926 resultados para Prime-Producing Polynomials
Resumo:
Serotonin-producing tumors of the pancreas are rare endocrine neoplasms composed of enterochromaffin (EC) cells that have been mainly described in the literature as case reports. This study analyzes the clinicopathologic features of a series of pancreatic EC cell neoplasms and their similarities to and differences from intestinal EC cell tumors.
Resumo:
This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided.
Resumo:
Abstract This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided.
Resumo:
During the past decade, extended-spectrum beta-lactamase (ESBL)-producing Enterobacteriaceae have become a matter of great concern in human medicine. ESBL-producing strains are found in the community, not just in hospital-associated patients, which raises a question about possible reservoirs. Recent studies describe the occurrence of ESBL-producing Enterobacteriaceae in meat, fish, and raw milk; therefore, the impact of food animals as reservoirs for and disseminators of such strains into the food production chain must be assessed. In this pilot study, fecal samples of 59 pigs and 64 cattle were investigated to determine the occurrence of ESBL-producing Enterobacteriaceae in farm animals at slaughter in Switzerland. Presumptive-positive colonies on Brilliance ESBL agar were subjected to identification and antibiotic susceptibility testing including the disc diffusion method and E-test ESBL strips. As many as 15.2% of the porcine and 17.1% of the bovine samples, predominantly from calves, yielded ESBL producers. Of the 21 isolated strains, 20 were Escherichia coli, and one was Citrobacter youngae. PCR analysis revealed that 18 strains including C. youngae produced CTX-M group 1 ESBLs, and three strains carried genes encoding for CTX-M group 9 enzymes. In addition, eight isolates were PCR positive for TEM beta-lactamase, but no bla(SHV) genes were detected. Pulsed-field gel electrophoresis showed a high genetic diversity within the strains. The relatively high rates of occurrence of ESBLproducing strains in food animals and the high genetic diversity among these strains indicate that there is an established reservoir of these organisms in farm animals. Further studies are necessary to assess future trends.
Resumo:
The goal of this paper is to contribute to the understanding of complex polynomials and Blaschke products, two very important function classes in mathematics. For a polynomial, $f,$ of degree $n,$ we study when it is possible to write $f$ as a composition $f=g\circ h$, where $g$ and $h$ are polynomials, each of degree less than $n.$ A polynomial is defined to be \emph{decomposable }if such an $h$ and $g$ exist, and a polynomial is said to be \emph{indecomposable} if no such $h$ and $g$ exist. We apply the results of Rickards in \cite{key-2}. We show that $$C_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,(z-z_{1})(z-z_{2})...(z-z_{n})\,\mbox{is decomposable}\},$$ has measure $0$ when considered a subset of $\mathbb{R}^{2n}.$ Using this we prove the stronger result that $$D_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,\mbox{There exists\,}a\in\mathbb{C}\,\,\mbox{with}\,\,(z-z_{1})(z-z_{2})...(z-z_{n})(z-a)\,\mbox{decomposable}\},$$ also has measure zero when considered a subset of $\mathbb{R}^{2n}.$ We show that for any polynomial $p$, there exists an $a\in\mathbb{C}$ such that $p(z)(z-a)$ is indecomposable, and we also examine the case of $D_{5}$ in detail. The main work of this paper studies finite Blaschke products, analytic functions on $\overline{\mathbb{D}}$ that map $\partial\mathbb{D}$ to $\partial\mathbb{D}.$ In analogy with polynomials, we discuss when a degree $n$ Blaschke product, $B,$ can be written as a composition $C\circ D$, where $C$ and $D$ are finite Blaschke products, each of degree less than $n.$ Decomposable and indecomposable are defined analogously. Our main results are divided into two sections. First, we equate a condition on the zeros of the Blaschke product with the existence of a decomposition where the right-hand factor, $D,$ has degree $2.$ We also equate decomposability of a Blaschke product, $B,$ with the existence of a Poncelet curve, whose foci are a subset of the zeros of $B,$ such that the Poncelet curve satisfies certain tangency conditions. This result is hard to apply in general, but has a very nice geometric interpretation when we desire a composition where the right-hand factor is degree 2 or 3. Our second section of finite Blaschke product results builds off of the work of Cowen in \cite{key-3}. For a finite Blaschke product $B,$ Cowen defines the so-called monodromy group, $G_{B},$ of the finite Blaschke product. He then equates the decomposability of a finite Blaschke product, $B,$ with the existence of a nontrivial partition, $\mathcal{P},$ of the branches of $B^{-1}(z),$ such that $G_{B}$ respects $\mathcal{P}$. We present an in-depth analysis of how to calculate $G_{B}$, extending Cowen's description. These methods allow us to equate the existence of a decomposition where the left-hand factor has degree 2, with a simple condition on the critical points of the Blaschke product. In addition we are able to put a condition of the structure of $G_{B}$ for any decomposable Blaschke product satisfying certain normalization conditions. The final section of this paper discusses how one can put the results of the paper into practice to determine, if a particular Blaschke product is decomposable. We compare three major algorithms. The first is a brute force technique where one searches through the zero set of $B$ for subsets which could be the zero set of $D$, exhaustively searching for a successful decomposition $B(z)=C(D(z)).$ The second algorithm involves simply examining the cardinality of the image, under $B,$ of the set of critical points of $B.$ For a degree $n$ Blaschke product, $B,$ if this cardinality is greater than $\frac{n}{2}$, the Blaschke product is indecomposable. The final algorithm attempts to apply the geometric interpretation of decomposability given by our theorem concerning the existence of a particular Poncelet curve. The final two algorithms can be implemented easily with the use of an HTML
Resumo:
Therapeutic intravesical instillation of bacillus Calmette-Guérin (BCG) is effective at triggering inflammation and eliciting successful tumor immunity in patients with non-muscle invasive bladder cancer, with 50 to 70% clinical response. Therapeutic success relies on repeated instillations of live BCG administered as adjuvant therapy shortly after tumor resection; however, the precise mechanisms remain unclear. Using an experimental model, we demonstrate that after a single instillation, BCG could disseminate to bladder draining lymph nodes and prime interferon-γ-producing T cells. Nonetheless, repeated instillations with live BCG were necessary for a robust T cell infiltration into the bladder. Parenteral exposure to BCG before instillation overcame this requirement; after the first intravesical instillation, BCG triggered a more robust acute inflammatory process and accelerated T cell entry into the bladder, as compared to the standard protocol. Moreover, parenteral exposure to BCG before intravesical treatment of an orthotopic tumor markedly improved response to therapy. Indeed, patients with sustained preexisting immunity to BCG showed a significant improvement in recurrence-free survival. Together, these data suggest that monitoring patients' response to purified protein derivative, and, in their absence, boosting BCG responses by parenteral exposure before intravesical treatment initiation, may be a safe and effective means of improving intravesical BCG-induced clinical responses.