Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

MSC 2010: 30C10, 32A30, 30G35

Integral Representations of Functional Series with Members Containing Jacobi Polynomials

MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10

Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.

Relationship between Extremal and Sum Processes Generated by the same Point Process

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.

Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32

An LP-based inconsistency monitoring of pairwise comparison matrices

A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent linear programming problem. The results can be applied in the process of filling in the matrix as the decision maker gets automatic feedback. As soon as a serious error occurs among the matrix elements, even due to a misprint, a significant increase in the inconsistency index is reported. The high inconsistency may be alarmed not only at the end of the process of filling in the matrix but also during the completion process. Numerical examples are also provided.

Algebraic duality theorems for infinite LP problems

In this paper we consider a primal-dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces, therefore our results are algebraic duality theorems. As an application, we consider transferable utility cooperative games with arbitrarily many players.

Three Essays on Extremal Quantiles

Extremal quantile index is a concept that the quantile index will drift to zero (or one)

as the sample size increases. The three chapters of my dissertation consists of three

applications of this concept in three distinct econometric problems. In Chapter 2, I

use the concept of extremal quantile index to derive new asymptotic properties and

inference method for quantile treatment effect estimators when the quantile index

of interest is close to zero. In Chapter 3, I rely on the concept of extremal quantile

index to achieve identification at infinity of the sample selection models and propose

a new inference method. Last, in Chapter 4, I use the concept of extremal quantile

index to define an asymptotic trimming scheme which can be used to control the

convergence rate of the estimator of the intercept of binary response models.

Lipoprotein-associated phospholipase A2 (Lp-PLA2) as a therapeutic target to prevent retinal vasopermeability during diabetes

Lipoprotein-associated phospholipase A2 (Lp-PLA2) hydrolyses oxidized low-density lipoproteins into proinflammatory products, which can have detrimental effects on vascular function. As a specific inhibitor of Lp-PLA2, darapladib has been shown to be protective against atherogenesis and vascular leakage in diabetic and hypercholesterolemic animal models. This study has investigated whether Lp-PLA2 and its major enzymatic product, lysophosphatidylcholine (LPC), are involved in blood-retinal barrier (BRB) damage during diabetic retinopathy. We assessed BRB protection in diabetic rats through use of species-specific analogs of darapladib. Systemic Lp-PLA2 inhibition using SB-435495 at 10 mg/kg (i.p.) effectively suppressed BRB breakdown in streptozotocin-diabetic Brown Norway rats. This inhibitory effect was comparable to intravitreal VEGF neutralization, and the protection against BRB dysfunction was additive when both targets were inhibited simultaneously. Mechanistic studies in primary brain and retinal microvascular endothelial cells, as well as occluded rat pial microvessels, showed that luminal but not abluminal LPC potently induced permeability, and that this required signaling by the VEGF receptor 2 (VEGFR2). Taken together, this study demonstrates that Lp-PLA2 inhibition can effectively prevent diabetes-mediated BRB dysfunction and that LPC impacts on the retinal vascular endothelium to induce vasopermeability via VEGFR2. Thus, Lp-PLA2 may be a useful therapeutic target for patients with diabetic macular edema (DME), perhaps in combination with currently administered anti-VEGF agents.

Monogenic polynomials of four variables with binomial expansion

In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its stratification via homogeneous monogenic polynomials is a useful tool. In this paper we consider the structure of those polynomials of four real variables with binomial expansion. This allows a complete characterization of sequences of 4D generalized monogenic Appell polynomials by three different types of polynomials. A particularly important case is that of monogenic polynomials which are simply isomorphic to the integer powers of one complex variable and therefore also called pseudo-complex powers.

Random extremal solutions of differential inclusions

Given a Lipschitz continuous multifunction $F$ on ${\mathbb{R}}^{n}$, we construct a probability measure on the set of all solutions to the Cauchy problem $\dot x\in F(x)$ with $x(0)=0$. With probability one, the derivatives of these random solutions take values within the set $ext F(x)$ of extreme points for a.e.~time $t$. This provides an alternative approach in the analysis of solutions to differential inclusions with non-convex right hand side.

The lipid- and lipoprotein- [LDL-Lp(a)] apheresis techniques. Updating

Therapeutic plasmapheresis allows the extracorporeal removal of plasmatic lipoproteins (Lipid-apheresis) (LA). It can be non selective (non specific), semi - selective or selective low density lipoprotein-lipoprotein(a) (specific [LDL- Lp(a)] apheresis) (Lipoprotein apheresis, LDLa). The LDL removal rate is a perfect parameter to assess the system efficiency. Plasma-Exchange (PEX) cannot be considered either specific nor, selective. In PEX the whole blood is separated into plasma and its corpuscular components usually through centrifugation or rather filtration. The corpuscular components mixed with albumin solution plus saline (NaCl 0.9%) solution at 20%-25%, are then reinfused to the patient, to substitute the plasma formerly removed. PEX eliminates atherogenic lipoproteins, but also other essential plasma proteins, such as albumin, immunoglobulins, and hemocoagulatory mediators. Cascade filtration (CF) is a method based on plasma separation and removal of plasma proteins through double filtration. During the CF two hollow–fiber filters with pores of different diameter are used to eliminate the plasma components of different weight and molecular diameter. A CF system uses a first polypropylene filter with 0.55 µm diameter pores and a second one of diacetate of cellulose with 0.02 µm pores. The first filter separates the whole blood, and the plasma is then perfused through a second filter which allows the recovery of molecules with a diameter lower than 0.02 µm, and the removal of molecules larger in diameter as apoB100–containing lipoproteins. Since both albumin and immunoglobulins are not removed, or to a negligible extent, plasma-expanders, substitution fluids, and in particular albumin, as occurs in PEX are not needed. CF however, is characterized by lower selectivity since removes also high density lipoprotein (HDL) particles which have an antiatherogenic activity. In the 80’s, a variation of Lipid-apheresis has been developed which allows the LDL-cholesterol (LDLC) (-61%) and Lp(a) (-60%) removal from plasma through processing 3 liters of filtered plasma by means of lipid-specific thermofiltration, LDL immunoadsorption, heparin-induced LDL precipitation, LDL adsorption through dextran sulphate. More recently (90’s) the DALI®, and the Liposorber D® hemoperfusion systems, effective for apoB100- containing lipoproteins removal have been developed. All the above mentioned systems are established LDL-apheresis techniques referable to the generic definition of LDLa. However, this last definition cannot describe in an appropriate manner the removal of another highly atherogenic lipoprotein particle: the Lp(a). Thus it would be better to refer the above mentioned techniques to the wider scientific and technical concept of lipoprotein apheresis. Lipid apheresis - Lipoprotein apheresis - LDL-apheresis - Severe Dyslipidemia.