Abstract. In [2] a delta convex function on R is constructed which is strictly differentiable at 0 but it is not representable as a difference of two convex function of this property. We improve this result by constructing a delta convex function of class C(R) which cannot be represented as a difference of two convex functions differentiable at 0. Further we give an example of a delta convex function differentiable everywhere which is not strictly differentiable at 0.

Let $f\colon I\to X$ be a delta-convex mapping, where $I\subset \mathbb R $ is an open interval and $X$ a Banach space. Let $C_f$ be the set of critical points of $f$. We prove that $f(C_f)$ has zero $1/2$-dimensional Hausdorff measure.

INTRODUCTION:The objective of this study was to characterize the lactobacilli from the human oral cavity as a potential source of probiotic strains.METHODS:Samples were collected from four different locations within the oral cavity: surface of healthy tooth, oral mucous membrane, surface of tooth decay and deep tooth decay. On the basis of morphological and biochemical properties eight categories were formed and 26 isolates were selected for further characterization. The isolates were determined as Lactobacillus sp. using primers specific for 16S rDNA. Sequencing of 16S rDNA genes and repetitive sequence-based polymerase chain reactions were used for determination to species and subspecies levels.RESULTS:Predominant species were Lactobacillus fermentum, Lactobacillus plantarum, Lactobacillus salivarius and Lactobacillus paracasei subsp. paracasei, while Lactobacillus acidophilus, Lactobacillus cellobiosus, Lactobacillus delbrueckii subsp. lactis and Lactobacillus gasseri were also present. The isolates Lactobacillus salivarius BGHO1, Lactobacillus fermentum BGHO36 and BGHO64, Lactobacillus gasseri BGHO89 and Lactobacillus delbrueckii subsp. lactis BGHO99 exhibited antagonistic action on the growth of Staphylococcus aureus, Enterococcus faecalis, Micrococcus flavus, Salmonella enteritidis, Streptococcus pneumoniae and Streptococcus mutans, but not on growth of Candida albicans. Moreover, the isolates L. salivarius BGHO1 and L. gasseri BGHO89 were tolerant to low pH and high concentration of bile salts.CONCLUSION:Taken together, these findings imply that L. salivarius BGHO1 and L. gasseri BGHO89 might be subjects for additional investigation as potential probiotic strains.

We prove that the set of directions of (n - 2)-dimensional balls which are contained in the boundary partial derivative Kappa of a convex body K subset of R-n but in no (n - 1)-dimensional convex subset of partial derivative Kappa is sigma-1-rectifiable. We also show that there exists a close connection between smallness of the set of directions of line segments on partial derivative Kappa and smallness of the set of tangent hyperplanes to the graph of a d.c. (delta-convex) function on Rn-2. Using this connection, we construct K subset of R-3 such that the set of directions of segments on partial derivative K cannot be covered by countably many simple Jordan arcs having half-tangents at all points. Also new results on directions of r-dimensional balls in partial derivative Kappa parallel to a fixed linear subspace are proved.

Background The aim of this study was to confirm the presence of herpes simplex virus type 1 and 2 on the oral mucosa, in patients undergoing chemotherapy, by means of polymerase chain reaction (PCR). Methods The research was carried out on 40 patients receiving chemotherapy as treatment for different malignancies. The status of oral mucosa and viral presence were assessed in all patients at the initial examination (prior to chemotherapy), and at the control examination (two weeks after the initiation of the chemotherapeutic cycle). Results The presence of HSV-1 was detected in 28 patients (70%) prior to chemotherapy, of whom 7 (25%) manifested oral complications. The control examination showed the presence of HSV-1 in 35 patients (87.5%), of whom 23 (65.7%) presented oral mucosa changes. HSV-2 has not been detected in any of the patients.

Let $f:I\to X$ be a d.c. mapping, where $I\subset \R$ is an open interval and $X$ a Banach space. Let $C_f$ be the set of critical points of $f$. We prove that $f(C_f)$ has zero 1/2-dimensional Hausdorff measure.

If f is a d.c. function on R-2 (i.e., f = f(1) - f(2), where f(1), f(2) are convex) and C is the set of all critical points of f, then f (C) is a Lebesgue null set. This result was published by E. Landis in 1951 with a sketch of a proof which is based on the notion of "planar variation" of (discontinuous) functions on R-2. We present a similar complete proof based on the well-known theory of BV functions and on a recent result of Ambrosio, Caselles, Masnou and Morel on sets with finite perimeter. Moreover, we generalize Landis' result to the case of a d.c. mapping f : R-2 -> X, where X is a Banach space. Also results on Lipschitz BV2 functions on R-n are proved.