bluuebunny/crossref_metadata_2025 huggingface dataset:
Leptin Receptor Genotype at Gln223Arg is Associated With Body Composition, BMD, and Vertebral Fracture in Postmenopausal Danish Women
Authors: Fairbrother Una L , Tankó László B , Walley Andrew J , Christiansen Claus , Froguel Philippe , Blakemore Alexandra IF
Published: January 2007

Leptin is emerging as a key regulator of bone remodeling. In a population-based study of 1306 postmenopausal Danish women, nonsynonymous LEPR SNPs were associated with risk of adiposity, BMD, and vertebral fracture. Smoking exacerbates this LEPR-associated fracture risk.

Introduction: Nonsynonymous single nucleotide polymorphisms (SNPs) in the human LEPR gene have been associated with adiposity in a number of studies, but there have been no large-scale studies of their implications for BMD and osteoporotic fracture risk in postmenopausal women.

Materials and Methods: We carried out a population-based study of 1430 women. Three well-known nonsynonymous leptin receptor (LEPR) SNPs (Lys109Arg, Gln223Arg, and Lys656Asn) were genotyped for qualitative and quantitative association analysis. Phenotype characteristics of main interest were DXA measures of body fat and lean tissue mass, BMD, and radiographic vertebral fractures.

Results: Gln223Arg associated with risk of vertebral fracture (overall OR = 1.76; OR in smokers = 2.31; p = 0.0004), in addition to BMD of the femoral neck and total hip (p = 0.036 and 0.008, respectively). Heterozygote carriers showed lower BMD at both sites. Gln223Arg was also associated with adiposity (p = 0.001 for total fat mass). For adiposity, the at-risk allele was G (resulting in an arginine at position 223).

Conclusions: Variation in LEPR seemed to contribute to the variation in BMD and fracture risk in Danish postmenopausal women; the heterozygous genotype was associated with increased risk of manifest osteoporosis. Further studies are needed to replicate these data and to clarify the mechanisms involved.
Charge flipping combined with histogram matching to solve complex crystal structures from powder diffraction data
Authors: Baerlocher Christian , McCusker Lynne B. , Palatinus Lukas
Published: January 2007

The charge-flipping structure-solution algorithm introduced by Oszlányi and Süto in 2004 has been adapted to accommodate powder diffraction data. In particular, a routine for repartitioning the intensities of overlapping reflections has been implemented within the iterative procedure. This is done by modifiying the electron density map with a histogram-matching algorithm, and then using the Fourier coefficients obtained from this map to repartition the structure factor amplitudes within each overlap group. The effectiveness of the algorithm has been demonstrated with five test examples covering different classes of materials of varying complexity (ZSM-5 ([Si96O192]), cimetidine (C10H16N6S), a polysalicylide ((C7O2H)6), the low-temperature modification of 4-methylpyridine-N-oxide (C6H7NO) with 8 molecules in the asymmetric unit, and a zirconium phosphate phase (|(C5H6N)4 (H2O)2| [Zr12P16O60(OH)4F8])). It was also used to solve the structure of a layer silicate (|(CH3)4N)8 (H2O)20| [Si24 O56]), whose space group was unclear. These structures, with 17–64 non-H atoms in the asymmetric unit (68–288 in the unit cell), could all be solved in a straightforward manner. Histogram matching proved to be an essential component of the algorithm for the more complex structures. The clear advantages of the charge-flipping algorithm are that (1) all calculations are performed in P1, so space group ambiguities, which are common with powder diffraction data, are irrelevant, (2) no chemical information such as bond distances, bond angles, or connectivity are required, so there is no danger of making incorrect assumptions about the structure, (3) it is equally effective for both organic and inorganic structures, and (4) it is fast, requiring only seconds to minutes per run.
Dopedγ-Bi2O3: synthesis of microcrystalline samples and crystal chemical analysis of structural data
Authors: Poleti Dejan , Karanović Ljiljana , Hadži-Tonić Aleksandra
Published: January 2007

A series of microcrystalline products containing theγ-Bi2O3phase doped with Co, Fe, Mn, Pb, Sb, Si, Ti, V and Zn has been prepared by solid state reaction. Based on the heating temperature and heating time, the following order of increasing relative stability of the dopedγ-Bi2O3phases was established: Sb5+< Co2+≈ Mn4+< Fe3+≈ Si4+< Ti4+< V5+< Zn2+< Pb2+. The unit cell parameters of the prepared samples were compared with available structural data, which were also further analyzed concerning the geometrical parameters and overall reliability. The analysis confirmed the so-called Radaev’s model for the dopedγ-Bi2O3structure, which assumes the presence of Bi23+ions slightly displaced from the tetrahedral M site and corresponding vacancies (resulting from a lone pair on Bi23+) in the coordinating oxygen positions. In addition, the analysis suggested that this model can be further improved. The existence of an approximate linear relationship between the unit cell parameters of the dopedγ-Bi2O3phases and the ionic radii of the M cations was found.
Foetal fibroblasts introduced to cleaving mouse embryos contribute to full-term development
Authors: Piliszek Anna , Modliński Jacek A , Pyśniak Kazimiera , Karasiewicz Jolanta
Published: January 2007

Foetal fibroblasts (FFs) labelled with vital fluorescent dye were microsurgically introduced into eight-cell mouse embryos, three cells to each embryo. FFs were first identified in the inner cell mass (ICM) in about one-third of embryos, whereas in three quarters of embryos FFs were located among trophoblast cells. Some elimination of FFs from trophoblast occurred later on. Eventually, in blastocysts’ outgrowths, an equally high contribution from FFs progeny (60%) was found in both ICM and trophoblast. Three days after manipulation, FFs resumed proliferation in vitro. More than three FFs were found in 46.2% of embryos on day 4. On the 7th day in vitro in 70% of embryos more than 12 FFs were found, proving at least three cell divisions.

To study postimplantation development, the embryos with FFs were transferred to pseudopregnant recipients a day after manipulation. After implantation, FFs were identified by electrophoresis for isozymes of glucose phosphate isomerase (GPI). A single 11-day embryo delayed to day 8 proved chimeric by expressing both donor isozyme GPI-1B and recipient GPI-1A. Similar chimerism was found in the extraembryonic lineage of 11% of embryos by day 12. Starting from day 11 onwards, in 32% of normal embryos and in 57% of foetal membranes, hybrid GPI-1AB isozyme, as well as recipient isozyme, was present. Hybrid GPI-1AB can only be produced in hybrid cells derived by cell fusion, therefore, we suggest that during postimplantation development, FFs are rescued by fusion with recipient cells. In the mice born, hybrid isozyme was found in several tissues, including brain, lung, gut and kidney.

We conclude that somatic cells (FFs) can proliferate in earlyembryonic environment until early postimplantation stages. Foetuses and the mice born are chimeras between recipient cells and hybrid cells with contributions from the donor FFs. Transdifferentiation as opposed to reprogramming by cell fusion can be considered as underlying cellular processes in these chimeras.
Hypothyroidism prolongs corpus luteum function in the pregnant rat
Authors: Hapon María Belén , Motta Alicia B , Ezquer Marcelo , Bonafede Melisa , Jahn Graciela A
Published: January 2007

It has been shown that hypothyroidism in the rat produces a prolongation of pregnancy associated with a delay in the fall of circulating progesterone (P4) at term. The aim of the present work is to determine whether the delayed P4 decline in hypothyroid mother rats is due to a retarded induction of P4 degradation to 20αOH P4 or to a stimulation of its synthesis, and to investigate the possible mechanisms that may underlie the altered luteal function. We determined by RIA the circulating profile of the hormones (TSH, PRL, LH, P4, PGF2α, and PGE2) involved in luteal regulation at the end of pregnancy and, by semiquantitative RT-PCR, the expression of factors involved in P4 synthesis (CytP450scc, StAR, 3βHSD, PRLR) and metabolism (20αHSD, PGF2αR, iNOS and COX2). Our results show that the delay in P4 decline and parturition is the resultant of retarded luteal regression, caused by a combination of decreases in luteolytic factors, mainly luteal PGF2α, iNOS mRNA expression and also circulating LH, and increased synthesis or action of luteotrophic factors, such as luteal and circulating PGE2 and circulating PRL. All these changes may be direct causes of the decreased 20αHSD mRNA and protein (measured by western blot analysis) expression, which in the presence of unchanged expression of the factors involved in P4 synthesis results in elevated luteal and circulating P4 that prolonged pregnancy and also may favor longer survival of the corpus luteum.
BAX is involved in regulating follicular growth, but is dispensable for follicle atresia in adult mouse ovaries
Authors: Greenfeld Chuck R , Babus Janice K , Furth Priscilla A , Marion Sam , Hoyer Patricia B , Flaws Jodi A
Published: January 2007

Mammalian females are endowed with a finite number of primordial follicles at birth or shortly thereafter. Immediately following the formation of the primordial follicle pool, cohorts of these follicles are recruited to begin growth, and this recruitment continues until the primordial follicle population is depleted. Once recruited, a follicle will either grow and ovulate or undergo atresia. Follicle atresia results from the apoptotic death of follicular cells. Members of the BCL-2 family of proteins are important regulators of apoptosis in most cells including in the ovary. Here, we tested the hypothesis that the proapoptotic BAX is an important regulator of follicle survival. We used a variety of histological and biochemical techniques to investigate the impact of Bax deletion on follicle growth and death. We observed that the Bax deletion results in delayed vaginal opening and altered follicular growth. Young adult Bax-deficient ovaries contained increased numbers of primordial follicles and a trend towards reduced numbers of growing follicles. Bax deficiency led to a reduction in average litter size, and also a reduction in the number of oocytes ovulated in response to exogenous gonadotropins. In contrast, Bax deficiency did not alter follicle atresia. In conclusion, BAX appears to be an important regulator of follicle growth, but is dispensable for follicle atresia in mice.
Changes of testicular aromatase expression during fetal development in male pigs (sus scrofa)
Authors: Haeussler Susanne , Wagner Anna , Welter Harald , Claus Rolf
Published: January 2007

Male pig fetuses secrete considerable amounts of estrogens, but the location of aromatase activity within the fetal testis is not known. The location of aromatase expression was investigated by immunocytochemistry in fetal testes from week 6 (n = 5), weeks 10, 13, and 15 (each: n = 6) of gestation and additionally in neonates (n = 4). Blood was sampled from the umbilical artery of fetuses and jugular vein of neonates. Histological evaluation of testes involved morphological criteria and counting of Leydig cells, Sertoli cells, and gonocytes. Aromatase activity was localized immunocytochemically and quantified by the percentage of positive stained cells within the same cell type. Aromatase expression was further characterized by quantitative RT-PCR. Concentrations of estrogens, testosterone, FSH, and LH were measured in blood plasma. Total estrogens increased from week 10 to a maximum of 31.03 nmol/l in week 15. Increased testosterone concentrations were only measured at week 6 and were paralleled by slightly elevated estrogens. Thereafter, testosterone dropped and was low throughout. The increase of estrogens was not paralleled by a similar increase of FSH and LH but was related to the increase of the total number of Leydig cells. This increase was also found for mRNA expression. Both Leydig cells and gonocytes were identified as contributors to estrogen formation. Gonocytes were the main source of aromatase at week 10, when gene expression by Leydig cells is low due to the preparation of a wave of Leydig cell mitosis.
Adult-only exposure of male rats to a diet of high phytoestrogen content increases apoptosis of meiotic and post-meiotic germ cells
Authors: Assinder Stephen , Davis Ryan , Fenwick Mark , Glover Amy
Published: January 2007

Apoptosis plays a critical role in regulating sperm production. Removal of androgens and gonadotropins, or estrogen administration induces germ cell apoptosis. It is hypothesized that dietary phytoestrogens increase apoptosis of developing germ cells, decreasing sperm production. This study aimed to test this in rats fed a high phytoestrogen diet only during adulthood. Male Wistar rats used in this study were offspring of females maintained on a low phytoestrogen diet prior to conception through to weaning. After weaning, juveniles were fed the same low phytoestrogen diet into adulthood. A cohort of males were transferred to a high phytoestrogen diet for 24 days and subsequently testes were collected from all animals. In the high phytoestrogen fed group, homogenization-resistant sperm counts were significantly decreased, as were epididymal sperm counts. Morphometric analysis determined round and elongated spermatid volumes to be significantly decreased, but seminiferous tubule lumen diameters to be significantly increased. TUNEL analysis determined that apoptosis of spermatocytes and round spermatids was significantly greater in the high phytoestrogen fed rats. Neither plasma gonadotropin concentrations nor testicular testosterone were altered. In conclusion, exposure of the adult male rat to a high phytoestrogen diet disrupts spermatogenesis, increasing germ cell apoptosis. This effect is independent of the hypothalamo–pituitary–testicular axis and is likely due to disruption of estrogen’s actions in the testis.
Kinetics of murine decidual dendritic cells
Authors: Zarnani Amir-Hassan , Moazzeni Seyed-Mohammad , Shokri Fazel , Salehnia Mojdeh , Jeddi-Tehrani Mahmood
Published: January 2007

Dendritic cells (DCs) are professional antigen presenting cells (APC) capable of induction of primary immune responses as well as immunologic tolerance. Myeloid and lymphoid subsets of murine DCs are able to shift cytokine responses of T cells toward Th2 and Th1 profiles respectively. Thus, DCs would be suitable candidates to mediate the balance of maternal immune responses to conception. We analyzed pregnancy-related variations in uterus and splenic DCs in a murine model. C57BL/6-mated Balb/c female mice with vaginal plugs were scarified at early, middle, and late pregnancy. Frozen sections of uterus and spleen at each stage of pregnancy were immunostained with CD11c- and MHC-II-specific antibodies. Two-color immunohistochemistry was also carried out using anti-CD11c and one of the antibodies against CD11b, CD8α, CD86, and DEC-205. Using morphometric analysis, the average density of DCs and relative percentage of myeloid (CD11c+, CD11b+) and lymphoid DCs (CD11c+, CD8a+) were determined at each stage. Our results showed that DCs are present throughout the pregnancy in decidua. The average density of decidual DCs at early pregnancy was significantly higher relative to middle and late gestation or to those of endometrial DCs of non-pregnant mice. Interestingly, the average density of decidual and splenic DCs, followed the same variations at different stages of pregnancy. The relative percentage of decidual lymphoid DCs (LDC) was significantly higher at mid-gestation when compared with other stages of pregnancy or non-pregnant mice. Inversely, the frequency of myeloid DCs (MDC) and the MDC/LDC ratio were statistically lower at the middle stage of pregnancy. A majority of decidual DCs expressed MHC-II and CD86. At early pregnancy, DCs were more concentrated subadjacent to the luminal epithelial layers, whereas at mid-or late gestation, DCs were randomly distributed in the stroma and around the epithelium. Mid-pregnancy period was a critical point with regard to splenic DCs kinetics, as both the average density of DCs and the frequency of MDCs decreased significantly when compared with early or late pregnancy, although the relative percentage of splenic LDCs did not change. Our data suggest that the balance of MDC and LDC is finely tuned throughout pregnancy, pointing an eminent immunoregulatory role of DCs in the maintenance of pregnancy.
Trinexapac‐ethyl and Paclobutrazol Affect Kentucky Bluegrass Single‐Leaf Carbon Exchange Rates and Plant Growth
Authors: Beasley Jeffrey S. , Branham Bruce E.
Published: January 2007

Trinexapac‐ethyl (TE) [4‐(cyclopropyl‐α‐hydroxy‐methylene)‐3,5‐dioxocyclohexanecarboxylic acid ethyl ester] and paclobutrazol (PAC) [(2RS,3RS)‐1‐(4‐chlorophenyl)‐4,4‐dimethyl‐2‐(1H‐1,2,4‐triazol‐1‐yl)pentan‐3‐ol] are routinely used to suppress clipping production. Single‐leaf turfgrass C exchange rates (CERs) in response to plant growth regulator (PGR) treatment have not been characterized. Individual Kentucky bluegrass (KBG, Poa pratensis L.) plants received label rates of TE or PAC and were placed in growth chambers at 23/18 or 30/25°C. Photosynthetic efficiency and CER measurements were recorded every 4 d for 44 d. Total root length (TRL), root surface area (SA), and average root diameter were measured at the end of the study. Reductions in CERs of TE‐ or PAC‐treated plants were short lived with CERs suppressed 17 to 29% of control (POC) at 4 and 12 days after treatment (DAT), respectively. Plants treated at 23/18°C with PGRs typically had short‐lived increases in CERs following CER suppression. A similar pattern of CER response to PGR treatment was observed at the 30/25°C temperature regime. Quantum efficiency was unaffected, but plants treated with PGRs had reduced root growth. PAC caused the greatest reduction in TRL and SA while increasing root diameter. A decline in TRL and SA in conjunction with increased tillering indicates that PGR reduced TRL and SA on a tiller basis. Changes in single‐leaf CERs do not fully explain PGR‐induced changes in plant growth.
Characterization of Roundup Ready Flex Cotton, ‘MON 88913’, for Use in Ecological Risk Assessment: Evaluation of Seed Germination, Vegetative and Reproductive Growth, and Ecological Interactions
Authors: Horak Michael J. , Rosenbaum Eric W. , Woodrum Carrie L. , Martens Amy B. , Mery Ramon F. , Cothren J. Tom , Burns J. Austin , Nickson Thomas E. , Pester Todd A. , Jiang Changjian , Hart Jesse L. , Sammons Bernard
Published: January 2007

Biological and ecological data collected on a genetically modified crop and an appropriate control are useful for assessing potential ecological risk. Specific characteristics studied are selected on the basis of relevance to potential ecological effects, are well known, and are accepted by plant breeders. In these studies, germination, vegetative and reproductive growth, or ecological characteristics of Roundup Ready Flex cotton, MON 88913 were compared with a negative control, MON 88913(‐). Statistically significant differences, when detected, were considered in the context of the genetic variation known to occur in cotton and their potential impact on plant pest (weed) potential (ecological risk). Experimental results revealed no effects of the genetic modification that would result in increased pest potential or ecological risk of MON 88913 compared with MON 88913(‐).
Genotypic Variation for Three Physiological Traits Affecting Drought Tolerance in Soybean
Authors: Hufstetler E. Vicki , Boerma H. Roger , Carter Thomas E. , Earl Hugh J.
Published: January 2007

Three physiological traits that may affect performance of soybean [Glycine max (L.) Merr.] when soil water availability is limiting are (i) water use efficiency (WUE), (ii) regulation of whole plant water use in response to soil water content, and (iii) leaf epidermal conductance (ge) when stomata are closed. Six soybean plant introductions (PIs), eight breeding lines derived from them, and nine cultivars were compared for variability in these three traits during vegetative growth in two greenhouse studies. In the first experiment, whole plant water use, normalized both to plant size and evaporative demand (the normalized transpiration ratio, NTR), was monitored during a 10‐d cycle of gradually increasing drought stress and then for an additional 2 d following rewatering. The critical soil water content at which each plant began to reduce its water use (FTSWC), was determined. The WUE was estimated as the ratio of total plant dry weight to total water used. In the second experiment, ge was determined for these same 23 genotypes by measuring leaf water vapor exchange after a 36‐h dark adaptation. Substantial variation was found among genotypes for WUE, FTSWC, ge, and also the extent to which NTR recovered on rewatering. Generally, adapted cultivars had greater WUE and lower ge than did PIs. However, PI 471938 and its progeny N98‐7264 were clear exceptions to this trend. An unexpected finding was that WUE was significantly negatively correlated with ge across genotypes.
A Quantitative Analysis of Resistance to Mycosphaerella Blight in Field Pea
Authors: Zhang Roger , Hwang Sheau-Fang , Gossen Bruce D. , Chang Kan-Fa , Turnbull George D.
Published: January 2007

Mycosphaerella blight, caused mainly by Mycosphaerella pinodes (Berk. and Blox.) Vestergren, is the most important foliar disease on field pea (Pisum sativum L.) in western Canada. A quantitative trait analysis of resistance to M. pinodes was undertaken on five crosses with reciprocals of P. sativum to examine broad‐sense (H2) and narrow‐sense (h2) heritability, minimum number of genes involved (MNG), midparent heterosis (MPH), cytoplasmic inheritance, and epistasis. Mean H2 was 0.75 (range 0.67–0.80) and mean h2 was 0.59 (range 0.41–0.70), indicating that additive variance is important and that improvement in resistance can be achieved through breeding. Mean MNG was 2.16 genes (range 0.06–6.22), indicating that genes for resistance differed among parent lines. Mean MPH was 50% (range 47–57%), indicating that heterosis did not influence the expression of resistance to M. pinodes There was no difference between the mean of any F1 population and its reciprocal, indicating lack of maternal inheritance. The mean of the epistatic points was −0.01 (range −0.1 to 0.12), indicating that epistasis was not important in these crosses. These results will further the understanding of the natural genetic diversity for disease resistance to M. pinodes in P. sativum
Growth, Gas Exchange, Chlorophyll Fluorescence, and Ion Content of Naked Oat in Response to Salinity
Authors: Zhao G. Q. , Ma B. L. , Ren C. Z.
Published: January 2007

Understanding of the physiological responses of crop plants to salinity stress is of paramount importance for selection of genotypes with improved tolerance to salt stress. Two naked oat (Avena sativa L.) genotypes, ‘VAO‐7’ and ‘VAO‐24‘, were subjected to different salt concentrations (0, 50, 100, 150, 200, and 250 mM NaCl) to determine the effects of salt levels and stress duration on seedling growth, ion content, and photosynthetic productivity. Relative growth rate (RGR) and leaf chlorophyll were determined at weekly intervals after salinity was imposed. Total leaf area, plant dry weight, photosynthetic parameters, and plant tissue ion concentrations were determined at 25 d after salinity application. Under salt stress conditions, germination rates varied greatly among the genotypes. The differences between VAO‐7 and VAO‐24 for most parameters measured were significant after 2 wk of stress introduction at 200 and 250 mM NaCl. Salt stress at the lowest level (50 mM) reduced total leaf area by 35% and plant dry matter by 52%. At 25 d after salt stress, plants treated with the 250 mM NaCl accumulated 36‐fold more Na+, 79% more Ca2+, and 2.4‐fold less K+ than the control. Salt treatment resulted in the reduction of almost all the growth parameters and coincident increases in plant Na+ and Ca2+ concentrations. Our results indicate that there is great variability for salt tolerance among naked oat germplasms, and greater photosynthesis capacity, higher RGR, and relatively lower tissue Na+ accumulation at high salt concentrations appeared to be associated with salt tolerance in naked oats.
Pollen‐Based Screening of Soybean Genotypes for High Temperatures
Authors: Salem Mohammed A. , Kakani Vijaya Gopal , Koti Sailaja , Reddy K. Raja
Published: January 2007

Soybean [Glycine max (L.) Merr.] reproduction is sensitive to temperatures > 35°C. Two studies were conducted to determine temperature effects on soybean pollen germination (PG) and to detect genotypic differences. Pollen collected from 44 genotypes (Maturity Groups III to VI) grown outdoors was subjected to in vitro temperatures from 15 to 50°C at 5°C intervals. Genotypes differed significantly for in vitro PG percentage (mean of 81%) and tube length (mean of 437 μm). Mean cardinal temperatures (Tmin, Topt, and Tmax) were 13.2, 30.2, and 47.2°C for PG and 12.1, 36.1, and 47.0°C for pollen tube growth. Genotypes differed for leaf cell membrane thermostability (CMTS), but CMTS did not correlate with pollen parameters. Cumulative temperature response index, CTRI (unitless), of each genotype calculated as the sum of eight individual stress responses (ISRs) derived from maximum PG, maximum pollen tube length (PTL), and the maximum (Tmax), minimum (Tmin), and optimum (Topt) temperatures for PG and for PTLs was used to group genotypes for temperature tolerance. Heat‐tolerant genotype (DG 5630RR) was less sensitive to high temperature (38/30°C) compared with heat‐intermediate (PI 471938) and heat‐sensitive (Stalwart III) genotypes that had deformed pollen, with reduced apertures and collumellae heads. Hence, pollen can be used as a screening tool for heat tolerance. Most sensitive to temperature was D88‐5320 with a CTRI of 6.8, while AG 4403RR was most tolerant with a CTRI of 7.5. Elevated [CO2] did not modify reproductive parameters or CTRI. The study also revealed that heat tolerance of vegetative tissue had little or no relationship with the heat tolerance of reproductive tissue. Maturity groups lacked a specific trend for tolerance to high temperature. The identified high temperature‐tolerant genotypes and temperature‐dependent pollen response functions might be useful in soybean breeding and modeling programs, respectively.
Saint Genet: Actor and Martyr
Authors: Sartre Jean-Paul
Published: January 2007

Genet is related to that family of people who are nowadays referred to by the barbaric name of passéistes. An accident riveted him to a childhood memory, and this memory became sacred. In his early childhood, a liturgical drama was performed, a drama of which he was the officiant; he knew paradise and lost it, he was a child and was driven from his childhood. No doubt this “break” is not easy to localize. It shifts back and forth, at the dictate of his moods and myths, between the ages of ten and fifteen. But that is unimportant. What matters is that it exists and that he believes in it. His life is divided into two heterogeneous parts: before and after the sacred drama. Indeed, it is not unusual that the memory condenses into a single mythical moment the contingencies and perpetual re-beginnings of an individual history.
Image, Movement, and Actor: Restoration of Potentiality
Authors: Feldenkrais Moshe
Published: January 2007

Moshe Feldenkrais is a master in judo, holder of the Black Belt, and author of several books in this field. Dr. Feldenkrais is also an influential kinesthetic therapist and theorist. This exposition of Feldenkrais' ideas and techniques of movement-training is taken from two of his essays, “L'Expression Corporelle” and “Mind and Body.” This material is interspersed with selections from an interview with Feldenkrais by Richard and Helen Schechner in Tel-Aviv during June, 1965.

Feldenkrais uses “body-image” and “self-image” interchangeably; he claims that there is no valid distinction to be made between the “self” and the “mind/body.” I have followed his not-quite-arbitrary usage.

This exposition suffers, no doubt, from brevity. No attempt has been made to offer the available (and substantial) supporting demonstrations, argumentation, and data. Feldenkrais’ concerns and practice are clearly applicable to theatre training; and, although he does not allude to it here, he has worked with the Habima Theatre in Israel. Interested specialists may contact Dr. Feldenkrais directly. His address is: 49 Nachmani Street, Tel-Aviv, Israel.
Elementary Methods of Treatment of Circular, Hyperbolic and Elliptic Functions
Authors: Miller W.
Published: January 2007

In the traditional text-book presentation and evaluation of logarithmic, exponential, circular and hyperbolic functions there is a lack of uniformity of method, and the demands on the analytical powers of the average student are considerable, if not excessive It has been shown in The Mathematical Gazette of June, 1926, that logarithmic and exponential functions may readily be evaluated by ab initio arithmetical methods. Incidentally it may be noted that the theory of the method is independent of the theory of indices. The definition of loge a is virtually and leads to a simple assignment of meaning to irrational and imaginary powers of a number.
A Problem in Probability
Authors: Jackson C. S.
Published: January 2007

In the Greenwich meteorological observations, Table XIII, gives the excess of the arithmetic mean of the daily maximum and minimum over the true mean daily temperature for each day in the year.
A Graphic Solution of the Equation
Authors: Lodge A.
Published: January 2007

zn − pz + q = 0. .....(1)

The usual method of solution by means of a fixed curve and varying line is to draw the curve y = zn, and find where it is cut by the line y=pz − q.

The following method is quicker, and has some aspects of theoretic interest to recommend it. It consists in taking p, q as coordinates, and in drawing the curve given by the parametric equation

2

which is the condition that the given equation (1) shall have equal roots.
Probability and Statistics
Authors: Sheppard W. F.
Published: January 2007

Statistical method is coming to be so extensively applied, that those who use it must from time to time feel the need of assuring themselves as to the security of its foundations. For this assurance they will naturally turn to books on the subject. But do these give much help?
On Some Properties of the Epipedon
Authors: Watkin E. L.
Published: January 2007

The solid which is the three-dimensional analogue of the plane quadrilateral appears to have been neglected by geometers, possibly on account of the difficulty of visualising it adequately from a plane figure. A model, however, makes an interesting object and is readily constructed from thin stiff wire and thread. The extraordinary number of collinearities, which are its principal feature, then become at once obvious. For the benefit of any one who wishes to construct such a model I would suggest the desirability of commencing with the external diagonal triangle PQR and the line P′Q′R′ (see Figs. 1 and 2), as otherwise it is difficult to get a compact model.
Some Old Text-Books
Authors: Hooker J. H.
Published: January 2007

This product of Queen Anne’s reign consists of five parts: I. Arithmetick, Vulgar and Decimal. II. Algebra or Arithmetick in Species. III. The Elements of Geometry. IV. Conick Sections. V. The Arithmetick of Infinites explained, with its application to Superficial and Solid Geometry. To these is added an Appendix of Practical Gauging, and in the eighth edition is also found the History of Logarithms.
Extension of Some Definitions and Propositions in Euclid’s Book XI. And Remarks
Authors: Muirhead R. F.
Published: January 2007

Euclid does not define the inclination to one another, or the mutual perpendicularity of non-intersecting straight lines. (For brevity I shall omit the adjective straight before lines.)

The following definition is justified by the 10th Proposition of Bk. XI. Def. : The inclination of two non-intersecting lines to one another, or the “ angle between them ” is the angle between two intersecting straight lines which are parallel to them respectively.
Constructions in Geometry. What is Legitimate?
Authors: Godfrey C.
Published: January 2007

Construction. As we depart widely from Euclid’s ideas in the proofs of Stage B, it seems to be thought by many people that go-as-you-please methods are good enough for constructions as well. Now, “trial” methods of construction are sometimes useful in more advanced work ; but they are tolerated only when a geometrical method is impossible ; they are means to get a solution, but there is no instruction to be had from such a method. We would therefore urge that a certain severity be still maintained in problems of construction.
Summer Schools for Advanced Mathematical Study
Authors: Chapman Sydney
Published: January 2007

The following remarks are based on the assumption, which I believe to be a true one, that there is a desire for more advanced mathematical knowledge among many people in this country, such as those engaged in teaching mathematics in secondary schools, technological institutions, and colleges, as well as others not professionally associated with mathematics. At present the means of satisfying this desire, at least as regards organised courses of post-graduate study available for persons employed in teaching or otherwise, are almost entirely lacking in England. The most that is available, and that only in a few university centres, consists of occasional lectures given under the auspices of universities and such bodies as mathematical societies and branches of the Mathematical Association. Able and interesting as these lectures may be, the knowledge to be acquired from them must, in the nature of things, be somewhat disconnected and superficial. Their value lies in the introductory glimpse which they give of unfamiliar branches of study, or in their rapid survey of a wide field of knowledge. They are useful complements to more systematic study, but are not a substitute for it.
A First Chapter on Elliptic Functions
Authors: Elliott E. B.
Published: January 2007

There is, of course, nothing really new to be said about the elementary theory of the Elliptic Functions sn, cn, dn; but it may be not too late in the day for a didactic note on the existence and one-formedness of these functions to have some usefulness. One reason, and perhaps the chief one, why the older analysis has fallen into disfavour in the treatment of elliptic functions is the obscurity on the subject of one-formedness which prevails in so many presentations of the early parts of the theory. Halphen’s Fonctions Elliptiques is exceptionally valuable in that it neither avoids nor postpones the difficulty; but it is common for analysts who follow the older methods either to pass the matter over without proper emphasis, or to confess weakness by appealing to the ideas of the general theory of functions, thus encouraging a belief that the newer analysis is absolutely necessary for soundness.
The Approach to the Calculus
Authors: Picken D. K.
Published: January 2007

Now that the Infinitesimal Calculus is becoming part of regular school courses in Mathematics, the question of how the subject should be introduced takes on correspondingly increased importance. And the question is really of fundamental importance; for it is only when the average person, as distinguished from those of special aptitude for a subject, has to be considered, that we are driven back upon the necessity for a sound common-sense basis of theory. Recent articles in the Gazette are evidence of the growing interest in this question—discussion of the perennial issue of e being only a part of this wider inquiry.
The Stieltjes Integral in Harmonic Analysis
Authors: Burkill J. C.
Published: January 2007

The object of this paper is to exhibit the application of the Stieltjes integral to harmonic analysis.
The Slide Rule
Authors: Barrell F.R.
Published: January 2007

Having accepted with some mental reservation the assurance of the Editor of this Gazette that the Slide Rule, although invented by Gunter as far back as 1624, is still unknown to many mathematicians, the writer has ventured to make this article explanatory and descriptive. To such then as are unenlightened he offers the good news that half-a-guinea will purchase an instrument capable of multiplying and dividing, of squaring and cubing, of extracting square and cube roots, of solving triangles and performing rapidly many similar combinations of arithmetic and trigonometric operations, all without any mental effort and to an accuracy of from ⅕ to ⅓ %. To examiners having to reduce marks to percentages the Slide Rule is invaluable, to physicists it is indispensable, to engineers it is both invaluable and indispensable.
Some Isochordic Circles Related to the Triangle
Authors: Taylor W. W.
Published: January 2007

Taking ABC as the triangle of reference, with the usual notation for its sides and angles, let l = s − a, m = s− b, n = s − c. Let I, I1, I2, I3 be the centres of the inscribed and escribed circles DEF, D1E1F1, D2E2F2, D3E3F3.

Through A, B, C draw parallels to the opposite sides forming the triangle A1B1C1, so that AAl, BB1, CC1 are the medians of the triangle ABC, and there are then ten triangles like ABB1, ACB1, etc., of the same area.
Suggested Notation for Ratios and Cross-Ratios
Authors: Lodge Alfred
Published: January 2007

I wish to call attention to the value, for some purposes, ot the notation for the ratio ; and for the cross-ratio .

For instance: in Menelaus’ theorem for the property of a transversal meeting the sides of a triangle ABC in the points P, Q, R, the first mentioned notation makes the property shine out very clearly The equation in the form is

,

which conspicuously separates the points on the transversal from the angular points of the triangle.
Quadrature-Formulae in Relation to Moments
Authors: Sheppard W. F.
Published: January 2007

Writers on mensuration do not seem to call attention to the convenience of quadrature-formulae for determining positions of centres of gravity, magnitudes of moments of inertia, etc.
The Simple Pendulum
Authors: Greenhill G.
Published: January 2007

Mr. D.K. Picken has done well to direct attention to the unsatisfactory nature of the elementary discussion of the Simple Pendulum, current in the text-books.

What is usually passed off as a proof is a downright wicked deceit, and deserves the serious attention of the advocate of rigour, when he can spare time to look elsewhere, beyond a fundamental axiom or a convergency test.
Appeciative Remarks on the Theory of Groups
Authors: Miller G. A.
Published: January 2007

While it is clearly impossible for the average high school teacher of mathematics to become familiar with all the modern branches of this subject, it is desirable that he should not be totally ignorant of any extensive branch. The views of a number of eminent mathematicians often furnish one of the simplest as well as one of the most reliable introductions to the nature and the scope of a difficult subject. The following list of quotations has been prepared for the purpose of providing such an introduction for one subject. The list could easily be extended, but the variety and the standing of the mathematicians quoted are perhaps sufficient to inspire confidence. The qnotations are arranged chronologica1ly, beginning with 1892. several of them were published in the American Mathematical Monthly, volume x. 1903, p. 87
The Geometrical Treatment of Trigonometrical Series
Authors: Whipple F. J. W.
Published: January 2007

In the standard text-books on trigonometry the object of the authors is to reduce geometry to algebra, to give geometrical proofs of a few fundamental formulae and afterwards to develop the subject on algebraic lines. When alternative geometrical proofs are given they are not often designed to illustrate the steps in the algebra. De Morgan’s Double Algebra and Hayward’s Vector Algebra may be mentioned as works in which free use is made of geometry, but the emphasis laid on the interpretation of a vector as a complex quantity makes their method appear rather advanced. The slides which I shewed to the annual meeting were intended to illustrate the
The Scientific Results and Aims of Modern Applied Mechanics
Authors: Sommerfeld A.
Published: January 2007

It is very far from my purpose to construct an antithesis between a purely scientific and a technical conception of the Problem of Mechanics. The conflict which undoubtedly existed some years ago, and at times was waged with bitterness, has come to a satisfactory conclusion; and a generous appreciation of the two different directions of investigation has taken the place of unseemly strife. From my personal knowledge of the Technical High School in Aachen, I at least can lay stress on the fact that I have been encouraged in the most ready manner by my technical colleagues of all departments.
The Achievements of Great Britian in the Realm of Mathematics
Authors: Loria Gino
Published: January 2007

The inhabitants of the three kingdoms which constitute Great Britain did not come into contact with the civilisation of the ancient East. Nor, as far as we know, did they have the advantage of direct relations with the Greeks—that race, beloved of Nature, which succeeded in placing all the sciences and all the fundamental arts on so secure a basis as to defy for two thousand years any attempt at radical innovation.
A Geometrical Construction for a Cardioid
Authors: Piggott H. E.
Published: January 2007

One of the best-known examples of a caustic curve in Geometrical Optics is that obtained by reflection from the arc of a circle of rays emanating from a point on the circumference of the circle. The enveloping curve is known to be a cardioid. It has not, however, I think, been pointed out that the analysis •of this problem leads to a very simple construction from which a cardioid •can be rapidly and accurately drawn.
Comparison Between Rhumb-Line and Great-Circle Courses
Authors: Heawood P. J.
Published: January 2007

IT is well known that, while the shortest course between two points on a sphere is a great circle, the course which is easiest for navigation is a rhumb line, i.e. a course which cuts all the successive meridians at the same angle, so that the ship always steers in a direction making an angle of the same number of degrees with due north or due south. Such a course is represented by a straight line on a Mercator’s chart, which thus makes it appear more direct than it really is. On a great circle, though the course is the shortest, you are (except on the equator or a meridian) continually altering your direction as measured by the angle which it makes with the north. Between any two points there is thus a difference in favour of great-circle sailing; but to demonstrate rigorously the greatest value which this difference can possibly take is a somewhat difficult and attractive mathematical problem. I have heard it stated that it is not susceptible of rigorous mathematical treatment. The following is suggested as giving a complete solution of the question: it would be interesting to learn whether any shorter or more direct method is available, which makes no unwarranted assumption. For the abstract treatment of the problem (though indeed in the Pacific or the Southern Ocean fairly extended courses are practically available) we suppose the globe cleared of all such inconvenient encumbrances as continents or islands: moreover, we treat it as a perfect sphere; and to word the question more exactly we should say: Find two points such that the difference between the shortest great-circle course and the shortest rhumb-line course joining them is a maximum; for the great circle through two points will (in general) consist of a major and a minor arc, and on the other hand a rhumb line might start the longer way round the earth, or indeed make any number of revolutions about the pole before reaching its objective. In either case it is the shortest course of the kind with which we deal.
That Pure and Applied Mathematics Ought to be Taught and Developed Pari Passu in Boys’ Secondary Schools
Authors: Dakin A.
Published: January 2007

It is now a commonplace of History, that Pure Mathematics had its origin in the practical needs of man, and that at intervals it has renewed its vitality by turning to its practical application. It has, during recent years, become increasingly recognised that the bases of mathematical education are the concrete and the practical; and this Association, by the Reports and Papers published in the Gazette, has emphasised the view that “the utilitarian aspect and application of Mathematics should receive a due share of attention in the mathematical course.” This increasing respect for the concrete and practical has not only led to considerable changes in the teaching of Arithmetic, Geometry and Algebra, but has brought into the Schools closer co-operation between the teachers of Mathematics and Science, and has resulted in a very desirable correlation of the syllabuses in these subjects.
Mechanical Similitude
Authors: Greenhill G.
Published: January 2007

After Geometrical Similitude has been retained by making two structures, animal, machine, or steamship, from the same drawing but to a different scale, there is still the remaining variable of the material of construction to be taken into account ; and a further question arises of the Mechanical Similitude in a calculation of the relative velocity and stress in the parts.

The first statement of the problem is to be found in the Principia, Book II, Section VII, Prop. XXXII, Theorem XXVI.

In its application to the steamship the principle goes by the name of Froude's Law; it is applied to infer the performance of the full size steamer by calculation on the record of the model in the experimental tank.
Discussion on the Report on the Teaching of Arithmetic: II The Syllabus in detail (p. 235)
Authors: Greenhill G.
Published: January 2007

Farming is still an important industry in England, although neglected and depressed by comparison with Manufacture and Navigation ; so it is useful still to teach the old agricultural units, mile, furlong, chain, perch, acre, rood, . . inherited from earliest civilisation through the Roman and Greek, and based on physical unchangeable qualities, nob likely to be displaced by an artificial Metric System.

Consult the lecture to the Society of Arts, December 1915, by Sir Charles M. Watson, on The Origin of the English Measures of Length, and Herodotus Ii 149 on Greek Measures.

But it is surprising no mention is made in the Report of the geographical units employed universally by the sailor of all countries, based on the measurement of the Earth, and the 24 hours of the day.

In these units there is never mention of the diameter or radius of the Earth, or of the military land-mile. The day being divided into 24 hours, and the equator also, longitude is reckoned in hours, each of 15 degrees or 60 minutes of time on the chronometer, and the degree is divided into 60 minutes of angle or 15 seconds of time. The length along the equator or a meridian of one minute of angle is then made the geographical sea-mile, le mille marin.
Mathematical Clubs in Schools.
Authors: Brown I. M.
Published: January 2007

I Think that everyone here will agree with me that we, who try to teach mathematics, have a heavily loaded curriculum and we are apt to become the slaves of public examinations. According to the age of our pupils, Intermediate or Matriculation hangs like the sword of Damocles above us, and we dare not be led far astray from the mark-gaining part of our work.
On the Teaching and Applications of Dynamics
Authors: Gray A.
Published: January 2007

I am not going to inflict a sermon on you; but if I had to give out a text for my discourse I should, I think, choose the words, “The letter killeth, the spirit maketh alive.” This is a very general truth, but it seems to me to have special force in connection with dynamical science. I shall leave the application to be traced by yourselves as I proceed.