Congruences for Overpartitions with Restricted Odd Differences

In recent work, Bringmann et al. used q-difference equations to compute a two-variable q-hypergeometric generating function for the number of overpartitions where (i) the difference between two successive parts may be odd only if the larger of the two is overlined, and (ii) if the smallest part is odd then it is overlined, given by t ¯ ( n ) . They also established the two-variable generating function for the same overpartitions where (i) consecutive parts differ by a multiple of ( k + 1 ) unless the larger of the two is overlined, and (ii) the smallest part is overlined unless it is divisible by k + 1 , enumerated by t ¯ ( k ) ( n ) . As an application they proved that t ¯ ( n ) = 0 ( mod 3 ) if n is not a square. In this paper, we extend the study of congruence properties of t ¯ ( n ) , and we prove congruences modulo 3 and 6 for t ¯ ( n ) , congruences modulo 2 and 4 for t ¯ ( 3 ) ( n ) and t ¯ ( 7 ) ( n ) , congruences modulo 4 and 5 for t ¯ ( 4 ) ( n ) , and congruences modulo 3, 6 and 12 for t ¯ ( 8 ) ( n )

Determination of radionuclides in soil samples taken from Gura Topp (Jos) using sodium iodide thallium detector Nai(Ti)

The activity concentrations of natural radionuclides 40K, 226Ra and 232Th in soil samples taken from the tin mining area in Gura top, Jos were measured by gamma spectrometry using Sodium Iodide detector. The average specific activity concentrations of 40K, 226Ra and 232Th determined in the soil sample ranged from 11.26±3.16Bq/Kg to 543.35±0.64Bq/Kg with mean activity concentration of 161.96±7.56Bq/Kg for 40K, that of 226Ra ranged from 7.19±1.23Bq/Kg to 144.20±10.18Bq/Kg with the mean activity of 46.47±5.19Bq/Kg while 232Th ranged from 76.08±3.38Bq/Kg to 1267.91±15.37Bq/Kg, with mean activity concentration of 396.17±7.69Bq/Kg. The results indicates that the activity concentration of 40K was found to be below the world average while that of 232Th and 226Ra were detected to be above the world average value. This suggests that t the study area has excess thorium and radium activities which pose significant health hazard and is considered radio-logically unsafe for human to cultivate on the land.Keywords: Activity concentration, Gamma spectrometry, Natural radionuclides and Sodium, Iodide detecto

Supernovae as a probe of particle physics and cosmology

It has very recently been demonstrated by Csaki, Kaloper and Terning (CKT) that the faintness of supernovae at high redshift can be accommodated by mixing of a light axion with the photon in the presence of an intergalactic magnetic field, as opposed to the usual explanation of an accelerating universe by a dark energy component. In this paper we analyze further aspects of the CKT mechanism and its generalizations. The CKT mechanism also passes various cosmological constraints from the fluctuations of the CMB and the formation of structure at large scales, without requiring an accelerating phase in the expansion of the Universe. We investigate the statistical significance of current supernova data for pinning down the different components of the cosmological energy-momentum tensor and for probing physics beyond the standard models.Comment: 17 pages, LaTeX, 4 figures; v2: typos corrected, minor changes, references added; v3: updated figures, details regarding fits include

Leptogenesis and Low-energy Observables

We relate leptogenesis in a class of theories to low-energy experimental observables: quark and lepton masses and mixings. With reasonable assumptions motivated by grand unification, one can show that the CP-asymmetry parameter takes a universal form. Furthermore the dilution mass is related to the light neutrino masses. Overall, these models offer a natural explanation for a lepton asymmetry in the early universe.Comment: 10 pages, revised discussion on light neutrino masse

Vacuum polarization of a scalar field in wormhole spacetimes

An analitical approximation of $$ for a scalar field in a static spherically symmetric wormhole spacetime is obtained. The scalar field is assumed to be both massive and massless, with an arbitrary coupling $\xi$ to the scalar curvature, and in a zero temperature vacuum state.Comment: 10 pages, RevTeX, two eps figure

Electromagnetic waves in a wormhole geometry

We investigate the propagation of electromagnetic waves through a static wormhole. It is shown that the problem can be reduced to a one-dimensional Schr\"odinger-like equation with a barrier-type potential. Using numerical methods, we calculate the transmission coefficient as a function of the energy. We also discuss the polarization of the outgoing radiation due to this gravitational scattering.Comment: LaTex file, 5 pages, 2 figures, one reference added, accepted for publication in PR

Design and Simulation of Extended Interaction Cavities for a Ka band Multi beam Klystron

This article reports about the design approach, electromagnetic simulation and analysis results of high-frequency ladder-type input, output, and intermediate RF cavaties for Ka-band multi-beam extended interaction klystron. Several parameters of the cavity, such as quality factor, shunt impedance, etc., have been investigated by the assistance of electromagnetic software CST microwave studio

Time-dependent Stochastic Modeling of Solar Active Region Energy

A time-dependent model for the energy of a flaring solar active region is presented based on a stochastic jump-transition model (Wheatland and Glukhov 1998; Wheatland 2008; Wheatland 2009). The magnetic free energy of the model active region varies in time due to a prescribed (deterministic) rate of energy input and prescribed (random) flare jumps downwards in energy. The model has been shown to reproduce observed flare statistics, for specific time-independent choices for the energy input and flare transition rates. However, many solar active regions exhibit time variation in flare productivity, as exemplified by NOAA active region AR 11029 (Wheatland 2010). In this case a time-dependent model is needed. Time variation is incorporated for two cases: 1. a step change in the rates of flare jumps; and 2. a step change in the rate of energy supply to the system. Analytic arguments are presented describing the qualitative behavior of the system in the two cases. In each case the system adjusts by shifting to a new stationary state over a relaxation time which is estimated analytically. The new model retains flare-like event statistics. In each case the frequency-energy distribution is a power law for flare energies less than a time-dependent rollover set by the largest energy the system is likely to attain at a given time. For Case 1, the model exhibits a double exponential waiting-time distribution, corresponding to flaring at a constant mean rate during two intervals (before and after the step change), if the average energy of the system is large. For Case 2 the waiting-time distribution is a simple exponential, again provided the average energy of the system is large. Monte Carlo simulations of Case~1 are presented which confirm the analytic estimates. The simulation results provide a qualitative model for observed flare statistics in active region AR 11029.Comment: 25 pages, 9 figure

Static and dynamic traversable wormhole geometries satisfying the Ford-Roman constraints

It was shown by Ford and Roman in 1996 that quantum field theory severely constrains wormhole geometries on a macroscopic scale. The first part of this paper discusses a wide class of wormhole solutions that meet these constraints. The type of shape function used is essentially generic. The constraints are then discussed in conjunction with various redshift functions. Violations of the weak energy condition and traversability criteria are also considered. The second part of the paper analyzes analogous time-dependent (dynamic) wormholes with the aid of differential forms. It is shown that a violation of the weak energy condition is not likely to be avoidable even temporarily.Comment: 16 pages AMSTe

A study of the zero modes of the Faddeev-Popov operator in Euclidean Yang-Mills theories in the Landau gauge in d=2,3,4 dimensions

Examples of normalizable zero modes of the Faddeev-Popov operator in SU(2) Euclidean Yang-Mills theories in the Landau gauge are constructed in d=2,3,4 dimensions.Comment: 18 pages. Text modifications. References added. Version accepted for publication in the EPJ