On the Calculation of the Finite Hankel Transform Eigenfunctions

In the recent years considerable attention has been focused on the numerical computation of the eigenvalues and eigenfunctions of the nite (truncated) Hankel transform, important for numerous applications. However, due to the very special behavior of the Hankel transform eigenfunctions, their direct numerical calculation often causes an essential loss of accuracy. Here, we discuss several simple, e cient and robust numerical techniques to compute Hankel transform eigenfunctions via the associated singular self-adjoint Sturm-Liouville operator. The properties of the proposed approaches are compared and illustrated by means of numerical experiments

The Application of Shooting to Singular Boundary Value Problems

This project was supported by th

Halting the Spread of Herpes Simplex Virus-1: The Discovery of an Effective Dual αvβ6/αvβ8 Integrin Ligand

Over recent years, αvβ6 and αvβ8 Arg-Gly-Asp (RGD) integrins have risen to prominence as interchangeable co-receptors for the cellular entry of herpes simplex virus-1 (HSV-1). In fact, the employment of subtype-specific integrin-neutralizing antibodies or gene-silencing siRNAs has emerged as a valuable strategy for impairing HSV infectivity. Here, we shift the focus to a more affordable pharmaceutical approach based on small RGD-containing cyclic pentapeptides. Starting from our recently developed αvβ6-preferential peptide [RGD-Chg-E]-CONH2 (1), a small library of N-methylated derivatives (2-6) was indeed synthesized in the attempt to increase its affinity toward αvβ8. Among the novel compounds, [RGD-Chg-(NMe)E]-CONH2 (6) turned out to be a potent αvβ6/αvβ8 binder and a promising inhibitor of HSV entry through an integrin-dependent mechanism. Furthermore, the renewed selectivity profile of 6 was fully rationalized by a NMR/molecular modeling combined approach, providing novel valuable hints for the design of RGD integrin ligands with the desired specificity profile

Selective Targeting of Integrin αvβ8 by a Highly Active Cyclic Peptide

Integrins play important roles in physiological and pathophysiological processes. Among the RGD-recognizing integrin subtypes, the αvβ8 receptor is emerging as an attractive target because of its involvement in various illnesses, such as autoimmune diseases, viral infections, and cancer. However, its functions have, so far, not been investigated in living subjects mainly because of the lack of a selective αvβ8 ligand. Here, we report the design and potential medical applications of a cyclic octapeptide as the first highly selective small-molecule ligand for αvβ8. Remarkably, this compound displays low nanomolar αvβ8 binding affinity and a strong discriminating power of at least 2 orders of magnitude versus other RGD-recognizing integrins. Peptide functionalization with fluorescent or radioactive labels enables the selective imaging of αvβ8-positive cells and tissues. This new probe will pave the way for detailed characterization of the distinct (patho)physiological role of this relatively unexplored integrin, providing a basis to fully exploit the potential of αvβ8 as a target for molecular diagnostics and personalized therapy regimens

A unified approach to singular problems arising in the membrane theory

summary:We consider the singular boundary value problem $$(t^nu'(t))'+ t^nf(t,u(t))=0, \quad \lim _{t\to 0+}t^nu'(t)=0, \quad a_0u(1)+a_1u'(1-)=A,$$ where $f(t,x)$ is a given continuous function defined on the set $(0,1]\times (0,\infty )$ which can have a time singularity at $t=0$ and a space singularity at $x=0$. Moreover, $n\in \Bbb N$, $n\ge 2$, and $a_0$, $a_1$, $A$ are real constants such that $a_0\in (0,\infty )$, whereas $a_1,A\in [0,\infty )$. The main aim of this paper is to discuss the existence of solutions to the above problem and apply the general results to cover certain classes of singular problems arising in the theory of shallow membrane caps, where we are especially interested in characterizing positive solutions. We illustrate the analytical findings by numerical simulations based on polynomial collocation