Calculation of the Equilibrium Configuration of Shopping Facility Sizes

This paper presents a range of methods for computing the equilibrium configuration of shopping facility sizes. First, the presently available range of quasi-balancing factor methods is considered and built into a theoretical framework in which further algorithms may be defined. Then the use of the gradient method is considered, which is a general method of solution of nonlinear equations. Last, it is shown that a special case exists in which a closed form solution may be obtained.

Download Full-text

A CLOSED-FORM SOLUTION OF THE EVOLUTION OPERATOR IN TWO-LEVEL SYSTEMS

Modern Physics Letters B ◽

10.1142/s0217984994000534 ◽

1994 ◽

Vol 08 (08n09) ◽

pp. 505-508 ◽

Cited By ~ 1

Author(s):

XIAN-GENG ZHAO

Keyword(s):

Closed Form ◽

Lie Algebra ◽

Evolution Operator ◽

Closed Form Solution ◽

Form Solution ◽

Time Dependent ◽

Arbitrary Time ◽

Two Level Systems ◽

Special Case

It is demonstrated by using the technique of Lie algebra SU(2) that the problem of two-level systems described by arbitrary time-dependent Hamiltonians can be solved exactly. A closed-form solution of the evolution operator is presented, from which the results for any special case can be deduced.

Download Full-text

A General Method for a Closed-Form Solution to Robot Kinematics Problems

Robotic Systems ◽

10.1007/978-94-011-2526-0_2 ◽

1992 ◽

pp. 11-18

Author(s):

Carlo Galletti ◽

Pietro Fanghella

Keyword(s):

Closed Form ◽

Closed Form Solution ◽

Form Solution ◽

Robot Kinematics ◽

General Method

Download Full-text

Spontaneous potential log response expressed as convolution

Geophysics ◽

10.1190/1.1441395 ◽

1982 ◽

Vol 47 (9) ◽

pp. 1335-1337

Author(s):

E. A. Nosal

Keyword(s):

Closed Form ◽

Signal Analysis ◽

Closed Form Solution ◽

Form Solution ◽

The Other ◽

Individual Contribution ◽

Spontaneous Potential ◽

The Earth ◽

The Individual ◽

Special Case

A special case of spontaneous potential (SP) logging, which has a closed‐form solution, will be expressed as a convolutional operation. Such a formal demonstration serves two purposes. First, it separates the individual contribution of the tool from that of the earth. Second, it places this logging device within the mathematical context of signal analysis. The special case for which a closed‐form solution is known is that where all resistivities are equal. Fourier analysis applied to this solution leads to a product of two functions, of which one is identified as the contribution of the earth and the other of the tool.

Download Full-text

Closed-Form Solution of a Special Case of a Vehicle Longitudinal Motion Model

Vehicles ◽

10.3390/vehicles1010007 ◽

2019 ◽

Vol 1 (1) ◽

pp. 116-126 ◽

Cited By ~ 1

Author(s):

Blagojevic ◽

Djudurovic ◽

Bajic

Keyword(s):

Mathematical Model ◽

Closed Form ◽

Closed Form Solution ◽

Large Data ◽

Form Solution ◽

Longitudinal Motion ◽

Data Set ◽

Engineering Research ◽

Complex Mathematical Model ◽

Special Case

One of the most common approaches in modern engineering research, including vehicle dynamics, is to formulate an accurate, but typically complex, mathematical model of a system or phenomenon and then use a software package to solve it. Typically, the solution is obtained in the form of a large data set, which may be difficult to analyse and interpret. This paper represents a purely theoretical analysis of a special case of vehicle longitudinal motion. Starting from a simplified mathematical model, a set of transcendental equations was derived that represents the exact solution of the model (i.e., in a closed form). The equations are analysed and interpreted in terms of what is their physical meaning. Although the equations derived here have only limited application in studying real world problems, due to the simplicity of the mathematical model, they offer a deeper insight into the nature of vehicle longitudinal motion.

Download Full-text

Closed Form Solution for Outage and Average Bit Error Rate of Asymmetric Relaying System

International Journal of Innovative Technology and Exploring Engineering - Special Issue ◽

10.35940/ijitee.k2438.0981119 ◽

2019 ◽

Vol 8 (11) ◽

pp. 3304-3310

Keyword(s):

Closed Form ◽

Fading Channels ◽

Bit Error Rate ◽

Error Rate ◽

Signal To Noise Ratio ◽

Closed Form Solution ◽

Form Solution ◽

Amplify And Forward ◽

Severity Factor ◽

Special Case

In this paper, closed form solution of outage and bit error rate (BER) is evaluated for the purpose of performance analysis of the amplify and forward relaying scheme under the asymmetric fading environment. In this dual hop system, we have used Rayleigh fading along source S to relay R and Mixture Gamma fading along relay R to destination D. First, we have derived closed form solution of outage and then we have used this derived expression for getting closed form solution of bit error rate (BER) for different kinds of modulation. Since Mixture Gamma fading channel represents many fading channels as its special case, so proposed closed form solution of outage and bit error rate may be used for analysis of outage and bit error rate under various fading scenarios. Specifically, in this paper, for analysis of outage and bit error rate (BER), we have taken Nakagami-m fading as a particular case of Mixture Gamma fading and analyzed the performance of proposed system after observing effect of fading severity factor and signal to noise ratio (SNR) on outage probability and bit error rate (BER)

Download Full-text