On Rogers-Ramanujan functions, binary quadratic froms and eta-quotients

Cataloged from PDF version of article.In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the Rogers-Ramanujan functions. We observe that the function that appears in Ramanujan's identities can be obtained from a Hecke action on a certain family of eta products. We establish further Hecke-type relations for these functions involving binary quadratic forms. Our observations enable us to find new identities for the Rogers-Ramanujan functions and also to use such identities in return to find identities involving binary quadratic forms. © 2013 American Mathematical Society

Perfect valley filter in strained graphene with single barrier region

We present a single barrier system to generate pure valley-polarized current in monolayer graphene. A uniaxial strain is applied within the barrier region, which is delineated by localized magnetic field created by ferromagnetic stripes at the regions boundaries. We show that under the condition of matching magnetic field strength, strain potential, and Fermi energy, the transmitted current is composed of only one valley contribution. The desired valley current can transmit with zero reflection while the electrons from the other valley are totally reflected. Thus, the system generates pure valley-polarized current with maximum conductance. The chosen parameters of uniaxial strain and magnetic field are in the range of experimental feasibility, which suggests that the proposed scheme can be realized with current technology

Ramanujan's identities and representation of integers by certain binary and quaternary quadratic forms

We revisit old conjectures of Fermat and Euler regarding the representation of integers by binary quadratic form x2+5y2. Making use of Ramanujan's 1ψ1 summation formula, we establish a new Lambert series identity for Σ∞n,m=-∞qn2+5m2 Conjectures of Fermat and Euler are shown to follow easily from this new formula. But we do not stop there. Employing various formulas found in Ramanujan's notebooks and using a bit of ingenuity, we obtain a collection of new Lambert series for certain infinite products associated with quadratic forms such as x2+6y2, 2x2+3y2, x2+15y2, 3x2+5y2, x2+27y2, x2+5(y2+z2+w2), 5x2+y2+z2+w2. In the process, we find many new multiplicative eta-quotients and determine their coefficients. © 2009 Springer Science+Business Media, LLC

Ge/SiGe Quantum Well p-i-n Structures for Uncooled Infrared Bolometers

Cataloged from PDF version of article.The temperature dependence of current is investigated experimentally for silicon–germanium (Si-Ge) multi-quantum-well p-i-n devices on Si substrates as uncooled bolometer active layers. Temperature coefficient of resistance values as high as −5.8%/K are recorded. This value is considerably higher than that of even commercial bolometer materials in addition to being well above the previous efforts based on CMOS compatible materials

Local differences of the position of the mental foramen

The mental foramen has been reported to vary in position in different ethnic groups. Repeated failures during injections and operative procedures involving the mental foramen suggest the presence of local differences in a given population. The aim of the present study was to investigate possible local differences of the mental foramen in Eastern Anatolian individuals in the Turkish population. The present investigation is based on the examination of 70 adult mandibles. The study consisted of three measurements, to include the relations of the mental foramen to the following: 1) the lower teeth; 2) the body of mandible; 3) the mandibular symphysis and posterior border of the ramus of the mandible. The most common position of the foramen was in line with the longitudinal axis of the second premolar tooth (relation IV), at the midpoint of the mandibular body height and at 1/3.5 of the distance from the mandibular symphysis to the posterior border of the ramus. Local differences of the mental foramen may occur in a population. Prior to surgery knowledge of the most common location of the foramen peculiar to a local population may enable effective mental block anaesthesia to be provided. (Folia Morphol 2008; 67: 32-35)