Groups with the same prime graph as the simple group Dn(5)

Let G be a finite group. The prime graph of G is denoted by Γ(G). Let G be a finite group such that Γ(G)=Γ(Dn(5)), where n≥6. In the paper, as the main result, we show that if n is odd, then G is recognizable by the prime graph and if n is even, then G is quasirecognizable by the prime graph.Нехай G — скшченна група. Простий граф групи GG позначимо через Γ(G). Нехай G — скінченна група така, що Γ(G)=Γ(Dn(5)), де n≥6. Як основний результат роботи доведено, що для непарних n група G розтзнається простим графом, а для парних n група G є такою, що квазiрозпiзнається простим графом

The electromagnetic field near a dielectric half-space

We compute the expectations of the squares of the electric and magnetic fields in the vacuum region outside a half-space filled with a uniform non-dispersive dielectric. This gives predictions for the Casimir-Polder force on an atom in the `retarded' regime near a dielectric. We also find a positive energy density due to the electromagnetic field. This would lead, in the case of two parallel dielectric half-spaces, to a positive, separation-independent contribution to the energy density, besides the negative, separation-dependent Casimir energy. Rough estimates suggest that for a very wide range of cases, perhaps including all realizable ones, the total energy density between the half-spaces is positive.Comment: Latex2e, IOP macros, 15 pages, 2 eps figure

MULTI-DIMENSIONAL COSMOLOGY AND DSR–GUP

A multi-dimensional cosmology with FRW type metric having four-dimensional spacetime and d-dimensional Ricci-flat internal space is considered with a higher-dimensional cosmological constant. The classical cosmology in commutative and Doubly Special Relativity–Generalized Uncertainty Principle (DSR–GUP) contexts is studied and the corresponding exact solutions for negative and positive cosmological constants are obtained. In the positive cosmological constant case, it is shown that unlike the commutative as well as GUP cases, in DSR–GUP case both scale factors of internal and external spaces after accelerating phase will inevitably experience decelerating phase leading simultaneously to a big crunch. This demarcation from GUP originates from the difference between the GUP and DSR–GUP algebras. The important result is that unlike GUP which results in eternal acceleration, DSR–GUP at first generates acceleration but prevents the eternal acceleration at late-times and turns it into deceleration

Multi-Dimensional Cosmology and GUP

We consider a multidimensional cosmological model with FRW type metric having 4-dimensional space-time and $d$-dimensional Ricci-flat internal space sectors with a higher dimensional cosmological constant. We study the classical cosmology in commutative and GUP cases and obtain the corresponding exact solutions for negative and positive cosmological constants. It is shown that for negative cosmological constant, the commutative and GUP cases result in finite size universes with smaller size and longer ages, and larger size and shorter age, respectively. For positive cosmological constant, the commutative and GUP cases result in infinite size universes having late time accelerating behavior in good agreement with current observations. The accelerating phase starts in the GUP case sooner than the commutative case. In both commutative and GUP cases, and for both negative and positive cosmological constants, the internal space is stabilized to the sub-Planck size, at least within the present age of the universe. Then, we study the quantum cosmology by deriving the Wheeler-DeWitt equation, and obtain the exact solutions in the commutative case and the perturbative solutions in GUP case, to first order in the GUP small parameter, for both negative and positive cosmological constants. It is shown that good correspondence exists between the classical and quantum solutions.Comment: 21 pages, 15 figures, minor revision, references adde

Effect of gold nanoparticles on prostate dose distribution under Ir-192 internal and 18 MV external radiotherapy procedures using gel dosimetry and monte carlo method

Background: Gel polymers are considered as new dosimeters for determining radiotherapy dose distribution in three dimensions. Objective: The ability of a new formulation of MAGIC-f polymer gel was assessed by experimental measurement and Monte Carlo (MC) method for studying the effect of gold nanoparticles (GNPs) in prostate dose distributions under the internal Ir-192 and external 18MV radiotherapy practices. Method: A Plexiglas phantom was made representing human pelvis. The GNP shaving 15 nm in diameter and 0.1 mM concentration were synthesized using chemical reduction method. Then, a new formulation of MAGIC-f gel was synthesized. The fabricated gel was poured in the tubes located at the prostate (with and without the GNPs) and bladder locations of the phantom. The phantom was irradiated to an Ir-192 source and 18 MV beam of a Varian linac separately based on common radiotherapy procedures used for prostate cancer. After 24 hours, the irradiated gels were read using a Siemens 1.5 Tesla MRI scanner. The absolute doses at the reference points and isodose curves resulted from the experimental measurement of the gels and MC simulations following the internal and external radiotherapy practices were compared. Results: The mean absorbed doses measured with the gel in the presence of the GNPs in prostate were 15 and 8 higher than the corresponding values without the GNPs under the internal and external radiation therapies, respectively. MC simulations also indicated a dose increase of 14 and 7 due to presence of the GNPs, for the same experimental internal and external radiotherapy practices, respectively. Conclusion: There was a good agreement between the dose enhancement factors (DEFs) estimated with MC simulations and experiment gel measurements due to the GNPs. The results indicated that the polymer gel dosimetry method as developed and used in this study, can be recommended as a reliable method for investigating the DEF of GNPs in internal and external radiotherapy practices. © 2015 Shiraz University of Medical Sciences. All Rights Reserved