Cycle Index Research Articles

Product action

This paper studies the cycle indices of products of permutation groups. The main focus is on the product action of the direct product of permutation groups. The number of orbits of the product on n-tuples is trivial to compute from the numbers of orbits of the factors; on the other hand, computing the cycle index of the product is more intricate. Reconciling the two computations leads to some interesting questions about formal power series. We also discuss what happens for infinite (oligomorphic) groups and give detailed examples. Finally, we briefly turn our attention to generalised wreath products, which are a common generalisation of both the direct product with the product action and the wreath product with the imprimitive action.

Prevention of changes in airway function facilitates Strongyloides venezuelensis infection in rats

Alterations in lung function and pulmonary symptoms have been described in patients infected with helminths with a lung cycle. We have previously shown that infection with the nematode Strongyloides venezuelensis induced a significant increase in airway hyperreactivity in infected rats. The aim of the present study was to test the hypothesis that bronchodilation during the lung phase of parasite migration would favor completion of the life cycle and infection indices. For this purpose, S. venezuelensis infected rats were treated with salbutamol during the first 48 h after the nematode infection. At the dose used (0.25 mg/mL for 10 min every 4 h), treatment with salbutamol prevented changes in lung function during the parasite migration. This was accompanied by a significant increase in parasite burden, as assessed in the lung and the small intestine. Parasite infected and salbutamol-treated animals also showed a significant increase in concentration of IL-10 and IL-4 in homogenates of lungs during the worm migration that was followed by stronger lung eosinophilic inflammation at 5 dpi, after the larvae had left the host lung. Our data indicates that airway hyperactivity reduce parasite progression through the lung, facilitating the action of innate or adaptive immune mechanisms.

Combinatorial enumeration of three-dimensional trees as stereochemical models of alkanes: an approach based on Fujita’s proligand method and dual recognition as uninuclear and binuclear promolecules

Three-dimensional (3D) trees, which are defined as a 3D extension of trees, are enumerated by Fujita’s proligand method (Fujita, Theor. Chem. Acc. 113 (2005) 73–79 and 80–86; 115 (2006) 37–53). Such 3D-trees are dually recognized as uninuclear promolecules and as binuclear ones. The 3D-trees regarded as uninuclear promolecules are enumerated to give the gross number of 3D-trees, which suffers from redundancy due to contaminants. To evaluate the number of such contaminants, the 3D-trees are alternatively enumerated as binuclear promolecules. Cycle indices with chirality fittingness (CI-CFs) composed of three kinds of sphericity indices (SIs), i.e., a d for homospheric cycles, c d for enantiospheric cycles, and b d for hemispheric cycles are obtained for evaluating promolecules of the two kinds. The CI-CFs for the uninuclear promolecules and those for the related binuclear promolecules are compared in terms of the dichotomy between balanced 3D-trees and unbalanced 3D-trees. Thereby, the redundancy due to such contaminants is deleted effectively so as to give the net number of 3D-trees. The validity of this procedure is proved in three ways, all of which are based on the respective modes of the correspondence between uninuclear promolecules and binuclear ones. In order to enumerate 3D-trees by following this procedure, the CI-CFs are converted into functional equations by substituting the SIs for a(x d ), c(x d ), and b(x d ). Thereby, the numbers of 3D-trees or equivalently those of alkanes as stereoisomers are calculated under various conditions and collected up to 20 carbon content in a tabular form. Now, the stereochemical problems (on the number of stereoisomers) by van’t Hoff (van’t~Hoff, Arch. Neerlandaises des Sci. Exactes et Nat, 9 (1874) 445–454”) and by LeBel (LeBel, Bull. Soc. Chim. Fr. (2), 22 (1874) 337–347) and the enumeration problems (on the number of trees) by Cayley (Cayley, Philos. Mag. 47 (1874) 444–446), both initiated in the 1870s, have been solved in a common theoretical framework, which satisfies both chemical and mathematical requirements.

Numbers of Monosubstituted Alkanes as Stereoisomers

Monosubstituted alkanes as stereoisomers, not as constitutional isomers, are regarded as planted three-dimensional (3D) trees, which are defined as a 3D extension of planted trees (graphs). They are thus recognized as 3D-objects (planted promolecules) and enumerated by Fujita's proligand method (Fujita S (2005) Theor. Chem. Acc. 113:73–79, 113:80–86, Fujita S (2006) Theor. Chem. Acc. 115:37–53). By starting from three kinds of sphericity indices, i.e., ad for homospheric cycles, cd for enantiospheric cycles, and bd for hemispheric cycles, cycle indices with chirality fittingness (CI-CFs) are obtained to enumerate planted 3D-trees or equivalently monosubstituted alkanes as stereoisomers. Functional equations a(x), c(x2), and b(x) for recursive calculations are derived from the CI-CFs and programmed in three ways by means of the Maple programming language. The three recursive procedures for calculating the numbers of planted 3D-trees are executed to give identical results, which are collected up to 100 carbon content in a tabular form. The results are compared with the enumeration of planted trees (as graphs).

Crioconservação em sementes de cebola

O presente trabalho teve como objetivo avaliar os efeitos de diferentes técnicas de crioconservação na qualidade fisiológica, composição química e índice mitótico de sementes de cebola. Sementes de cebola, cultivar Baia Periforme, foram expostas, durante uma hora, a duas técnicas de crioconservação: (a) sem e (b) com crioprotetor (glicerol 50%), seguidas de três métodos de descongelamento: (1) temperatura ambiente de 25°C, durante duas horas; (2) banho-maria a 37°C, durante cinco minutos; (3) microondas em potência de 70W, durante cinco minutos. Antes e após a crioconservação, foram realizadas as seguintes avaliações: teor de água, germinação, vigor (envelhecimento acelerado, primeira contagem de germinação e comprimento de raiz e de parte aérea das plântulas), composição química (teor de açúcar solúvel, proteínas e amido), análise do ciclo celular e índice mitótico. A imersão em nitrogênio líquido, sem o uso de crioprotetor, é uma técnica adequada para a crioconservação de sementes de cebola, não altera a percentagem de germinação e a composição química das sementes, sendo também o tratamento que proporciona maior número de células em divisão celular após o descongelamento das sementes. O tratamento criogênico, com uso de glicerol 50% como crioprotetor, é prejudicial à qualidade fisiológica e altera a composição química de sementes de cebola. O descongelamento das sementes em microondas é mais adequado do que em temperatura ambiente ou banho-maria, porém este último possibilita maior índice mitótico que os demais tratamentos.

On an Identity for the Cycle Indices of Rooted Tree Automorphism Groups

This note deals with a formula due to G. Labelle for the summed cycle indices of all rooted trees, which resembles the well-known formula for the cycle index of the symmetric group in some way. An elementary proof is provided as well as some immediate corollaries and applications, in particular a new application to the enumeration of $k$-decomposable trees. A tree is called $k$-decomposable in this context if it has a spanning forest whose components are all of size $k$.

Modeling of Three-Phase Uniform Symmetrical Sampling Digital PWM for Power Converter

A mathematical approach of modeling and analyzing three-phase pulsewidth modulation (PWM) is presented. The three-phase flyback converter required a unique pattern of PWM to optimize the power transfer in the magnetic circuit used in the converter. The three-phase PWM is generated digitally based on uniform symmetrical sampling technique using Xilinx chip. The generated PWM pattern is able to reduce the magnitude of the low order of harmonic components present in the input ac supply. Although software simulation could simulate the PWM pattern, it does not represent the exact pattern as being generated digitally. The mathematical approach used is to model the PWM pattern exactly as being created digitally. The proposed mathematical technique could also be used to analyze any digital PWM. The result of the mathematical analysis on the PWM pattern could be used to study the characteristics of the pattern such as maximum and minimum value of duty cycle, pulsewidth, turn-on time, turn-off time, and modulation index. To verify the validity of the proposed technique, the results obtained from the mathematical model, experimental, and simulation using PSpice were compared

Graphs to chemical structures. 4: Combinatorial enumeration of planted three-dimensional trees as stereochemical models of monosubstituted alkanes

Planted three-dimensional (3D) trees, which are defined as a 3D version of planted trees, are enumerated by means of Fujita’s proligand method formulated in Parts 1–3 of this series [Fujita in Theor Chem Acc 113:73–79, 80–86, 2005; Fujita in Theor Chem Acc 115:37–53, 2006]. By starting from the concepts of proligand and promolecule introduced previously [Fujita in Tetrahedron 47:31–46, 1991], a planted promolecule is defined as a 3D object in which the substitution positions of a given 3D skeleton are occupied by a root and proligands. Then, such planted promolecules are introduced as models of planted 3D-trees. Because each of the proligands in a given planted promolecule is regarded as another intermediate planted promolecule in a nested fashion, the given planted promolecule is recursively constructed by a set of such intermediates planted promolecules. The recursive nature of such intermediate planted promolecules is used to derive generating functions for enumerating planted promolecules or planted 3D-trees. The generating functions are based on cycle indices with chirality fittingness (CI-CFs), which are composed of three kinds of sphericity indices (SIs), i.e., a d for homospheric cycles, c d for enantiospheric cycles, and b d for hemispheric cycles. For the purpose of evaluating c d recursively, the concept of diploid is proposed, where the nested nature of c d is demonstrated clearly. The SIs are applied to derive functional equations for recursive calculations, i.e., a(x), c(x 2), and b(x). Thereby, planted 3D-trees or equivalently monosubstituted alkanes as stereoisomers are enumerated recursively by counting planted promolecules. The resulting values are collected up to 20 carbon content in a tabular form. Now, the enumeration problem initiated by mathematician Cayley [Philos Mag 47(4):444–446, 1874] has been solved in such a systematic and integrated manner as satisfying both mathematical and chemical requirements.

Graphs to chemical structures 5. Combinatorial enumeration of centroidal and bicentroidal three-dimensional trees as stereochemical models of alkanes

Three-dimensional trees (3D-trees), which are defined as a 3D version of trees, are enumerated by Fujita’s proligand method formulated in Part 1 to Part 3 of this series (Fujita in Theor Chem Acc 113:73–79, 113:80–86, 2005; 115:37–53, 2006). Such 3D-trees are classified into centroidal and bicentroidal 3D-trees, which correspond to respective promolecules having proligands as substituents. In order to enumerate such centroidal and bicentroidal 3D-trees, cycle indices with chirality fittingness (CI-CFs) are formulated as being composed of three kinds of sphericity indices, i.e., ad for homospheric cycles, cd for enantiospheric cycles, and bd for hemispheric cycles. The CI–CFs are capable of giving itemized results with respect to chiral and achiral 3D-trees so that they are applied to derive functional equations (a(x), c(x2), and b(x)). The generating functions of planted 3D-trees, which are formulated and calculated elsewhere, are introduced into such functional equations. Thereby, the numbers of 3D-trees or equivalently those of alkanes as stereoisomers are calculated and collected up to a carbon content of 20 in a tabular form. Now, the enumeration problem initiated by a mathematician Cayley (Philos Mag 47(4):444–446, 1874) has been solved in such a systematic and integrated manner as satisfying both mathematical and chemical requirements.

Biological implications of the inhibition of survivin by RNA interference in human androgen-independent prostate carcinoma with highly metastatic potential

To determine the expression level of survivin in androgen-independent prostate carcinoma, and to investigate the biological role of survivin in invasion and metastasis of androgen-independent prostate carcinoma. Highly metastatic prostatic cancer cell line PC-3M-1E8 was stably transfected with pSilencer plasmid targeting survivin expression by RNA interference. The biological effects were observed, including anchorage-independent growth, in vitro invasion by soft agar colony formation and Boyden chamber assay, and also in vivo tumorigenesis in nude mice. Cell cycle and apoptosis indices were evaluated by flow cytometry and Western blot analysis of bioactive fragments of caspase 3. The expression of survivin in transfected PC-3M-1E8 cells was markedly depressed at both mRNA and protein levels (about 78% to 80%) as compared with control. The growth of tumor cells was retarded by anchorage-independent growth assay. The survivin transfectants formed smaller and fewer colonies (14.33 +/- 3.51) than the negative (52.33 +/- 6.81) and blank controls (54.00 +/- 6.00). Inhibition of survivin expression was correlated with enhanced apoptosis of tumor cells (percentages of apoptotic cells of the negative control, blank control and experimental groups were 5.88 +/- 0.99, 6.97 +/- 1.60, 16.40 +/- 1.95 respectively), along with an increased expression of activated caspase 3, and cell cycle inhibition at G(0)/G(1) phase (the relative number of cells at G(0)/G(1) phase were 43.65 +/- 3.44, 43.59 +/- 1.83 and 52.71 +/- 1.10, respectively). In addition, multinucleated giant cells were observed along with a marked inhibition of invasion as reflected by fewer penetrating cells by Boyden chamber assay (46.07 +/- 9.97, 47.87 +/- 9.58 and 38.67 +/- 6.59, respectively). Survivin expression is high in androgen-independent prostate cancer cells and likely may be related to the apoptosis, growth and invasion of the tumor cells. Targeting the survivin pathway by RNA interference appears to be a promising approach for clinical treatment of androgen-independent prostate cancer.

Experimental study on lung injury and cell cycle changes in mice induced by bitumen fume

To investigate the carcinogenic and mutagenic mechanism of bitumen fume. The experimental mice were forced to inhale the bitumen fume at different exposure level (55 mg/m(3), 165 mg/m(3)) and in different time (30 days, 60 days). The pathological changes of the lung tissue in mice were observed with H.E staining. The content of the DNA in the lung tissue of mice and the cell circles were determined with flow cytometry. The lesion of the lung tissue in mice comprised the atypical hyperplasia of different levels and the carcinoma in situ with the increase of the containment time and dosage; the cycle index was changed: the number of the G 1 phase cells was decreased, the S phase was retarded, the cells entering the G 2/S phase were decreased, the cell proliferation index (P I) was increased and the heteroploid DNA index (DI) was increased (P < 0.05). The cell index in the 55 mg/m(3) group and the 165 mg/m(3) group was higher than that in the control group when the containment time was same. The heteroploid DNA index (DI) in the 55 mg/m(3) group was significantly higher than that in the 165 mg/m(3) group (P < 0.05 or P < 0.01). When the containment dosage was same, the DI in the 60 days treatment group (1.16 +/- 1.51 x 10(-2), 1.20 +/- 2.3 x 10(-2)) was all significantly higher than those in the 30 days treatment group (1.14 +/- 8.8 x 10(-2), 1.16 +/- 1.47 x 10(-2)) (P < 0.05). The precancerous lesion in the lung tissue of the mice induced by the bitumen fume may be related with the changes of the cell cycle.

Sphericities of Double Cosets, Double Coset Representations, and Fujita’s Proligand Method for Combinatorial Enumeration of Stereoisomers

The concepts of double coset representations and sphericities of double cosets are proposed to characterize stereoisomerism, where double cosets are classified into three types, i.e., homospheric double cosets, enantiospheric double cosets, or hemispheric double cosets. They determine modes of substitutions (i.e., chirality fittingness), where homospheric double cosets permit achiral ligands only; enantiospheric ones permit achiral ligands or enantiomeric pairs; and hemispheric ones permit achiral and chiral ligands. The sphericities of double cosets are linked to the sphericities of cycles which are ascribed to right coset representations. Thus, each cycle is assigned to the corresponding sphericity index (a d , c d , or b d ) so as to construct a cycle indices with chirality fittingness (CI-CFs). The resulting CI-CFs are proved to be identical with CI-CFs introduced in Fujita’s proligand method (S. Fujita, Theor. Chem. Acc. 113 (2005) 73–79 and 80–86). The versatility of the CI-CFs in combinatorial enumeration of stereoisomers is demonstrated by using methane derivatives as examples, where the numbers of achiral plus chiral stereoisomers, those of achiral stereoisomers, and those of chiral stereoisomers are calculated separately by means of respective generating functions.

Infertility, Ovulation Induction Treatments and the Incidence of Breast Cancer—a Historical Prospective Cohort of Israeli Women

Ovulation induction drugs may be associated with increased breast cancer risk. Results so far have been inconclusive. To evaluate the association between infertility, exposure to ovulation induction drugs and the incidence of breast cancer. Historical prospective cohort and nested case-control study. Institutional practice About 5,788 women attending five infertility centers in Israel between 1964 and 1984. Abstracting of medical records and telephone interviews. Breast cancer incidence was determined through linkage with the National Cancer Registry database. Standardized incidence ratios (SIRs) and 95% confidence intervals were computed by comparing the observed to the expected cancer rates in the general population. In addition, a nested case-control study within the cohort was performed with interviews of breast cancer cases and two matched controls. The study cohort included 120,895 women years of follow-up. Compared to 115.2 expected breast cancer cases, 131 cases were observed (SIR = 1.1; 95% CI 0.9-1.4). Risk for breast cancer was significantly higher for women treated with clomiphene citrate (SIR = 1.4; 95% CI 1.0-1.8). Similar results were noted when comparisons were carried out between treated and untreated women, and when multivariate models were applied. In the nested case-control study, higher cycle index (OR = 2.2; 95% CI 1.0-4.8) and treatment with clomiphene citrate (OR=2.7; 95% CI 1.3-5.7) were associated with higher risk for breast cancer. Infertility and usage of infertility drugs in general are not associated with increased risk for breast cancer. However, for infertile women treated with clomiphene citrate, breast cancer risk is elevated.

A Statistical Study of Transequatorial Loops

We identify 356 transequatorial loops (TLs) from the data set of Yohkoh Soft X-Ray Telescope (SXT) in the period of solar cycles 22 and 23. The classification of the TLs can be made on two bases. One is according to the magnetic polarities of the footpoints of TLs, and the other is according to the number of TLs in the same region. Based on the first criterion, TLs fall into two categories: PTLs in which the magnetic polarities of the footpoints are the same as the preceding polarities and FTLs in which the footpoint polarities are the same as the following polarities of active regions, respectively. It is found that PTLs have a preference; about 66% of the TLs are PTLs, and this preference of PTLs is independent of the solar cycle. The percentage of FTLs is about 34%. Based on the second criterion, TLs are also divided into two categories: the number of TLs in a region is either single (STLs) or multiple (MTLs). In addition, we find that the number of TLs, PTLs, and FTLs have good correlations with solar cycle indices. By comparing the number of TLs and the number of active regions in each year, we obtain the ratio between them. The separation of footpoints and their yearly variations are calculated, and we find that our result is consistent with sporer's law.

Cycle index methods for finite groups of orthogonal type in odd characteristic

This is the third in a series of papers whose object is to show how cycle index methods for finite classical groups, developed by Fulman [Jason Fulman. Cycle indices for the classical groups. J. Group Theory2 (1999), 251–289.], may be extended to other almost simple groups of classical type. In [John R. Britnell. Cyclic, separable and semisimple transformations in the special unitary groups over a finite field. J. Group Theory9 (2006), 547–569.] we treated the special unitary groups, and in [John R. Britnell. Cyclic, separable and semisimple transformations in the finite conformal groups. J. Group Theory9 (2006), 571–601.] the general symplectic and general orthogonal groups. In this paper we shall treat various subgroups of the general orthogonal group over a field of odd characteristic. We shall focus at first on Ω± (d, q), the commutator subgroup of Ο±(d, q). Subsequently we shall look at groups G in the range

Cyclic, separable and semisimple transformations in the special unitary groups over a finite field

Let A be a linear transformation with minimum polynomial mA(t) and characteristic polynomial cA(t). We say that A is cyclic if mA(t) = cA(t), semisimple if mA(t) has no repeated factors, and separable if it is both cyclic and semisimple. The proportions of elements of GL(d, q) which are cyclic or separable have been investigated by, amongst others, Neumann and Praeger [7], Wall [10], and Fulman [4] who also studies semisimple elements. Making use of their results, we gave estimates in [1] for these proportions in SL(d, q). Fulman, Neumann and Praeger [5] have recently found good estimates for the corresponding proportions in the finite classical groups, U(d, q2), Sp(2m, q) and O±(d, q). They raise the question of whether similar methods may be used to calculate the proportions in various subgroups and supergroups of the classical groups. In a series of three papers, we shall show how this may be done. In this, the first paper, we deal with the special unitary groups SU(d, q2), consisting of unitary transformations with determinant 1. In the second paper [2] we shall focus on the conformal groups GSp(2m, q) and GO±(d, q), and in the third paper [3] we shall consider how the method may be extended to a number of groups of orthogonal type, including the special orthogonal group and the derived group of the orthogonal group. Our method in [1] involved the vector space cycle index of Kung [6] and Stong [8], which we describe briefly in Section 2. Similarly, in the current series

Common Factors in Latin America's Business Cycles

This paper constructs new business cycle indices for Argentina, Brazil, Chile, and Mexico based on common dynamic factors extracted from a comprehensive set of sectoral output, external data, and fiscal and financial variables spanning over a century. The constructed indices are used to derive a business cycle chronology for these countries and characterize a set of new stylized facts. In particular, we show that all four countries have historically displayed a striking combination of high business cycle and persistence relative to benchmark countries, and that such volatility has been time-varying, with important differences across policy regimes. We also uncover a sizeable common factor across the four economies which has greatly limited scope for regional risk sharing.

東京都都有施設における環境配慮型建築の環境・コスト評価システムの開発(環境工学)

In response to amplifying the problems of global environment, the municipality has been expected to take integrated countermeasure to contribute to building of a sustainable society. Tokyo metropolitan government draws up the guideline of government building planning to design the building considering the environment. This paper introduces a developed evaluating system in order to confirm consideration level of guideline by calculating some life cycle indices and grading a casbee tool. We can analyze the effect of reduction CO_2, emission and cost-benefit on public facilities, public high school and public hospital by adoption of environmental technologies by using the indices.

Graph Theory for Fused Cubic Clusters of Water Dodecamer

The stable structures of the fused cubic water cluster (H2O)12 are examined using graph theoretical techniques and ab initio calculations. The calculations are obtained by scanning the symmetry of digraph structures of hydrogen-bond network spanning 12 oxygen atom vertexes. Using the Pólya theorem the cycle index expressions for 12 vertexes and 20 edges of a cuboid in point-group symmetry D(4h) are developed. A total of 91 energy-allowed fused cubic structures are obtained, which are classified by 8 point-group symmetries: 1 D(2h), 2 S4, 5 C4, 1 D2, 11 C2, 10 C(i), 1 C(s), and 60 C1. An energy level diagram of the structures reveals 14 bands that correspond to 14 unique two-colored graphs derived from the distributions of four free hydrogens of the cluster.

Life cycle of remanufactured engines

The life cycle index of remanufactured engines was assessed by using the method of life cycle assessment (LCA). A remanufactured engine of a certain domestic brand was taken as researching object. Engine reproducing engineering was investigated from three aspects which were energy, material and environment. The application of LCA on remanufacturing engines was discussed in detail with a practical case. The results indicate that remanufacturing an engine can save 55 kg steels, 8.3 kg aluminum and 113 kW · h electric powers and reduce emissions of 565 kg CO2, 6.09 kg CO, 1.01 kg NOx, 3.985 kg SOx and 288.725 kg solid waste. The remanufacturing of engines possesses great economic value and practicability.