on a hidden rigid body motion. Specially shaped rod, rigidly connected to the hidden body is extended to the ouside of hiding object so that a camera may catch the motion data. Every motion can be described with translatio and rotation. But translation can be explanied with ratation with a infinitly far centroid. Motion analysis is to find the instantaneous centroid and ratation angle. With this theory jaw motion is analyzed in this paper.

• Asia pacific journal of information systems
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• v.20 no.1
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• pp.81-99
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• 2010

Lately, in consumers' markets the number of new items is rapidly increasing at an overwhelming rate while consumers have limited access to information about those new products in making a sensible, well-informed purchase. Therefore, item providers and customers need a system which recommends right items to right customers. Also, whenever new items are released, for instance, the recommender system specializing in new items can help item providers locate and identify potential customers. Currently, new items are being added to an existing system without being specially noted to consumers, making it difficult for consumers to identify and evaluate new products introduced in the markets. Most of previous approaches for recommender systems have to rely on the usage history of customers. For new items, this content-based (CB) approach is simply not available for the system to recommend those new items to potential consumers. Although collaborative filtering (CF) approach is not directly applicable to solve the new item problem, it would be a good idea to use the basic principle of CF which identifies similar customers, i,e. neighbors, and recommend items to those customers who have liked the similar items in the past. This research aims to suggest a hybrid recommendation procedure based on the preference boundary of target customer. We suggest the hybrid recommendation procedure using the preference boundary in the feature space for recommending new items only. The basic principle is that if a new item belongs within the preference boundary of a target customer, then it is evaluated to be preferred by the customer. Customers' preferences and characteristics of items including new items are represented in a feature space, and the scope or boundary of the target customer's preference is extended to those of neighbors'. The new item recommendation procedure consists of three steps. The first step is analyzing the profile of items, which are represented as k-dimensional feature values. The second step is to determine the representative point of the target customer's preference boundary, the centroid, based on a personal information set. To determine the centroid of preference boundary of a target customer, three algorithms are developed in this research: one is using the centroid of a target customer only (TC), the other is using centroid of a (dummy) big target customer that is composed of a target customer and his/her neighbors (BC), and another is using centroids of a target customer and his/her neighbors (NC). The third step is to determine the range of the preference boundary, the radius. The suggested algorithm Is using the average distance (AD) between the centroid and all purchased items. We test whether the CF-based approach to determine the centroid of the preference boundary improves the recommendation quality or not. For this purpose, we develop two hybrid algorithms, BC and NC, which use neighbors when deciding centroid of the preference boundary. To test the validity of hybrid algorithms, BC and NC, we developed CB-algorithm, TC, which uses target customers only. We measured effectiveness scores of suggested algorithms and compared them through a series of experiments with a set of real mobile image transaction data. We spilt the period between 1st June 2004 and 31st July and the period between 1st August and 31st August 2004 as a training set and a test set, respectively. The training set Is used to make the preference boundary, and the test set is used to evaluate the performance of the suggested hybrid recommendation procedure. The main aim of this research Is to compare the hybrid recommendation algorithm with the CB algorithm. To evaluate the performance of each algorithm, we compare the purchased new item list in test period with the recommended item list which is recommended by suggested algorithms. So we employ the evaluation metric to hit the ratio for evaluating our algorithms. The hit ratio is defined as the ratio of the hit set size to the recommended set size. The hit set size means the number of success of recommendations in our experiment, and the test set size means the number of purchased items during the test period. Experimental test result shows the hit ratio of BC and NC is bigger than that of TC. This means using neighbors Is more effective to recommend new items. That is hybrid algorithm using CF is more effective when recommending to consumers new items than the algorithm using only CB. The reason of the smaller hit ratio of BC than that of NC is that BC is defined as a dummy or virtual customer who purchased all items of target customers' and neighbors'. That is centroid of BC often shifts from that of TC, so it tends to reflect skewed characters of target customer. So the recommendation algorithm using NC shows the best hit ratio, because NC has sufficient information about target customers and their neighbors without damaging the information about the target customers.

• Structural Engineering and Mechanics
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• v.45 no.1
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• pp.69-93
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• 2013

The present study deals with the dynamics of the flapwise (out-of-plane) vibrations of a rotating, internally damped (Kelvin-Voigt model) tapered Bernoulli-Euler beam carrying a heavy tip mass. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The equation of motion and the corresponding boundary conditions are derived via the Hamilton's Principle, leading to a differential eigenvalue problem. Afterwards, this eigenvalue problem is solved by using Frobenius Method of solution in power series. The resulting characteristic equation is then solved numerically. The numerical results are tabulated for a variety of nondimensional rotational speed, tip mass, tip mass offset, mass moment of inertia, internal damping parameter, hub radius and taper ratio. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.191-207
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• 2015

Let $\mathcal{R}$ be a prime ring of characteristic different from 2, $\mathcal{Q}_r$ be its right Martindale quotient ring and $\mathcal{C}$ be its extended centroid. Suppose that $\mathcal{G}$ is a nonzero generalized skew derivation of $\mathcal{R}$, ${\alpha}$ is the associated automorphism of $\mathcal{G}$, f($x_1$, ${\cdots}$, $x_n$) is a non-central multilinear polynomial over $\mathcal{C}$ with n non-commuting variables and $$\mathcal{S}=\{f(r_1,{\cdots},r_n)\left|r_1,{\cdots},r_n{\in}\mathcal{R}\}$$. If $\mathcal{G}$ acts as a Jordan homomorphism on $\mathcal{S}$, then either $\mathcal{G}(x)=x$ for all $x{\in}\mathcal{R}$, or $\mathcal{G}={\alpha}$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1651-1657
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• 2013

Let R be a prime ring, I a nonzero ideal of R, $d$ a derivation of R, $m({\geq}1)$, $n({\geq}1)$ two fixed integers and $a{\in}R$. (i) If $a((d(x)y+xd(y)+d(y)x+yd(x))^n-(xy+yx))^m=0$ for all $x,y{\in}I$, then either $a=0$ or R is commutative; (ii) If $char(R){\neq}2$ and $a((d(x)y+xd(y)+d(y)x+yd(x))^n-(xy+yx)){\in}Z(R)$ for all $x,y{\in}I$, then either $a=0$ or R is commutative.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.573-586
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• 2018

Let R be a noncommutative prime ring of characteristic different from 2, Q be its maximal right ring of quotients and C be its extended centroid. Suppose that $f(x_1,{\ldots},x_n)$ be a noncentral multilinear polynomial over $C,b{\in}Q,F$ a b-generalized derivation of R and d is a nonzero derivation of R such that d([F(f(r)), f(r)]) = 0 for all $r=(r_1,{\ldots},r_n){\in}R^n$. Then one of the following holds: (1) there exists ${\lambda}{\in}C$ such that $F(x)={\lambda}x$ for all $x{\in}R$; (2) there exist ${\lambda}{\in}C$ and $p{\in}Q$ such that $F(x)={\lambda}x+px+xp$ for all $x{\in}R$ with $f(x_1,{\ldots},x_n)^2$ is central valued in R.

• Journal of the Korean Society of Safety
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• v.13 no.1
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• pp.3-12
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• 1998

On the stability of the cantilever beam subjected to a follower force at the free end, the influences of the translational spring and the moment of inertia of a tip mass at the free end have been studied by numerical methods. The centroid of a tip mass is offset from the free end of a Beam and is located along its extended axis to vary the value of moment of inertia of a tip mass. It is proved that as the constants of a spring supporting the free end are augmented, the critical flutter loads of the above system decrease, whereas they increase without a tip mass.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.73-81
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• 2021

Let R be a prime ring, Qr be the right Martindale quotient ring and C be the extended centroid of R. If �� be a nonzero generalized skew derivation of R and f(x1, x2, ⋯, xn) be a multilinear polynomial over C such that (��(f(x1, x2, ⋯, xn)) - f(x1, x2, ⋯, xn)) ∈ C for all x1, x2, ⋯, xn ∈ R, then either f(x1, x2, ⋯, xn) is central valued on R or R satisfies the standard identity s4(x1, x2, x3, x4).

• Korean Journal of Applied Biomechanics
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• v.18 no.1
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• pp.203-212
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• 2008

The purpose of this study is to propose appropriate model for 3 staged Didimsae movement to Jajinmori rhythm and to provide information for ideal foot step movements. For the locational change of body center, the height of body center is lowered at the moment of forward step and during forward intersection of the feet, forward direction linear motion is converted to vertical motion to maintain stability. Speed change of body center reduces flow of body on step forward moment and controls rapid forward movement for stabled movement and position when preventing fast forward horizontal direction movement of centroid speed while knee joint and foot joint are vertically risen for heel bone contacts the ground. For angle changes of joints, in order to prevent hyperextension of lower leg, hip joint is extended and knee joint is curved to secure stability of movement for smooth curves and extension. When centroid of foot joint is moved from top of the feet to whole foot sole and when left foot makes dorsal curve, stabled movement is accomplished.