Basal Cell Carcinoma: What’s New Under the Sun

Basal cell carcinoma (BCC) is the most common skin cancer in white populations with an increasing incidence worldwide, thereby imposing an important public health problem. Its etiology is still unclear, but existing data indicate that the risk for BCC development is of multifactorial origin and results from the interplay of both constitutional and environmental factors. Yet, UV radiation (UVR) is believed to be the predominant causative risk factor in the pathogenesis of BCC. For years, BCC and squamous cell carcinoma (SCC) have been grouped together as “nonmelanoma skin cancer.” However, it seems that there are considerable biologic differences between BCC and SCC, and thus each type of epithelial cancer should be addressed separately. The present review provides an overview of the intriguing etiologic link of BCC with UVR and attempts a comprehensive review of recent epidemiologic and molecular evidence that supports this association.     

Relationships Between Various Outer Measures Induced by Lattice Measures

In this paper, we work with lattice spaces. (A lattice space is an ordered pair consisting of a set X and a lattice on X). As is known, each lattice measure µ induces six outer measures on P(X), one of which is the well-known "induced outer measure" µ^*(in case µ is countably additive); the others are µ, µ, µ,, and .In the first part of the paper, we consider an arbitrary lattice measure and discover various relationships involving two or more of the seven set functions under consideration, on P(X) and on various special subsets of P(X), under various conditions on the measure or on the lattice.In the second part of the paper, we consider two lattice measures related by "domination" and obtain similar results.In the third part of the paper, we consider two lattice measures related by "restriction" and obtain similar results.     

On an extension of a lattice-continuous mapping with embeddability applications

It is well known that ifX andY are completely regularT ₂ spaces, then any continuous function,f, fromX toY, has a unique continuous extension,(f), fromX toY, whereX andY are the Stone—ech compactifications ofX andY, respectively. This function plays an important role in Stone—ech Theory, especially in questions pertaining to embeddability.In this paper, we first extend this construction to general Wallman spaces, and then apply the results to extend well-known embeddability theorems.     

Trace elements in skin epitheliomas

Skin tissue samples from 41 patients suffering from skin epitheliomas were analyzed by the PIXE method. Skin samples from the non-affected areas and blood serum were also analyzed for the same patients. The elements determined were K, Ca, Cr, Mn, Fe, Ni, Cu, Zn, Br, Rb, and Pb. Their concentrations in the healthy skin and the serum were normal. The concentrations in the lesions were nearly the same for both basal cell and squamus cell epitheliomas (BCE and SCC) except for higher zinc and lower bromine values in the BCE samples. However, substantial differences were observed between the affected and non-affected skin.Supported in part by the Hellenic Anticancer Society.     

Melanocortin 1 receptor variants: functional role and pigmentary associations

The significance of human cutaneous pigmentation lies in its protective role against sun-induced DNA damage and photocarcinogenesis. Fair skin and red hair are characterized by a low eumelanin to pheomelanin ratio, and have been associated with increased risk of skin cancer. Cutaneous pigmentation is a complex genetic trait, with more than 120 genes involved in its regulation, among which the melanocortin 1 receptor gene (MC1R) plays a key role. Although a large number of single nucleotide polymorphisms (SNPs) have been identified in pigmentation genes, very few SNPs have been examined in relation to human pigmentary phenotypes and skin cancer risk. Recent GWAS have identified new candidate determinants of pigmentation traits, but MC1R remains the best characterized genetic determinant of human skin and hair pigmentation as well as the more firmly validated low-penetrance skin cancer susceptibility gene. In this review, we will address how the melanocortin system regulates pigmentation, the effect of MC1R variants on the physiologic function of the MC1 receptor, and how specific MC1R variants are associated with distinct human pigmentation phenotypes.     

Lattice repleteness and some of its applications to topology

We deal with the general concept of lattice repleteness. Specifically, we systematize the study of several important special cases of repleteness, namely, realcompactness, α-completeness, N-compactness, and Borel-completeness; we apply our general results on repleteness to specific lattices in topological spaces, in particular, to analytic spaces; we utilize the concept of $\text{G}$_δ-closure to obtain necessary or sufficient conditions for repleteness (this portion of our work generalizes important theorems of Mrówka on Stone-?echcompactification, of Frolik on realcompact spaces, and of Wenjen on realcompact spaces); finally, we extend the measure representation material of Varadarajan and then we utilize the results to obtain further applications to repleteness.     

Lattice measures and associated outer measures

In this paper, we consider lattice measures and introduce certain associated outer measures (not the usual induced outer measures), study their properties, and investigate the associated classes of measureable sets. We utilize some of these outer measures to characterize normality and investigate lattice separation properties; also, to extend the notion of regularity of measures to weak regularity of measures. We give applications of our results to specific topological lattices.     

Some applications of the adjoint to lattice regular measures

Summary In this paper, the principal role is played by the adjoint of a certain bounded linear mapping, whose domain and range are Banach spaces of lattice regular measures. First, the general properties of the adjoint are investigated and it is shown, in particular, how this mapping yields generalizations of many results in Stone-ech Theory, especially matters related to embeddibility. Then, the investigation continues with the mapping properties of the adjoint, and a variety of applications is given to Topological Measure Theory, strong measure repleteness, tightness, and relative compactness.