1,139 research outputs found
Extensions of Watson's theorem and the Ramanujan-Guinand formula
No full text© 2023 World Scientific Publishing Company.Ramanujan provided several results involving the modified Bessel function Kz(x) in his Lost Notebook. One of them is the famous Ramanujan-Guinand formula, equivalent to the functional equation of the non-holomorphic Eisenstein series on SL2(ℤ). Recently, this formula was generalized by Dixit, Kesarwani, and Moll. In this paper, we first obtain a generalization of a theorem of Watson and, as an application of it, give a new proof of the result of Dixit, Kesarwani, and Moll. Watson's theorem is also generalized in a different direction using muλ) which is itself a generalization of Kz(x). Analytic continuation of all these results are also given.11Nsciescopu
Explicit transformations of certain Lambert series
No full textAn exact transformation, which we call the \emph{master identity}, is
obtained for the first time for the series
for and Re.
New modular-type transformations when is a non-zero even integer are
obtained as its special cases. The precise obstruction to modularity is
explicitly seen in these transformations. These include a novel companion to
Ramanujan's famous formula for . The Wigert-Bellman identity
arising from the case of the master identity is derived too. When is
an odd integer, the well-known modular transformations of the Eisenstein series
on , that of the Dedekind eta function
as well as Ramanujan's formula for are derived from the master
identity. The latter identity itself is derived using Guinand's version of the
Vorono\"{\dotlessi} summation formula and an integral evaluation of
N.~S.~Koshliakov involving a generalization of the modified Bessel function
. Koshliakov's integral evaluation is proved for the first time. It
is then generalized using a well-known kernel of Watson to obtain an
interesting two-variable generalization of the modified Bessel function. This
generalization allows us to obtain a new modular-type transformation involving
the sums-of-squares function . Some results on functions
self-reciprocal in the Watson kernel are also obtained.Comment: The earlier title of the paper is modified to the current one. This
paper has now been accepted for publication in 'Research in the Mathematical
Sciences
Arbitration and Dispute Settlement in Foreign Indirect Investment. The increasing significance and use of arbitration in international loan agreements, syndicated loans and international bond issues
No full textThis dissertation examines the suitability of arbitration for the resolution of securities regulatory claims and it adoption globally, which has resulted in international arbitration becoming the favoured dispute resolution mechanism in the securities industry. The author explains that disputes arising out of international bilateral and syndicated loan agreements are generally considered to be arbitrable, while international bond disputes are often derived from the controversies over the application of mandatory national laws and the compliance with securities regulation provisions - so the arbitrability of international bond disputes depends on the acceptance of the arbitrability of securities regulatory claims
A monolithically integrated power JFET and Junction Barrier Schottky diode in 4H silicon carbide
No full textEfficiency of power management circuits depends significantly on their constituent switches and rectifiers. The demands of technology are increasingly running up against the intrinsic properties of Si based power devices. 4H-Silicon Carbide (SiC) has superior properties that make it attractive for high power applications. SiC rectifiers are already a competitive choice and SiC switches have also been commercialized recently. Junction Barrier Schottky (JBS) diodes, which combine the advantages of PN and Schottky, have higher Figure of Merit (FOM) as rectifiers. Among switches, a robust and mature process has been developed for Silicon Carbide Vertical Junction Field Effect Transistors (VJFETs), which currently gives it the highest unipolar FOM. Switches are frequently combined with anti-parallel diodes in power circuits. This thesis describes the development of a SiC-based monolithically integrated power switch and diode. Monolithic integration increases reliability and efficiency, and reduces cost. Because of their superior properties and similarities in fabrication, we chose the SiC VJFET and JBS diode as the switch and rectifier. Detailed design, fabrication and characterization of the integrated switch to block above 800 V and conduct current beyond 100 A/cm2 is explained. In this process, the first physics-based 2-D compact model is developed for reverse leakage in a JBS diode as a function of design parameters. Since the gate-channel junctions of SiC VJFETs cannot be assumed to be abrupt, an existing analytical model for Si VJFETs is extended to account for graded gate-channel junctions. Using these analytical models, design rules are developed for the VJFET and JBS diode. Finite element simulations are used to find the best anode layout of the JBS diode and optimize electric field termination in the integrated device to ensure their capability to operate at high voltage. Finally, a spin-on glass based process is developed for filling the gate trenches of the VJFET to improve long-term robustness in extreme environments. The integrated power switch developed in this thesis points to the attractions of monolithic integration in SiC power circuits. Analytical compact design equations derived here will facilitate faster and easier design of switches and rectifiers for desired circuit operation.Ph. D.Includes bibliographical referencesIncludes vitaby Rahul Radhakrishna
The generalized modified Bessel function Kz,w(x) at z=1/2 and Humbert functions,
No full textRecently Dixit, Kesarwani, and Moll introduced a generalization Kz,w(x) of the modified Bessel function Kz(x) and showed that it satisfies an elegant theory similar to Kz(x). In this paper, we show that while K12(x) is an elementary function, K12,w(x) can be written in the form of an infinite series of Humbert functions. As an application of this result, we generalize the transformation formula for the logarithm of the Dedekind eta function ?(z)
Form Tester: Website Test Automation Using Form-Oriented Models
No full textFull text is available to authenticated members of The University of Auckland only.Whilst Model Based Testing (MBT) is an improvement over manual test specification, the leap from manual testing to MBT can be hard. Current MBT tools only allow development of models from scratch, without reuse of existing manual test specifications. Conversely, current MBT tools do not facilitate partial automation of manual test cases, e.g. to automate only the test initialization procedure. Finally, existing MBT tools do not identify areas of the system that are not testable due to defects, which may in turn conceal other defects. We propose a new MBT approach that addresses these shortcomings. The approach uses a form-oriented model that clearly represents the actions, pages and fields of a web application. Instead of having to specify a test model from scratch, existing manual test cases can be used without modification as part of a test model specification. This means that developers can move from manual testing to MBT without any additional cost. Furthermore, the approach allows developers to use test models to partially automate manual tests. A test model can be used to automate the initialization step of manual test cases, hence making it easier to specify manual tests. Finally, the proposed approach can identify areas of the application that are unreachable due to defects using an online testing strategy. This provides an overview of all testable parts that have been covered, as well as areas where additional defects may be concealed. The approach was implemented in a novel MBT tool called FormTester, and evaluated with real web applications. One small and one mid-sized application were tested using manually specified tests; one large, complex application was automated using the MBT tool. The tool's performance gains over manual specification were evaluated. Manual test cases were used to specify the model, and their test initializations were generated automatically. This improved time spent developing test cases (Minutes/Test) by about 30%. The same types and similar numbers of defects were discovered using the tool as manual specification, indicating a similar effectiveness in defect detection
Correlating Middle Manager Recommendations In Portfolio Management Outcomes
No full textAbstractDecision-making is fundamental to any business. Decision-making happens at all levels of the enterprise and in all parts of the organization. This research focusses on decision-making processes in the defense industry. The US defense industry has undergone over 2-decades of consolidations through acquisitions and mergers. Given over $100B in annual opportunities for product development, to succeed in this monopsony marketplace, portfolio managers within these enterprises must repeatedly make the right pursue-abandon decisions. One of the key differentiators for successful defense companies is how they execute Portfolio Management (PM) and New Product Development (NPD) processes. Product management is seen as both science and art and depends on the goals on hand. This research seeks to validate the researcher’s anecdotal multi-decade observations on portfolio-management decision-making practices in the defense industry, especially regarding new product development opportunities. The observations suggest a framework that ties market factors with decision-making processes and includes moderating and modifying effects due to organizational value propositions and risk tolerance. These concepts were vetted via an extensive literature survey that tracked major research streams to identify a decision-making framework, and then to follow evolution of these research ideas through the various citations that flowed from the benchmark papers, to seek correlation of the factors with business outcome. The major gaps in literature were that published literature mostly addressed commercial free-market situations, were often from an outsider’s point of view (ETIC), and rarely connected early pursue-abandon decisions with later-term production award business impact. To address these gaps, a modified Delphi methods study was designed to assess qualitatively (explorative) and quantitative (confirmatory) correlation between decision-making processes and later-term production awards. The qualitative research was conducted via face-to-face individual interviews with subject matter experts and industry middle-management decision makers engaged in portfolio management. These open-ended interviews were guided by the cue-words that were extracted from the literature review. The interviews yielded a set of closed-ended questions that helped create a wide-area survey instrument. The survey instrument was deployed across a broad cross-section of industry decision makers to assess quantitative correlation between early pursue-abandon decisions and later term production awards. The resultant data was analyzed for correlation between factors and decision outcome. After dimensionality reduction and regression analysis, the study was able to obtain R2 (adjusted) up to 44.8% to link the independent variables to the business outcome (the dependent variable). This is a significant advancement in the field that ties defense industry early phase pursue-abandon PM and NPD decision making with later-term (production phase) business outcome. For the first time, an attempted correlation of ‘how’ to ‘thus’ was attempted, with acceptable success. The results revealed that factors related to market conditions impact company’s decision processes, which are themselves moderated and mediated by value proposition factors and risk tolerance factors. The significance of this research extends to other low-velocity industries and can be a valuable governance guide for procurement reform within the customer community, and for bid-development best-practices within the industry participants
Barriers to career advancement: Asian Americans in the U.S. aerospace industry
No full textThis qualitative study explored the lack of Historically Underrepresented Population (HUP) inclusion in management and leadership roles. Specifically, why Asian Americans (AA) do not reach executive levels in southern California aerospace and defense companies (SCDCs). The AA members of HUP are among the highest educated and display model-behavior characteristics, yet, somehow do not thrive in management assignments. The U.S. defense industry has operated in a single-customer market, and that customer (the U.S. Government) is imposing social change agendas, to establish a leadership that is reflective of the company’s diversity. Exacerbating the underrepresentation of AAs is a shrinking domestic defense appropriations budget and business growth opportunities overseas. These conditions present the need for the development of a diverse management pipeline that can provide needed agility in industry leadership to enable both compliance and growth. In the course of this research, a pilot group and a main study sample of subjects were interviewed to characterize both the employee traits and their experience within the corporate environment. The study exposed environmental factors such as micro-aggressions (i.e., bullying) and other corporate impediments, as well as AA behavior traits that make this population conflict and risk averse. These qualities keep them from entering the management pipeline during their early career, where they could acquire the skills and develop the soft skills needed for later career senior management and leadership assignments. A proposed path forward to motivate aspirants onto the management track, as well as corporate behavior transformation to institutionalize AA pipelining, is recommended. The outcomes of this study provide an opportunity for transforming the leadership of the southern California defense contractors
Detection of Image Region Duplication through Digital Forensics
No full textDigital images, being the major information carriers in today's digital world, act as the primary sources of evidence towards any event in the court of law as well as media and broadcast industries. Nonetheless, the relative simplicity of editing and manipulating digital images, have made their reliability and trustworthiness largely questionable. In fact, seeing is no more believing, due to the fact that in today's digital age, there is an expanding number of vindictively altered pictures. Exploiting the present-day vast availability of an extensive variety of efficient and easy–to–use image processing software and desktop tools, digital image manipulations by an adversary has become extremely common and simple. One of the major issues in crime scene investigation depicted in an image, is figuring out whether the image is genuine or doctored. This can be a critical assignment when images are utilized as fundamental proof to impact legal judgement, for instance, in the court of law.
Digital Forensics is a branch of science that deals with the investigation, verification and recovery of digital data and evidences remnant in digital devices such as computers, digital cameras and video recorders. In this research, we deal with digital image forensics. We focus on a specific class of image forgery, viz. copy–move forgery or region duplication, and its subsequent detection and localization. In this type of forgery, one part of the image is copied and moved into another region of the same image, with the malicious intent of repeating or obscuring significant image objects of interest. This form of digital image forgery becomes all the more difficult to be detected, when the adversary performs additional intelligent attacks, such as edge blurring, brightness adjustment, noise enhancement of the forged regions, or geometric attacks such as rotation or re–scale of the forged regions before duplicating those. Majorly, this research focuses on the development and performance analysis of copy–move forgery detection and localization techniques, while addressing the additional challenge of detecting geometric and post-processing based attacks. In this dissertation, we present a survey of state–of–the–art copy–move forgery detection techniques, along with the motivation and objectives of this research. We present, efficient proposed techniques for region duplication detection (both block based and key–point based), and detailed experimental and comparison results pertaining to those. Finally, we conclude with significant future research directions
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