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Peroxisome proliferator-activated receptor δ (Pparδ) is a nuclear receptor that plays critical roles in lipid metabolism, glucose metabolism, and cell growth and differentiation. Several recent studies have shown that Pparδ promotes blastocyst hatching in vitro. However, the mechanism by which it promotes preimplantation embryonic development in vitro remains unclear. In this study, oocytes and parthenotes were treated with a specific agonist of PPARδ, GW501516. The activation of PPARδ had no effect on oocyte maturation for 1 μM and 10 μM GW501516 compared with the control group. Additionally, the PPARδ agonist did not affect blastocyst formation (77.79 ± 3.59% [10 μM], 79.00 ± 5.53% [50 μM], and 79.64 ± 6.00% [100 μM] vs. 81.69 ± 2.61% [control]). However, the blastocyst hatching rate was significantly greater for parthenotes treated with 10 and 50 μM agonist, and did not differ between those treated with 100 μM agonist and the control group (61.80 ± 3.03% [10 μM], 65.10 ± 5.25% [50 μM], and 38.85 ± 7.45% [100 μM] vs. 41.77 ± 10.88% [0 μM]). Activation of PPARδ also increased blastocyst quality and cell number, as well as ATP production. There were no clear differences in mitochondrial membrane potential, mitochondrion copy number, or glucose consumption between the treatment and control groups. However, PPARδ activation enhanced lipid accumulation via Fabp3 and Fabp5. Fatty acid oxidation also increased in response to treatment with the agonist via the rate-limiting gene Cpt2. Reactive oxygen species were modified and REDOX maintenance-related gene expression increased significantly in GW501516-exposed blastocysts. In addition, the activation of PPARδ resulted in changes in miRNA content. After treatment with the PPARδ agonist, miR-99 increased and miR-32 decreased. These data showed that PPARδ has a positive impact on blastocyst hatching via the regulation of lipid metabolism.

A theoretical scheme to employ the principle of minimal sensitivity for choosing the optimal values of nonlinear parameters is proposed for the multistate Rayleigh–Ritz variational method. Anharmonic oscillators are particularly considered in this paper. Applications of the present scheme to the one-dimensional Morse and two double-well potentials indicate that it provides much more accurate and faster convergent approximations to the exact energy eigenvalues than several schemes existing in the literatures.

For the generalized statistical mechanics based on the Tsallis entropy, a variational perturbation approximation method with the principle of minimal sensitivity is developed by calculating the generalized free energy up to the third order in variational perturbation expansion. The approximation up to the first order amounts to a variational approach which covers the variational method developed by E.K. Lenzi, L.C. Malacarne, R.S. Mendes [Phys. Rev. Lett. 80 (1998) 218] and the approximations up to higher orders can systematically improve variational results. As an illustrated example, the generalized free energy for a classical harmonic oscillator (considered in the Lenzi's joint work) are calculated up to the third order, and the resultant approximations up to the first, second, and third orders are numerically compared with the exact result.

Combining an optimized expansion scheme in the spirit of the background field method with the Coleman's normal-ordering renormalization prescription, we calculate the effective potential of sine-Gordon field theory beyond the Gaussian approximation. The first-order result is just the sine-Gordon Gaussian effective potential (GEP). For the range of the coupling beta^2, 9 pages and 4 EPS figures, the revised version with literal changes and minor corrections to typo errors in equations

Within the framework of the Gaussian wave-functional approach, we investigate the influences of quantum and finite-temperature effects on the Z_2-symmetry(\phi \to -\phi) of the (1+1)-dimensional massive sine-Gordon field theory. It is explicitly demonstrated that by quantum effects the Z_2-symmetry can be restored in one region of the parameter space and dynamically spontaneously broken in another region. Moreover, a finite-temperature effect can further restore the Z_2-symmetry only.

The Gaussian wavefunctional approach is developed in thermofield dynamics. We manufacture thermal vacuum wavefunctional, its creation as well as annihilation operators,and accordingly thermo-particle excited states. For a (D+1)-dimensional scalar field system with an arbitrary potential whose Fourier representation exists in a sense of tempered distributions, we calculate the finite temperature Gaussian effective potential (FTGEP), one- and two-thermo-particle-state energies. The zero-temperature limit of each of them is just the corresponding result in quantum field theory, and the FTGEP can lead to the same one of each of some concrete models as calculated by the imaginary time Green function., Comment: the revised version of hep-th/9807025, with one equation being added, a few sentences rewritten, and some spelling mistakes corrected. 7 page, Revtex, no figure

Within the framework of thermofield dynamics, the wavefunctions of the thermalized displaced number and squeezed number states are given in the coordinate representation. Furthermore, the time evolution of these wavefunctions is considered by introducing a thermal coordinate representation, and we also calculate the corresponding probability densities, average values and variances of position coordinate, which are consistent with results in the literature., Comment: 12 pages, no figures, Revtex. v3: substantially revised

Using the Gaussian wave functional as variational ground state, we study the excited states of the double sine-Gordon model in dimensions. We find, i) for there exist two particle bound states, their energy decreases with increasing coupling; ii) also for , the phase shift of the two-particle scattering state is always positive; iii) for the investigation on the interaction between the particles shows that the theory is trivial.

It is shown that for a (D+1)-dimensional scalar field system with an arbitrary potential whose Fourier representation exists in the sense of tempered distributions, the effective potential and multi-particle-state energies by the Bogoliubov transformation technique are identical to those calculated by the Gaussian wavefunctional approach. However, the Bogoliubov transformation technique differs from the latter as it can be applied to quantizing a static soliton without difficulty.

Through the calculation of the effective potential and the excited state energies for the sinh-Gordon and the sine-Gordon models in dimensions, we show that the variational technique of Bogoliubov transformations is equivalent to the Gaussian wave-functional approach.

The Gaussian wave-functional approach is used to variationally study the two-particle states of the sinh-Gordon and sine-Gordon fields in (1+1) dimensions. We find that in the sine-Gordon model there exist two-particle bound states for a certain range of the coupling constant, where the vacuum state is stable, and in the sinh-Gordon model there are no two-particle bound states. The scattering behaviour of both models has also been investigated in detail.

In this paper, we develop Schiff's discretization procedure for calculating the phase shifts in the $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ model in ($D+1$)-dimensional space-time ($Dg0$) with the Gaussian wave-functional approach. In 1+1 and 2+1 dimensions, the phase shifts are negative, which indicates the interaction between two pions is repulsive. In 3+1 dimensions, the phase shifts vanish. We also discuss the dependences of the phase shifts upon the scattering energy in detail.

The (1+1)-dimensional sine-Gordon model is studied in the framework of the variational Gaussian wave functionals. The renormalized mass depends on two dimensionless parameters. In the phase diagram a first-order phase transition will replace the second-order phase transition for large bare mass. The spectrum of the two-particle states consists of a continuum of scattering states and the isolated values connected to the excitonlike bound states. The energy of the bound states and the phase shifts of the scattering states are explicitly calculated.

Scattering two-particle states of the sine-Gordon and sinh-Gordon models in D + 1 dimensions are investigated for all values of the coupling constant with the Gaussian wave-functional approach. In 1 + 1 and 2 + 1 dimensions, the phase shifts of the scattering states are obtained. We find that the phase shifts are positive for the sine-Gordon field theory and negative for the sinh-Gordon field theory. In the higher dimensions, the phase shifts vanish, which is coincident with the triviality of the two field theories.

In this paper, expectation values of exponential fields in the 2-dimensional Euclidean sine-Gordon field theory are calculated with variational perturbation approach up to the second order. Our numerical analysis indicates that for not large values of the exponential-field parameter $a$, our results agree very well with the exact formula conjectured by Lukyanov and Zamolodchikov in Nucl. Phys. B 493, 571 (1997)., only abbreviated the original, 12 pages, 2 EPS figures, to be published in Phys. Lett. B

An optimized Rayleigh-Schr\"{o}dinger expansion scheme of solving the functional Schr\"odinger equation with an external source is proposed to calculate the effective potential beyond the Gaussian approximation. For a scalar field theory whose potential function has a Fourier representation in a sense of tempered distributions, we obtain the effective potential up to the second order, and show that the first-order result is just the Gaussian effective potential. Its application to the $\lambda\phi^4$ field theory yields the same post-Gaussian effective potential as obtained in the functional integral formalism., Comment: Revtex, 8 pages, no figures, revised version with literal changes

A Rayleigh-Schr\"odinger perturbation theory based on the Gaussian wave functional is constructed. The method can be used for calculating the energies of both the vacuum and the excited states. A model calculation is carried out for the vacuum state of the $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ field theory.

For a class of system, the potential of whose Bosonic Hamiltonian has a Fourier representation in the sense of tempered distributions, we calculate the Gaussian effective potential within the framework of functional integral formalism. We show that the Coleman's normal-ordering prescription can be formally generalized to the functional integral formalism., 6 pages, revtex; With derivation details and an example added. To appear in J. Phys. A

In this paper, a variational perturbation scheme for nonrelativistic many-Fermion systems is generalized to a Bosonic system. By calculating the free energy of an anharmonic oscillator model, we investigated this variational expansion scheme for its efficiency. Using the modified Feynman rules for the diagrams, we obtained the analytical expression of the free energy up to the fourth order. Our numerical results at various orders are compared with the exact and other relevant results., Comment: 9 pages, 3 EPS figures. With a few typo errors corrected. to appear in J. Phys. A

Using the Gaussian wave-functional approach with the normal-ordering renormalization prescription, we show that for the (3+1)-dimensional massive lambda phi^4 theory, ``precarious'' and ``autonomous'' phi^4s can exist if and only if the normal-ordering mass is equal to the classical masses at the symmetrc and asymmetric vacua, respectively., Comment: 6 pages, no figures, Revtex file, accepted for publication in Mod. Phys. Lett. A

The ground, one- and two-particle states of the (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of the model-parameter space, the vacuum of the field system is asymmetrical. Furthermore, it is shown that two-particle bound state can exist upon the asymmetric vacuum for a part of the aforementioned region. Besides, for the bosonic equivalent to the massive Schwinger model, the masses of the one boson and two-boson bound states agree with the recent second-order results of a fermion-mass perturbation calculation when the fermion mass is small., Comment: Latex, 11 pages, 8 figures (EPS files)

Through the explicit calculation to the Gaussian effective potential in the sine-Gordon model in (1+1) dimensions with the normal-ordering prescription of renormalization, we find that the "m" in Coleman's formalism in operator notation can be regarded as the renormalized mass.