• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.617-629
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• 2019

A term is called linear if each variable which occurs in the term, occurs only once. A hypersubstitution is said to be linear if it maps any operation symbol to a linear term of the same arity. Linear hypersubstitutions have some importance in Theoretical Computer Science since they preserve recognizability [7]. We show that the collection of all linear hypersubstitutions forms a monoid. Linear hypersubstitutions are used to define linear hyperidentities. The set of all linear term operations of a given algebra forms with respect to certain superposition operations a function algebra. Hypersubstitutions define endomorphisms on this function algebra.

• Water for future
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• v.20 no.3
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• pp.229-235
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• 1987

The purpose of this study is to estimate the parameters of linear reservoir models in order to derive the Instantaneous unit hydrograph from a given small experimental watershed. The linear reservoir model is a conceptual model, consisting of cascade or parallel equal linear reservoirs, preceded by a linear channel which involved Nash, SLR(single linear reservoir) and 2-PLR(two-parallel linear Reservoir) model. the Nash model have two parameters N and K, single linear reseroir has one parameter $K_I$ and two-parallel linear reservoirs have two parameters $K_1,\;K_2$; where N denote the number of reservoirs and K is the storage coefficient of each reservoirs.

• Coupled systems mechanics
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• v.12 no.4
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• pp.297-313
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• 2023

This paper deals with delamination analysis of non-linear viscoelastic multilayered beam subjected to bending in the plane of the layers. For this purpose, first, a non-linear viscoelastic model is presented. In order to take into account the non-linear viscoelastic behaviour, a non-linear spring and a non-linear dashpot are assembled in series with a linear spring connected in parallel to a linear dashpot. The behaviours of the non-linear spring and dashpot are described by applying non-linear stress-strain and stress-rate of strain relationships, respectively. The constitutive law of the model is derived. Due to the non-linear spring and dashpot, the constitutive law is non-linear. This law is used for describing the time-dependent mechanical behaviour of the beam under consideration. The material properties involved in the constitutive law vary along the beam length due to the continuous material inhomogeneity of the layers. Solution of the strain energy release rate for the delamination is obtained by analyzing the balance of the energy with considering of the non-linear viscoelastic behaviour. The strain energy release rate is found also by using the complementary strain energy for verification. A parametric study is carried-out by using the solution obtained. The solutions derived and the results obtained help to understand the time-dependent delamination of non-linear viscoelastic beams under loading in the plane of layers.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.55 no.1
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• pp.16-20
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• 2006

The proposed paper presents an integrated linear actuator which combines Transverse Flux Linear Motor(TFLM) for Household elelctric applications. They both use the same primary magnetic circuit, but they have different secondary movers. The paper presents a new design of linear motor for a new electromagnetic linear actuator, an tintegrated TFLM. The calculated tthrust force is good agreement with experiments. We have studied a transient response of a linear actuator with a damping ratio, spring constant and specially a pressed power patterns for a constant stroke control.

• Journal of Environmental Science International
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• v.3 no.4
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• pp.349-356
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• 1994

The purpose of this study is to develop a linear reservoir model with Kalman filter using Kalman filter theory which removes a physical uncertainty of :ainfall-runoff process. A linear reservoir model, which is the basic model of Kalman filter, is used to calculate runoff from rainfall in river basin. A linear reservoir model with Kalman filter is composed of a state-space model using a system model and a observation model. The state-vector of system model in linear. The average value of the ordinate of IUH for a linear reservoir model with Kalman filter is used as the initial value of state-vector. A .linear reservoir model with Kalman filter shows better results than those by linear reserevoir model, and decreases a physical uncertainty of rainfall-runoff process in river basin.

• International conference on construction engineering and project management
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• 2005.10a
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• pp.917-923
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• 2005

Scheduling is one of the main functions in construction project to determine the sequence of activities necessary to complete a project. The scheduling techniques provide important information crucial to a project's success. Highway construction project the paving activity can be considered a linear activity. Linear scheduling technique may be better suited for linear projects than other scheduling techniques. A new type of scheduling in linear project is calling Linear Scheduling Model (LSM). The Project monitoring and controlling is very ease to identify that all the stage of linear project and have more advantages.

• International Journal of Precision Engineering and Manufacturing
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• v.2 no.3
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• pp.61-68
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• 2001

A linear motor has a lot of advantages in comparison with conventional feed mechanisms: high transitional speed, acceleration, high control performance and good positioning at high speed. Through the omission of a power transfer element, the linear motor shows no wear and no backlash, has along lifetime and is easy to assemble. Recently, the two types of linear motors, asynchronous and synchronous linear motors, are often applied to machine tools as a fast feed mechanism. In this paper, a comparison between the two types of linear motors as to power loss and thermal behavior is made. The heat sources of the linear motor-the electrical power loss in the motor and the frictional heat on the linear guidance-are measured and compared. Also, the temperature on the linear motor and machine structure is measured and presented.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.1 s.178
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• pp.129-135
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• 2006

In this study, a two-axis ultra-precision stage driven by piezoelectric elements is presented. The stage has a flexure-type parallel linear guide mechanism consisting of quad-symmetric simple parallel linear springs and quad-symmetric double compound linear springs. While the simple parallel linear springs guide the linear motion of a moving plate in the stage, the double compound linear springs follow the motion of the simple parallel linear spring as well as compensate the parasitic motions caused by the simple parallel linear springs. The linear springs are designed by rectangular beam type flexures that are deformed by bending deflection rather than axial extension, because the axial extension is smaller than the bending deflection at the same force. The designed guide mechanism is analyzed by finite element method(FEM). Then two-axis parallel linear stage is implemented by the linear guide mechanism combined with piezoelectric elements and capacitance type displacement sensors. It is shown that the manufactured ultra-precision stage achieves 3 nm of resolution in x- and y-axis within 30 ${\mu}m$ of operating range.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.871-882
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• 2012

For a connected graph G of order $n$, an ordered set $S=\{u_1,u_2,{\cdots},u_k\}$ of vertices in G is a linear edge geodetic set of G if for each edge $e=xy$ in G, there exists an index $i$, $1{\leq}i$ < $k$ such that e lie on a $u_i-u_{i+1}$ geodesic in G, and a linear edge geodetic set of minimum cardinality is the linear edge geodetic number $leg(G)$ of G. A graph G is called a linear edge geodetic graph if it has a linear edge geodetic set. The linear edge geodetic numbers of certain standard graphs are obtained. Let $g_l(G)$ and $eg(G)$ denote the linear geodetic number and the edge geodetic number, respectively of a graph G. For positive integers $r$, $d$ and $k{\geq}2$ with $r$ < $d{\leq}2r$, there exists a connected linear edge geodetic graph with rad $G=r$, diam $G=d$, and $g_l(G)=leg(G)=k$. It is shown that for each pair $a$, $b$ of integers with $3{\leq}a{\leq}b$, there is a connected linear edge geodetic graph G with $eg(G)=a$ and $leg(G)=b$.

• Proceedings of the Korea Water Resources Association Conference
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• 1987.07a
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• pp.151-158
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• 1987

The purpose of thes study is to estimate the parameters of linear reservoir models in order to derive the instantaneous unit hydrograph from a given small experimental watershed. The linear reservoir model is a conceptual model, consisting of cascade or parallel equal linear reservoirs, preceded by a linear channel which involved NASH, SLR(single linear reservoir)and 2-PLR(two-parallel linear reservoir)model. The NASH model have two parameters N and K, single linear reservoir has one parameter K1 and two-parallel linear reservoirs have two parameters K1, K2;where N denote the number of reservoirs and K is the storage coefficient of each reservoirs.