arXiv subjects
Publications and source records attributed to S. Sivasubramanian.
In this paper, we consider the class of strongly bi-close-to-convex functions of order $α$ and bi-close-to-convex functions of order $β$. We obtain an upper bound estimate for the second Hankel determinant for functions belonging to these classes. The results in this article improve some earlier result obtained for the class of bi-convex functions.
We consider general theoretical models of water and in particular the nature of the motions of the hydrogen nuclei. If the motion of hydrogen nuclei is classical, then the thermodynamic pressure equation of state for heavy water wherein the hydrogen nuclei are deuterons is identical to the pressure equation of state for light water wherein the hydrogen nuclei are protons. Since the experimental thermodynamic phase diagram for light water is clearly measurably different from the experimental thermodynamic phase diagram for heavy water, one may deduce that the motions of hydrogen nuclei are quantum mechanical in nature. This conclusion is in physical agreement with a recent analysis of X-ray, neutron and deep inelastic neutron scattering data.
A rigorous thermodynamic expression is derived for the total biological information capacity per unit length of a DNA molecule. The total information includes the usual four letter coding sequence information plus that excess information coding often erroneously referred to as "junk". We conclude that the currently understood human DNA code is about a hundred megabyte program written on a molecule with about a ten gigabyte memory. By far, most of the programing code is not presently understood.
Chemical reactions can be induced at a distance due to the propagation of electromagnetic signals during intermediate chemical stages. Although it is well known at optical frequencies, e.g. photosynthetic reactions, electromagnetic signals hold true for much lower frequencies. In E. coli bacteria such electromagnetic signals can be generated by electric transitions between energy levels describing electrons moving around DNA loops. The electromagnetic signals between different bacteria within a community is a "wireless" version of intercellular communication found in bacterial communities connected by "nanowires". The wireless broadcasts can in principle be of both the AM and FM variety due to the magnetic flux periodicity in electron energy spectra in bacterial DNA orbital motions.
Soft multi-photon radiation from hard higher energy reaction sources can be employed to describe three major well established properties of biophoton radiation; Namely, (i) the mild radiation intensity decreases for higher frequencies, (ii) the coherent state Poisson counting statistics, and (iii) the time delayed luminescence with a hyperbolic time tail. Since the soft photon frequencies span the visible to the ultraviolet frequency range, the hard reaction sources have energies extending into the nuclear transmutation regime.
Geographic location search engines allow users to constrain and order search results in an intuitive manner by focusing a query on a particular geographic region. Geographic search technology, also called location search, has recently received significant interest from major search engine companies. Academic research in this area has focused primarily on techniques for extracting geographic knowledge from the web. In this paper, we study the problem of efficient query processing in scalable geographic search engines. Query processing is a major bottleneck in standard web search engines, and the main reason for the thousands of machines used by the major engines. Geographic search engine query processing is different in that it requires a combination of text and spatial data processing techniques. We propose several algorithms for efficient query processing in geographic search engines, integrate them into an existing web search query processor, and evaluate them on large sets of real data and query traces.
The phenomenological equations of motion for the relaxation of ordered phases of magnetized and polarized crystal phases can be developed in close analogy with one another. For the case of magnetized systems, the driving magnetic field intensity toward relaxation was developed by Gilbert. For the case of polarized systems, the driving electric field intensity toward relaxation was developed by Khalatnikov. The transport times for relaxation into thermal equilibrium can be attributed to viscous sound wave damping via magnetostriction for the magnetic case and electrostriction for the polarization case.
Recent studies of turbulence in superfluid Helium indicate that turbulence in quantum fluids obeys a Kolmogorov scaling law. Such a law was previously attributed to classical solutions of the Navier-Stokes equations of motion. It is suggested that turbulence in all fluids is due to quantum fluid mechanical effects. Employing a field theoretical view of the fluid flow velocity, vorticity appears as quantum filamentary strings. This in turn leads directly to the Kolmogorov critical indices for the case of fully developed turbulence.
A cylindrical flexible cable made up of pure fluid water can be experimentally spanned across a spatial gap with cable endpoints fixed to the top edges of two glass beakers. The cable has been called a water bridge in close analogy to iron cables employed to build ordinary span bridges. A necessary condition for the construction of a water bridge is that a large electric field exists parallel to and located within the water cable. Presently, there is no accepted detailed theory which quantitatively explains the forces which hold up the bridge. Our purpose is to present such theory based on the Maxwell pressure tensor induced by the electric field albeit within the condensed matter dielectric fluid cable.
The degree partition of a simple graph is its degree sequence rearranged in weakly decreasing order. The polytope of degree partitions (respectively, degree sequences) is the convex hull of all degree partitions (respectively, degree sequences) of a fixed length. We think of the degree sequence polytope as the symmetrization of the degree partition polytope and the degree partition polytope as the asymmetric part of the degree sequence polytope. The degree sequence polytope is a well studied object with formulas (generating functions) known for its face numbers, volume, and number of lattice points. We study the degree partition polytope and determine its extreme points, edges, and facets. In particular, the degree partition polytope on n vertices has 2^{n-1} extreme points.
Molecular quantum electrodynamics leads to photon frequency shifts and thus to changes in condensed matter free energies often called the Casimir effect. Strong quantum electrodynamic coupling between radiation and molecular motions can lead to an instability beyond which one or more photon oscillators undergo a displacement phase transition. The phase boundary of the transition can be located by a Casimir free energy instability.
The cross section for a gravitational wave antenna to absorb a graviton may be directly expressed in terms of the non-local viscous response function of the metallic crystal. Crystal viscosity is dominated by electronic processes which then also dominate the graviton absorption rate. To compute this rate from a microscopic Hamiltonian, one must include the full Coulomb interaction in the Maxwell electric field pressure and also allow for strongly non-adiabatic transitions in the electronic kinetic pressure. The view that the electrons and phonons constitute ideal gases with a weak electron phonon interaction is not sufficiently accurate for estimating the full strength of the electronic interaction with a gravitational wave.
We consider light waves propagating clockwise and other light waves propagating counterclockwise around a closed path in a plane (theoretically with the help of stationary mirrors). The time difference between the two light propagating path orientations constitutes the Sagnac effect. The general relativistic expression for the Sagnac effect is discussed. It is shown that a gravitational wave incident to the light beams at an arbitrary angle will not induce a Sagnac effect so long as the wave length of the weak gravitational wave is long on the length scale of the closed light beam paths. The gravitational wave induced Sagnac effect is thereby null.
Employing Maxwell's equations as the field theory of the photon, quantum mechanical operators for spin, chirality, helicity, velocity, momentum, energy and position are derived. The photon ``Zitterbewegung'' along helical paths is explored. The resulting non-commutative geometry of photon position and the quantum version of the Pythagorean theorem is discussed. The distance between two photons in a polarized beam of given helicity is shown to have a discrete spectrum. Such a spectrum should become manifest in measurements of two photon coincidence counts. The proposed experiment is briefly described.
Electromagnetic methods recently proposed for detecting gravitational waves modify the Michelson phase shift analysis (historically employed for special relativity). We suggest that a frequency modulation analysis is more suited to general relativity. An incident photon in the presence of a very long wavelength gravitational wave will have a finite probability of being returned as a final photon with a frequency shift whose magnitude is equal to the gravitational wave frequency. The effect is due to the non-linear coupling between electromagnetic and gravitational waves. The frequency modulation is derived directly from the Maxwell-Einstein equations.
The notion of ``radiating'' and ``non-radiating'' current sources in classical electrodynamics plays an important role in calculations of direct and inverse electromagnetic scattering problems. Such a decomposition of the current is central for the notion of localized non-radiating electromagnetic modes. A completely quantum electrodynamic view is explored in this work. Photon emission and absorption current sources are classified as being either radiating or non-radiating. This quantum classification corresponds, respectively and exactly, to the notion of ``real'' and ``virtual'' photon processes. Causal properties of both real and virtual electromagnetic fields are discussed.
The conventional Clausius-Mossotti polarization equation of state is known to be unstable for polar liquids having molecules with high polarizability. Room temperature water is an important example. The instability in the polarization equation of state is of the typical loop form requiring an ``equal area'' construction for studying the stable ordered phase. The ordered phase of a Clausius-Mossotti polar liquid then consists of domains each having a net polarization. The polarization may vary in direction from domain to domain. The ordered phases are quite similar to those previously discussed on the basis of Dicke superradiance.
The quantum statistical dynamics of a position coordinate x coupled to a reservoir requires theoretically two copies of the position coordinate within the reduced density matrix description. One coordinate moves forward in time while the other coordinate moves backward in time. It is shown that quantum dissipation induces, in the plane of the forward and backward motions, a noncommutative geometry. The noncommutative geometric plane is a consequence of a quantum dissipation induced phase interference which is closely analogous to the Aharanov-Bohm effect.