We provide strong evidence for the conjecture that analogue of Kontsevich's matrix Airy function, with cubic potential $\mathrm{Tr}(\Phi^3)$ replaced by a quartic term $\mathrm{Tr}(\Phi^4)$, obeys blobbed topological recursion Borot and Shadrin. identify in Kontsevich model three families correlation functions which we establish interwoven loop equations. One family consists symmetric meromorph...

the aim of this study was to identify the effect of spermine and salicylic acid on several growth parameters, such as shoot length, shoot fresh and dry weights, amount of protein and carbohydrate, of badami and qazvini pistachio cultivated variety under copper stress. the experiment design was completely randomized with three replicates per treatment and four levels of copper (o.5, 30, 45, 60 µ...

Modulation theory is developed for a periodic peakon solution of the Camassa-Holm equation. An explicit simple wave solution of these modulation equations is then derived; this simple wave describing the evolution into an undular bore of an initial step. The characteristic on which the expansion fan occurs (propagating at a nonlinear group velocity) has a turning point, illustrating the fact th...

Spectrally modulated Airy-based pulses peak amplitude modulation (PAM) in linear dispersive media is investigated, designed, and numerically simulated. As it is shown here, it is possible to design the spectral modulation of the initial Airy-based pulses to obtain a pre-defined PAM profile as the pulse propagates. Although optical pulses self-amplitude modulation is a well-known effect under no...

We report on the first realization of an ultrafast Airy beam optical parametric oscillator (OPO). By introducing intracavity cubic phase modulation to the resonant Gaussian signal in a synchronously-pumped singly-resonant OPO cavity and its subsequent Fourier transformation, we have generated 2-dimensional Airy beam in the output signal across a 250 nm tuning range in the near-infrared. The gen...

Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the energy levels of the physical system. We consider the case when the n× n external source matrix has two distinct real eigenvalues: a with multiplicity r and z...

We investigate and analyze temporal soliton interactions with a dispersive truncated Airy pulse traveling in a nonlinear fiber at the same center wavelength (or frequency), via split step Fourier numerical simulation. Truncated Airy pulses, which remain self-similar during propagation and have a ballistic trajectory in the retarded time frame, can interact with a nearby soliton by its accelerat...

We consider a family of chiral non-Hermitian Gaussian random matrices in the unitarily invariant symmetry class. The eigenvalue distribution in this model is expressed in terms of Laguerre polynomials in the complex plane. These are orthogonal with respect to a non-Gaussian weight including a modified Bessel function of the second kind, and we give an elementary proof for this. In the large n l...

We prove a Tracy-Widom type formula for the generating function of occupancy numbers on several disjoint intervals higher order Airy point processes. The is related to new vector-valued Painlevé II hierarchy we define, together with its Lax pair.

In this paper, an improved refined shear and normal deformation theory is used in order to investigate the vibration behavior of functionally graded rectangular plates. theory, displacements various points plate are assumed be due in-plane middle plane transverse displacement. Transverse displacement divided into three parts: bending, shear, thickness stretching. Using Airy stress function, cor...