scholarly journals Cantor series constructions of sets of normal numbers

2012 ◽  
Vol 156 (3) ◽  
pp. 223-245 ◽  
Author(s):  
Bill Mance
Keyword(s):  
Normal Numbers ◽  
Cantor Series

scholarly journals Number theoretic applications of a class of Cantor series fractal functions, II

2015 ◽  
Vol 11 (02) ◽  
pp. 407-435 ◽  
Author(s):  
Brian Li ◽  
Bill Mance
Keyword(s):  
Theoretical Result ◽  
Real Number ◽  
Arithmetic Progression ◽  
Relative Frequency ◽  
Series Expansions ◽  
Basic Fact ◽  
Normal Numbers ◽  
Fractal Functions ◽  
Cantor Series

It is well known that all numbers that are normal of order k in base b are also normal of all orders less than k. Another basic fact is that every real number is normal in base b if and only if it is simply normal in base bkfor all k. This may be interpreted to mean that a number is normal in base b if and only if all blocks of digits occur with the desired relative frequency along every infinite arithmetic progression. We reinterpret these theorems for the Q-Cantor series expansions and show that they are no longer true in a particularly strong way. The main theoretical result of this paper will be to reduce the problem of constructing normal numbers with certain pathological properties to the problem of solving a system of Diophantine relations.

scholarly journals Normal Numbers and Limit Computable Cantor Series

2017 ◽  
Vol 58 (2) ◽  
pp. 215-220 ◽  
Author(s):  
Achilles Beros ◽  
Konstantinos Beros
Keyword(s):  
Normal Numbers ◽  
Cantor Series

scholarly journals Adult Mice With Targeted Mutation of the Interleukin-11 Receptor (IL11Ra) Display Normal Hematopoiesis

Blood ◽  
1997 ◽  
Vol 90 (6) ◽  
pp. 2148-2159 ◽  
Author(s):  
Harshal H. Nandurkar ◽  
Lorraine Robb ◽  
David Tarlinton ◽  
Louise Barnett ◽  
Frank Köntgen ◽  
...  
Keyword(s):  
Bone Marrow ◽  
Peripheral Blood ◽  
Blood Cells ◽  
Bone Marrow Cells ◽  
White Blood Cells ◽  
Null Mutation ◽  
Wild Type ◽  
Normal Numbers ◽  
Interleukin 11 ◽  
Marrow Cells

Abstract Interleukin-11 (IL-11) is a pleiotropic growth factor with a prominent effect on megakaryopoiesis and thrombopoiesis. The receptor for IL-11 is a heterodimer of the signal transduction unit gp130 and a specific receptor component, the α-chain (IL-11Rα). Two genes potentially encode the IL-11Rα: the IL11Ra and IL11Ra2 genes. The IL11Ra gene is widely expressed in hematopoietic and other organs, whereas the IL11Ra2 gene is restricted to only some strains of mice and its expression is confined to testis, lymph node, and thymus. To investigate the essential actions mediated by the IL-11Rα, we have generated mice with a null mutation of IL11Ra (IL11Ra−/−) by gene targeting. Analysis of IL11Ra expression by Northern blot and reverse transcriptase-polymerase chain reaction, as well as the absence of response of IL11Ra−/− bone marrow cells to IL-11 in hematopoietic assays, further confirmed the null mutation. Compensatory expression of the IL11Ra2 in bone marrow cells was not detected. IL11Ra−/− mice were healthy with normal numbers of peripheral blood white blood cells, hematocrit, and platelets. Bone marrow and spleen contained normal numbers of cells of all hematopoietic lineages, including megakaryocytes. Clonal cultures did not identify any perturbation of granulocyte-macrophage (GM), erythroid, or megakaryocyte progenitors. The number of day-12 colony-forming unit-spleen progenitors were similar in wild-type and IL11Ra−/− mice. The kinetics of recovery of peripheral blood white blood cells, platelets, and bone marrow GM progenitors after treatment with 5-flurouracil were the same in IL11Ra−/− and wild-type mice. Acute hemolytic stress was induced by phenylhydrazine and resulted in a 50% decrease in hematocrit. The recovery of hematocrit was comparable in IL11Ra−/− and wild-type mice. These observations indicate that IL-11 receptor signalling is dispensable for adult hematopoiesis.

A class of normal numbers To the memory of Isamu Kobayashi

1990 ◽  
Vol 16 (1) ◽  
pp. 17-29 ◽  
Author(s):  
Yoshinobu NAKAI ◽  
Iekata SHIOKAWA
Keyword(s):  
Normal Numbers

scholarly journals Murine myeloproliferative disorder as a consequence of impaired collaboration between dendritic cells and CD4 T cells

Blood ◽  
2019 ◽  
Vol 133 (4) ◽  
pp. 319-330 ◽  
Author(s):  
Stéphanie Humblet-Baron ◽  
John S. Barber ◽  
Carlos P. Roca ◽  
Aurelie Lenaerts ◽  
Pandelakis A. Koni ◽  
...  
Keyword(s):  
T Cells ◽  
Dendritic Cells ◽  
Mhc Class Ii ◽  
Cd4 T Cells ◽  
Adaptive Immune Response ◽  
Extramedullary Hematopoiesis ◽  
Myeloproliferative Disorder ◽  
Myeloid Differentiation ◽  
Normal Numbers ◽  
Congenital Deficiency

Abstract Dendritic cells (DCs) are a key cell type in the initiation of the adaptive immune response. Recently, an additional role for DCs in suppressing myeloproliferation was discovered. Myeloproliferative disorder (MPD) was observed in murine studies with constitutive depletion of DCs, as well as in patients with congenital deficiency in DCs caused by mutations in GATA2 or IRF8. The mechanistic link between DC deficiency and MPD was not predicted through the known biology and has remained an enigma. Prevailing models suggest numerical DC deficiency leads to MPD through compensatory myeloid differentiation. Here, we formally tested whether MPD can also arise through a loss of DC function without numerical deficiency. Using mice whose DCs are deficient in antigen presentation, we find spontaneous MPD that is characterized by splenomegaly, neutrophilia, and extramedullary hematopoiesis, despite normal numbers of DCs. Disease development was dependent on loss of the MHC class II (MHCII) antigen-presenting complex on DCs and was eliminated in mice deficient in total lymphocytes. Mice lacking MHCII and CD4 T cells did not develop disease. Thus, MPD was paradoxically contingent on the presence of CD4 T cells and on a failure of DCs to activate CD4 T cells, trapping the cells in a naive Flt3 ligand–expressing state. These results identify a novel requirement for intercellular collaboration between DCs and CD4 T cells to regulate myeloid differentiation. Our findings support a new conceptual framework of DC biology in preventing MPD in mice and humans.

scholarly journals On the Cantor series

1968 ◽  
Vol 18 (1) ◽  
pp. 25-56 ◽  
Author(s):  
Tibor Šalát
Keyword(s):  
Cantor Series

scholarly journals effects of anemia education using web-based she smart to improve knowledge, attitudes, and practice in adolescent girls

2022 ◽  
Vol 5 (1) ◽  
pp. 44-49
Author(s):  
Ernawati Ernawati ◽  
Yusring Sanusi Baso ◽  
Healthy Hidayanty ◽  
Syafruddin Syarif ◽  
Aminuddin Aminuddin ◽  
...  
Keyword(s):  
Adolescent Girls ◽  
Statistical Tests ◽  
Sampling Technique ◽  
P Value ◽  
Growth Disorders ◽  
Normal Numbers ◽  
Web Based ◽  
Before And After ◽  
Smart Education ◽  
The Impact

Anemia is a state of hemoglobin levels in the bloodless than normal numbers according to the sex and age group. The impact of anemia in adolescents is a decrease in achievement and learning spirit and can cause symptoms such as paleness, lethargy, decreased appetite, and growth disorders. Anemia has an impact not only on the health of adolescent girls but can have a long impact on the health of the mother and fetus. You can see the influence of anemia education on knowledge, attitudes, and practice. Uses the Pre-experimental method with the design of one group pretest and posttest. Sampling technique using purposive sampling with the number of 47 adolescent girls. The research was conducted at Senior High School 12 Makassar in September-October 2021. Data analysis using the McNemar test. From the results of statistical tests showed that there was an influence on the use of web-based she smart education model on the use of adolescent girls about anemia with p-value = 0.000 (p<0.05), attitude p-value = 0.016 (p<0.05) and action p-value = 0.001 (p<0.05). Anemia education using web-based she smart can improve knowledge, attitudes, and practice before and after an intervention.

scholarly journals Immature dense granules in platelets from mice with platelet storage pool disease

Blood ◽  
1987 ◽  
Vol 69 (5) ◽  
pp. 1300-1306 ◽  
Author(s):  
M Reddington ◽  
EK Novak ◽  
E Hurley ◽  
C Medda ◽  
MP McGarry ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Dense Granule ◽  
Mutant Mice ◽  
Normal Numbers ◽  
Group Of Seven ◽  
Dense Granules ◽  
Storage Pool ◽  
Platelet Storage ◽  
Transmission Electron ◽  
Storage Pool Disease

Mepacrine uptake into platelets and bone marrow megakaryocytes was analyzed to further characterize the dense granule defects in a group of seven mouse pigment mutants that have characteristics of platelet storage pool disease (SPD). In contrast to our previous studies using electron microscopy, this method revealed that all mutants had normal numbers of dense granules. However, total mepacrine uptake in all mutant platelets was significantly diminished to less than 50% of normal uptake. Also, the flashing phenomenon observed when normal dense granules are irradiated with ultraviolet light was either greatly diminished or absent when platelets of individual mutants were similarly irradiated. Therefore the principal defect in the mutant platelets is an inability to accumulate dense granule contents rather than an absence of the granules. Mepacrine uptake into megakaryocytes was indistinguishable in normal and mutant mice. This indicates the mutant dense granule defects appear either very late in megakaryocyte development or early in platelet formation in correlation with development of the mature dense granule. By standard transmission electron microscopy we have not been able to detect gross structural or subcellular abnormalities in either platelets or megakaryocytes of mutant mice. It appears all seven mutants produce immature or functionally abnormal dense granules.

scholarly journals Hematologic engraftment and immune reconstitution posttransplantation with anti-B1 purged autologous bone marrow

Blood ◽  
1987 ◽  
Vol 69 (2) ◽  
pp. 597-604
Author(s):  
KC Anderson ◽  
J Ritz ◽  
T Takvorian ◽  
F Coral ◽  
H Daley ◽  
...  
Keyword(s):  
Bone Marrow ◽  
T Cells ◽  
B Cells ◽  
Immune Reconstitution ◽  
Autologous Bone Marrow ◽  
Normal Numbers ◽  
Autologous Bone ◽  
Total Body ◽  
One Year

Hematologic engraftment and immune reconstitution were examined in patients who received cyclophosphamide and total body irradiation therapy followed by infusion of autologous bone marrow purged with anti- B1 monoclonal antibody (MoAb) and complement as therapy for non- Hodgkin's lymphoma. Hematologic engraftment was prompt with return of greater than or equal to 0.5 X 10(3)/microL granulocytes and greater than or equal to 2 X 10(4)/microL platelets at a median of 26 and 29 days posttransplant, respectively. Immunologic reconstitution, in contrast, was prolonged. Normal numbers of circulating B cells were consistently noted by five months posttransplant, whereas return of normal immunoglobulin levels in some patients did not occur for one year. Normal numbers of T cells were evident within the first month posttransplant, but a reversed T4:T8 ratio persisted in some patients up to three years. In vitro responses of either B cells to triggers of activation or of T cells to mitogens and antigens were not normal for at least three months posttransplant. Natural killer (NK) cells predominated early after transplant and may demonstrate cytotoxicity against tumor cells. Our studies demonstrate that transplantation with anti-B1 purged autologous bone marrow results in complete hematologic and delayed immunologic engraftment. No significant acute or chronic clinical toxicities have been observed.

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