Ω-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem

In this paper we study generalised prime systems for which the integer counting function NP(x) is asymptotically well behaved, in the sense that NP(x)=ρx+O(xβ), where ρ is a positive constant and . For such systems, the associated zeta function ζP(s) is holomorphic for . We prove that for , for any ε>0, and also for ε=0 for all such σ except possibly one value. The Dirichlet divisor problem for generalised integers concerns the size of the error term in NkP(x)−Ress=1(ζPk(s)xs/s), which is O(xθ) for some θ<1. Letting αk denote the infimum of such θ, we show that

Analogue and digital linear modulation techniques for mobile satellite

The choice of modulation format for a mobile satellite service is complex. The subjective performance is summarized of candidate schemes and voice coder technologies. It is shown that good performance can be achieved with both analogue and digital voice systems, although the analogue system gives superior performance in fading. The results highlight the need for flexibility in the choice of signaling format. Linear transceiver technology capable of using many forms of narrowband modulation is described

Reconsidering \u3cem\u3eIn re Technology Licensing Corporation\u3c/em\u3e and the Right to Jury Trial in Patent Invalidity Suits

Over the past decade, the Federal Circuit and the Supreme Court have lessened the role of the jury in patent cases, both by classifying patent issues as questions of law for the judge, and by limiting the situations in which jury trial is available as of right. Recently, In re Technology Licensing Corporation, the Federal Circuit held that there is no right to a jury trial in a declaratory judgment action seeking a declaration of patent invalidity, where the defendant counterclaims with alleged infringement and seeks an injunction as the sole remedy. In line with Supreme Court precedent, the Technology Licensing majority applied a two-pronged historical analog test: (1) compare the statutory action to eighteenth-century actions from England, as they existed prior to the merger of the courts of law and equity; and (2) determine whether the remedy sought is legal or equitable in nature. Under the first prong, the Federal Circuit majority determined that the closest historical analog to the declaratory judgment action for patent invalidity was the inverted form of the action: a patent infringement suit where the defendant alleges patent invalidity. A review of eighteenth-century English patent law, however, in combination with a closer look at the nature of the present-day patent invalidity action, suggests that the writ of scire facias—a legal action-is a more appropriate historical analog to the declaratory judgment action for patent invalidity, and that the right to jury trial should therefore attach. At a minimum, the uncertainty as to what the appropriate analog might be suggests that the Federal Circuit should have followed the Supreme Court\u27s approach in Markman v. Westview Instruments. In Markman, the Court had recognized that there was no clear historical analog to patent claim construction, and therefore looked instead to functional considerations and policy concerns. Under that approach, the highly fact-intensive nature of patent invalidity issues dictates that the right to jury trial should be preserved

Reconsidering \u3cem\u3eIn re Technology Licensing Corporation\u3c/em\u3e and the Right to Jury Trial in Patent Invalidity Suits

Over the past decade, the Federal Circuit and the Supreme Court have lessened the role of the jury in patent cases, both by classifying patent issues as questions of law for the judge, and by limiting the situations in which jury trial is available as of right. Recently, In re Technology Licensing Corporation, the Federal Circuit held that there is no right to a jury trial in a declaratory judgment action seeking a declaration of patent invalidity, where the defendant counterclaims with alleged infringement and seeks an injunction as the sole remedy. In line with Supreme Court precedent, the Technology Licensing majority applied a two-pronged historical analog test: (1) compare the statutory action to eighteenth-century actions from England, as they existed prior to the merger of the courts of law and equity; and (2) determine whether the remedy sought is legal or equitable in nature. Under the first prong, the Federal Circuit majority determined that the closest historical analog to the declaratory judgment action for patent invalidity was the inverted form of the action: a patent infringement suit where the defendant alleges patent invalidity. A review of eighteenth-century English patent law, however, in combination with a closer look at the nature of the present-day patent invalidity action, suggests that the writ of scire facias—a legal action-is a more appropriate historical analog to the declaratory judgment action for patent invalidity, and that the right to jury trial should therefore attach. At a minimum, the uncertainty as to what the appropriate analog might be suggests that the Federal Circuit should have followed the Supreme Court\u27s approach in Markman v. Westview Instruments. In Markman, the Court had recognized that there was no clear historical analog to patent claim construction, and therefore looked instead to functional considerations and policy concerns. Under that approach, the highly fact-intensive nature of patent invalidity issues dictates that the right to jury trial should be preserved

Feasibility study of an Integrated Program for Aerospace vehicle Design (IPAD). Volume 3: Support of the design process

The user requirements for computer support of the IPAD design process are identified. The user-system interface, language, equipment, and computational requirements are considered

Relativistic and Radiative Corrections to the Mollow Spectrum

The incoherent, inelastic part of the resonance fluorescence spectrum of a laser-driven atom is known as the Mollow spectrum [B. R. Mollow, Phys. Rev. 188, 1969 (1969)]. Starting from this level of description, we discuss theoretical foundations of high-precision spectroscopy using the resonance fluorescence light of strongly laser-driven atoms. Specifically, we evaluate the leading relativistic and radiative corrections to the Mollow spectrum, up to the relative orders of (Z alpha)^2 and alpha(Z alpha)^2, respectively, and Bloch-Siegert shifts as well as stimulated radiative corrections involving off-resonant virtual states. Complete results are provided for the hydrogen 1S-2P_{1/2} and 1S-2P_{3/2} transitions; these include all relevant correction terms up to the specified order of approximation and could directly be compared to experimental data. As an application, the outcome of such experiments would allow for a sensitive test of the validity of the dressed-state basis as the natural description of the combined atom-laser system.Comment: 20 pages, 1 figure; RevTe