Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 18683

# Search results for: number of order

##### 18683 The Theory of Number "0"

Authors: Iryna Shevchenko

Abstract:

The science of mathematics was originated at the order of count of objects and subsequently for the measurement of size and quality of objects using the logical or abstract means. The laws of mathematics are based on the study of absolute values. The number 0 or "nothing" is the purely logical (as the opposite to absolute) value as the "nothing" should always assume the space for the something that had existed there; otherwise the "something" would never come to existence. In this work we are going to prove that the number "0" is the abstract (logical) and not an absolute number and it has the absolute value of “∞” (infinity). Therefore, the number "0" might not stand in the row of numbers that symbolically represents the absolute values, as it would be the mathematically incorrect. The symbolical value of number "0" in the row of numbers could be represented with symbol "∞" (infinity). As a result, we have the mathematical row of numbers: epsilon, ...4, 3, 2, 1, ∞. As the conclusions of the theory of number “0” we presented the statements: multiplication and division by fractions of numbers is illegal operation and the mathematical division by number “0” is allowed. Downloads 460
##### 18682 A Second Order Genetic Algorithm for Traveling Salesman Problem

Authors: T. Toathom, M. Munlin, P. Sugunnasil

Abstract:

The traveling salesman problem (TSP) is one of the best-known problems in optimization problem. There are many research regarding the TSP. One of the most usage tool for this problem is the genetic algorithm (GA). The chromosome of the GA for TSP is normally encoded by the order of the visited city. However, the traditional chromosome encoding scheme has some limitations which are twofold: the large solution space and the inability to encapsulate some information. The number of solution for a certain problem is exponentially grow by the number of city. Moreover, the traditional chromosome encoding scheme fails to recognize the misplaced correct relation. It implies that the tradition method focuses only on exact solution. In this work, we relax some of the concept in the GA for TSP which is the exactness of the solution. The proposed work exploits the relation between cities in order to reduce the solution space in the chromosome encoding. In this paper, a second order GA is proposed to solve the TSP. The term second order refers to how the solution is encoded into chromosome. The chromosome is divided into 2 types: the high order chromosome and the low order chromosome. The high order chromosome is the chromosome that focus on the relation between cities such as the city A should be visited before city B. On the other hand, the low order chromosome is a type of chromosome that is derived from a high order chromosome. In other word, low order chromosome is encoded by the traditional chromosome encoding scheme. The genetic operation, mutation and crossover, will be performed on the high order chromosome. Then, the high order chromosome will be mapped to a group of low order chromosomes whose characteristics are satisfied with the high order chromosome. From the mapped set of chromosomes, the champion chromosome will be selected based on the fitness value which will be later used as a representative for the high order chromosome. The experiment is performed on the city data from TSPLIB. Downloads 198
##### 18681 Characterization of Number of Subgroups of Finite Groups

Authors: Khyati Sharma, A. Satyanarayana Reddy

Abstract:

The topic of how many subgroups exist within a certain finite group naturally arises in the study of finite groups. Over the years, different researchers have investigated this issue from a variety of angles. The significant contributions of the key mathematicians over the time have been summarized in this article. To this end, we classify finite groups into three categories viz. (a) Groups for which the number of subgroups is less than |G|, (b) equals to |G|, and finally, (c) greater than |G|. Because every element of a finite group generates a cyclic subgroup, counting cyclic subgroups is the most important task in this endeavor. A brief survey on the number of cyclic subgroups of finite groups is also conducted by us. Furthermore, we also covered certain arithmetic relations between the order of a finite group |G| and the number of its distinct cyclic subgroups |C(G)|. In order to provide pertinent context and possibly reveal new novel areas of potential research within the field of research on finite groups, we finally pose and solicit a few open questions. Downloads 8
##### 18680 Numerical Solutions of Fractional Order Epidemic Model

Abstract:

The dynamical study of the carriers play an essential role in the evolution and global transmission of infectious diseases and will be discussed in this study. To make this approach novel, we will consider the fractional order model which is generalization of integer order derivative to an arbitrary number. Since the integration involved is non local therefore this property of fractional operator is very useful to study epidemic model for infectious diseases. An extended numerical method (ODE solver) is implemented on the model equations and we will present the simulations of the model for diﬀerent values of fractional order to study the eﬀect of carriers on transmission dynamics. Global dynamics of fractional model are established by using the reproduction number. Downloads 442
##### 18679 Core Number Optimization Based Scheduler to Order/Mapp Simulink Application

Abstract:

Over these last years, the number of cores witnessed a spectacular increase in digital signal and general use processors. Concurrently, significant researches are done to get benefit from the high degree of parallelism. Indeed, these researches are focused to provide an efficient scheduling from hardware/software systems to multicores architecture. The scheduling process consists on statically choose one core to execute one task and to specify an execution order for the application tasks. In this paper, we describe an efficient scheduler that calculates the optimal number of cores required to schedule an application, gives a heuristic scheduling solution and evaluates its cost. Our proposal results are evaluated and compared with Preesm scheduler results and we prove that ours allows better scheduling in terms of latency, computation time and number of cores. Downloads 205
##### 18678 Workforce Optimization: Fair Workload Balance and Near-Optimal Task Execution Order

Authors: Alvaro Javier Ortega

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##### 18677 Analysis of Slip Flow Heat Transfer between Asymmetrically Heated Parallel Plates

Abstract:

In the present study, analysis of heat transfer is carried out in the slip flow region for the fluid flowing between two parallel plates by employing the asymmetric heat fluxes at surface of the plates. The flow is assumed to be hydrodynamically and thermally fully developed for the analysis. The second order velocity slip and viscous dissipation effects are considered for the analysis. Closed form expressions are obtained for the Nusselt number as a function of Knudsen number and modified Brinkman number. The limiting condition of the present prediction for Kn = 0, Kn2 = 0, and Brq1 = 0 is considered and found to agree well with other analytical results. Downloads 295
##### 18676 Model Order Reduction for Frequency Response and Effect of Order of Method for Matching Condition

Abstract:

In this paper, model order reduction method is used for approximation in linear and nonlinearity aspects in some experimental data. This method can be used for obtaining offline reduced model for approximation of experimental data and can produce and follow the data and order of system and also it can match to experimental data in some frequency ratios. In this study, the method is compared in different experimental data and influence of choosing of order of the model reduction for obtaining the best and sufficient matching condition for following the data is investigated in format of imaginary and reality part of the frequency response curve and finally the effect and important parameter of number of order reduction in nonlinear experimental data is explained further. Downloads 317

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##### 18674 Analysis of Evolution of Higher Order Solitons by Numerical Simulation

Abstract:

Solitons are stable solution of nonlinear Schrodinger equation. Their stability is due to the exact combination between nonlinearity and dispersion which causes pulse broadening. Higher order solitons are born when nonlinear length is N multiple of dispersive length. Soliton order is determined by the number N itself. In this paper, evolution of higher order solitons is illustrated by simulation using Matlab. Results show that higher order solitons change their shape periodically, the reason why they are bad for transmission comparing to fundamental solitons which are constant. Partial analysis of a soliton of higher order explains that the periodic shape is due to the interplay between nonlinearity and dispersion which are not equal during a period. This class of solitons has many applications such as generation of supercontinuum and the impulse compression on the Femtosecond scale. As a conclusion, the periodicity which is harmful to transmission can be beneficial in other applications.

Keywords: dispersion, nonlinearity, optical fiber, soliton

##### 18673 A Remote Sensing Approach to Calculate Population Using Roads Network Data in Lebanon

Abstract:

In developing countries, such as Lebanon, the demographic data are hardly available due to the absence of the mechanization of population system. The aim of this study is to evaluate, using only remote sensing data, the correlations between the number of population and the characteristics of roads network (length of primary roads, length of secondary roads, total length of roads, density and percentage of roads and the number of intersections). In order to find the influence of the different factors on the demographic data, we studied the degree of correlation between each factor and the number of population. The results of this study have shown a strong correlation between the number of population and the density of roads and the number of intersections. Downloads 79
##### 18672 Automatic Number Plate Recognition System Based on Deep Learning

Abstract:

In the last few years, Automatic Number Plate Recognition (ANPR) systems have become widely used in the safety, the security, and the commercial aspects. Forethought, several methods and techniques are computing to achieve the better levels in terms of accuracy and real time execution. This paper proposed a computer vision algorithm of Number Plate Localization (NPL) and Characters Segmentation (CS). In addition, it proposed an improved method in Optical Character Recognition (OCR) based on Deep Learning (DL) techniques. In order to identify the number of detected plate after NPL and CS steps, the Convolutional Neural Network (CNN) algorithm is proposed. A DL model is developed using four convolution layers, two layers of Maxpooling, and six layers of fully connected. The model was trained by number image database on the Jetson TX2 NVIDIA target. The accuracy result has achieved 95.84%.

Keywords: ANPR, CS, CNN, deep learning, NPL

##### 18671 An Optimal and Efficient Family of Fourth-Order Methods for Nonlinear Equations

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In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect. Downloads 241
##### 18670 Second-Order Slip Flow and Heat Transfer in a Long Isothermal Microchannel

Authors: Huei Chu Weng, Chien-Hung Liu

Abstract:

This paper presents a study on the effect of second-order slip and jump on forced convection through a long isothermally heated or cooled planar microchannel. The fully developed solutions of thermal flow fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and Smoluchowski jump boundary conditions. Results reveal that the second-order term in the Karniadakis slip boundary condition is found to contribute a negative velocity slip and then to lead to a higher pressure drop as well as a higher fluid temperature for the heated-wall case or to a lower fluid temperature for the cooled-wall case. These findings are contrary to predictions made by the Deissler model. In addition, the role of second-order slip becomes more significant when the Knudsen number increases. Downloads 384
##### 18669 Flow of a Second Order Fluid through Constricted Tube with Slip Velocity at Wall Using Integral Method

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The steady flow of a second order fluid through constricted tube with slip velocity at wall is modeled and analyzed theoretically. The governing equations are simplified by implying no slip in radial direction. Based on Karman Pohlhausen procedure polynomial solution for axial velocity profile is presented. An expressions for pressure gradient, shear stress, separation and reattachment points and radial velocity are also calculated. The effect of slip and no slip velocity on velocity, shear stress, pressure gradient are discussed and depicted graphically. It is noted that when Reynolds number increases velocity of the fluid decreases in both slip and no slip conditions. It is also found that the wall shear stress, separation and reattachment points are strongly effected by Reynolds number. Downloads 308
##### 18668 Study the Effect of Roughness on the Higher Order Moment to Extract Information about the Turbulent Flow Structure in an Open Channel Flow

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The present study was carried out to understand the extent of effect of roughness and Reynolds number in open channel flow (OCF). To this extent, four different types of bed surface conditions consisting smooth, distributed roughness, continuous roughness, natural sand bed and two different Reynolds number for each bed surfaces were adopted in this study. Particular attention was given on mean velocity, turbulence intensity, Reynolds shear stress, correlation, higher order moments and quadrant analysis. Further, the extent of influence of roughness and Reynolds number in the depth-wise direction also studied. Increasing Reynolds shear stress near rough beds are noticed due to arrays of discrete roughness elements and flow over these elements generating a series of wakes which contributes to the generation of significantly higher Reynolds shear stress. Downloads 196
##### 18667 Introduction to Paired Domination Polynomial of a Graph

Authors: Puttaswamy, Anwar Alwardi, Nayaka S. R.

Abstract:

One of the algebraic representation of a graph is the graph polynomial. In this article, we introduce the paired-domination polynomial of a graph G. The paired-domination polynomial of a graph G of order n is the polynomial Dp(G, x) with the coefficients dp(G, i) where dp(G, i) denotes the number of paired dominating sets of G of cardinality i and γpd(G) denotes the paired-domination number of G. We obtain some properties of Dp(G, x) and its coefficients. Further, we compute this polynomial for some families of standard graphs. Further, we obtain some characterization for some specific graphs. Downloads 149
##### 18666 Generic Polynomial of Integers and Applications

Authors: Nidal Ali

Abstract:

Consider an algebraic number field K of degree n, A0 K is its ring of integers and a prime number p inert in K. Let F(u1, . . . , un, x) be the generic polynomial of integers of K. We will study in advance the stability of this polynomial and then, we will apply it in order to obtain all the monic irreducible polynomials in Fp[x] of degree d dividing n. Downloads 276
##### 18665 Air Pollution and Respiratory-Related Restricted Activity Days in Tunisia

Authors: Mokhtar Kouki Inès Rekik

Abstract:

This paper focuses on the assessment of the air pollution and morbidity relationship in Tunisia. Air pollution is measured by ozone air concentration and the morbidity is measured by the number of respiratory-related restricted activity days during the 2-week period prior to the interview. Socioeconomic data are also collected in order to adjust for any confounding covariates. Our sample is composed by 407 Tunisian respondents; 44.7% are women, the average age is 35.2, near 69% are living in a house built after the 1980, and 27.8% have reported at least one day of respiratory-related restricted activity. The model consists on the regression of the number of respiratory-related restricted activity days on the air quality measure and the socioeconomic covariates. In order to correct for zero-inflation and heterogeneity, we estimate several models (Poisson, Negative binomial, Zero inflated Poisson, Poisson hurdle, Negative binomial hurdle and finite mixture Poisson models). Bootstrapping and post-stratification techniques are used in order to correct for any sample bias. According to the Akaike information criteria, the hurdle negative binomial model has the greatest goodness of fit. The main result indicates that, after adjusting for socioeconomic data, the ozone concentration increases the probability of positive number of restricted activity days. Downloads 177
##### 18664 Nonhomogeneous Linear Fractional Differential Equations Will Bessel Functions of the First Kind Giving Hypergeometric Functions Solutions

Authors: Fernando Maass, Pablo Martin, Jorge Olivares

Abstract:

Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α. Downloads 111
##### 18663 A Study on Stochastic Integral Associated with Catastrophes

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We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t). Downloads 550
##### 18662 A Polynomial Time Clustering Algorithm for Solving the Assignment Problem in the Vehicle Routing Problem

Authors: Lydia Wahid, Mona F. Ahmed, Nevin Darwish

Abstract:

The vehicle routing problem (VRP) consists of a group of customers that needs to be served. Each customer has a certain demand of goods. A central depot having a fleet of vehicles is responsible for supplying the customers with their demands. The problem is composed of two subproblems: The first subproblem is an assignment problem where the number of vehicles that will be used as well as the customers assigned to each vehicle are determined. The second subproblem is the routing problem in which for each vehicle having a number of customers assigned to it, the order of visits of the customers is determined. Optimal number of vehicles, as well as optimal total distance, should be achieved. In this paper, an approach for solving the first subproblem (the assignment problem) is presented. In the approach, a clustering algorithm is proposed for finding the optimal number of vehicles by grouping the customers into clusters where each cluster is visited by one vehicle. Finding the optimal number of clusters is NP-hard. This work presents a polynomial time clustering algorithm for finding the optimal number of clusters and solving the assignment problem. Downloads 273
##### 18661 Presence of Nesting Parrot (Psittacula krameri borealis) Order Psitaciforme, Family Psittacidea in District Mirpurkhas Sindh Pakistan

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The parrot (Psittacula krameri borealis) commonly known as ‘Tota’ belongs to the order ‘Psittaciformes’ and family ‘Psittacidea’. Its range inhabits tropical to subtropical regions. The parrot (Psittacula krameri borealis) has been categorized as least concern species. The core aim of the present study is to investigate the nesting of parrot (Psittacula krameri borealis); site observation was done a different interval from various adjoining areas of District Mirpurkhas from June 2017 to May 2018. During the study period, altogether 15 nests were observed, number of nests were high in June’s month (33.3%), July (13.3%), August (20.0 %), March (13.3%), April (13.3%) while the lowest number of nest was observed in September’s month (6.6%) and the nest was absent from October to February. It investigates that the number of nests was high June’s month when temperature range between '20 °C' and '45 °C'. Downloads 80
##### 18660 Second-Order Complex Systems: Case Studies of Autonomy and Free Will

Authors: Eric Sanchis

Abstract:

Although there does not exist a definitive consensus on a precise definition of a complex system, it is generally considered that a system is complex by nature. The presented work illustrates a different point of view: a system becomes complex only with regard to the question posed to it, i.e., with regard to the problem which has to be solved. A complex system is a couple (question, object). Because the number of questions posed to a given object can be potentially substantial, complexity does not present a uniform face. Two types of complex systems are clearly identified: first-order complex systems and second-order complex systems. First-order complex systems physically exist. They are well-known because they have been studied by the scientific community for a long time. In second-order complex systems, complexity results from the system composition and its articulation that are partially unknown. For some of these systems, there is no evidence of their existence. Vagueness is the keyword characterizing this kind of systems. Autonomy and free will, two mental productions of the human cognitive system, can be identified as second-order complex systems. A classification based on the properties structure makes it possible to discriminate complex properties from the others and to model this kind of second order complex systems. The final outcome is an implementable synthetic property that distinguishes the solid aspects of the actual property from those that are uncertain. Downloads 120
##### 18659 Improvement of Central Composite Design in Modeling and Optimization of Simulation Experiments

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Simulation modeling can be used to solve real world problems. It provides an understanding of a complex system. To develop a simplified model of process simulation, a suitable experimental design is required to be able to capture surface characteristics. This paper presents the experimental design and algorithm used to model the process simulation for optimization problem. The CO2 liquefaction based on external refrigeration with two refrigeration circuits was used as a simulation case study. Latin Hypercube Sampling (LHS) was purposed to combine with existing Central Composite Design (CCD) samples to improve the performance of CCD in generating the second order model of the system. The second order model was then used as the objective function of the optimization problem. The results showed that adding LHS samples to CCD samples can help capture surface curvature characteristics. Suitable number of LHS sample points should be considered in order to get an accurate nonlinear model with minimum number of simulation experiments. Downloads 85
##### 18658 Effect of Nanoparticle Diameter of Nano-Fluid on Average Nusselt Number in the Chamber

Authors: A. Ghafouri, N. Pourmahmoud, I. Mirzaee

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In this numerical study, effects of using Al2O3-water nanofluid on the rate of heat transfer have been investigated numerically. The physical model is a square enclosure with insulated top and bottom horizontal walls while the vertical walls are kept at different constant temperatures. Two appropriate models are used to evaluate the viscosity and thermal conductivity of nanofluid. The governing stream-vorticity equations are solved using a second order central finite difference scheme, coupled to the conservation of mass and energy. The study has been carried out for the nanoparticle diameter 30, 60, and 90 nm and the solid volume fraction 0 to 0.04. Results are presented by average Nusselt number and normalized Nusselt number in the different range of φ and D for mixed convection dominated regime. It is found that different heat transfer rate is predicted when the effect of nanoparticle diameter is taken into account. Downloads 310
##### 18657 Basins of Attraction for Quartic-Order Methods

Authors: Young Hee Geum

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We compare optimal quartic order method for the multiple zeros of nonlinear equations illustrating the basins of attraction. To construct basins of attraction effectively, we take a 600×600 uniform grid points at the origin of the complex plane and paint the initial values on the basins of attraction with different colors according to the iteration number required for convergence. Downloads 201
##### 18656 Automatic Teller Machine System Security by Using Mobile SMS Code

Authors: Husnain Mushtaq, Mary Anjum, Muhammad Aleem

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The main objective of this paper is used to develop a high security in Automatic Teller Machine (ATM). In these system bankers will collect the mobile numbers from the customers and then provide a code on their mobile number. In most country existing ATM machine use the magnetic card reader. The customer is identifying by inserting an ATM card with magnetic card that hold unique information such as card number and some security limitations. By entering a personal identification number, first the customer is authenticated then will access bank account in order to make cash withdraw or other services provided by the bank. Cases of card fraud are another problem once the user’s bank card is missing and the password is stolen, or simply steal a customer’s card & PIN the criminal will draw all cash in very short time, which will being great financial losses in customer, this type of fraud has increase worldwide. So to resolve this problem we are going to provide the solution using “Mobile SMS code” and ATM “PIN code” in order to improve the verify the security of customers using ATM system and confidence in the banking area. Downloads 295
##### 18655 Portfolio Optimization with Reward-Risk Ratio Measure Based on the Mean Absolute Deviation

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In problems of portfolio selection, the reward-risk ratio criterion is optimized to search for a risky portfolio with the maximum increase of the mean return in proportion to the risk measure increase when compared to the risk-free investments. In the classical model, following Markowitz, the risk is measured by the variance thus representing the Sharpe ratio optimization and leading to the quadratic optimization problems. Several Linear Programming (LP) computable risk measures have been introduced and applied in portfolio optimization. In particular, the Mean Absolute Deviation (MAD) measure has been widely recognized. The reward-risk ratio optimization with the MAD measure can be transformed into the LP formulation with the number of constraints proportional to the number of scenarios and the number of variables proportional to the total of the number of scenarios and the number of instruments. This may lead to the LP models with huge number of variables and constraints in the case of real-life financial decisions based on several thousands scenarios, thus decreasing their computational efficiency and making them hardly solvable by general LP tools. We show that the computational efficiency can be then dramatically improved by an alternative model based on the inverse risk-reward ratio minimization and by taking advantages of the LP duality. In the introduced LP model the number of structural constraints is proportional to the number of instruments thus not affecting seriously the simplex method efficiency by the number of scenarios and therefore guaranteeing easy solvability. Moreover, we show that under natural restriction on the target value the MAD risk-reward ratio optimization is consistent with the second order stochastic dominance rules. Downloads 324
##### 18654 Effects of a Dwarfing Gene sd1-d (Dee-Geo-Woo-Gen Dwarf) on Yield and Related Traits in Rice: Preliminary Report

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The sd1-d allele at the sd1 locus on chromosome 1, originating from Taiwanese variety Dee-geo-woo-gen, has been playing important role for developing short-culm and lodging-resistant indica varieties such as IR36 in rice. The dominant allele SD1 for long culm at the locus is differentiated into SD1-in and SD1-ja which are harbored in indica and japonica subspecies’s, respectively. The sd1-d of an indica variety IR36 was substituted with SD1-in or SD1-ja by recurrent backcrosses of 17 times with IR36, and two isogenic tall lines regarding the respective dominant alleles were developed by using an indica variety IR5867 and a japonica one ‘Koshihikari’ as donors, which were denoted by '5867-36' and 'Koshi-36', respectively. The present study was conducted to examine the effect of sd1-d on yield and related traits as compared with SD1-in and SD1-ja, by using the two isogenic tall lines. Seedlings of IR36 and the two isogenic lines were transplanted on an experimental field of Kochi University, by the planting distance of 30 cm × 15 cm with two seedlings per hill, on May 3, 2017. Chemical fertilizers were supplied by basal application and top-dressing at a rate of 8.00, 6.57 and 7.52 g/m², respectively, for N, P₂O₅ and K₂O in total. Yield, yield components, and other traits were measured. Culm length (cm) was in the order of 5867-36 (101.9) > Koshi-36 (80.1) > IR36 (60.0), where '>' indicates statistically significant difference at the 5% level. Accordingly, sd1-d reduced culm by 41.9 and 20.1 cm, compared with SD1-in and SD1-ja, respectively, and the effect of elongating culm was higher in the former allele than in the latter one. Total brown rice yield (g/m²), including unripened grains, was in the order of IR36 (611) ≧ 5867-36 (586) ≧ Koshi-36 (572), indicating non-significant differences among them. Yield-1.5mm sieve (g/m²) was in the order of IR36 (596) ≧ 5867-36 (575) ≧ Koshi-36 (558). Spikelet number per panicle was in the order of 5867-36 (89.2) ≧ IR36 (84.7) ≧ Koshi-36 (79.8), and 5867-36 > Koshi-36. Panicle number per m² was in the order of IR36 (428) ≧ Koshi-36 (403) ≧ 5867-36 (353), and IR36 > 5867-36, suggesting that sd1-d increased number of panicles compared with SD1-in. Ripened-grain percentage-1.5mm sieve was in the order of Koshi-36 (86.0) ≧ 5867-36 (85.0) ≧ IR36 (82.7), and Koshi-36 > IR36. Thousand brown-rice-grain weight-1.5mm sieve (g) was in the order of 5867-36 (21.5) > Koshi-36 (20.2) ≧ IR36 (19.9). Total dry weight at maturity (g/m²) was in the order of 5867-36 (1404 ) ≧ IR36 (1310) ≧ Kosihi-36 (1290). Harvest index of total brown rice (%) was in the order of IR36 (39.6) > Koshi-36 (37.7) > 5867-36 (35.5). Hence, sd1-d did not exert significant effect on yield in indica genetic background. However, lodging was observed from the late stage of maturity in 5867-36 and Koshi-36, particularly in the former, which was principally due to their long culms. Consequently, sd1-d enables higher yield with higher fertilizer application, by enhancing lodging resistance, particularly in indica subspecies.

Keywords: rice, dwarfing gene, sd1-d, SD1-in, SD1-ja, yield