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Boolos, John P. Burgess, Richard C. Jeffrey Publisher: Cambridge University Press Abstract: Computability theory, which investigates computable functions and computable sets, lies at the foundation of logic and computer science.
For the statements 7 - 11 above will all be found in various mathematics textbooks called, e. I'll be teaching logic to graduate students in philosophy this coming semester. Its classical presentations usually involve a fair amount of Goedel encodings.
Jeffrey Publisher: Cambridge University Press. There is a difference of emphasis, however.
I sat in Soare's class in the hope some of the techniques in computability would help my research in complexity for the most part they haven't and have gone to a few logic seminars. Jerome Keisler et al. Everything I do they call "zero. The study of computability theory in computer science is closely related to the study of computability in mathematical logic.
This page intentionally left blankComputability and Logic, Fourth EditionThis fourth edition of one of the classic logic textbooks has been thoroughly revised by JohnBurgess. Undeland, William P. Semiconductor switching into magnetic components is not unusual in power electronics, for example, the flyback converter.
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Power Electronics: Converters , Applications, and Design, 3rd edition. The expression "soft switching" actually refers to the operation of power electronic switches as zero-voltage switches ZVS or zero-current switches ZCS. ALD's EH42xx is another voltage step-up converter designed for energy harvesting sources. Very generalised statistical module, useful to be done with GER Most reviews I have read mentions that some of the modules covered have been taught in JC Mathematics, and I heard that graphic calculators are not allowed for this.
Dr Yuan Ye TA: My advice is that you focus on understanding the next few topics as there will be heavy emphasis on them and keep practicing the methods.
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Gone are the Finals! To find out more, including how to control cookies, see here: These are all personal opinions and do note that assessment of the mods may differ depending on which year they are taken.
Then some questions were just duplicates until the nots just skips them. Redo these questions without referring to your notes to check your application.
These difficult computational problemsolving needs have now fostered many complexities in virtually all computing technologies, while driving up costs and operational aspects of the technology environments.
However, this advanced computing collaboration capability is indeed required in almost all areas of industrial and business problem solving, ranging from scientific studies to commercial solutions to academic endeavors.
It is a difficult challenge across all the technical communities to achieve this level of resource collaboration needed for solving these complex and dynamic problems, within the bounds of the necessary quality requirements of the end user. To further illustrate this environment and oftentimes very complex set of technology challenges, let us consider some common use case scenarios one might have already encountered, which will begin to examine the many values of a Grid Computing solution environment.
These simple use cases, for purposes of introduction to the concepts of Grid Computing, are as follows: A financial organization processing wealth management application collaborates with the different departments for more computational power and software modeling applications. It pools a number of computing resources, which can thereby perform faster with real-time executions of the tasks and immediate access to complex pools of data storage, all while managing complicated data transfer tasks.
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This ultimately results in increased customer satisfaction with a faster turnaround time. A group of scientists studying the atmospheric ozone layer will collect huge amounts of experimental data, each and every day. These scientists need efficient and complex data storage capabilities across wide and geographically dispersed storage facilities, and they need to access this data in an efficient manner based on the processing needs.
This ultimately results in a more effective and efficient means of performing important scientific research.
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Massive online multiplayer game scenarios for a wide community of international gaming participants are occurring that require a large number of gaming computer servers instead of a dedicated game server.
This allows international game players to interact among themselves as a group in a real-time manner. This involves the need for on-demand allocation and provisioning of computer resources, provisioning and self-management of complex networks, and complicated data storage resources. This on-demand need is very dynamic, from momentto-moment, and it is always based upon the workload in the system at any given moment in time. This ultimately results in larger gaming communities, requiring more complex infrastructures to sustain the traffic loads, delivering more profits to the bottom lines of gaming corporations, and higher degrees of customer satisfaction to the gaming participants.
A government organization studying a natural disaster such as a chemical spill may need to immediately collaborate with different departments in order to plan for and best manage the disaster.
These organizations may need to simulate many computational models related to the spill in order to calculate the spread of the spill, effect of the weather on the spill, or to determine the impact on human health factors.
This ultimately results in protection and safety matters being provided for public safety issues, wildlife management and protection issues, and ecosystem protection matters: Needles to say all of which are very key concerns. Today, Grid Computing offers many solutions that already address and resolve the above problems. Grid Computing solutions are constructed using a variety of technologies and open standards. Grid Computing, in turn, provides highly scalable, highly secure, and extremely high-performance mechanisms for discovering and negotiating access to remote computing resources in a seamless manner.
This makes it possible for the sharing of computing resources, on an unprecedented scale, among an infinite number of geographically distributed groups. This serves as a significant transformation agent for individual and corporate implementations surrounding computing practices, toward a general-purpose utility approach very similar in concept to providing electricity or water.
These electrical and water types of utilities, much like Grid Computing utilities, are available "on demand," and will always be capable of providing an always-available facility negotiated for individual or corporate utilization.
In this new and intriguing book, we will begin our discussion on the core concepts of the Grid Computing system with an early definition of grid. In addition to these qualifications of coordinated resource sharing and the formation of dynamic virtual organizations, open standards become a key underpinning. It is important that there are open standards throughout the grid implementation, which also accommodate a variety of other open standardsbased protocols and frameworks, in order to provide interoperable and extensible infrastructure environments.
Grid Computing environments must be constructed upon the following foundations: Coordinated resources. W e should avoid building grid systems with a centralized control; instead, we must provide the necessary infrastructure for coordination among the resources, based on respective policies and service-level agreements.
Open standard protocols and framew orks. The use of open standards provides interoperability and integration facilities. These standards must be applied for resource discovery, resource access, and resource coordination.
Another basic requirement of a Grid Computing system is the ability to provide the quality of service QoS requirements necessary for the end-user community. These QoS validations must be a basic feature in any Grid system, and must be done in congruence with the available resource matrices. These QoS features can be for example response time measures, aggregated performance, security fulfillment, resource scalability, availability, autonomic features such as event correlation and configuration management, and partial fail over mechanisms.
There have been a number of activities addressing the above definitions of Grid Computing and the requirements for a grid system. The most notable effort is in the standardization of the interfaces and protocols for the Grid Computing infrastructure implementations.
W e will cover the details later in this book. Let us now explore some early and current Grid Computing systems and their differences in terms of benefits. Early Grid Activities Over the past several years, there has been a lot of interest in computational Grid Computing worldwide. W e also note a number of derivatives of Grid Computing, including compute grids, data grids, science grids, access grids, knowledge grids, cluster grids, terra grids, and commodity grids.
As we explore careful examination of these grids, we can see that they all share some form of resources; however, these grids may have differing architectures. One key value of a grid, whether it is a commodity utility grid or a computational grid, is often evaluated based on its business merits and the respective user satisfaction.
User satisfaction is measured based on the QoS provided by the grid, such as the availability, performance, simplicity of access, management aspects, business values, and flexibility in pricing.
The business merits most often relate to and indicate the problem being solved by the grid. For instance, it can be job executions, management aspects, simulation workflows, and other key technology-based foundations. Earlier Grid Computing efforts were aligned with the overlapping functional areas of data, computation, and their respective access mechanisms.
Let us further explore the details of these areas to better understand their utilization and functional requirements.
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Data The data aspects of any Grid Computing environment must be able to effectively manage all aspects of data, including data location, data transfer, data access, and critical aspects of security. The core functional data requirements for Grid Computing applications are: The ability to integrate multiple distributed, heterogeneous, and independently managed data sources.
The ability to provide efficient data transfer mechanisms and to provide data where the computation will take place for better scalability and efficiency. The ability to provide necessary data discovery mechanisms, which allow the user to find data based on characteristics of the data.
The capability to implement data encryption and integrity checks to ensure that data is transported across the network in a secure fashion. Computation The core functional computational requirements for grid applications are: The ability to allow for independent management of computing resources The ability to provide mechanisms that can intelligently and transparently select computing resources capable of running a user's job The understanding of the current and predicted loads on grid resources, resource availability, dynamic resource configuration, and provisioning Failure detection and failover mechanisms Ensure appropriate security mechanisms for secure resource management, access, and integrity Let us further explore some details on the computational and data grids as they exist today.
Computational and Data Grids In today's complex world of high speed computing, computers have become extremely powerful as to that of let's say five years ago.
Even the home-based PCs available on the commercial markets are powerful enough for accomplishing complex computations that we could not have imagined a decade prior to today.
The quality and quantity requirements for some business-related advanced computing applications are also becoming more and more complex. These requirements can actually exceed the demands and availability of installed computational power within an organization. Sometimes, we find that no single organization alone satisfies some of these aforementioned computational requirements. This advanced computing power applications need is indeed analogous to the electric power need in the early s, such that to provide for the availability of electrical power, each user has to build and be prepared to operate an electrical generator.
Thus, when the electric power grid became a reality, this changed the entire concept of the providing for, and utilization of, electrical power.
This, in turn, paved the way for an evolution related to the utilization of electricity. In a similar fashion, the computational grids change the perception on the utility and availability of the computer power. Thus the computational Grid Computing environment became a reality, which provides a demanddriven, reliable, powerful, and yet inexpensive computational power for its customers.
Later in this book, in the "Grid Anatomy" section, we will see that this definition has evolved to give more emphasis on the seamless resource sharing aspects in a collaborative virtual organizational world.
But the concept still holds for a computational grid where the sharable resource remains a computing power. As of now, the majority of the computational grids are centered on major scientific experiments and collaborative environments.
The requirement for key data forms a core underpinning of any Grid Computing environment. For example, in data-intensive grids, the focus is on the management of data, which is being held in a variety of data storage facilities in geographically dispersed locations. These data sources can be databases, file systems, and storage devices. The grid systems must also be capable of providing data virtualization services to provide transparency for data access, integration, and processing.
In addition to the above requirements, security and privacy requirements of all respective data in a grid system is quite complex. W e can summarize the data requirements in the early grid solutions as follows: The ability to discover data The access to databases, utilizing meta-data and other attributes of the data The provisioning of computing facilities for high-speed data movement The capability to support flexible data access and data filtering capabilities As one begins to realize the importance of extreme high performance-related issues in a Grid Computing environment, it is recommended to store or cache data near to the computation, and to provide a common interface for data access and management.
It is interesting to note that upon careful examination of existing Grid Computing systems, readers will learn that many Grid Computing systems are being applied in several important scientific research and collaboration projects; however, this does not preclude the importance of Grid Computing in business-, academic-, and industry-related fields.
The commercialization of Grid Computing invites and addresses a key architectural alignment with several existing commercial frameworks for improved interoperability and integration. As we will describe in this book, many current trends in Grid Computing are toward service-based architectures for grid environments.
This "architecture" is built for interoperability and is again based upon open standard protocols. W e will provide a full treatment including many of the details toward this architecture throughout subsequent sections in this book. Current Grid Activities As described earlier, initially, the focused Grid Computing activities were in the areas of computing power, data access, and storage resources.
The definition of Grid Computing resource sharing has since changed, based upon experiences, with more focus now being applied to a sophisticated form of coordinated resource sharing distributed throughout the participants in a virtual organization.
This application concept of coordinated resource sharing includes any resources available within a virtual organization, including computing power, data, hardware, software and applications, networking services, and any other forms of computing resource attainment. This concept of coordinated resource sharing is depicted in Figure 1. Figure 1. Dynamic benefits of coordinated resource sharing in a virtual organization. As depicted in the previous illustration, there are a number of sharable resources, hardware and software applications, firmware implementations, and networking services, all available within an enterprise or service provider environment.
Rather than keeping these resources isolated within an atomic organization, the users can acquire these resources on a "demand" basis. Through implementing this type of Grid Computing environment, these resources are immediately available to the authenticated users for resolving specific problems.
These problems may be a software capability problem e. W hile on another level, these problems may be related to a networking bandwidth availability problem, the need for immediate circuit provisioning of a network, a security event or other event correlation issue, and many more types of critical environmental needs.
Based upon the specific problem dimension, any given problem may have one or more resolution issues to address. For example, in the above case there is two sets of users, each with a need to solve two different types of problems.
Y ou will note that one has to resolve the weather prediction problem, while the other has to provide a financial modeling case. Based upon these problem domains noted by each of the user groups, their requirements imply two types of virtual organizations.
These distinct virtual organizations are formulated, sustained, and managed from a computing resource viewpoint according to the ability to access the available resources. Let us further explore this concept of "virtualization " by describing in more detail the usage patterns found within each of the virtual organizations.
A virtual organization for w eather prediction.
For example, this virtual organization requires resources such as weather prediction software applications to perform the mandatory environmental simulations associated with predicting weather.
Likewise, they will require very specific hardware resources to run the respective software, as well as high-speed data storage facilities to maintain the data generated from performing the simulations. A virtual organization for financial modeling. For example, this virtual organization requires resources such as software modeling tools for performing a multitude of financial analytics, virtualized blades  to run the above software, and access to data storage facilities for storing and accessing data.
These virtual organizations manage their resources and typically will provision additional resources on an "as-needed" basis. This on-demand approach provides tremendous values toward scalability, in addition to aspects of enhanced reusability.
This approach is typically found in any "on-demand" environment.A virtual organization for financial modeling. As a matter of fact the complexity and dynamic nature of industrial problems in today's world are much more intensive to satisfy by the more traditional, single computational platform approaches.
For example, in data-intensive grids, the focus is on the management of data, which is being held in a variety of data storage facilities in geographically dispersed locations. Rather than keeping these resources isolated within an atomic organization, the users can acquire these resources on a "demand" basis. The provisioning of secure access methods to the resources, and bindings with the local security mechanisms based upon the autonomic control policies.
Its classical presentations usually involve a fair amount of Goedel encodings. This delivery of utility-based power has become second nature to many of us, worldwide. With that said — Hexalock seems tough to beat when it comes to cloning — I now have hexaloock useless coasters from trying to duplicate the discs using every available known application — with no success.