Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

Existence and uniqueness of Q-processes with a given finite μ-invariant measure

Let Q be a stable and conservative Q-matrix over a countable state space S consisting of an irreducible class C and a single absorbing state 0 that is accessible from C. Suppose that Q admits a finite mu-subinvariant measure in on C. We derive necessary and sufficient conditions for there to exist a Q-process for which m is mu-invariant on C, as well as a necessary condition for the uniqueness of such a process.

On the efficiency of some finite groups

We describe a new technique for finding efficient presentations for finite groups. We use it to answer three previously unresolved questions about the efficiency of group and semigroup presentations.

Classification of the Maximal Subsemigroups of the Semigroup of all Partial Order-Preserving Transformations

Илинка А. Димитрова, Цветелина Н. Младенова - Моноида P Tn от всички частични преобразования върху едно n-елементно множество относно операцията композиция на преобразования е изучаван в различни аспекти от редица автори. Едно частично преобразование α се нарича запазващо наредбата, ако от x ≤ y следва, че xα ≤ yα за всяко x, y от дефиниционното множество на α. Обект на разглеждане в настоящата работа е моноида P On състоящ се от всички частични запазващи наредбата преобразования. Очевидно P On е под-моноид на P Tn. Направена е пълна класификация на максималните подполугрупи на моноида P On. Доказано е, че съществуват пет различни вида максимални подполугрупи на разглеждания моноид. Броят на всички максимални подполугрупи на POn е точно 2^n + 2n − 2.

On Nilpotent Subsemigroups in some Matrix Semigroups

2000 Mathematics Subject Classification: 20M20, 20M10.

Regular homomorphisms of minimal sets

The classification of minimal sets is a central theme in abstract topological dynamics. Recently this work has been strengthened and extended by consideration of homomorphisms. Background material is presented in Chapter I. Given a flow on a compact Hausdorff space, the action extends naturally to the space of closed subsets, taken with the Hausdorff topology. These hyperspaces are discussed and used to give a new characterization of almost periodic homomorphisms. Regular minimal sets may be described as minimal subsets of enveloping semigroups. Regular homomorphisms are defined in Chapter II by extending this notion to homomorphisms with minimal range. Several characterizations are obtained. In Chapter III, some additional results on homomorphisms are obtained by relativizing enveloping semigroup notions. In Veech's paper on point distal flows, hyperspaces are used to associate an almost one-to-one homomorphism with a given homomorphism of metric minimal sets. In Chapter IV, a non-metric generalization of this construction is studied in detail using the new notion of a highly proximal homomorphism. An abstract characterization is obtained, involving only the abstract properties of homomorphisms. A strengthened version of the Veech Structure Theorem for point distal flows is proved. In Chapter V, the work in the earlier chapters is applied to the study of homomorphisms for which the almost periodic elements of the associated hyperspace are all finite. In the metric case, this is equivalent to having at least one fiber finite. Strong results are obtained by first assuming regularity, and then assuming that the relative proximal relation is closed as well.

Pipkiiα Is Widely Expressed In Hematopoietic-derived Cells And May Play A Role In The Expression Of Alpha- And Gamma-globins In K562 Cells.

Characterized for the first time in erythrocytes, phosphatidylinositol phosphate kinases (PIP kinases) belong to a family of enzymes that generate various lipid messengers and participate in several cellular processes, including gene expression regulation. Recently, the PIPKIIα gene was found to be differentially expressed in reticulocytes from two siblings with hemoglobin H disease, suggesting a possible relationship between PIPKIIα and the production of globins. Here, we investigated PIPKIIα gene and protein expression and protein localization in hematopoietic-derived cells during their differentiation, and the effects of PIPKIIα silencing on K562 cells. PIPKIIα silencing resulted in an increase in α and γ globins and a decrease in the proliferation of K562 cells without affecting cell cycle progression and apoptosis. In conclusion, using a cell line model, we showed that PIPKIIα is widely expressed in hematopoietic-derived cells, is localized in their cytoplasm and nucleus, and is upregulated during erythroid differentiation. We also showed that PIPKIIα silencing can induce α and γ globin expression and decrease cell proliferation in K562 cells.

The Clinical Impact Of Cerebellar Grey Matter Pathology In Multiple Sclerosis.

The cerebellum is an important site for cortical demyelination in multiple sclerosis, but the functional significance of this finding is not fully understood. To evaluate the clinical and cognitive impact of cerebellar grey-matter pathology in multiple sclerosis patients. Forty-two relapsing-remitting multiple sclerosis patients and 30 controls underwent clinical assessment including the Multiple Sclerosis Functional Composite, Expanded Disability Status Scale (EDSS) and cerebellar functional system (FS) score, and cognitive evaluation, including the Paced Auditory Serial Addition Test (PASAT) and the Symbol-Digit Modalities Test (SDMT). Magnetic resonance imaging was performed with a 3T scanner and variables of interest were: brain white-matter and cortical lesion load, cerebellar intracortical and leukocortical lesion volumes, and brain cortical and cerebellar white-matter and grey-matter volumes. After multivariate analysis high burden of cerebellar intracortical lesions was the only predictor for the EDSS (p<0.001), cerebellar FS (p = 0.002), arm function (p = 0.049), and for leg function (p<0.001). Patients with high burden of cerebellar leukocortical lesions had lower PASAT scores (p = 0.013), while patients with greater volumes of cerebellar intracortical lesions had worse SDMT scores (p = 0.015). Cerebellar grey-matter pathology is widely present and contributes to clinical dysfunction in relapsing-remitting multiple sclerosis patients, independently of brain grey-matter damage.

Dna Extraction From Filter-paper Spots Of Vaginal Samples Collected After Sexual Violence.

To detect the presence of male DNA in vaginal samples collected from survivors of sexual violence and stored on filter paper. A pilot study was conducted to evaluate 10 vaginal samples spotted on sterile filter paper: 6 collected at random in April 2009 and 4 in October 2010. Time between sexual assault and sample collection was 4-48hours. After drying at room temperature, the samples were placed in a sterile envelope and stored for 2-3years until processing. DNA extraction was confirmed by polymerase chain reaction for human β-globin, and the presence of prostate-specific antigen (PSA) was quantified. The presence of the Y chromosome was detected using primers for sequences in the TSPY (Y7/Y8 and DYS14) and SRY genes. β-Globin was detected in all 10 samples, while 2 samples were positive for PSA. Half of the samples amplified the Y7/Y8 and DYS14 sequences of the TSPY gene and 30% amplified the SRY gene sequence of the Y chromosome. Four male samples and 1 female sample served as controls. Filter-paper spots stored for periods of up to 3years proved adequate for preserving genetic material from vaginal samples collected following sexual violence.

Analysis Of The Dna Fourier Transform-infrared Microspectroscopic Signature Using An All-reflecting Objective.

The Fourier transform-infrared (FT-IR) signature of dry samples of DNA and DNA-polypeptide complexes, as studied by IR microspectroscopy using a diamond attenuated total reflection (ATR) objective, has revealed important discriminatory characteristics relative to the PO2(-) vibrational stretchings. However, DNA IR marks that provide information on the sample's richness in hydrogen bonds have not been resolved in the spectral profiles obtained with this objective. Here we investigated the performance of an all reflecting objective (ARO) for analysis of the FT-IR signal of hydrogen bonds in DNA samples differing in base richness types (salmon testis vs calf thymus). The results obtained using the ARO indicate prominent band peaks at the spectral region representative of the vibration of nitrogenous base hydrogen bonds and of NH and NH2 groups. The band areas at this spectral region differ in agreement with the DNA base richness type when using the ARO. A peak assigned to adenine was more evident in the AT-rich salmon DNA using either the ARO or the ATR objective. It is concluded that, for the discrimination of DNA IR hydrogen bond vibrations associated with varying base type proportions, the use of an ARO is recommended.

Antiangiogenic And Finasteride Therapies: Responses Of The Prostate Microenvironment In Elderly Mice.

The aim of this study was to evaluate the structural and molecular effects of antiangiogenic therapies and finasteride on the ventral prostate of senile mice. 90 male FVB mice were divided into: Young (18 weeks old) and senile (52 weeks old) groups; finasteride group: finasteride (20mg/kg); SU5416 group: SU5416 (6 mg/kg); TNP-470 group: TNP-470 (15 mg/kg,) and SU5416+TNP-470 group: similar to the SU5416 and TNP-470 groups. After 21 days, prostate ventral lobes were collected for morphological, immunohistochemical and Western blotting analyses. The results demonstrated atrophy, occasional proliferative lesions and inflammatory cells in the prostate during senescence, which were interrupted and/or blocked by treatment with antiangiogenic drugs and finasteride. Decreased AR and endostatin reactivities, and an increase for ER-α, ER-β and VEGF, were seen in the senile group. Decreased VEGF and ER-α reactivities and increased ER-β reactivity were verified in the finasteride, SU5416 groups and especially in SU5416+TNP-470 group. The TNP-470 group showed reduced AR and ER-β protein levels. The senescence favored the occurrence of structural and/or molecular alterations suggesting the onset of malignant lesions, due to the imbalance in the signaling between the epithelium and stroma. The SU5416+TNP-470 treatment was more effective in maintaining the structural, hormonal and angiogenic factor balance in the prostate during senescence, highlighting the signaling of antiproliferation via ER-β.

An Efficient Protocol For The Generation Of Monocyte Derived Dendritic Cells Using Serum-free Media For Clinical Applications In Post Remission Aml Patients.

Protocols for the generation of dendritic cells (DCs) using serum as a supplementation of culture media leads to reactions due to animal proteins and disease transmissions. Several types of serum-free media (SFM), based on good manufacture practices (GMP), have recently been used and seem to be a viable option. The aim of this study was to evaluate the results of the differentiation, maturation, and function of DCs from Acute Myeloid Leukemia patients (AML), generated in SFM and medium supplemented with autologous serum (AS). DCs were analyzed by phenotype characteristics, viability, and functionality. The results showed the possibility of generating viable DCs in all the conditions tested. In patients, the X-VIVO 15 medium was more efficient than the other media tested in the generation of DCs producing IL-12p70 (p=0.05). Moreover, the presence of AS led to a significant increase of IL-10 by DCs as compared with CellGro (p=0.05) and X-Vivo15 (p=0.05) media, both in patients and donors. We concluded that SFM was efficient in the production of DCs for immunotherapy in AML patients. However, the use of AS appears to interfere with the functional capacity of the generated DCs.

Changes In The Bacterial Community Of Soil From A Neutral Mine Drainage Channel.

Mine drainage is an important environmental disturbance that affects the chemical and biological components in natural resources. However, little is known about the effects of neutral mine drainage on the soil bacteria community. Here, a high-throughput 16S rDNA pyrosequencing approach was used to evaluate differences in composition, structure, and diversity of bacteria communities in samples from a neutral drainage channel, and soil next to the channel, at the Sossego copper mine in Brazil. Advanced statistical analyses were used to explore the relationships between the biological and chemical data. The results showed that the neutral mine drainage caused changes in the composition and structure of the microbial community, but not in its diversity. The Deinococcus/Thermus phylum, especially the Meiothermus genus, was in large part responsible for the differences between the communities, and was positively associated with the presence of copper and other heavy metals in the environmental samples. Other important parameters that influenced the bacterial diversity and composition were the elements potassium, sodium, nickel, and zinc, as well as pH. The findings contribute to the understanding of bacterial diversity in soils impacted by neutral mine drainage, and demonstrate that heavy metals play an important role in shaping the microbial population in mine environments.

Malignant Transformation Of An Odontogenic Cyst In A Period Of 10 Years.

Primary intraosseous carcinoma of the jaws (PIOSCC) might arise from odontogenic epithelium, more commonly from a previous odontogenic cyst. The aim of this case is to illustrate that the clinician should consider that an apparent benign dentigerous cyst can suffer malignant transformation and that all material removed from a patient must be evaluated histologically. A 44-year-old man presented in a routine periapical X-ray an impacted lower left third molar with radiolucency over its crown. Ten years later, the patient complained of pain in the same region and the tooth was extracted. After one month, the patient still complained of pain and suffered a fracture of the mandible. A biopsy was performed and carcinoma was diagnosed. The patient was treated surgically with adjuvant radio- and chemotherapy and after 8 years, he is well without signs of recurrences. This report describes a central mandibular carcinoma probably developed from a previous dentigerous cyst.