A Treatise on the differential calculus and the elements of the integral calculus : with numerous examples /

Mode of access: Internet.

An elementary treatise on the differential calculus : containing the theory of plane curves, with numerous examples /

Includes index.

The principles of the differential calculus; with its application to curves and curve surfaces ...

Mode of access: Internet.

Descriptive Sets and the Topology of Nonseparable Banach Spaces

This paper was extensively circulated in manuscript form beginning in the Summer of 1989. It is being published here for the first time in its original form except for minor corrections, updated references and some concluding comments.

Representable Banach Spaces and Uniformly Gateaux-Smooth Norms

It is proved that a representable non-separable Banach space does not admit uniformly Gâteaux-smooth norms. This is true in particular for C(K) spaces where K is a separable non-metrizable Rosenthal compact space.

Radon Measures on Banach Spaces with their Weak Topologies

The main concern of this paper is to present some improvements to results on the existence or non-existence of countably additive Borel measures that are not Radon measures on Banach spaces taken with their weak topologies, on the standard axioms (ZFC) of set-theory. However, to put the results in perspective we shall need to say something about consistency results concerning measurable cardinals.

Application of Fractional Calculus in the Dynamical Analysis and Control of Mechanical Manipulators

Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40

Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s

Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05.

Nonlinear Time-Fractional Differential Equations in Combustion Science

MSC 2010: 34A08 (main), 34G20, 80A25

Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions

2010 Mathematics Subject Classification: 47B33, 47B38.

A broadcast authentication and integrity augmentation for trusted differential GPS in marine navigation

In this paper we propose an efficient authentication and integrity scheme to support DGPS corrections using the RTCM protocol, such that the identified vulnerabilities in DGPS are mitigated. The proposed scheme is based on the TESLA broadcast protocol with modifications that make it suitable for the bandwidth and processor constrained environment of marine DGPS.

Calculating shades of meaning in semantic spaces

This thesis introduces the problem of conceptual ambiguity, or Shades of Meaning (SoM) that can exist around a term or entity. As an example consider President Ronald Reagan the ex-president of the USA, there are many aspects to him that are captured in text; the Russian missile deal, the Iran-contra deal and others. Simply finding documents with the word “Reagan” in them is going to return results that cover many different shades of meaning related to "Reagan". Instead it may be desirable to retrieve results around a specific shade of meaning of "Reagan", e.g., all documents relating to the Iran-contra scandal. This thesis investigates computational methods for identifying shades of meaning around a word, or concept. This problem is related to word sense ambiguity, but is more subtle and based less on the particular syntactic structures associated with or around an instance of the term and more with the semantic contexts around it. A particularly noteworthy difference from typical word sense disambiguation is that shades of a concept are not known in advance. It is up to the algorithm itself to ascertain these subtleties. It is the key hypothesis of this thesis that reducing the number of dimensions in the representation of concepts is a key part of reducing sparseness and thus also crucial in discovering their SoMwithin a given corpus.

An advanced implicit meshless approach for fractional partial differential equation in computational mechanics

Recently, the numerical modelling and simulation for fractional partial differential equations (FPDE), which have been found with widely applications in modern engineering and sciences, are attracting increased attentions. The current dominant numerical method for modelling of FPDE is the explicit Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of time fractional diffusion equations. The discrete system of equations is obtained by using the RBF meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modelling and simulation for FPDE.

Exploiting system fluctuations. Differential training in physical prevention and rehabilitation programs for health and exercise

Background: Traditional causal modeling of health interventions tends to be linear in nature and lacks multidisciplinarity. Consequently, strategies for exercise prescription in health maintenance are typically group based and focused on the role of a common optimal health status template toward which all individuals should aspire. ----- ----- Materials and methods: In this paper, we discuss inherent weaknesses of traditional methods and introduce an approach exercise training based on neurobiological system variability. The significance of neurobiological system variability in differential learning and training was highlighted.----- ----- Results: Our theoretical analysis revealed differential training as a method by which neurobiological system variability could be harnessed to facilitate health benefits of exercise training. It was observed that this approach emphasizes the importance of using individualized programs in rehabilitation and exercise, rather than group-based strategies to exercise prescription.----- ----- Conclusion: Research is needed on potential benefits of differential training as an approach to physical rehabilitation and exercise prescription that could counteract psychological and physical effects of disease and illness in subelite populations. For example, enhancing the complexity and variability of movement patterns in exercise prescription programs might alleviate effects of depression in nonathletic populations and physical effects of repetitive strain injuries experienced by athletes in elite and developing sport programs.