In this paper, the Touchard-based Laguerre–Gould–Hopper polynomials are introduced by using operational techniques. We investigate many properties of such polynomials. In particular, generating functions, series definitions, integral representations, and summation formulas are analyzed. Further, we derive some new identities satisfied by these polynomials by using umbral calculus methods.

Let C[0, T] denote an analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. For a partition \(0=t_0

In this paper, we present a fast boundary integral equation method for the numerical conformal mapping and its inverse of bounded multiply connected regions onto a disk and annulus with circular slits regions. The method is based on two uniquely solvable boundary integral equations with Neumann-type and generalized Neumann kernels. The integral equations related to the mappings are solved numerically

In this paper, we study some ternary Diophantine equations of the form \(Aa^n+Bb^n=Cc^m\), where \(m \in \{2,3\} \), and \(n\geqslant 7 \) is a prime. In fact, we completely solve some particular cases: \(A=5^{\alpha }, ~B=64,~ C=3\), when \(m=2\); \(A=2^{\alpha },~ B=27, ~C \in \{7,13\}\), when \(m=3\).

Weaving Hilbert space frames have been introduced recently by Bemrose et al. to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle. In this regard, not only we obtain new properties in weaving frame theory related to dual frames but also we bring up new approaches for manufacturing pairs of woven frames. Specifically

We show that if the following delay differential equation of rational coefficients $$\begin{aligned} w^k(z)\sum _{\mu =1}^se_\mu (z)w(z+c_\mu )+a(z)\frac{w^{(n)}(z)}{w(z)}= \frac{\sum _{i=0}^pa_i(z)w^i}{\sum _{j=0}^qb_j(z)w^j} \end{aligned}$$ admits a transcendental entire solution w of hyper-order less than one, then it reduces into a delay differential equation of rational coefficients $$\begin{aligned}

Fourth-order tensors play a fundamental role in signal processing, wireless communication systems, image processing, data analysis and higher-order statistics. In this paper, we introduce a Z-identity tensor and establish two Z-eigenvalue inclusion sets for fourth-order tensors, which are sharper than some existing results. Numerical examples are proposed to verify the efficiency of the obtained results

In this paper, we show that the Carathéodory function \(\varphi _{\mathrm{Ne}}(z)=1+z-z^3/3\) maps the open unit disk \(\mathbb {D}\) onto the interior of the nephroid, a 2-cusped kidney-shaped curve, $$\begin{aligned} \left( (u-1)^2+v^2-\frac{4}{9}\right) ^3-\frac{4 v^2}{3}=0, \end{aligned}$$ and introduce new Ma–Minda-type function classes \(\mathcal {S}^*_{\mathrm{Ne}}\) and \(\mathcal {C}_{\mathrm{Ne}}\)