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XIV, 284 p. ; 24 cm

XIV, 284 p. ; 24 cm

This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension of some useful techniques from these two fields to a much wider class of problems. In particular, combining certain finite-dimensional techniques from convex analysis with measure theoretic techniques from mathematical finance, we are able to close the duality gap in some situations where traditional topological arguments fail.

This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension of some useful techniques from these two fields to a much wider class of problems. In particular, combining certain finite-dimensional techniques from convex analysis with measure theoretic techniques from mathematical finance, we are able to close the duality gap in some situations where traditional topological arguments fail.

Mathematical Programming 1987: Volume 37 , Issue Index. Digitized from IA1652525-04 . Next issue: sim_mathematical-programming_1987-02_37_1 .

Mathematical Programming 1990: Volume 46 , Issue Index. Digitized from IA1653230-05 . Previous issue: sim_mathematical-programming_1989-12_45_3_0 . Next issue: sim_mathematical-programming_1990-01_46_1_0 .

Mathematical Programming 1998: Volume 83 , Issue Index. Digitized from IA1653230-03 . Previous issue: sim_mathematical-programming_1998-08-01_82_3_0 . Next issue: sim_mathematical-programming_1998-09-01_83_1_0 .

Cluster analysis involves the problem of optimal partitioning of a given set of entities into a pre-assigned number of mutually exclusive and exhaustive clusters. Here the problem is formulated in two different ways with the distance function (a) of minimizing the within groups sums of squares and (b) minimizing the maximum distance within groups. These lead to different kinds of linear and non-linear (0-1) integer programming problems. Computational difficulties are discussed.

Activity and research in Nondifferentiable Optimization (NDO) and Discrete Optimization are described. (1) Conjugate descent methods have been extended to constrained NDO problems. (2) A robust and efficient algorithm for the minimization of an arbitrarty convex univariate function has been devised. (3) Substantial improvements have been made to subgradient optimization ('relaxation') methods for solving large systems of linear inequalities. (4) The subadditive characterization of facets of integer programming polyhedra has been extended to a very general class of pure integer problems. (5) Work has continued on use of subadditive functions to give a satisfactory duality theory for integer programming, to provide pricing information, and eventually to solve problems. (6) The theories of blocking pairs of polyhedra and anti-blocking pairs of polyhedra have been extended, and we have characterized pairs of polyhedra which are, respectively, the blocker and anti-blocker of some unspecified third polyhedron.

The Eleventh Annual Conference on the Mathematical Foundations of Programming Semantics, and featured invited addresses by six international researchers, two special sessions and twenty-four talks selected from papers submitted by researchers from all over the world. The conference attracted 77 participants from 9 countries, and the ONR grant helped provide support for the six invited speakers, for the participants in the special session, and for women and minority participants who participated in the meeting. The conference published its Proceedings as the first volume of the new series Electronic Notes in Theoretical Computer Science, which is published electronically on the World Wide Web using the facilities and under the auspices of Elsevier Science B.V. This Proceedings can be accessed via the URL: http://www.elsevier.nl/locate/entcs/volumel.html. A further Proceedings consisting of expanded, journal-length papers selected from the papers presented at the meeting is in preparation. This will appear on a special issue of the journal Theoretical Computer Science. The funding was used to support the invited speakers to the meeting, to help support participants in the two special sessions, and to underwrite general conference support costs including support of graduate students, women and members of minority groups.

The economic, technical and strategic factors are the three most important factors in examining the cropping patterns in Iran. Iran is geographically located in a part of the planet with specific climate constraints. Drought is one of the constraints that has been a major challenge to agricultural development for many years and has always been the subject of discussions and investigations. On the other hand, constraints such as agricultural soils, economic factors, climate change, agricultural workforce, etc., multiply the production challenges in the country. Despite such constraints, planning a coherent and targeted program for the cultivation of crops and overcome the existing problems is inevitable. The present study introduced a model for optimization of regional cropping pattern decisions, which is one of the subsets of the Multi-Objective Structural Planning (MOSP) approach, and addressed different objectives, such as economic, social and environmental objectives, separately and jointly. However, it is important to address the exchange of crops in different areas in order to achieve the fundamental objectives of determining the optimal cropping pattern. Therefore, in the proposed model of optimal regional cropping pattern, issues such as the transportation of crops and, consequently, virtual water and energy exchanges were also considered. In order to evaluate the proposed model, agricultural arable lands located in the political-geographic divisions of 23 counties of Isfahan province (Iran) were selected for examination. The results showed that in the main groups of grains and forage, a significant reduction was observed in the optimal crop area of the multi-objective model by 26% and 5%, respectively. Increasing the crop area of horticultural products by 10% in the optimal pattern of multi-objective model was another important factor in the analysis of the results. In general, in order to achieve the economic, social and environmental objectives mentioned in this study within the framework of a multi-objective planning, a 16% reduction in the level of the crop area in Isfahan province is inevitable. The results of this measure are reduction in the irrigation water consumption by 17%, increase in the profit by 58% and increase in the production by 11%. Regarding the fact that in the structural planning of cropping pattern, different and sometimes conflicting objectives are considered and the compromise between the objectives is possible in the multi-objective structural planning model, the decision makers are recommended to use this model.

The economic, technical and strategic factors are the three most important factors in examining the cropping patterns in Iran. Iran is geographically located in a part of the planet with specific climate constraints. Drought is one of the constraints that has been a major challenge to agricultural development for many years and has always been the subject of discussions and investigations. On the other hand, constraints such as agricultural soils, economic factors, climate change, agricultural workforce, etc., multiply the production challenges in the country. Despite such constraints, planning a coherent and targeted program for the cultivation of crops and overcome the existing problems is inevitable. The present study introduced a model for optimization of regional cropping pattern decisions, which is one of the subsets of the Multi-Objective Structural Planning (MOSP) approach, and addressed different objectives, such as economic, social and environmental objectives, separately and jointly. However, it is important to address the exchange of crops in different areas in order to achieve the fundamental objectives of determining the optimal cropping pattern. Therefore, in the proposed model of optimal regional cropping pattern, issues such as the transportation of crops and, consequently, virtual water and energy exchanges were also considered. In order to evaluate the proposed model, agricultural arable lands located in the political-geographic divisions of 23 counties of Isfahan province (Iran) were selected for examination. The results showed that in the main groups of grains and forage, a significant reduction was observed in the optimal crop area of the multi-objective model by 26% and 5%, respectively. Increasing the crop area of horticultural products by 10% in the optimal pattern of multi-objective model was another important factor in the analysis of the results. In general, in order to achieve the economic, social and environmental objectives mentioned in this study within the framework of a multi-objective planning, a 16% reduction in the level of the crop area in Isfahan province is inevitable. The results of this measure are reduction in the irrigation water consumption by 17%, increase in the profit by 58% and increase in the production by 11%. Regarding the fact that in the structural planning of cropping pattern, different and sometimes conflicting objectives are considered and the compromise between the objectives is possible in the multi-objective structural planning model, the decision makers are recommended to use this model.

The economic, technical and strategic factors are the three most important factors in examining the cropping patterns in Iran. Iran is geographically located in a part of the planet with specific climate constraints. Drought is one of the constraints that has been a major challenge to agricultural development for many years and has always been the subject of discussions and investigations. On the other hand, constraints such as agricultural soils, economic factors, climate change, agricultural workforce, etc., multiply the production challenges in the country. Despite such constraints, planning a coherent and targeted program for the cultivation of crops and overcome the existing problems is inevitable. The present study introduced a model for optimization of regional cropping pattern decisions, which is one of the subsets of the Multi-Objective Structural Planning (MOSP) approach, and addressed different objectives, such as economic, social and environmental objectives, separately and jointly. However, it is important to address the exchange of crops in different areas in order to achieve the fundamental objectives of determining the optimal cropping pattern. Therefore, in the proposed model of optimal regional cropping pattern, issues such as the transportation of crops and, consequently, virtual water and energy exchanges were also considered. In order to evaluate the proposed model, agricultural arable lands located in the political-geographic divisions of 23 counties of Isfahan province (Iran) were selected for examination. The results showed that in the main groups of grains and forage, a significant reduction was observed in the optimal crop area of the multi-objective model by 26% and 5%, respectively. Increasing the crop area of horticultural products by 10% in the optimal pattern of multi-objective model was another important factor in the analysis of the results. In general, in order to achieve the economic, social and environmental objectives mentioned in this study within the framework of a multi-objective planning, a 16% reduction in the level of the crop area in Isfahan province is inevitable. The results of this measure are reduction in the irrigation water consumption by 17%, increase in the profit by 58% and increase in the production by 11%. Regarding the fact that in the structural planning of cropping pattern, different and sometimes conflicting objectives are considered and the compromise between the objectives is possible in the multi-objective structural planning model, the decision makers are recommended to use this model.

programming

Journal of Research of the National Bureau of Standards

Computer Science - Number System Conversion and mathematical operation behind Programming

Computer Science - Number System Conversion and mathematical operation behind Programming

Book Source: Digital Library of India Item 2015.194103 dc.contributor.author: Purshotam Lal Jolly dc.date.accessioned: 2015-07-08T03:56:28Z dc.date.available: 2015-07-08T03:56:28Z dc.date.digitalpublicationdate: 2005-08-28 dc.identifier.barcode: 1990010092368 dc.identifier.origpath: /rawdataupload/upload/0092/368 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/194103 dc.description.scannerno: 5 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 190 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: In Public Domain dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Natural Sciences dc.subject.classification: Mathematics dc.subject.classification: Geometry dc.title: Some Contributions To Mathematical Programming

Book Source: Digital Library of India Item 2015.194103 dc.contributor.author: Purshotam Lal Jolly dc.date.accessioned: 2015-07-08T03:56:28Z dc.date.available: 2015-07-08T03:56:28Z dc.date.digitalpublicationdate: 2005-08-28 dc.identifier.barcode: 1990010092368 dc.identifier.origpath: /rawdataupload/upload/0092/368 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/194103 dc.description.scannerno: 5 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 190 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: In Public Domain dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Natural Sciences dc.subject.classification: Mathematics dc.subject.classification: Geometry dc.title: Some Contributions To Mathematical Programming

Mathematical Programming 1995: Volume 69 , Issue Index. Digitized from IA1652525-04 . Previous issue: sim_mathematical-programming_1995-03-02_68_3 . Next issue: sim_mathematical-programming_1995-07-25_69_1 .

Mathematical Programming 1996: Volume 74 , Issue Index. Digitized from IA1653230-03 . Previous issue: sim_mathematical-programming_1996-06-30_73_3_0 . Next issue: sim_mathematical-programming_1996-07-31_74_1_0 .

Mathematical Programming Study 1987: Volume 30 , Issue CONTENTS. Digitized from IA1653230-01 . Next issue: sim_mathematical-programming-study_1987-02_30_0 .

Mathematical Programming 1987: Volume 37 , Issue Index. Digitized from IA1653230-05 . Next issue: sim_mathematical-programming_1987-02_37_1_0 .

Mathematical Programming 1990: Volume 47 , Issue Index. Digitized from IA1653230-05 . Previous issue: sim_mathematical-programming_1990-04_46_3_0 . Next issue: sim_mathematical-programming_1990-05_47_1_0 .

Mathematical Programming 1991: Volume 50 , Issue Index. Digitized from IA1652525-04 . Previous issue: sim_mathematical-programming_1991-01_49_3 . Next issue: sim_mathematical-programming_1991-03_50_1 .

Mathematical Programming 1998: Volume 82 , Issue Index. Digitized from IA1653230-03 . Previous issue: sim_mathematical-programming_1998-05-01_81_3_0 . Next issue: sim_mathematical-programming_1998-06-01_82_1-2_0 .

The paper presents two new approaches to modeling the interaction of small and medium pricetaking traders with a stock exchange. In the framework of these approaches, the traders can form and manage their portfolios of financial instruments traded on a stock exchange with the use of linear, integer, and mixed programming techniques. Unlike previous authors publications on the subject, besides standard securities, the present publication considers derivative financial instruments such as futures and options contracts.

We show that for mathematical programming problems an optimization algorithm must encapsulate implicitly or explicitly a quadratic internal model of the problem to be solved which represents the essence of the problem from the view point of the algorithm. Optimization models are coming from the conservation laws. For systems which obey the principle of least action the Noether’s theorem expresses the equivalence between the conservation laws and symmetries. But mathematically, symmetries are expressed by quadratic forms. Therefore, at the heart of every real optimization model is a quadratic form. The quadratic internal model principle says that this quadratic form modified in order to imbed the main ingredients of the optimization algorithm represents the quadratic internal model of the optimization algorithm.

We show that for mathematical programming problems an optimization algorithm must encapsulate implicitly or explicitly a quadratic internal model of the problem to be solved which represents the essence of the problem from the view point of the algorithm. Optimization models are coming from the conservation laws. For systems which obey the principle of least action the Noether’s theorem expresses the equivalence between the conservation laws and symmetries. But mathematically, symmetries are expressed by quadratic forms. Therefore, at the heart of every real optimization model is a quadratic form. The quadratic internal model principle says that this quadratic form modified in order to imbed the main ingredients of the optimization algorithm represents the quadratic internal model of the optimization algorithm.

Accompanied by 3.5" disc

Accompanied by 3.5" disc

260p

260p

Book Source: Digital Library of India Item 2015.270391 dc.contributor.author: Poonam dc.date.accessioned: 2015-07-27T20:42:51Z dc.date.available: 2015-07-27T20:42:51Z dc.identifier.barcode: 05990010890378 dc.identifier.origpath: /data58/upload/0092/095 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/270391 dc.description.scannerno: 20003547 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 147 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Bundelkhand Uni Jhansi dc.source.library: Bundelkhand Uni Jhansi dc.subject.classification: Philosophy dc.title: Applications Of Mathematical Programming In The Development Of Some Models dc.type: ptiff dc.type: pdf

Book Source: Digital Library of India Item 2015.270391 dc.contributor.author: Poonam dc.date.accessioned: 2015-07-27T20:42:51Z dc.date.available: 2015-07-27T20:42:51Z dc.identifier.barcode: 05990010890378 dc.identifier.origpath: /data58/upload/0092/095 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/270391 dc.description.scannerno: 20003547 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 147 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Bundelkhand Uni Jhansi dc.source.library: Bundelkhand Uni Jhansi dc.subject.classification: Philosophy dc.title: Applications Of Mathematical Programming In The Development Of Some Models dc.type: ptiff dc.type: pdf

Book Source: Digital Library of India Item 2015.270391 dc.contributor.author: Poonam dc.date.accessioned: 2015-07-27T20:42:51Z dc.date.available: 2015-07-27T20:42:51Z dc.identifier.barcode: 05990010890378 dc.identifier.origpath: /data58/upload/0092/095 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/270391 dc.description.scannerno: 20003547 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 147 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Bundelkhand Uni Jhansi dc.source.library: Bundelkhand Uni Jhansi dc.subject.classification: Philosophy dc.title: Applications Of Mathematical Programming In The Development Of Some Models dc.type: ptiff dc.type: pdf

Approved for public release, distribution unlimited.

mathematical programming for data mining(1)

Binary optimization is one of the central problems in mathematical optimization and it captures an abundance of applications. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with Equilibrium Constraints (MPECs). We first reformulate the binary program as an equivalent augmented biconvex optimization problem with a bilinear equality constraint, then we propose two penalization/regularization methods (exact penalty and alternating direction) to solve it. The resulting algorithms seek desirable solutions to the original problem via solving a sequence of linear programming convex relaxation subproblems. In addition, we prove that both the penalty function and augmented Lagrangian function, induced by adding the complementarity constraint to the objectives, are exact, i.e., they have the same local and global minima with those of the original binary program when the penalty parameter is over some threshold. The convergence of both algorithms can be guaranteed since they essentially reduce to block coordinate descent in the literature. Finally, we demonstrate the effectiveness and versatility of our methods on several important problems, including graph bisection, constrained image segmentation, dense subgraph discovery, modularity clustering and Markov random fields. Extensive experiments show that our methods outperform existing popular techniques, such as iterative hard thresholding, linear programming relaxation and semidefinite programming relaxation.

Binary optimization is one of the central problems in mathematical optimization and it captures an abundance of applications. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with Equilibrium Constraints (MPECs). We first reformulate the binary program as an equivalent augmented biconvex optimization problem with a bilinear equality constraint, then we propose two penalization/regularization methods (exact penalty and alternating direction) to solve it. The resulting algorithms seek desirable solutions to the original problem via solving a sequence of linear programming convex relaxation subproblems. In addition, we prove that both the penalty function and augmented Lagrangian function, induced by adding the complementarity constraint to the objectives, are exact, i.e., they have the same local and global minima with those of the original binary program when the penalty parameter is over some threshold. The convergence of both algorithms can be guaranteed since they essentially reduce to block coordinate descent in the literature. Finally, we demonstrate the effectiveness and versatility of our methods on several important problems, including graph bisection, constrained image segmentation, dense subgraph discovery, modularity clustering and Markov random fields. Extensive experiments show that our methods outperform existing popular techniques, such as iterative hard thresholding, linear programming relaxation and semidefinite programming relaxation.

Binary optimization is one of the central problems in mathematical optimization and it captures an abundance of applications. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with Equilibrium Constraints (MPECs). We first reformulate the binary program as an equivalent augmented biconvex optimization problem with a bilinear equality constraint, then we propose two penalization/regularization methods (exact penalty and alternating direction) to solve it. The resulting algorithms seek desirable solutions to the original problem via solving a sequence of linear programming convex relaxation subproblems. In addition, we prove that both the penalty function and augmented Lagrangian function, induced by adding the complementarity constraint to the objectives, are exact, i.e., they have the same local and global minima with those of the original binary program when the penalty parameter is over some threshold. The convergence of both algorithms can be guaranteed since they essentially reduce to block coordinate descent in the literature. Finally, we demonstrate the effectiveness and versatility of our methods on several important problems, including graph bisection, constrained image segmentation, dense subgraph discovery, modularity clustering and Markov random fields. Extensive experiments show that our methods outperform existing popular techniques, such as iterative hard thresholding, linear programming relaxation and semidefinite programming relaxation.

Binary optimization is one of the central problems in mathematical optimization and it captures an abundance of applications. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with Equilibrium Constraints (MPECs). We first reformulate the binary program as an equivalent augmented biconvex optimization problem with a bilinear equality constraint, then we propose two penalization/regularization methods (exact penalty and alternating direction) to solve it. The resulting algorithms seek desirable solutions to the original problem via solving a sequence of linear programming convex relaxation subproblems. In addition, we prove that both the penalty function and augmented Lagrangian function, induced by adding the complementarity constraint to the objectives, are exact, i.e., they have the same local and global minima with those of the original binary program when the penalty parameter is over some threshold. The convergence of both algorithms can be guaranteed since they essentially reduce to block coordinate descent in the literature. Finally, we demonstrate the effectiveness and versatility of our methods on several important problems, including graph bisection, constrained image segmentation, dense subgraph discovery, modularity clustering and Markov random fields. Extensive experiments show that our methods outperform existing popular techniques, such as iterative hard thresholding, linear programming relaxation and semidefinite programming relaxation.

The aim of this study was to investigate the effect of the Scratch and Lego Mindstorms Ev3 programming activities on academic achievement with respect to computer programming, and on the problem-solving and logical-mathematical thinking skills of students. This study was a semi-experimental, pretest-posttest study with two experimental groups and a control groups. A total of 75 students were divided among all three groups. Scratch-based game activities were applied to Study Group I. Lego Mindstorms Ev3-based design activities were applied to Study Group II. A C++ editor-based teaching activity was applied to the control group. The academic achievement test was developed within the scope of this study (Kr-20 = 0.71). The Logical-Mathematical Intelligence Sub-Scale was used (Cronbach alpha is 0,925). Problem-Solving Inventory was used (Cronbach alpha is 0,86). Data was evaluated using frequency, percentage, arithmetic mean, standard deviation, and Anova analyses. The educational program based on Scratch-related game activities made a more positive contribution to the logical-mathematical thinking skills of students than the educational programs based on Lego Mindstorms Ev3 design activities and traditional teaching activities, and this contribution was especially significant for the mathematical relationship factor.

Trimester 1 2016/2017

Network characterizations are developed for effecting contacts between accounting and mathematical programming. En route to these objectives some of the customary uses of double entry accounting are altered and related to suitable generalizations of classical network ideas such as the Kirchhoff node conservation laws. Extensions of the usual node-link incidence relations provide a basis for effecting these contacts. Concrete illustrations are supplied including a goods-flow-funds-flow model which is preceded by a simpler example involving a PERT-Critical Path application. The latter is examined in the context of a uni-dimensional physical flow involving time only while the former suggests how double entry can be extended to flows that involve a variety of different dimensions. A possibility for joint coordinated uses of programming and accounting of management planning is indicated and amplified and some of the implications for alterations in accounting practice are then examined. Suggestions for further extensions include probabilistic formulations and multi-dimensional objectives.

The report is a user's guide to available mathematical programming (MP) computer codes and to NELC's capabilities in numerically solving MP problems. It defines the general MP problem; lists and evaluates the MP codes operational on the NELCIBM 360/65 computers; and provides guidelines for modifying the MP problem when, in its first form, it is cumbersome; or there is not information enough to start computation; or the available codes do not yield all the needed information.

This thesis refines an earlier demonstrated methodology which combines response surface methodology and experimental design concepts to describe the output of a deterministic model. In an effort to maximize the combat power delivered to a theater commander, several critical factors are varied to determine their impact upon the delivery of men and equipment to the objective area. The effects of time, materials handling equipment capability, airfield ramp space, distance between the Aerial Port of Debarkation and Forward Operating Location, the availability and capabilities of different aircraft, and the impact of aircraft attrition are examined in the model. This model does not use metric ton-miles per day as a measure of effectiveness, but rather it places a time dependent value on the delivery of combat units to the objective area. The deterministic model includes 168 equations and 288 different variables. A response surface was generated using an appropriate experimental design, with the response surface predictions averaging greater than a 96 percent level of accuracy.

Bibliography: p. [43-44]

Mathematical Programming 1988: Volume 41 , Issue Index. Digitized from IA1653230-05 . Previous issue: sim_mathematical-programming_1988-04_42_1_0 . Next issue: sim_mathematical-programming_1988-05_41_1_0 .