A Proof of the Riemann hypothesis The new version contains a change in Definition 3.4, resulting in simpler proofs of theorems in Sections 3 and 4. Also, important proof in Sec.5 has been modified, for completeness and clarity

The function $G(z) = \int_0^\infty \xi^{z-1}(1+\exp(\xi))^{-1} \, d\xi$ is analytic and has the same zeros as the Riemann zeta function in the critical strip $D = \{z \in {\mathbf C} : 0 < \Re z < 1\}$. This paper combines some novel methods about indefinite integration, indefinite convolutions and inversions of Fourier transforms with numerical ranges of operators to prove the Riemann hypothesis.Comment: 26 pages in .pdf This version changes Definition 3.4, enabling changes the statements of Theorems in Sec.4, and thus enabling a clearer proof in Sec.

Where to find Christian philosophy?: Spatiality in John Chrysostom’s counter to Greek Paideia

This article examines the use of the concept philosophia in the writings and homilies of John Chrysostom. Although Chrysostom in his discussion of intellectual achievements draws on a long-standing tradition of Christian apologetics, he lends a new direction to the debate by highlighting the spatiality of philosophy. He not only counters Hellenic paideia with Christian wisdom, but locates these two types of philosophy in the city and the countryside, respectively. The article argues that the spatial dimension is vital to Chrysostom’s view of philosophy as he aims to extend the rural ideal of asceticism to the polis to create a healthy Christian community within the city

Closed fluid system without moving parts controls temperature

Closed fluid system maintains a constant temperature in an insulated region without the use of any moving parts. Within the system, the energy for thermodynamic cycling of two-phase heat transfer fluid and a hydraulic fluid is entirely supplied by the heat generated in the thermally insulated region

Study of phase transitions and properties of tetragonal (Pb, La) (Zr, Ti)O3 ceramics—III : Transitions induced by electric fields

The phase diagram of electrically poled, tetragonal PLZT materials has been investigated. In the higher La concentration range, a tetragonal, so-called β-phase occurs, which has no clear FE properties. The transition to the FEt phase has first order character and takes place only after a strong electric field has been applied to the material. The energetics of theβt ah FEt transition were investigated in several ways. The heat-effects associated with this transition have a small value of 6–20cal/mol, dependent on composition. The transition βt ah FEt is accompanied by a relatively large activation energy ΔG2. The ΔG2(T) curve shows a minimum for materials, which do not show a spontaneous transition to the FEt phase. This minimum value of ΔG2 (1–2.5 cal/mol) is large in comparison to the average thermal energy kT and prevents the spontaneous transition from the βt phase to the FEt phase

Tunneling conductance in semiconductor-superconductor hybrid structures

We study the differential conductance for charge tunneling into a semiconductor wire--superconductor hybrid structure, which is actively investigated as a possible scheme for realizing topological superconductivity and Majorana zero modes. The calculations are done based on a tight-binding model of the heterostructure using both a Blonder-Tinkham-Klapwijk approach and a Keldysh non-equilibrium Green's function method. The dependence of various tunneling conductance features on the coupling strength between the semiconductor and the superconductor, the tunnel barrier height, and temperature is systematically investigated. We find that treating the parent superconductor as an active component of the system, rather than a passive source of Cooper pairs, has qualitative consequences regarding the low-energy behavior of the differential conductance. In particular, the presence of sub-gap states in the parent superconductor, due to disorder and finite magnetic fields, leads to characteristic particle-hole asymmetric features and to the breakdown of the quantization of the zero-bias peak associated with the presence of Majorana zero modes localized at the ends of the wire. The implications of these findings for the effort toward the realization of Majorana bound states with true non-Abelian properties are discussed.Comment: published version, 15+ pages, 12 figure

Social Network Sites (SNS): do they match ? Definitions and methods for social sciences and marketing research

Social Networks Sites (SNS) such as Facebook, MySpace, Skyrock.com or Linkedin have become new fields of investigation for marketing. Even though the phenomenon has met with an amazing popular success, only a few scientific works have been published on this subject. This article proposes initially to evaluate the situation by a review of the experts' discourses and, then, a an analysis of the texts in core disciplines specialising in social networks analysis (mainly sociometry, anthropology and sociology). Finally this work will help us to propose a definition for SNS as a research subject and to design a methodology for marketing research

How Teenagers Deal with their Privacy on Social Network Sites? Results from a National Survey in France

This paper proposes to examine the case of privacy concerns and privacy management for teenagers on Social Network Sites, according to a national survey being carried out in France since January 2008 by two University research teams in management sciences, sociology and computing, for the French National Postal Service.