Abstract:
In the research it was examined the changes in total phenolic contents and seven major phenolic compounds (gallic acids, +(–) catechin, catechol, Chlorogenic acid, o-coumaric acid, rutin and quercetin) of two litchi cultivars (Purbi and Bedana) shoot tips and fruits (for zygotic embryos) collected in different months, in order to determine their effects on the explants browning during establishment stage of shoot tip culture. The concentrations of phenolic compounds varied depending on the cultivars and the months. Phenolic compounds showed various correlation coefficients with the explants browning. Total phenolic content and some individual phenolic compounds including +(–) catechin, catechol, gallic acid, chlorogenic acid and rutin quantified in this study showed significant positive correlations with the explants browning, while o-coumaric acid and quercetin did not exhibit any significant one. According to our results, explants browning are affected by the phenolic compounds at different ranges. In both litchi cultivars, shoot tips and fruits (for zygotic embryos) collected in March exhibited the lowest explants browning during the establishment stage as compared to those collected in the other months. So it may be possible to increase the success of shoot tip and zygotic embryo culture with the selection of the most suitable terms of explants collection. Browning of explants could be controlled by the use of antioxidants both in semi-solid and liquid culture.

Abstract:
The article concentrates on the role of fluctuating parameters for removable population from the incubated class in a susceptible-incubated-infected model. The discrete analogous of this model is also investigated. Conditions for local asymptotic stability are derived for both the disease free and endemic cases. Numerical simulations are performed to validate the theoretical results.

Abstract:
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential equations in the arena of discrete phase space and continuous time. The scalar field and electromagnetic fields are quantized with commutation relations. The spin-1/2 field is quantized with anti-commutation relations. Moreover, the total momentum, energy and charge of these free relativisitic quantized fields in the discrete phase space and continuous time are computed exactly. The results agree completely with those computed from the relativisitic fields defned on the space-time continuum.

Abstract:
In the arena of the discrete phase space and continuous time, the theory of S-marix is formulated. In the special case of Quantum-Electrodynamics (QED), the Feynman rules are precisely developed. These rules in the fourmomentum turn out to be identical to the usual QED, except for the vertex function. The new vertex function is given by an infinite series which can only be treated in an asymptotic approximation at the present time. Preliminary approximations prove that the second order self-energies of a fermion and a photon in the discrete model have convergent improper integrals. In the final section, a sharper asymptotic analysis is employed. It is proved that in case the number of external photon or fermion lines is at least one, then the S-matrix elements converge in all orders. Moreover, there are no infra-red divergences in this formulation.

Abstract:
The classical relativistic wave equations are presented as partial difference equations in the arena of covariant discrete phase space. These equations are also expressed as difference-differential equations in discrete phase space and continuous time. The relativistic invariance and covariance of the equations in both versions are established. The partial difference and difference-differential equations are derived as the Euler-Lagrange equations from the variational principle. The difference and difference-differential conservation equations are derived. Finally, the total momentum, energy, and charge of the relativistic classical fields satisfying difference-differential equations are computed.

Abstract:
A cosmology is considered driven by a stress-energy tensor consisting of a perfect fluid, an inhomogeneous pressure term (which we call a ``tachyonic dust'' for reasons which will become apparent) and a cosmological constant. The inflationary, radiation dominated and matter dominated eras are investigated in detail. In all three eras, the tachyonic pressure decreases with increasing radius of the universe and is thus minimal in the matter dominated era. The gravitational effects of the dust, however, may still strongly affect the universe at present time. In case the tachyonic pressure is positive, it enhances the overall matter {\em density} and is a candidate for dark matter. In the case where the tachyonic pressure is negative, the recent acceleration of the universe can be understood without the need for a cosmological constant. The ordinary matter, however, has positive energy density at all times. In a later section, the extension to a variable cosmological term is investigated and a specific model is put forward such that recent acceleration and future re-collapse is possible.

Abstract:
This paper studies wormhole solutions to Einstein gravity with an arbitrary number of time dependent compact dimensions and a matter-vacuum boundary. A new gauge is utilized which is particularly suited for studies of the wormhole throat. The solutions possess arbitrary functions which allow for the description of infinitely many wormhole systems of this type and, at the stellar boundary, the matter field is smoothly joined to vacuum. It turns out that the classical vacuum structure differs considerably from the four dimensional theory and is therefore studied in detail. The presence of the vacuum-matter boundary and extra dimensions places interesting restrictions on the wormhole. For example, in the static case, the radial size of a weak energy condition (WEC) respecting throat is restricted by the extra dimensions. There is a critical dimension, D=5, where this restriction is eliminated. In the time dependent case, one \emph{cannot} respect the WEC at the throat as the time dependence actually tends the solution towards WEC violation. This differs considerably from the static case and the four dimensional case.

Abstract:
A general class of solutions is obtained which describe a spherically symmetric wormhole system. The presence of arbitrary functions allows one to describe infinitely many wormhole systems of this type. The source of the stress-energy supporting the structure consists of an anisotropic brown dwarf ``star'' which smoothly joins the vacuum and may possess an arbitrary cosmological constant. It is demonstrated how this set of solutions allows for a non-zero energy density and therefore allows positive stellar mass as well as how violations of energy conditions may be minimized. Unlike examples considered thus far, emphasis here is placed on construction by manipulating the matter field as opposed to the metric. This scheme is generally more physical than the purely geometric method. Finally, explicit examples are constructed including an example which demonstrates how multiple closed universes may be connected by such wormholes. The number of connected universes may be finite or infinite.