WE SHOW THAT A CODED SYSTEM IS MIXING IF AND ONLY IF IT HAS STRONG PROPERTY P IF AND ONLY IF IT IS TOTALLY TRANSITIVE.THEN WE GIVE SOME RESULTS ON SPACING SHIFTS. LET (SP, SP) BE THE SPACE OF A SPACING SHIFT WHERE (FORMULA) SHOW THAT (SP, SP) IS CODED IF AND ONLY IF P IS COFINITE OR K N FOR SOME KÎ N.

THE EFFECT OF MONO SIZE LINEAR POLYSTYRENE (PS), LINEAR AND CROSS LINKED STYRENE ACRYLONITRILE (SAN, XSAN) COPOLYMER WITH 25 WT% OF ACRYLONITRILE PARTICLES AND AVERAGE MOLECULAR WEIGHT OF 500 KG/MOLE ON RELATIVE PERCENTAGE OF BETA POLYMORPHISM OF POLYPROPYLENE WAS INVESTIGATED UTILIZING POLARIZED OPTICAL MICROSCOPE (POM), X-RAY DIFFRACTION (XRD) AND DIFFERENTIAL SCANNING CALORIMETERY (DSC). THE RELATIVE PERCENTAGE OF B POLYMORPHISM IN PP CONTAINING SAN, PS AND XSAN AFTER ANNEALING AT 115OC FOR 10 MINUTES WAS 34, 14 AND 6%, RESPECTIVELY. THE DIFFERENCE IN B NUCLEATION EFFICIENCY OF THESE PARTICLES WAS ATTRIBUTED TO THE AVERAGE PHENYL D-SPACING OF STYRENE MONOMERS IN THE BACKBONE OF PS, SAN AND XSAN NANO PARTICLES.

BACKGROUND: THE CHEMICAL MODIFICATION OF LAYERED SILICATES IS BASED ON CATIONIC EXCHANGE REACTION BETWEEN THE CLAY INORGANIC CATIONS AND THE CATIONS OF THE ORGANIFIER (INTERCALATING AGENT) USUALLY AN AMMONIUM OR PHOSPHONIUM-BASED SURFACTANT [1, 2]. …

EXISTING GEOMETRIC DESIGN GUIDANCE RELATED TO INTERCHANGE RAMP IS NOT SPEED-DEPENDENT EVEN THOUGHINTUITION INDICATES SPACING AND SPEED ARE RELATED. UNDERSTANDING THE RELATIONSHIP BETWEEN INTERCHANGERAMP SPACING, SPEED, AND FREEWAY OPERATIONS IS IMPORTANT. THE OBJECTIVES OF THIS PAPER WERE TO INVESTIGATERELATIONSHIPS BETWEEN WEAVING LENGTH AND SPEED. WITHIN THE RESEARCH TASKS SEVERAL METHODS WERE UTILIZEDTO ASSIST IN DEVELOPING GUIDANCE ON RAMP SPACING LENGTHS. THE METHODS OR RESOURCES USED TO GENERATEPOTENTIAL LENGTHS INCLUDED: FINDINGS FROM FIELD STUDIES AT SEVEN STUDY SITES, FINDINGS FROM SIMULATIONCONDUCTED AS PART OF THIS RESEARCH. SUGGESTED RAMP SPACINGS WERE DEVELOPED FOR THE ENTRANCE RAMP TO EXITRAMP.

NUMERICAL SOLUTION PROCEDURES OCCUPY AN EXTREMELY IMPORTANT PART IN MANY AREAS OF SCIENCE AND ENGINEERING. A VARIETY OF NUMERICAL METHODS ARE AVAILABLE TODAY FOR SOLVING THE INITIAL-AND/OR BOUNDARY VALUE PROBLEMS IN PHYSICAL SCIENCE AND ENGINEERING. IN RECENT YEARS, THE DIFFERENTIAL QUADRATURE (DQ) METHOD HAS BECOME AN INCREASINGLY POPULAR NUMERICAL TECHNIQUE FOR THE RAPID AND EFFICIENT SOLUTION OF A VARIETY OF SCIENCE AND ENGINEERING PROBLEMS. THE DQ METHOD MAY BE NOT WELL KNOWN TO THE ENGINEERING COMMUNITY. IN THIS PAPER, WE STUDY THE DQ METHOD AND ITS APPLICATIONS. IN THIS STUDY, SEVEN GENERAL RULES FOR CHOOSING SAMPLING POINTS ARE PRESENTED. THE RELATIONS BETWEEN THE OPTIMAL TYPES OF GRID SPACING’S AND TRUNCATION ERRORS ARE DISCUSSED. IN CONTINUING, WE PRESENT THE ABOVE CASES WITH REAL MODEL.