Contemporary Approaches to the Solution of the Integer Programming Problem

The purpose of this thesis is to provide analysis of the modem development of the methods for solution to the integer linear programming problem. The thesis simultaneously discusses some main approaches that lead to the development of the algorithms for the solution to the integer linear programming problem. Chapter 1 introduces the Generalized Linear Programming Problem alongside with the properties of a solution to the Linear Programming Problem. The simplex procedure presented to solve the Linear Programming Problem by adding slack variables along with the artificial-basis technique. Chapter 2 refers to the primal-dual simplex procedure. The dual simplex algorithm reflects the dual simplex procedure. Chapter 3 discusses the mixed and alternative formulations of the integer programming problem. Chapter 4 considers the optimality conditions with the imposed relaxations to solve the Linear Programming Relaxation Problem. The methods of the Integer Programming are introduced for the Linear Programming Relaxation. Chapter 5 discusses the concepts of the Branch-and Bound method followed by the direct application of the Branch-and-Bound method. Chapter 6 introduces the fundamental concepts of the cutting method. The main concept of the valid inequalities presented for the Linear Programming Problem as well as for the Integer Programming Problem. Gomory\u27s Fractional cutting plane Algorithm represents the desired step to obtain the solution for the Integer Programming Problem. Furthermore, the mixed integer cuts generalizes the concepts to provide the corresponding solution for the Integer Programming Problem. Chapter 7 describes the Gomory method for the pure Integer Program followed by the Gomory method for the mixed Integer Program. In the Appendix the computer program LINDO is used. Throughout the whole thesis this computer program is applied to emphasize the very helpful tool in Linear Programming. All above mentioned chapters include the variety of examples corresponding to the Linear Programming Problem and the Integer Program

The advanced defuzzification methods of the convex α – cut fuzzy sets

The main features of the fuzzy sets and their corresponding membership functions were presented in terms of the fuzzification process and further by the de-fuzzification operation. The convexity of the α -(alfa) cuts of the fuzzy sets is used in the decomposition of the fuzzy sets. The alfa cuts of the fuzzy sets were defined precisely in terms of the pair of functions and their lowest upper and greatest lower bounds. The convex combination of the intervals of the sub-regions of the fuzzy sets and their membership function were considered as the points of the defuzzified values of the fuzzy sets. The methods of the de-fuzzification to the crisp sets were presented by the formulas to find the defuzzification regions and de-fuzzified values. The compositional concepts of the inference as the expansion of the extension principle were introduced to formalize further the fuzzy reasoning by the set of fuzzy rules based on the approximate reasoning

Study of Populus euphrafica OLfV. community in the margin of Karoon river

Populus euphratica Oliv. In Iran is distributed naturally in vast regions. But the largest area is located along the margins of the large rivers in Khuzistan province, such as Karkheh, Dez and some area in Maroon(nearly 20,000 ha). It is spread in the from of coppices covering at the large area, which are very important from the economical point of view and environmental purposes because of production of wood, animals fodder, protection and stabilization of the river border. Also it can be useful for the protection of the natural ecosystem and wildlife. P. euphratica in Khuzistan is adapted to arid and semi-arid regions. Also the dry period consider to Ombrothermic curves is between 7 and 8 month per year (late Feb. to late Oct). The mean annual rainfall is between 230-340 mm, and the mean annual temperature is between 23-25°C. Soil of the studied sites are alluvial which contribute from erosion of lime, marl and salty matters of Zagroos formations. Soil texture of upper horizons is sandy-loam and lower horizons change to loam. Electrical conductivity (EC) value is higher in south and western than north regions. The overall hydrological characteristics such as, meander, flood river and light texture of soil are the reasons for presence of P. euphratica communities in the natural regions. The number per hectare of stands was 357 and 329, the crown cover percentage of stands was 72.6 and 68.4. Also the mean annual diameter increament was 9.6 mm and 9.5 mm and the approximate age estimated 35 and 36 years

Co-liquefaction with acetone and GC analysis of volatile compounds in exhaled breath as lung cancer biomarkers

Introduction: A simple, rapid and low cost method for enrichment of volatile organic compounds (VOCs) from exhaled breath (EB) is presented. Methods: A 1000 mL home-made extraction device was filled with EB. The VOCs were extracted and condensed in 0.5 mL acetone. Recognition of volatiles in the real studied EB samples was performed by a GC-MS. Results: The method displays an extraction efficiency of >86% with the enrichment factor of 1929 for octanal. Limits of detection and quantification, and linear dynamic range were 0.008, 0.026 and 0.026-400 ng/mL respectively. Analysis of real samples showed the existence of more than 100 compounds in EB of healthy volunteers and patients with lung cancer before and after treatment. Exhaled octanal concentration was significantly higher in lung cancer patient than in healthy volunteers and lung cancer patient after treatment. Conclusion: Having used the proposed approach, high extraction recovery (up to 86%) was attained for the lung cancer marker, octanal, as an important biomarker. Our findings on smaples of EB of healthy controls and patients with lung cancer before and after treatment provide complelling evidence upon the effectiveness of the developed method

Modelling of Retention Factors of Analytes in Chromatography with Ternary Solvent Mobile Phases

Article on the modelling of retention factors of analytes in chromatography with ternary solvent mobile phases