Some Properties of Weak Block Designs

The necessary conditions for the existence of weak designs are given in the form of two inequalities in this paper. The relations among weak block designs (WBDs) , Balanced incomplete block designs ( BIBDs) and differential balanced block designs (DBBDs) are researched.

Splitting Balanced Incomplete Block Designs with Block Size 2×k

This paper investigated the existence of splitting balanced incomplete block designs with blck size 2× k .The necessary conditions for such a design are λ(v-1) ≡0(mod k ),and λv(v- 1)≡0(mod 2 k 2).It will show that the above necessary conditions are also sufficient for k =3 with the definite exception( v,λ )=(10,1) and with several possible exceptions.

CONSTRUCTION OF NONSYSTEMATIC LOW-DENSITY PARITY-CHECK CODES BASED ON SYMMETRIC BALANCED INCOMPLETE BLOCK DESIGN

This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes con-structed based on SBIBD is presented.Their characteristics include:both generator matrices andparity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbi-trary rate codes can be easily constructed,so they are rate-compatible codes.Because there aresparse generalized inverses of generator matrices,the performance of the proposed codes is only0.15dB away from that of the traditional systematic LDPC codes.

A New Method of Construction of Robust Second Order Rotatable Designs Using Balanced Incomplete Block Designs

The following article has been retracted due to the investigation of complaints received against it. Title: A New Method of Construction of Robust Second Order Rotatable Designs Using Balanced Incomplete Block Designs Authors: Bejjam Re. Victorbabu, Kottapalli Rajyalakshmi. The above paper is a copy of Dr. Rabindra Nath Das’s former article, entitled '“Robust second order rotatable designs (Part I)”. The scientific community takes a very strong view on this matter and we solemnly withdrawn?the paper from the journal OJS. This paper published in OJS Vol.2 No.1, 39-47, 2012, has been retracted.

Variable Selection in Randomized Block Design Experiment

In the experimental field, researchers need very often to select the best subset model as well as reach the best model estimation simultaneously. Selecting the best subset of variables will improve the prediction accuracy as noninformative variables will be removed. Having a model with high prediction accuracy allows the researchers to use the model for future forecasting. In this paper, we investigate the differences between various variable selection methods. The aim is to compare the analysis of the frequentist methodology (the backward elimination), penalised shrinkage method (the Adaptive LASSO) and the Least Angle Regression (LARS) for selecting the active variables for data produced by the blocked design experiment. The result of the comparative study supports the utilization of the LARS method for statistical analysis of data from blocked experiments.

FURTHER RESULTS ON THE EXISTENCE OF LABELED RESOLVABLE BLOCK DESIGNS

It was proved in this paper that there exists a labeled resolvable block design LRB (4,3; v ) if and only if v ≡0 (mod 4) and v ≥8, with 8 possible exceptions. It was also proved that there exists a nearly Kirkman system NKS (2,4; v ) if and only if v ≡0 (mod 12) and v ≥24, except possibly when v =264 or 372.

U-Type Designs via New Generalized Partially Balanced Incomplete Block Designs with <i>m</i>= 4, 5 and 7 Associated Classes

The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes (m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns (w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method (s). For n or l even and s divisor of n or l, the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U-type designs U (wnl;) (r is the repetition number of each treatment in our resolvable PBIB design).

SUZUKI GROUPS Sz(q) AND 2-(v,k,1) BLOCK DESIGNS

It is proved that if D be a 2|(v,k,1) design with G≤ Aut D block primitive then G does not have a Suzuki group Sz(q) as the socle.

EMBEDDINGS OF SIMPLE TWO-FOLD BALANCED INCOMPLETE BLOCK DESIGNS WITH BLOCK SIZE FOUR

The necessary and sufficient conditions for the existence of simple incomplete block design （v, ω; 4, 2）-IPBDs are determined. As a consequence, the necessary and sufficient conditions for the embeddings of simple two-fold balanced incomplete block designs with block size 4 are also determined.

On the Existence of (v,3×3,λ)-Splitting Balanced Incomplete Block Design with λ between 2 to 9

Let （v, u × c,λ）-splitting BIBD denote a （v, u × c,λ）-splitting balanced incomplete block design of order v with block size u × c and index A. The necessary conditions for the existence of a （v, u × c,λ）-splitting BIBD are v ≥ uc, λ（v- 1） -- 0 0 mod （c（u- 1）） and Av（v- 1） - 0 mod （c^2u（u- 1））. In this paper, for 2 ≤λ≤ 9 the necessary conditions for the existence of a （v, 3 × 3, λ）-splitting BIBD are also sufficient with one possible exception for （v, λ） = （39, 9）.

General Solution of Normal Equations in the Intra-Block Analysis of PBIB Designs with Four Associates

General solution of normal equations in the general intra-block analysis of partially balanced incomplete block designs involving four associates is presented in this talk as they are quite useful in practice. Only intra-block estimates are given as the necessary formulae for inter-block estimates can be derived from them by changing the parameters as discussed in Rao[5]. We have obtained the general formulae for computation of four types of efficiencies, the average efficiency factor and the variance of the estimated elementary treatment contrast of the four types of comparisons irrespective of the type of association scheme a PBIB Design follows.

Landscape Planning and Design of Folk Culture Block Based on Theory of Three Elements of Landscape

This paper firstly defined the concept of folk culture block,and then analyzed the significance and planning principle of landscape design in folk culture block,and at last expounded landscape planning and design of folk culture block based on theory of three elements of landscape.

ORTHOGONAL GEOMETRIES OVER FINITE FIELDS WITH CHARACTERISTIC≠2 AND BLOCK DESIGNS

By taking as blocks certain subspace-pairs of an orthogonal geometry over a finite field with characteristic≠2 we construct some new types of BIB designs and PBIB designs whose parameters are also given.

Some Construction Methods of Optimum Chemical Balance Weighing Designs III

Methods of constructing the optimum chemical balance weighing designs from symmetric balanced incomplete block designs are proposed with illustration. As a by-product pairwise efficiency and variance balanced designs are also obtained.

Some results on resolvable incomplete block designs

This paper is concerned with the uniformity of a certain kind of resolvable incomplete block (RIB for simplicity) design which is called the PRIB design here. A sufficient and necessary condition is obtained, under which a PRIB design is the most uniform in the sense of a discrete discrepancy measure, and the uniform PRIB design is shown to be connected. A construction method for such designs via a kind of U-type designs is proposed, and an existence result of these designs is given. This method sets up an important bridge between PRIB designs and U-type designs.

CONSTRUCTION OF OPTIMAL BLOCKING SCHEMES FOR ROBUST PARAMETER DESIGNS

Robust parameter design （RPD） is an important issue in experimental designs. If all experimental runs cannot be performed under homogeneous conditions, blocking the units is effective. In this paper, we obtain the correspondence relation between fractional factorial RPDs and the blocking schemes for full factorial RPDs. In addition, we provide a construction of optimal blocking schemes that make all main effects and control-by-noise two-factor interactions estimable.

Die design and process optimization of die cast V6 engine blocks

The use of aluminum, particularly for engine blocks, has grown considerably in the past ten years, and continues to rise in the automotive industry. In order to enhance the quality and engineering functionality of die cast engine blocks, die design and processes have to be optimized. In this study, a computer simulation software, MAGMAsoft, as an advanced tool for optimizing die design and casting process, was employed to virtually visualize cavity filling and patterns of a V6 engine block. The original die design and process was simulated first to establish a baseline. A reality check was used to verify the predicted results. Then, the die modification with a different runner system was made by using a CAD software, Unigraphics (UG). The simulation on combinations of the modified die design and revised process was performed to examine the effect of die modification and process change on flow filling of V6 engine blocks. The simulated prediction indicates that the enhancement of cavity filling due to the die and process modification minimizes the occurrence of defects during casting, and consequently improves the quality of blocks. The results of mechanical testing show a significant increase in fatigue strengths, and a moderately improvement on tensile properties for the blocks die cast with the new die design and process in comparison with those produced by the original ones.

OPTIMIZATION DESIGN OF HYDRAULIC MANIFOLD BLOCKS BASED ON HUMAN-COMPUTER COOPERATIVE GENETIC ALGORITHM

Optimization design of hydraulic manifold blocks (HMB) is studied as acomplex solid spatial layout problem. Based on comprehensive research into structure features anddesign rules of HMB, an optimal mathematical model for this problem is presented. Usinghuman-computer cooperative genetic algorithm (GA) and its hybrid optitation strategies, integratedlayout and connection design schemes of HMB can be automatically optimized. An example is given totestify it.

Comparative Analysis on Space Form of Block in Arid Region and Ecological Design Strategy

Due to unique geographical position and climatic characteristics,there are more economic,social,resource,environmental and other problems in urban construction of arid region. Old urban block of Kashgar and typical block of Masdar ecological city of Abu Dhabi are taken as the research objects. Based on summarizing the characteristics of traditional block and newly built ecological block in arid region,comparative analysis on their space forms and environmental designs is conducted,and the association mechanism between ecological adaptability and space form is generalized. From the aspects of block layout,block space,open space and architectural form,ecological design strategy of the block in arid region is proposed,which could provide the reference for development and construction of ecological city in arid region of China.

Block-Transitive 4-(v,k,4) Designs and Ree Groups

This article is a contribution to the study of the automorphism groups of designs. Let be a non-trivial design where for some positive integer , and is block-transitive. If the socle of G is isomorphic to the simple groups of lie type, then G is not flag-transitive.