On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis

By using the generalized Littlewood theorem about a contour integral involving the logarithm of an analytic function, we show how an infinite number of integral equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis can be established and present some of them as an example. It is shown that all earlier known equalities of this type, viz., the Wang equality, Volchkov equality, Balazard–Saias–Yor equality, and an equality established by one of the authors, are certain special cases of our general approach.Показано як за допомогою узагальненої теореми Лiттлвуда про контурний iнтеграл, що мiстить логарифм аналiтичної функцiї, можна отримати нескiнченну кiлькiсть iнтегральних рiвностей, що мiстять iнтеграли вiд логарифма ζ-функцiї Рiмана i є еквiвалентними гiпотезi Рiмана, i наведено кiлька таких рiвностей у якостi прикладу. Показано, що деякi вiдомi рiвностi такого типу, а саме, рiвностi Ванга, Волчкова, Балазарда – Сайаса – Йора та рiвнiсть, що встановлена одним iз авторiв, є частинними випадками нaшого загального пiдход

Laser nanotraps and nanotweezers for cold atoms: 3D gradient dipole force trap in the vicinity of Scanning Near-field Optical Microscope tip

Using a two-dipole model of an optical near-field of Scanning Near-field Optical Microscope tip, i. e. taking into account contributions of magnetic and electric dipoles, we propose and analyze a new type of 3D optical nanotrap found for certain relations between electric and magnetic dipoles. Electric field attains a minimum value in vacuum in the vicinity of the tip and hence such a trap is quite suitable for manipulations with cold atoms.Comment: 9 pages, 6 figure

An Optical Fiber-Based Nanomotion Sensor for Rapid Antibiotic and Antifungal Susceptibility Tests.

The emergence of antibiotic and antifungal resistant microorganisms represents nowadays a major public health issue that might push humanity into a post-antibiotic/antifungal era. One of the approaches to avoid such a catastrophe is to advance rapid antibiotic and antifungal susceptibility tests. In this study, we present a compact, optical fiber-based nanomotion sensor to achieve this goal by monitoring the dynamic nanoscale oscillation of a cantilever related to microorganism viability. High detection sensitivity was achieved that was attributed to the flexible two-photon polymerized cantilever with a spring constant of 0.3 N/m. This nanomotion device showed an excellent performance in the susceptibility tests of Escherichia coli and Candida albicans with a fast response in a time frame of minutes. As a proof-of-concept, with the simplicity of use and the potential of parallelization, our innovative sensor is anticipated to be an interesting candidate for future rapid antibiotic and antifungal susceptibility tests and other biomedical applications

Single Atom Electron Emission from the Silicon Tip Coated by Calcium Fluoride with Samarium Dopant Ions

We present the first experimental results of the studying of field electron emission from sharp silicon tips covered by thin dielectric CaF2 layers containing Sm dopant ions. Some indications on the resonant tunneling of electrons from sharp silicon tip through dopant samarium ions inside the coating have been observed, which can be regarded as an implementation of one-atom electron source of a new type, based on dielectric coating of emitting tip

Can Dissipative Properties of Single Molecules Be Extracted from a Force Spectroscopy Experiment?

We performed dynamic force spectroscopy of single dextran and titin I27 molecules using small-amplitude and low-frequency (40-240 Hz) dithering of an atomic force microscope tip excited by a sine wave voltage fed onto the tip-carrying piezo. We show that for such low-frequency dithering experiments, recorded phase information can be unambiguously interpreted within the framework of a transparent theoretical model that starts from a well-known partial differential equation to describe the dithering of an atomic force microscope cantilever and a single molecule attached to its end system, uses an appropriate set of initial and boundary conditions, and does not exploit any implicit suggestions. We conclude that the observed phase (dissipation) signal is due completely to the dissipation related to the dithering of the cantilever itself (i.e., to the change of boundary conditions in the course of stretching). For both cases, only the upper bound of the dissipation of a single molecule has been established as not exceeding 3⋅10(-7)kg/s. We compare our results with previously reported measurements of the viscoelastic properties of single molecules, and we emphasize that extreme caution must be taken in distinguishing between the dissipation related to the stretched molecule and the dissipation that originates from the viscous damping of the dithered cantilever. We also present the results of an amplitude channel data analysis, which reveal that the typical values of the spring constant of a I27 molecule at the moment of module unfolding are equal to 4±1.5mN/m, and the typical values of the spring constant of dextran at the moment of chair-boat transition are equal to 30-50mN/m

Field - and Photoassisted Field Emission Studies of Calcium Fluoride Coated Silicon Tips

Measurements of field emission current-voltage and Fowler-Nordheim characteristics of Si tips covered by 100 nm-thick CaF2 epitaxial layers have been for the first time performed. It was found that in spite of dielectric nature of the coating, the tips demonstrate high emissivity comparable with the diamond coated tips. Results of high resolution photoassisted field emission investigations of CaF2/Si structures are presented

Force-induced globule-coil transition in laminin binding protein and its role for viral-cell membrane fusion.

The specific interactions of the pairs laminin binding protein (LBP)-purified tick-borne encephalitis viral surface protein E and certain recombinant fragments of this protein, as well as West Nile viral surface protein E and certain recombinant fragments of that protein, are studied by combined methods of single-molecule dynamic force spectroscopy (SMDFS), enzyme immunoassay and optical surface waves-based biosensor measurements. The experiments were performed at neutral pH (7.4) and acid pH (5.3) conditions. The data obtained confirm the role of LBP as a cell receptor for two typical viral species of the Flavivirus genus. A comparison of these data with similar data obtained for another cell receptor of this family, namely human αVβ3 integrin, reveals that both these receptors are very important. Studying the specific interaction between the cell receptors in question and specially prepared monoclonal antibodies against them, we could show that both interaction sites involved in the process of virus-cell interaction remain intact at pH 5.3. At the same time, for these acid conditions characteristic for an endosome during flavivirus-cell membrane fusion, SMDFS data reveal the existence of a force-induced (effective already for forces as small as 30-70 pN) sharp globule-coil transition for LBP and LBP-fragments of protein E complexes. We argue that this conformational transformation, being an analog of abrupt first-order phase transition and having similarity with the famous Rayleigh hydrodynamic instability, might be indispensable for the flavivirus-cell membrane fusion process. Copyright © 2014 John Wiley & Sons, Ltd

Probing hidden sectors with a muon beam: Implication of spin-0 dark matter mediators for the muon (g-2) anomaly and the validity of the Weiszäcker-Williams approach

In addition to vector (V) type new particles extensively discussed previously, both CP-even (S) and CP-odd (P) spin-0 dark matter (DM) mediators can couple to muons and be produced in the bremsstrahlung reaction μ-+N→μ-+N+S(P). Their possible subsequent invisible decay into a pair of Dirac DM particles, S(P)→χχ¯, can be detected in fixed target experiments through missing energy signature. In this paper, we focus on the case of experiments using high-energy muon beams. For this reason, we derive the differential cross sections involved using the phase space Weiszäcker-Williams approximation and compare them to the exact-tree-level calculations. The formalism derived can be applied in various experiments that could observe muon-spin-0 DM interactions. This can happen in present and future proton beam-dump experiments such as NA62, SHIP, HIKE, and SHADOWS; in muon fixed target experiments as NA64μ, MUonE and M3; in neutrino experiments using powerful proton beams such as DUNE. In particular, we focus on the NA64μ experiment case, which uses a 160 GeV muon beam at the CERN Super Proton Synchrotron accelerator. We compute the derived cross sections, the resulting signal yields and we discuss the experiment projected sensitivity to probe the relic DM parameter space and the (g-2)μ anomaly favored region considering 1011 and 1013 muons on target.ISSN:1550-7998ISSN:0556-2821ISSN:1550-236