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steps approach for complex problems

Lecture Practical business math procedures (10/e): Chapter 5 - Jeffrey Slater

Lecture Practical business math procedures (10/e): Chapter 5 - Jeffrey Slater

Chapter 5 - Solving for the unknown: a how-to approach for solving equations. After you have mastered the material in this chapter, you will be able to: Explain the basic procedures used to solve equations for the unknown; list the five rules and the mechanical steps used to solve for the unknown in seven situations; know how to check the answers; list the steps for solving word problems; complete blueprint aids to solve word problems; check the solutions.
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SELF ORGANIZING MAPS APPLICATIONS AND NOVEL ALGORITHM DESIGN PART 4 PPT

SELF ORGANIZING MAPS APPLICATIONS AND NOVEL ALGORITHM DESIGN PART 4 PPT

In the research area of computer science, a method called self-organizing map (SOM) has been developed and utilized (Kohonen (2001)). SOM is one of the neural network systems, which models the column structure of visual cortex (V1) in animal brains (Van Hulle (2000)) and learns based on an unsupervised machine learning algorithm. SOMs have been applied to problems in many fields such as data visualization, dimensional reduction, clustering, etc. In this chapter, we focus on the multi-media content broadcasted on the Internet with the streaming technique. To serve most users by utilizing the bandwidth of the Internet, it is ideal to broadcast only important portions of the content that viewers really want to watch. If this is realized, viewers can avoid wasting their time by watching the portions that they do not desire to watch. Moreover, by not broadcasting less important portions unnecessary network traffic is decreased.
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MULTIMEDIA – A MULTIDISCIPLINARY APPROACH TO COMPLEX ISSUES PPT

MULTIMEDIA – A MULTIDISCIPLINARY APPROACH TO COMPLEX ISSUES PPT

1. Introduction With the rapid growth of multimedia application technologies and network technologies, especially the proliferation of Web 2.0 and digital cameras, there has been an explosion of images and videos in the Internet. For example, the volume of videos uploaded to the YouTube every minute is amounting to 48 hours by May 2011, having doubled in the last two years. Such huge video collections hold useful yet implicit and nontrivial knowledge about various domains. To manage and utilize these resources effectively, video concept detection becomes a very important subject of intensive research by a large research community (Over et al., 2008). It is an integral part of visual data mining that is automatically extracting such knowledge from the huge unstructured visual data. It aims to automatically annotate video shots or keyframes with respect to a semantic concept (Tang et al., 2012). Ranging from objects like airplane and car to scenes like urban street and sky , semantic concepts serve as good intermediate semantic features for video content indexing and understanding, and thus, spurring much research attention (Jiang et al., 2010; Naphade & Smith, 2004; Snoek et al., 2006; Zheng et al., 2008). Essentially, concept detection is a classification task, in which a binary classifier is usually learned to predict the presence of a certain concept in a video shot or keyframe (image). Traditional concept detection methods are mainly global classification: use supervised machine learning techniques, such as single Support Vector Machine (SVM), etc., over whole training dataset.
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SELF ORGANIZING MAPS APPLICATIONS AND NOVEL ALGORITHM DESIGNE PART 4 POT

SELF ORGANIZING MAPS APPLICATIONS AND NOVEL ALGORITHM DESIGNE PART 4 POT

In the research area of computer science, a method called self-organizing map (SOM) has been developed and utilized (Kohonen (2001)). SOM is one of the neural network systems, which models the column structure of visual cortex (V1) in animal brains (Van Hulle (2000)) and learns based on an unsupervised machine learning algorithm. SOMs have been applied to problems in many fields such as data visualization, dimensional reduction, clustering, etc. In this chapter, we focus on the multi-media content broadcasted on the Internet with the streaming technique. To serve most users by utilizing the bandwidth of the Internet, it is ideal to broadcast only important portions of the content that viewers really want to watch. If this is realized, viewers can avoid wasting their time by watching the portions that they do not desire to watch. Moreover, by not broadcasting less important portions unnecessary network traffic is decreased.
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BÁO CÁO NGHIÊN CỨU KHOA HỌC   BETTER BREEDS OF COMMON CARP  CYPRINUS CARPIO L   FOR SMALL SCALE FISH FARMERS   MS6   PDF

BÁO CÁO NGHIÊN CỨU KHOA HỌC BETTER BREEDS OF COMMON CARP CYPRINUS CARPIO L FOR SMALL SCALE FISH FARMERS MS6 PDF

4. Introduction & Background The general aim of this project is to identify better breeds of common carp and increase the utilisation of such fish by small-scale farmers as means of increasing yields and lowering costs, and thereby contributing significantly to poverty alleviation and income generation for communities heavily dependent on fish aquaculture for livelihoods and food security.
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BÁO CÁO Y HỌC   OUTCOMES OF SINGLE STAGE TOTAL ARCH REPLACEMENT VIA CLAMSHELL INCISION  PDF

BÁO CÁO Y HỌC OUTCOMES OF SINGLE STAGE TOTAL ARCH REPLACEMENT VIA CLAMSHELL INCISION PDF

disease involving the descending aorta replaced through a left thoracotomy have been excluded from this study. In 2008 and 2009 the modified arch-first technique was used by our institution by two surgeons for 38 con- secutive cases, comprising 20 males and 18 females with an average age of 71 years (range: 42 - 93 years). There were 12 true aneurysms, 6 ruptured aortic aneurysms, 5 acute and 8 chronic type B aortic dissections and 7 acute type A aortic dissections, all with distal arch aortic disease. Eighteen cases underwent emergency surgery. Concomitant procedures consisted of aorto-coronary bypass grafting, Bentall operation, aortic valve replace- ment and aorto-femoral bypass grafting. There were 10 cases of repeat surgery, with the previous surgery con- sisting of three ascending aortic replacements, one aortic valve procedure, one coronary artery bypass and five cases of abdominal aortic repair. In all cases, the arch vessels were reconstructed with a commercially available four-branched graft (Hemashield; Boston Scientific, Natick, MA).
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INNOVATION THROUGH DESIGN  THINKING AN APPROACH TO INVENT EXCITING PRODUCTS AND IDENTIFY POSSIBLE FUTURES

INNOVATION THROUGH DESIGN THINKING AN APPROACH TO INVENT EXCITING PRODUCTS AND IDENTIFY POSSIBLE FUTURES

TRANG 1 INNOVATION THROUGH DESIGN THINKING An approach to invent exciting products, identify possible futures, and solve wicked problems.[r]
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EVAPORATION CONDENSATION AND HEAT TRANSFER PART 15 PDF

EVAPORATION CONDENSATION AND HEAT TRANSFER PART 15 PDF

efficiency. Moreover, evaporation rates differ depending on paper grade and production volume. A hood balance should be carried out for the production volume requiring the highest evaporation rates in the dryers. Depending upon the type of hood present in an existing paper machine dryer section, the optimal amounts of total ‘supply’ and exhaust air required per unit mass of water evaporated will vary. The required hood balance (defined as the ratio of total ‘supply’ to total exhaust air) is largely influenced by the hood type i.e., whether the hood is an open, conventional closed or high-humidity closed hood. The hood balance for a modern paper machine with a closed hood should be close to 0.8, while that for an older machine with open hood should be between 0.3 and 0.4. If the hood balance is too high then this results in spillage from the hood into the machine room. A low balance results in sweating, runnability problems and poor profile in the cross direction (CD). Conditions around the machine may become uncomfortable and troubleshooting, broke cleaning and operations may become difficult. In many machines, an actual hood balance is rarely carried out. The importance of air balance is often ignored potentially losing opportunity to improve drying efficiency (Sundqvist, 1996; Ghosh, 2005).
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MULTIPROCESSOR SCHEDULING PART 5 PPT

MULTIPROCESSOR SCHEDULING PART 5 PPT

8. Summary and Conclusions In this study we combine two metaheuristic search techniques, the Augmented Neural Networks and Genetic Algorithms approach to create a hybrid metaheuristic called the NeuroGenetic approach. We apply this hybrid approach to a multiprocessor scheduling problem, the job-shop scheduling problem to test if the hybridization helps improve the solution. The hybridization of AugNN and GA is achieved by interleaving the two approaches. Since the GA approach is better at diversification or global search whereas AugNN is better at intensification or local search, the combination provides improved solutions than either GA or AugNN search with the same number of iterations. Computational results showed that such hybridization provided improvements in the solutions, than if each technique was used alone. Given the encouraging results, more research needs to be done in this area. Such hybrid techniques can be applied to other scheduling problems and also on the job shop scheduling problem by applying other GA approaches that have performed well in the literature. The AugNN technique can also be hybridized with other non GA techniques such Tabu Search and Simulated Annealing approaches, which tend to give good results for the job-shop scheduling problem.
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ELECTRIC CIRCUITS, 9TH EDITION P76 PPT

ELECTRIC CIRCUITS, 9TH EDITION P76 PPT

To arrive at an equivalent circuit for these two magnetically coupled coils, we seek an arrangement of inductors that can be described by a set of equations equivalent to Eqs. C.l and C.2. The key to finding the arrange- ment is to regard Eqs. C.l and C.2 as mesh-current equations with i y and i 2
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TÀI LIỆU INCIDENT HANDLING FOUNDATIONS PPT

TÀI LIỆU INCIDENT HANDLING FOUNDATIONS PPT

• Determine cause and symptom • Improve defenses • Perform vulnerability analysis Before the system goes back online, an incident handler must make sure that they fix the problem or the vulnerability that the attacker used to compromise the system. Nuking the operating system from high orbit may be considered a shortcut in the handling process. While it is certainly true that total destruction of the contents of the disk will take care of any malevolent code, the opportunity for re-infection via the same channel after you reload the operating system still exists. There are tons of cases where handlers have taken systems down, reloaded the operating system, only to have the box compromised again a couple days later. The best course of action is to determine what the cause of the incident was, to find the vector of infection, and take action to prevent this from happening again.
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INTRODUCTION TO OPC

INTRODUCTION TO OPC

At the top of this figure is an OPC Server object . This is the COM object to which the application first connects. Below this is a collection of OPC Group Objects. These are created dynamically by the applications to hold lists of Tags and attributes (which OPC refers to as Items). An HMI might create a Group for each open picture. A report package might create a group to access data for each report. The contents of the Group and item collections may vary over time based on the needs of the applications. (Again this has no effect on the underlying control system). This is actually somewhat analogous to RowSets as used on OLEDB. There is a lot of data in the database, you want to look at a subset of it in your application., and that subset may vary based on your needs at the time.
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TỔNG HỢP VÀ ĐẶC TRƯNG XÚC TÁC TẨM CHẤT LỎNG ION (SILP) IMIDAZOL CHỨA PHỨC RODI MANG TRÊN CÁC CHẤT MANG RẮN CHO PHẢN ỨNG HYDROFORMYL HÓA ETYLEN

TỔNG HỢP VÀ ĐẶC TRƯNG XÚC TÁC TẨM CHẤT LỎNG ION (SILP) IMIDAZOL CHỨA PHỨC RODI MANG TRÊN CÁC CHẤT MANG RẮN CHO PHẢN ỨNG HYDROFORMYL HÓA ETYLEN

Recently, a novel approach to immobilizing homogeneous catalysts on solid supports supported ionic liquid phase – SILP catalyst has been reported, in which the hydroformylation complex c[r]
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Exploring general-purpose protein features for distinguishing enzymes and nonenzymes within the twilight zone

Exploring general-purpose protein features for distinguishing enzymes and nonenzymes within the twilight zone

Computational prediction of protein function constitutes one of the more complex problems in Bioinformatics, because of the diversity of functions and mechanisms in that proteins exert in nature. This issue is reinforced especially for proteins that share very low primary or tertiary structure similarity to existing annotated proteomes.
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UNIT 14.WRITING

UNIT 14.WRITING

Anticipated problems: - Students may not be familiar with format of an announcement and the language Used in it, so teacher should be ready to assist them.. Procedure: Time Steps Work ar[r]
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BÁO CÁO Y HỌC:

BÁO CÁO Y HỌC: "HUMAN DEPRESSION: A NEW APPROACH IN QUANTITATIVE PSYCHIATRY" PDF

Introduction The need for a deep, radical turning point in the world of psychiatry is rapidly growing. Present diagnostic meth- ods cannot continue to be considered acceptable because they are almost completely based on the psychiatrist's opinion, which does not have an objective diagnostic technology and thus has a very high error rate.
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TIẾNG ANH CHUYÊN NGHÀNH KẾT TOÁN KIỂM TOÁN   PHẦN 9 PPS

TIẾNG ANH CHUYÊN NGHÀNH KẾT TOÁN KIỂM TOÁN PHẦN 9 PPS

INVESTMENTS REQUIRING CONSOLIDATION CONCEPT OF CONTROL: You only need to casually review the pages of most any business press before you will notice a story about one business buying another. Such acquisitions are common and number in the thousands annually. Typically, such transactions are effected rather simply, by the acquirer simply buying a majority of the stock of the target company. This majority position enables the purchaser to exercise control over the other company; electing a majority of the board of directors, which in turn sets the direction for the company. Control is ordinarily established once ownership jumps over the 50% mark, but management contracts and other similar arrangements may allow control to occur at other levels.
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ARTIFICIAL INTELLIGENCE FOR WIRELESS SENSOR NETWORKS ENHANCEMENT PART 6 PPTX

ARTIFICIAL INTELLIGENCE FOR WIRELESS SENSOR NETWORKS ENHANCEMENT PART 6 PPTX

3. Cooperative Game Theoretic Model of Clustering Algorithms for Wireless Sen- sor Networks 3.1 Game and solution Game theory is a mathematical basis for capturing behavior in interactive decision situation. It provides a framework and analytical approach for predicting the results of complex and dynamic interactions between rational agents who try to maximize personal payoff (or min- imize private cost) according to strategies of other agents. The theory is generally divided into the non-cooperative game theory and the cooperative game theory. In non-cooperative games, the agents have distinct interests that interact by predefined mechanisms and deviate alone from a proposed solution, if it is in their interest, and do not themselves coordinate their moves in groups. In other words, for individually rational behaviors, they cannot reach an agreement or negotiate for cooperation. Contrarily, a cooperative game allows agents to com- municate for allocating resources before making decisions by an unspecified mechanism. It is concerned with coalitions which are composed of group of agents for coordinating actions and feasible allocations. Cooperative game theory is concerned with situations when groups of agents coordinate their actions. Consequently, Cooperative games focus how to assign the total benefits (or cost) among coalitions, taking into account individual and group incentives, as well as various fairness properties (Nisan et al., 2007).
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GOnet: A tool for interactive Gene Ontology analysis

GOnet: A tool for interactive Gene Ontology analysis

Biological interpretation of gene/protein lists resulting from -omics experiments can be a complex task. A common approach consists of reviewing Gene Ontology (GO) annotations for entries in such lists and searching for enrichment patterns.
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BÁO CÁO HÓA HỌC:

BÁO CÁO HÓA HỌC:" RESEARCH ARTICLE EXTENSION THEOREM FOR COMPLEX CLIFFORD ALGEBRAS-VALUED FUNCTIONS ON FRACTAL DOMAINS" PPT

He gives representations of both a gravitational and a constant magnetic field as such analogues in order to solve now the spatial problems of the separation of field as well as analytic extension through the surface and into the domain with sources. Our results can be applied to the study of the above problems in the more general context of domains with fractal boundaries, but the detailed discussion of this technical point is beyond the scope of this paper.
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MEGANBOOK VERSION 6.1 PART 86 POT

MEGANBOOK VERSION 6.1 PART 86 POT

Ed.rar.html Complex.IT.Project.Management.16.Steps.to.Success.rar.html PASSWORD: doungtawan Project.Management.Process.Improvement.rar.html PASSWORD: doungtawan Your.Successful.Project.M[r]
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Báo cáo hóa học:

Báo cáo hóa học: " Research Article Interference Robust Transmission for the Downlink of an OFDM-Based Mobile Communications " pptx

We show that the improved possibilities for interference suppression in case of real-valued symbols more than com- pensate for the loss in power efficiency and even signifi- cant gains are possible in an interference limited environ- ment with respect to a conventional OFDM scheme em- ploying coded QAM modulation with the same spectral e ffi - ciency. Performance of a QAM scheme in principle could be enhanced by successive interference cancellation (SIC) [18]. However, due to the presence of multiple interferers in prac- tical applications, SIC alone could not achieve an acceptable performance and hence, it would have to be combined with successive decoding [18]. Unfortunately, because desired sig- nal and interferers are usually not frame aligned and the code laws of the interferers are not known in general, successive decoding is not applicable here.
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LECTURE PERFORMANCE MANAGEMENT: SESSION 16 - OSMAN BIN SAIF

LECTURE PERFORMANCE MANAGEMENT: SESSION 16 - OSMAN BIN SAIF

In this chapter, the following content will be discussed: How strategic case analysis is used to simulate real-world experiences; how analyzing strategic management cases can help develop the ability to differentiate, speculate, and integrate when evaluating complex business problems; the steps involved in conducting a strategic management case analysis;...
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HARNESSING THE POWER OF CONTINUOUS AUDITING_1 DOCX

HARNESSING THE POWER OF CONTINUOUS AUDITING_1 DOCX

THE REAL DEFINITION One of the significant challenges facing internal audit, control specialists, enterprise risk management teams, and business managers all over the world is being able to understand what continuous auditing is and how the approach can be used effectively. As you read through this book, keep in mind that continuous auditing has been around for decades. As I travel and speak around the world on this topic, I have found each individual team, department, or company has its own definition of what it believes the approach represents and how to maximize its value. So let us start off this educational process by establishing a clear-cut definition of continuous auditing and understanding the characteristics that make it a unique tool. The definition will be broken down into two distinct parts: (1) the formal ‘‘book’’ definition for personnel familiar with the audit profession and (2) the ‘‘nonaudit’’ definition for clients to clearly understand the objective of the approach.
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LESSON ENTERPRISE SYSTEMS

LESSON ENTERPRISE SYSTEMS

Lesson Enterprise systems present the content: legacy system approach and the problems of information silos; enterprise system approach, improve business processes through enterprise systems; the challenges when implementing new enterprise systems.
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CHAPTER 26 – ASSOCIATED WITH ANTIGEN PROCESSING AND LOADING COMPLEX ESSENTIAL FOR CELLULAR IMMUNE RESPONSE

CHAPTER 26 – ASSOCIATED WITH ANTIGEN PROCESSING AND LOADING COMPLEX ESSENTIAL FOR CELLULAR IMMUNE RESPONSE

CHAPTER 26 – ASSOCIATED WITH ANTIGEN PROCESSING AND LOADING COMPLEX ESSENTIAL FOR CELLULAR IMMUNE RESPONSE CHAPTER 26 – ASSOCIATED WITH ANTIGEN PROCESSING AND LOADING COMPLEX ESSENTIAL FOR CELLULAR IMMUNE RESPONSE CHAPTER 26 – ASSOCIATED WITH ANTIGEN PROCESSING AND LOADING COMPLEX ESSENTIAL FOR CELLULAR IMMUNE RESPONSE CHAPTER 26 – ASSOCIATED WITH ANTIGEN PROCESSING AND LOADING COMPLEX ESSENTIAL FOR CELLULAR IMMUNE RESPONSE CHAPTER 26 – ASSOCIATED WITH ANTIGEN PROCESSING AND LOADING COMPLEX ESSENTIAL FOR CELLULAR IMMUNE RESPONSE
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Numerical solution of the problems for plates on some complex partial internal supports

Numerical solution of the problems for plates on some complex partial internal supports

The method is developed for plates on internal supports of more complex configurations. Namely, we examine the cases of symmetric rectangular and H-shape supports, where the computational domain after reducing to the first quadrant of the plate is divided into three subdomains. Also, we consider the case of asymmetric rectangular support where the computational domain needs to be divided into 9 subdomains. The problems under consideration are reduced to sequences of weak mixed boundary value problems for the Poisson equation, which are solved by difference method. The performed numerical experiments show the effectiveness of the iterative method.
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READ JAPANESE TODAY

READ JAPANESE TODAY

Japanese characters, called kanji, often intimidate potential students of the language with their complex and mysterious appearance. Read Japanese Today is a comprehensible and storylike approach to an often difficult language. Intended for people on the
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Fast genomic prediction of breeding values using parallel Markov chain Monte Carlo with convergence diagnosis

Fast genomic prediction of breeding values using parallel Markov chain Monte Carlo with convergence diagnosis

Running multiple-chain Markov Chain Monte Carlo (MCMC) provides an efficient parallel computing method for complex Bayesian models, although the efficiency of the approach critically depends on the length of the non-parallelizable burn-in period, for which all simulated data are discarded.
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Giải bài tập mạng máy tính Computer Networking A TopDown Approach Chapter 1 2 Problems

Giải bài tập mạng máy tính Computer Networking A TopDown Approach Chapter 1 2 Problems

Giải bài tập mạng máy tính Computer Networking A TopDown Approach Chapter 1 2 Problems
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HANDBOOK OF ALGORITHMS FOR PHYSICAL DESIGN AUTOMATION PART 104 PPSX

HANDBOOK OF ALGORITHMS FOR PHYSICAL DESIGN AUTOMATION PART 104 PPSX

model-based approach_ steps in, 792 topography variations dummy fill synthesis, 794–795 Markov chain approach, 323 Mask error enhancement factor MEEF, 727–729 Master-image style, 17 Math[r]
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ATMAD: ROBUST IMAGE ANALYSIS FOR AUTOMATIC TISSUE MICROARRAY DE-ARRAYING

ATMAD: ROBUST IMAGE ANALYSIS FOR AUTOMATIC TISSUE MICROARRAY DE-ARRAYING

We developed a novel de-arraying approach for TMA analysis. By combining wavelet-based detection, active contour segmentation, and thin-plate spline interpolation, our approach is able to handle TMA images with high dynamic, poor signal-to-noise ratio, complex background and non-linear deformation of TMA grid.
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A two-phase linear programming approach for redundancy allocation problems

A two-phase linear programming approach for redundancy allocation problems

Provision of redundant components in parallel is an efficient way to increase the system reliability, however, the weight, volume and cost of the system will increase simultaneously. This paper proposes a new two-phase linear programming approach for solving the nonlinear redundancy allocation problems subject to multiple linear constraints.
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LUẬN VĂN THẠC SĨ APPLICATIONS OF TASK BASED LANGUAGE APPROACH IN TEXTBOOKS FOR GRADE 10 STUDENTS IN DEVELOPING LISTENING SKILLS   AN ACTION RESEARCH

LUẬN VĂN THẠC SĨ APPLICATIONS OF TASK BASED LANGUAGE APPROACH IN TEXTBOOKS FOR GRADE 10 STUDENTS IN DEVELOPING LISTENING SKILLS AN ACTION RESEARCH

Basing on the background and stated problems of the study, the researcher conducted a classroom action research on _“APPLICATIONS OF TASK-BASED LANGUAGE _ _APPROACH IN TEXTBOOKS FOR GRAD[r]
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DISCRETE SIGNAL ANALYSIS AND DESIGN  P27 PPS

DISCRETE SIGNAL ANALYSIS AND DESIGN P27 PPS

Example 7-1: The Use of Eq. (7-2) Figure 7-2 is an example of the use of Eq. (7-2). The x ( n ) input signal voltage waveform in part (a) is a complex time sequence of cosine and sine waves. This Þ gure uses steps of 0.1 in the ( n ) values for better visual resolution, and this is the only place where x ( n ) is plotted. The two plots in part (a) are I ( n ) (real) and Q ( n ) (imaginary) sequences that we have looked at previously. Parts (b) and (c) are the DFT of part (a) that show the two-sided phasor frequency X ( k ) voltage values. The DFT uses ( k ) steps of 1.0 to avoid spectral leakage between ( k ) integers (Chapter 3). If a dc voltage is present, it shows up at k = 0 (see Fig. 1-2). In this example there is no dc, but it will be considered later. The integer values are suf Þ cient for a correct evaluation if there are enough of them to satisfy the requirements for adequate sampling.
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NUMERICAL PROBLEMS IN PHYSICAL CHEMISTRY FOR IITJEE

NUMERICAL PROBLEMS IN PHYSICAL CHEMISTRY FOR IITJEE

Numerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEE
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SUCCESS STEP ENGLISH 8 PPSX

SUCCESS STEP ENGLISH 8 PPSX

Of course, it helps to know the formula or method needed to solve a problem. But there are always those problems on the test that you don’t recognize or can’t remember how to do, and this may cause you a little anxiety. Even experienced math teachers experience that paralyzing feeling at times. But you shouldn’t allow anxiety to conquer you. Nor should you jump into a problem and start figuring madly without a careful reading and analysis of the problem.
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