Properties Of Special Functions Research Articles

Differentiation-Dependent Effects of a New Recombinant Manganese Superoxide Dismutase on Human SK-N-BE Neuron-Like Cells

We have recently isolated a new isoform of recombinant manganese superoxide dismutase (rMnSOD) which provides a potent antitumor activity and strongly counteracts the occurrence of oxidative stress and tissue inflammation. This isoform, in addition to the enzymatic action common to all SODs, also shows special functional and structural properties, essentially due to the presence of a first leader peptide that allows the protein to enter easily into cells. Among endogenous antioxidants, SOD constitutes the first line of natural defence against pathological effects induced by an excess of free radicals. Here, we firstly describe the effects of our rMnSOD administration on the proliferant and malignant undifferentiated human neuroblastoma SK-N-BE cell line. Moreover, we also test the effects of rMnSOD in the all trans retinoic-differentiated SK-N-BE neuron-like cells, a quiescent "not malignant" model. While rMnSOD showed an antitumor activity on proliferating cells, a poor sensitivity to rMnSOD overload in retinoid-differentiated neuron-like cells was observed. However, in the latter case, in presence of experimental-induced oxidative stress, overcharge of rMnSOD enhanced the oxidant effects, through an increase of H2O2 due to low activity of both catalase and glutathione peroxidase. In conclusion, our data show that rMnSOD treatment exerts differential effects, which depend upon both cell differentiation and redox balance, addressing attention to the potential use of the recombinant enzyme on differentiated neurons. These facts ultimately pave the way for further preclinical studies aimed at evaluation of rMnSOD effects in models of neurodegenerative diseases.

Stability application and research of astaxanthin integrated into food

Astaxanthin is a kind of keto carotenoid which is with higher activity compare to alpha-tocopherol and other carotenoids. Due to its strong antioxidant capacity and various special functional properties, it has been widely used in the food. Besides, it has high value in nutrtion. During food processing, Astaxanthin would be unstable, easily degraded, and the chemical reaction would be easy to occur. This paper discussed the effects of the common processes in food processing on the stability of astaxanthin, and the preservation techniques that integrated astaxanthin into food matrices to maintain its stability, such as microencapsulation, contained in liposomes, emulsions, suspensions, etc.

Hardy’s Inequalities for the Heisenberg Group

This article presents two types of Hardy’s inequalities for the Heisenberg group. The proofs are mainly based on estimates of the Fourier transform for atomic functions deduced by the horizontal Taylor formula and the properties of special Hermite functions on Heisenberg group.

Sharp $L^p$-bounds for the martingale maximal function

The paper studies sharp weighted $L^p$ inequalities for the martingale maximal function. Proofs exploit properties of certain special functions of four variables and self-improving properties of $A_p$ weights.

Proximal iteratively reweighted algorithm for low-rank matrix recovery

This paper proposes a proximal iteratively reweighted algorithm to recover a low-rank matrix based on the weighted fixed point method. The weighted singular value thresholding problem gains a closed form solution because of the special properties of nonconvex surrogate functions. Besides, this study also has shown that the proximal iteratively reweighted algorithm lessens the objective function value monotonically, and any limit point is a stationary point theoretically.

From Circular to Bessel Functions: A Transition through the Umbral Method

A common environment in which to place Bessel and circular functions is envisaged. We show, by the use of operational methods, that the Gaussian provides the umbral image of these functions. We emphasize the role of the spherical Bessel functions and a family of associated auxiliary polynomials, as transition elements between these families of functions. The consequences of this point of view and the relevant impact on the study of the properties of special functions is carefully discussed.

Novel nano-particulated exopolysaccharide produced by Klebsiella sp. PHRC1.001

In recent decades, microbial synthesis of polysaccharides with special functional properties has attracted increasing attention. This work reported a novel exopolysaccharide (EPS)-producing strain, Klebsiella sp. PHRC1.001 isolated from activated sludge. Physicochemical, rheological, emulsifying and toxicological properties of the obtained EPS were characterized. The EPS was mainly composed of d-glucose and l-arabinose, and was found to exist in aqueous solution in a nano-particulated form (∼50nm in diameter) with a strong tendency of aggregation. Rheological analysis showed that the EPS aqueous solution was a typical pseudoplastic fluid at higher concentration and could form weak gel upon alkaline treatment followed by neutralization. The EPS exhibited excellent emulsifying properties in stabilizing oil-in-water emulsions presumably by a Pickering mechanism owing to its nanoparticle structure. Acute toxicity test showed that 1.8g EPS per kg of body weight caused no toxic effect on mice. PHRC1.001 EPS has the potential to be a novel industrial polysaccharide.

Using Probabilistic Models to Study the Asymptotic Behavior of Bell Numbers

The use of probabilistic models is often useful for proving combinatorial identities and for studying the properties of special numbers and functions. The proof in this case becomes more simple, intuitive and natural compared to traditional combinatorial and algebraic-analytical methods. In this article we demonstrate the advantages of a probabilistic approach for studying the asymptotic behavior of Bell numbers.

Generating of spatial formations composed of carbon atoms as fullerenes and nanotubes type by applying of pulsed electrical discharges to the formation of graphite films on metallic surfaces

The present paper presents the results of experimental researchings concerning the technology for obtaining the graphite films on metallic surfaces by applying the method of electric pulsed discharges (DEI). It was established that the efficiency for the graphite film obtaining is according with the conecting mode for the workpiece subjected to treatment of electric pulsed discharges to the polarity of the electric pulse generator. Thin pellicles obtained after the electric pulsed discharges treatment, contain mostly carbon, but after of detailed and special analysis (termogravimetric analyses, electronic microscopy SEM and chemical analyses), it was found that different chemical forms of carbon other of graphite are generated. They are spatial formations made of carbon atoms the type of fullerenes and carbon nanotubes. This occurance explains the special functional properties of graphite films and that is to encapsulate small molecules such as N 2 in the case of fullerenes, or organic molecules in case of nanotubes with single wall.

Structural transitions in a NiTi alloy: a multistage loading-unload cycle

NiTi shape memory alloys (SMAs) are increasingly used in many engineering and medical applications, because they combine special functional properties, such as shape memory effect and pseudoelasticity, with good mechanical strength and biocompatibility. However, the microstructural changes associated with these functional properties are not yet completely known. In this work a NiTi pseudo-elastic alloy was investigated by means of X-ray diffraction in order to assess micro-structural transformations under mechanical uniaxial deformation. The structure after complete shape recovery have been compared with initial state.

Constructive Formulations of Resonant Maxwell's Equations

In this article we propose new constructive weak formulations for resonant time-harmonic wave equations with singular solutions. Our approach follows the limiting absorption principle and combines standard weak formulations of PDEs with properties of elementary special functions adapted to the singularity of the solutions, called manufactured solutions. We show the well-posedness of several formulations obtained by these means for the limit problem in dimension one, and propose a generalization in dimension two.

New analytical functions for a skin and storage effect – An insight to decouple fracture half-length and square-root of permeability

Several solutions to the double porosity model have been presented. There are solutions for closed outer boundary systems as well as infinite acting boundary conditions with constant rate or constant pressure inner boundary conditions. A common assumption in all of these solutions is that the fracture has a quadrilateral (linear) geometry. Very few solutions exist for cases were the fracture is assumed to have a circular geometry. This is the first work that presents approximate early and late time solutions for flow from fractures that have a circular geometry where the inter porosity transfer function is model with an unsteady state function. The result obtained from this analysis shows that the function behaves in a manner identical to production data from fractured horizontal wells in unconventional reservoirs (including early time data that is usually assumed to be obscured by skin and wellbore/fracture storage effects).The double porosity model was formulated for a fractured horizontal well in which the fractures were assumed to have a circular geometry. The associated mathematical model was then solved with Laplace transforms to obtain a closed form analytical solution in Laplace space. We then derive the approximate early and late time solutions by using special properties of Bessel functions and the Laplace space solution. The solutions were derived for a constant-pressure and constant-rate inner-boundary condition with a no flow outer-boundary condition.The approximate early time solution obtained is identical to the solution obtained when the fracture is assumed to have a quadrilateral geometry. But it has two additional parameters. A detailed sensitivity analysis showed that fracture thickness does not have a significant impact on the producing characteristics. The approximate late-time solution has a production history identical to that observed from field production data. The approximate late-time solution also has a slope of two on a log–log plot of rate verses time; this has not been report before in the literature. A comparison of the approximate late-time solution to traditional linear fracture solutions with skin and storage effect lead to the development of new skin and fracture storage functions. The significance of this result is that the new skin and fracture storage functions suggest that they can be used to decouple the product of fracture half-length and the square-root of permeability from early-time production data.

Branching particle systems and compound Poisson processes related to Pólya-Aeppli distributions

We establish numerous new refined local limit theorems for a class of com- pound Poisson processes with P´ olya-Aeppli marginals, and for a particular family of the branching particle systems which undergo critical binary branching and can be approxi- mated by the backshifted Feller diffusion. To this end, we also derive new results for the families of P´ olya-Aeppli and Poisson-exponential distributions. We relate a few of them to properties of certain special functions some of which were previously unknown. n ; n 1g is a sequence of geometrically distributed i.i.d. random vari- ables (or r.v.'s) whose range is N, and which are characterized by the probability of suc- cess 2 (0; 1). In addition, they are assumed to be independent of the Poisson counting process f � (t); t 0g with intensity � > 0. In view of (9), (26), (28), the marginals of both these classes of stochastic processes belong to the two-parameter P´ olya-Aeppli fam-

Limit curve of H-Bézier curves and rational Bézier curves in standard form with the same weight

The basis of H-Bézier curves of degree n is 1,t,…,tn−2, sinhαt and coshαt, for t∈[0,1]. We find the limit curve of H-Bézier curves of degree n as a parameter α goes to ∞, which is the Bézier curve of degree n−2, and prove it using mathematical induction and special properties of H-basis functions. We also compare it to the limit curve of rational Bézier curves of degree n in standard form with the same weight w as it goes to ∞, which is the rational Bézier curve of degree n−2.

New families of subordinators with explicit transition probability semigroup

There exist only a few known examples of subordinators for which the transition probability density can be computed explicitly along side an expression for its Lévy measure and Laplace exponent. Such examples are useful in several areas of applied probability. For example, they are used in mathematical finance for modeling stochastic time change. They appear in combinatorial probability to construct sampling formulae, which in turn is related to a variety of issues in the theory of coalescence models. Moreover, they have also been extensively used in the potential analysis of subordinated Brownian motion in dimension d≥2. In this paper, we show that Kendall’s classic identity for spectrally negative Lévy processes can be used to construct new families of subordinators with explicit transition probability semigroups. We describe the properties of these new subordinators and emphasize some interesting connections with explicit and previously unknown Laplace transform identities and with complete monotonicity properties of certain special functions.

A prophet inequality for $$L^p$$ L p -bounded dependent random variables

Let \(X=(X_n)_{n\ge 1}\) be a sequence of arbitrarily dependent nonnegative random variables satisfying the boundedness condition $$\begin{aligned} \sup _\tau \mathbb {E}X_\tau ^p\le t, \end{aligned}$$ where \(t>0\), \(1<p<\infty \) are fixed numbers and the supremum is taken over all finite stopping times of \(X\). Let \(M=\mathbb {E}\sup _n X_n\) and \(V=\sup _\tau \mathbb {E}X_\tau \) denote the expected supremum and the optimal expected return of the sequence \(X\), respectively. We establish the prophet inequality $$\begin{aligned} M\le V+\frac{V}{p-1}\log \left( \frac{te}{V^p}\right) \end{aligned}$$ and show that the bound on the right is the best possible. The proof of the inequality rests on Burkholder’s method and exploits properties of certain special functions. The proof of the sharpness is somewhat indirect, but we also provide an indication how the extremal sequences can be constructed.

Participation of leptin in the determination of the macrophage phenotype: an additional role in adipocyte and macrophage crosstalk

Macrophages develop into specialized cell types with special functional properties, depending on locally produced stimuli. Adipose tissue macrophages present particular characteristics, such as the M2 cell phenotype, and produce cytokines and chemokines usually produced by M1 cells. Our aim was to study the role of leptin, which is an adipokine produced and released by adipocytes, in the induction of these characteristics in macrophages found in the adipose tissue. Human CD14(+) cells were obtained and maintained in culture with IFN-γ (classical M1 phenotype), IL-4 (alternative M2 phenotype) or leptin for 5 d. Surface marker expression was then analyzed by cytometry. In addition, the release of tumor necrosis factor alpha (TNF-α), interleukin (IL)-6, IL-1β, IL-10, IL-1ra, MCP-1, MIP-1α, and RANTES was quantified by ELISA after an LPS stimulus, in the culture supernatant. Macrophages exposed to leptin in culture expressed surface markers that were more similar to the M2 phenotype, but they were able to produce TNF-α, IL-6, IL-1β, IL-1ra, IL-10, MCP-1, and MIP-1α, as observed for M1 cells. Results suggest that leptin strongly contributes to the phenotype observed in macrophages found in adipose tissue.

On the properties of special functions on the linear-type lattices

We present a general theory for studying the difference analogs of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a special kind of lattices: the linear type lattices. In particular, using the integral representation of the solutions we obtain several difference–recurrence relations for such functions. Finally, applications to q-classical polynomials are given.

Effect of Technological Parameters on Preparation of Mg-Based Foam Materials

As a novel material, Mg-based foam material not only has fantastic physical characteristics, such as low density, high specific surface area, high specific strength and stiffness, and good biocompatibility, but also has special functional properties, for example, electromagnetic wave shielding, vibration reduction, sound absorption, and so on. It can be widely applied to aeronautical and aerospace, military, shipbuilding, transportation, automotive and medical industries. Mg-based foam material was prepared by direct foaming in magnesium alloy liquid in this study, and the effect of technological parameters on the products, such as addition amount of and granularity of SiC particles and MgCO3 particles, stirring temperature, stirring time, stirring velocity, foaming temperature and foaming time, was investigated. The aim of this research was to develop a new technology which could fabricate large scale Mg-based foam material in air condition. The results showed that variations of technological parameters may affect preparation of the foam materials in some extent and resulted in the changes of the products in apparent density, porosity and structural uniformity. The light weight Mg-based foam with homogeneous pores could be obtained by suitable combination of the technological parameters.

Analytical solutions for a time-fractional axisymmetric diffusion–wave equation with a source term

In this paper, a time-fractional axisymmetric diffusion–wave equation with a source term is considered in cylindrical coordinates. The analytical solution is obtained with the help of an integral transform method and some properties of special functions. In addition, we discuss two kinds of different boundary conditions and different forms of the source term. Finally, we analyze the effects of the fractional derivative on the solutions by using numerical results and find that sub-diffusion phenomena and oscillations exist.