[en] We introduce the concept of cumulative conditional expectation function. This is a quantity that provides statistical support for making decisions in applied problems. The goal of this paper is to find an analytical expression for upper and lower bounds of this function, assuming stochastic dependence types as being the underlying random structure

[en] We investigate the spectral properties of self-adjoint Schrödinger operators with attractive δ-interactions of constant strength α>0 supported on conical surfaces in R³. It is shown that the essential spectrum is given by [−α²/4,+∞) and that the discrete spectrum is infinite and accumulates to − α²/4. Furthermore, an asymptotic estimate of these eigenvalues is obtained. (paper)

[en] We employ the matching method to analytically investigate the holographic superconductors with Lifshitz scaling in an external magnetic field. We discuss systematically the restricted conditions for the matching method and find that this analytic method is not always powerful to explore the effect of external magnetic field on the holographic superconductors unless the matching point is chosen in an appropriate range and the dynamical exponent z satisfies the relation z=d−1 or z=d−2. From the analytic treatment, we observe that Lifshitz scaling can hinder the condensation to be formed, which can be used to back up the numerical results. Moreover, we study the effect of Lifshitz scaling on the upper critical magnetic field and reproduce the well-known relation obtained from Ginzburg–Landau theory

[en] We consider one-dimensional nonlinear delay reaction-diffusion equations with varying transfer coefficients. We describe a few new methods for constructing exact solutions of such equations; these methods are based on using invariant subspaces for the corresponding nonlinear differential operators. A number of new exact generalized and functional separable solutions have been obtained. All of the equations and solutions involve several free parameters. The exact solutions obtained can be used to test approximate analytical and numerical methods for solving nonlinear delay reaction-diffusion equations

[en] In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov—Kuznetsov (ZK) and modified Zakharov—Kuznetsov (mZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie' modified Riemann—Liouville sense. (general)

[en] This article is devoted to describe the 't Hooft gauge electrodynamics by means of non-perturbative methods together with Heisenberg perturbation theory insights. The point is that this specific gauge choice introduces a non-linear photon field self interaction. So, this model is analyzed in a BRST framework in analogy to the non-Abelian cases. Finally, we show that the asymptotic transverse photon modes are the same as that of the linear gauge well known case while just the non-physical longitudinal sector get renormalized by such gauge self interaction. Then the physical gauge independence is explicitly verified.

[en] We investigate holography for asymptotically Schrödinger spacetimes, using a frame formalism based on the anisotropic scaling symmetry. We build on our previous work on $z<<!--\; <\; -->2$ to propose a dictionary for z = 2. For z = 2, the scaling symmetry does not act on the additional null direction, which implies that in our dictionary it does not correspond to one of the field theory directions. This is significantly different from previous analyses based on viewing Schrödinger as a deformation of AdS. We study this dictionary in the linearized theory and in an asymptotic expansion. We show that a solution exists in an asymptotic expansion for arbitrary sources for the relevant operators in the stress energy complex. (paper)

[en] In this study, we have submitted to literature a method newly extended which is called as Improved Bernoulli sub-equation function method based on the Bernoulli Sub-ODE method. The proposed analytical scheme has been expressed with steps. We have obtained some new analytical solutions to the nonlinear fractional-order biological population model by using this technique. Two and three dimensional surfaces of analytical solutions have been drawn by wolfram Mathematica 9. Finally, a conclusion has been submitted by mentioning important acquisitions founded in this study.

[en] Some results are proved on the exact asymptotic representation of large deviation probabilities for Gaussian processes in the Hoeder norm. The following classes of processes are considered: the Wiener process, the Brownian bridge, fractional Brownian motion, and stationary Gaussian processes with power-law covariance function. The investigation uses the method of double sums for Gaussian fields

[en] We consider the problem of constructing asymptotically exact (for Ω>>1) uniform (with respect to parameters t=(t₁,t₂,...,t_m) estimates for oscillatory integrals containing a large parameter Ω. We suggest a possible multidimensional analogue of Vinogradov's well-known estimate for one-dimensional integrals. Based on this suggestion, we estimate the integrals with singularities of type A_k, D₄^± (in Arnold's classification) and use the special case of D₅^± to discuss the possibility of generalizing our results