On a conjecture by Boyd

The aim of this note is to prove the Mahler measure identity $m(x+x^{-1}+y+y^{-1}+5) = 6 m(x+x^{-1}+y+y^{-1}+1)$ which was conjectured by Boyd. The proof is achieved by proving relationships between regulators of both curves

On a q-analogue of the multiple gamma functions

A $q$-analogue of the multiple gamma functions is introduced, and is shown to satisfy the generalized Bohr-Morellup theorem. Furthermore we give some expressions of these function.Comment: 8 pages, AMS-Late

Observation of Bell Inequality violation in B mesons

A pair of $B^0\bar B^0$ mesons from $\Upsilon(4S)$ decay exhibit EPR type non-local particle-antiparticle (flavor) correlation. It is possible to write down Bell Inequality (in the CHSH form: $S\le2$) to test the non-locality assumption of EPR. Using semileptonic $B^0$ decays of $\Upsilon(4S)$ at Belle experiment, a clear violation of Bell Inequality in particle-antiparticle correlation is observed: S=2.725+-0.167(stat)+-0.092(syst)Comment: Conference Proceeding for Garda Lake Workshop 2003 "Mysteries, Puzzles and Paradoxes in Quantum Mechanics

Congruence schemes

A new category of algebro-geometric objects is defined. This construction is a vast generalization of existing F1-theories, as it contains the the theory of monoid schemes on the one hand and classical algebraic theory, e.g. Grothendieck schemes, on the the other. It also gives a handy description of Berkovich subdomains and thus contains Berkovich's approach to abstract skeletons. Further it complements the theory of monoid schemes in view of number theoretic applications as congruence schemes encode number theoretical information as opposed to combinatorial data which are seen by monoid schemes

A two-stage ceramic tile grout sealing process using a high power diode laser Part I: Grout development and materials characteristics

Work has been conducted using a 60 W-cw high power diode laser (HPDL) in order to determine the feasibility and characteristics of sealing the void between adjoining ceramic tiles with a specially developed grout material having an impermeable enamel surface glaze. A two-stage process has been developed using a new grout material which consists of two distinct components: an amalgamated compound substrate and a glazed enamel surface; the amalgamated compound seal providing a tough, heat resistant bulk substrate, whilst the enamel provides an impervious surface. HPDL processing has resulted in crack free seals produced in normal atmospheric conditions. The basic process phenomena are investigated and the laser effects in terms of seal morphology, composition and microstructure are presented. Also, the resultant heat affects are analysed and described, as well as the effects of the shield gases, O2 and Ar, during laser processing. Tiles were successfully sealed with power densities as low as 500 W/cm2 and at rates up to 600 mm/min. Contact angle measurements revealed that due to the wettability characteristics of the amalgamated oxide compound grout (AOCG), laser surface treatment was necessary in order to alter the surface from a polycrystalline to a semi-amorphous structure, thus allowing the enamel to adhere. Bonding of the enamel to the AOCG and the ceramic tiles was identified as being principally due to van der Waals forces, and on a very small scale, some of the base AOCG material dissolving into the glaze

Integral representations of q-analogues of the Hurwitz zeta function

Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at non-positive integers of the q-analogue of the Hurwitz zeta function, and to study the classical limit of this q-analogue. All the discussion developed here is entirely different from the previous work in [4]Comment: 14 page

Imaging and quantifying ganglion cells and other transparent neurons in the living human retina

Ganglion cells are the primary building block of retinal neural circuitry, but have been elusive to observe and quantify in the living human eye. Here, we show a light microscopy modality that reveals not only the somas of these cells, but also their 3D packing geometry, primary subtypes, and spatial projection to other neurons. The method provides a glimpse of the rich tapestry of neurons, glia, and blood vessels that compose the retina, thus exposing the anatomical substrate for neural processing of visual information. Clinically, high-resolution images of retinal neurons in living eyes hold promise for improved diagnosis and assessing treatment of ganglion cell and other neuron loss in retinal disease., Ganglion cells (GCs) are fundamental to retinal neural circuitry, processing photoreceptor signals for transmission to the brain via their axons. However, much remains unknown about their role in vision and their vulnerability to disease leading to blindness. A major bottleneck has been our inability to observe GCs and their degeneration in the living human eye. Despite two decades of development of optical technologies to image cells in the living human retina, GCs remain elusive due to their high optical translucency. Failure of conventional imaging—using predominately singly scattered light—to reveal GCs has led to a focus on multiply-scattered, fluorescence, two-photon, and phase imaging techniques to enhance GC contrast. Here, we show that singly scattered light actually carries substantial information that reveals GC somas, axons, and other retinal neurons and permits their quantitative analysis. We perform morphometry on GC layer somas, including projection of GCs onto photoreceptors and identification of the primary GC subtypes, even beneath nerve fibers. We obtained singly scattered images by: (i) marrying adaptive optics to optical coherence tomography to avoid optical blurring of the eye; (ii) performing 3D subcellular image registration to avoid motion blur; and (iii) using organelle motility inside somas as an intrinsic contrast agent. Moreover, through-focus imaging offers the potential to spatially map individual GCs to underlying amacrine, bipolar, horizontal, photoreceptor, and retinal pigment epithelium cells, thus exposing the anatomical substrate for neural processing of visual information. This imaging modality is also a tool for improving clinical diagnosis and assessing treatment of retinal disease