Probabilistic degenerate Fubini polynomials associated with random variables

Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order $r$, namely the probabilisitc degenerate Fubini polynomials associated with Y and the probabilistic degenerate Fubini polynomials of order r associated with Y. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials.Comment: 1

Some Identities Involving the Reciprocal Sums of One-Kind Chebyshev Polynomials

We use the elementary and analytic methods and the properties of Chebyshev polynomials to study the computational problem of the reciprocal sums of one-kind Chebyshev polynomials and give several interesting identities for them. At the same time, we also give a general computational method for this kind of reciprocal sums

Detecting GPC3-Expressing Hepatocellular Carcinoma with L5 Peptide-Guided Pretargeting Approach: An In Vitro MRI Experiment

Background and Aim: Glypican-3 (GPC3) is a novel molecular target for hepatocellular carcinoma (HCC). This study investigated the potential of an L5 peptide-guided pretargeting approach to identify GPC3-expressing HCC cells using ultra-small super-paramagnetic iron oxide (USPIO) as the MRI probe.Methods: Immunofluorescence with carboxyfluorescein (FAM)-labeled L5 peptide was performed in HepG2 and HL-7702 cells. Polyethylene glycol-modified ultrasmall superparamagnetic iron oxide (PEG-USPIO) and its conjugates with streptavidin (SA-PEG-USPIO) were synthesized, and hydrodynamic diameters, zeta potential, T2 relaxivity, and cytotoxicity were measured. MR T2-weighted imaging of HepG2 was performed to observe signal changes in the pretargeting group, which was first incubated with biotinylated L5 peptide and then with SA-PEG-USPIO. Prussian blue staining of cells was used to assess iron deposition.Results: Immunofluorescence assays showed high specificity of L5 peptide for GPC3. SA-PEG-USPIO nanoparticles had ≈36 nm hydrodynamic diameter, low toxicity, negative charge and high T2 relaxivity. MR imaging revealed that a significant negative enhancement was only observed in HepG2 cells from the pretargeting group, which also showed significant iron deposition with Prussian blue staining.Conclusion: MR imaging with USPIO as the probe has potential to identify GPC3-expressing HCC through L5 peptide-guided pretargeting approach

On the two-term exponential sums and character sums of polynomials

The main aim of this paper is to use the analytic methods and the properties of the classical Gauss sums to research the computational problem of one kind hybrid power mean containing the character sums of polynomials and two-term exponential sums modulo p, an odd prime, and acquire several accurate asymptotic formulas for them

A Note on Cube-Full Numbers in Arithmetic Progression

We obtain an asymptotic formula for the cube-full numbers in an arithmetic progression n≡lmod q, where q,l=1. By extending the construction derived from Dirichlet’s hyperbola method and relying on Kloosterman-type exponential sum method, we improve the very recent error term with x118/4029<q

Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers

The aim of this paper is to research the structural properties of the Fibonacci polynomials and Fibonacci numbers and obtain some identities. To achieve this purpose, we first introduce a new second-order nonlinear recursive sequence. Then, we obtain our main results by using this new sequence, the properties of the power series, and the combinatorial methods

On Generalized Fibonacci Polynomials and Bernoulli Numbers 1

In this paper we use elementary methods to study the relationship between the generalized Fibonacci polynomials and the famous Bernoulli numbers, and give several interesting identities involving them. 1 Introduction an