Prime Index Research Articles

Elements with prime and small indices in bicyclic biquadratic number fields

We give necessary and sufficient conditions for the existence of primitive algebraic integers with index A in totally complex bicyclic biquadratic number fields where A is an odd prime or a positive rational integer at most 10. We also determine all these elements and prove that there are infinitely many totally complex bicyclic biquadratic number fields containing elements with index A.

Prime Power Indices in Factorised Groups

Let the group $G = AB$ be the product of the subgroups $A$ and $B$. We determine some structural properties of $G$ when the $p$-elements in $A\cup B$ have prime power indices in $G$, for some prime $p$. More generally, we also consider the case that all prime power order elements in $A\cup B$ have prime power indices in $G$. In particular, when $G = A = B$ we obtain as a consequence some known results.

Normal subgroups in limit groups of prime index

Abstract Motivated by their study of pro-p limit groups, D. H. Kochloukova and P. A. Zalesskii formulated in [15, Remark after Theorem 3.3] a question concerning the minimum number of generators d ⁢ ( N ) {d(N)} of a normal subgroup N of prime index p in a non-abelian limit group G (see Question*). It is shown that the analogous question for the rational rank has an affirmative answer (see Theorem A). From this result one may conclude that the original question of Kochloukova and Zalesskii has an affirmative answer if the abelianization G ab {G^{\mathrm{ab}}} of G is torsion free and d ⁢ ( G ) = d ⁢ ( G ab ) {d(G)=d(G^{\mathrm{ab}})} (see Corollary B), or if G is a special kind of one-relator group (see Theorem D).

The role of lipid peroxidation and myeloperoxidase in priming a respiratory burst in neutrophils under the action of combined constant and alternating magnetic fields

The enhancement of lipid peroxidation in neutrophils (the content of malonic dialdehyde increased by 10.2%) has been shown after a 1-h exposure to a combined constant (42 μT) magnetic field and a weak low-frequency magnetic field (1.0, 4.4, and 16.5 Hz; 860 nT) collinear to it. No correlation was found between this effect and the process of functional pre-activation (priming) of neutrophils as a result of the combined action of magnetic fields detected by chemiluminescence enhancement in response to the introduction of the bacterial peptide N-formyl–Met–Leu–Phe in the presence of luminol, since ionol (10 μM), an inhibitor of lipid peroxidation, did not reduce the neutrophil priming index in this case. Preliminary addition of histidine (0.1 and 1.0 mM), a singlet oxygen scavenger, also did not decrease the priming index. A myeloperoxidase inhibitor, sodium azide (0.1 mM), exerted a significant inhibitory effect on the chemiluminescence intensity of the neutrophil suspension; priming did not develop in the presence of this inhibitor after the action of combined magnetic fields.

A note on finite groups with the indice of some maximal subgroups being primes

‎The Theorem 12 in [A note on‎ ‎$p$-nilpotence and solvability of finite groups‎, ‎J‎. ‎Algebra 321‎ ‎(2009) 1555--1560.] investigated the non-abelian simple groups in‎ ‎which some maximal subgroups have primes indices‎. ‎In this note we‎ ‎show that this result can be applied to prove that the finite groups‎ ‎in which every non-nilpotent maximal subgroup has prime index are‎ ‎solvable‎.

The dynamical zeta function for commuting automorphisms of zero-dimensional groups

For a $\mathbb{Z}^{d}$-action $\unicode[STIX]{x1D6FC}$ by commuting homeomorphisms of a compact metric space, Lind introduced a dynamical zeta function that generalizes the dynamical zeta function of a single transformation. In this article, we investigate this function when $\unicode[STIX]{x1D6FC}$ is generated by continuous automorphisms of a compact abelian zero-dimensional group. We address Lind’s conjecture concerning the existence of a natural boundary for the zeta function and prove this for two significant classes of actions, including both zero entropy and positive entropy examples. The finer structure of the periodic point counting function is also examined and, in the zero entropy case, we show how this may be severely restricted for subgroups of prime index in $\mathbb{Z}^{d}$. We also consider a related open problem concerning the appearance of a natural boundary for the dynamical zeta function of a single automorphism, giving further weight to the Pólya–Carlson dichotomy proposed by Bell and the authors.

An evidence-based analysis of the National Lipid Association recommendations concerning non-HDL-C and apoB

The National Lipid Association (NLA) selected non-HDL-C as its prime index of the cardiovascular risk associated with the apoB lipoproteins. ApoB was recommended only as an optional secondary target after low-density lipoprotein cholesterol (LDL-C) and non-high-density lipoprotein cholesterol (HDL-C) targets were achieved. The aims of this analysis were to determine whether (1) all relevant uses of apoB were considered by the NLA; (2) all the relevant evidence was considered by the NLA panel; and (3) all the evidence that was considered was interpreted correctly. (1) The utility of apoB in the diagnosis of the atherogenic dyslipoproteinemias was not considered. (2) All the relevant observational studies were not identified, and some that were cited were incorrectly interpreted. In particular, an equal hazard ratio for two markers in a group does not mean they will predict risk equally in individuals within the group in whom they are discordant. This matters because discordance analysis consistently demonstrates apoB and LDL particle number are more accurate measures of cardiovascular risk than LDL-C/non-HDL-C. (3) The target levels of apoB selected by the NLA are too high relative to the levels selected for LDL-C and non-HDL-C. The review of the evidence by the NLA was incomplete. More complete examination of the evidence indicates that apoB is a more accurate marker of cardiovascular risk than non-HDL-C and that the practice of lipidology would be improved by inclusion of apoB along with lipoprotein lipids in routine clinical care.

Genetic diversity analysis and redundant identification in 48 core collections of Zingiber officinale Rosc. (Zingiberaceae)

Ginger (Zingiber officinale Rosc.) rhizome has great demand in food and pharmaceutical industry. Odisha is the second largest ginger-cultivating state, and considered as best suitable after Kerala, in India. Forty-eight germplasm from 10 agro-climatic zones of Odisha were genetically characterized and potential duplicates were identified employing 25 polymorphic markers (RAPD, ISSR, SSR). These markers together amplified 170 polymorphic, 136 monomorphic, and 2 unique bands. SSR markers were the most efficient in generating highest primer resolving power (44.85), primer index (10.28), and number of polymorphic bands (67). Genotype–environment interaction was clearly demonstrated from UPGMA dendrogram based on Jaccard’s similarity coefficients and SAHN clustering which divided 48 samples into 8 sub-clusters (showing 80 % congruence with their places of geographical origin). H (0.211), I (0.38), and Gst (0.239) indices revealed genetic diversity within and genetic differentiation among 10 populations. AMOVA showed higher genetic variability among populations (64 %) than within populations (36 %). Ginger accessions having a mean genetic distance less than 0.21 (threshold average genetic distance) were considered redundant. Forty-eight samples could be reduced to 11 genetically diverse groups (each group contains duplicates but is different from each other) which confirmed 77 % of the collection to be redundant. Identification of duplicates can be useful to eliminate confusion regarding synonyms among farmers, help selection of suitable ginger seed material, and facilitate judicious management of germplasm in conservatory. Genetic diversity analysis unraveled the scope of genetic improvement and breeding program. Clustering analysis showed grouping of majority of samples to respective agro-climatic zones and established the possible interaction between genotype and environment.

A Sufficient Condition for Subgroups with Prime Indices to Be Normal

SummaryWe extend two group theory exercises to determine a necessary condition for a prime index finite subgroup to be normal.

Individual differences in the cortisol-awakening response during the first two years of shift work: A longitudinal study in novice police officers

Cortisol acts as a critical biological intermediary through which chronic stressors like shift work impact upon multiple physiological, neuro-endocrine and hormonal functions. Therefore, the cortisol awakening response (CAR) is suggested as a prime index of shift work tolerance. Repeated assessments of the CAR (calculated as MnInc) in a group of 25 young novice police officers showed that in the interval between about 4 and 14 months after transitioning from regular day work to rotating shift work, mean values began to rise from baseline to significantly higher levels at about 14 months after they commenced shift work. Visual inspection of the individual trends revealed that a subgroup of 10 subjects followed a monotonically rising trend, whereas another 14 subjects, after an initial rise from about 4–14 months, reverted to a smaller, baseline level cortisol response at about 20 months after the start of shift work. If the initial increase in the cortisol response marks the development of a chronic stress response, the subsequent reversal to baseline levels in the subgroup of 14 participants might be indicative of a process of recovery, possibly the development of shift work tolerance.

A group-theoretical version of Hilbert's theorem 90

It is shown that for a normal subgroup N of a group G, G / N cyclic, the kernel of the map N ab → G ab satisfies the classical Hilbert 90 property (cf. Theorem A). As a consequence, if G is finitely generated, | G : N | < ∞ , and all abelian groups H ab , N ⊆ H ⊆ G , are torsion free, then N ab must be a pseudo-permutation module for G / N (cf. Theorem B). From Theorem A, one also deduces a non-trivial relation between the order of the transfer kernel and co-kernel which determines the Hilbert–Suzuki multiplier (cf. Theorem C). Translated into a number-theoretical setting, one obtains a strong form of Hilbert's theorem 94 (Theorem 4.1). In case that G is finitely generated and N has prime index p in G there holds a ‘generalized Schreier formula’ involving the torsion-free ranks of G and N and the ratio of the order of the transfer kernel and co-kernel (cf. Theorem D).

Triple Factorizations and Supersolubility of Finite Groups

AbstractIn this paper we analyse the structure of a finite group of minimal order among the finite non-supersoluble groups possessing a triple factorization by supersoluble subgroups of pairwise relatively prime indices. As an application we obtain some sufficient conditions for a triple factorized group by supersoluble subgroups of pairwise relatively prime indices to be supersoluble. Many results appear as consequences of our analysis.

Search for the periodicity of the prime Indian and American stock exchange indices using date-compensated discrete Fourier transform

The behaviour of Indian stock markets has a persistent close association with the behaviour of American stock exchange. The present work is an effort in this direction and the purpose of the present work is to investigate the periodicity of the two prime Indian stock market indices viz. SENSEX and NIFTY and the prime American stock market indices viz. DOW-JONES and S&P500. To serve the present purpose we have here used SENSEX logarithmic daily close data during the period from 1st January, 1990 to 31st December, 2013, NIFTY logarithmic daily close data during the period from 3rd July, 1990 to 31st December, 2013, DOW-JONES logarithmic daily close data during the period from 10th January, 1928 to 31st December, 2013 and S&P500 logarithmic daily close data during the period 3rd January, 1950 to 31st December, 2013. For the present analysis we have first used double exponential smoothing on all the four time series in order to remove the trend and next we have generated monthly averages of the smoothed time series in order to remove the irregular fluctuations. At the final stage Ferraz-Mello method of date-compensated discrete Fourier transform (DCDFT) has been applied on the present four double-smoothed monthly averaged time series. Study reveals periods for SENSEX of 11, 53 and 142 months; for NIFTY periods of 22, 38, 52 and 139 months; for DOW-JONES periods of 23, 25, 27, 30, 59, 107, 138, 194 and 494 months and for S&P500 periods of 28, 66, 74, 149 and 384 months. With this specific periodic behaviour we have also observed some pseudo-periods in the present four financial time series which certainly adds to the uncertainty in the process of prediction for the same.

Finite groups with elements of prime power index

Let G be a finite group and let π be a set of primes. For an element x of G, let Ind G(x) denote the index of CG(x) in G. We prove that if Ind 〈a,x〉(x) is a π-number for every element a of prime power order in G, then Ind G(x) is a π-number.

A note on elements of prime power index in finite groups

For an element \(x\) of a finite group \(G\), let Ind\(_{G}(x)\) denote the index of \(x\) in \(G\). In this note we prove that if Ind\(_{\langle a,b,x\rangle }(x)\) is a prime power for any \(a, b\in G\) of prime power order, then Ind\(_{G}(x)\) is a prime power.

Sums of Squares of Fibonacci Numbers with Prime Indices

In this paper we present some identities for the sums of squares of Fibonacci and Lucas numbers with consecutive primes, using maximal prime gap G(x)~log2x, as indices.

Consumer sentiment and government confidence: Is there a stable causal relationship?

Consumer confidence and perceived political confidence are known to play independently a crucial role in the economic growth of a country. Using French monthly economic and political data, we analyse the relationships between the president, the prime minister and consumer confidence during cohabitation and non-cohabitation periods, based on a SUR (seemingly unrelated regression) model. During cohabitation periods, whenever the president’s confidence index increased the prime minister index decreased. Further, confidence in the prime minister was useful for predicting consumer confidence. During non-cohabitation periods, consumer confidence helps to forecast both the president’s confidence and the prime minister’s confidence.

Debt Burden of Constituents of the Russian Federation and Its Determinant Factors

Expansion of expenditure obligations of the Russian Federation constituents and municipalities, which results in growing pressure on expenditure of territorial budgets, with preservation of current practice of revenue distribution between budgets of Russian budgeting system and reduction of cheap budget credits granted to regions - the situation when debt finance of budget expenditure and, accordingly, the increasing debt burden on regional budgets, are of current concern. This article analyses debt burden of Russian regions taken in conjunction with its prime budget and economic indices. On the basis of analysis we draw certain conclusions on factors that determine the level of debt burden and tendencies in regional debt behaviour, raise problems which, if solved successfully, will provide for improvement of debt situation in constituents of the Russian Federation. DOI: 10.5901/mjss.2014.v5n24p216

Sign changes of Fourier coefficients of cusp forms supported on prime power indices

Let f be an even integral weight, normalized, cuspidal Hecke eigenform over SL2(ℤ) with Fourier coefficients a(n). Let j be a positive integer. We prove that for almost all primes p the sequence (a(pjn))n≥0 has infinitely many sign changes. We also obtain a similar result for any cusp form with real Fourier coefficients that provide the characteristic polynomial of some generalized Hecke operator is irreducible over ℚ.

Developing and testing temperature models for regulated systems: A case study on the Upper Delaware River

Summary Water temperature is an important driver of many processes in riverine ecosystems. If reservoirs are present, their releases can greatly influence downstream water temperatures. Models are important tools in understanding the influence these releases may have on the thermal regimes of downstream rivers. In this study, we developed and tested a suite of models to predict river temperature at a location downstream of two reservoirs in the Upper Delaware River (USA), a section of river that is managed to support a world-class coldwater fishery. Three empirical models were tested, including a Generalized Least Squares Model with a cosine trend (GLScos), AutoRegressive Integrated Moving Average (ARIMA), and Artificial Neural Network (ANN). We also tested one mechanistic Heat Flux Model (HFM) that was based on energy gain and loss. Predictor variables used in model development included climate data (e.g., solar radiation, wind speed, etc.) collected from a nearby weather station and temperature and hydrologic data from upstream U.S. Geological Survey gages. Models were developed with a training dataset that consisted of data from 2008 to 2011; they were then independently validated with a test dataset from 2012. Model accuracy was evaluated using root mean square error (RMSE), Nash Sutcliffe efficiency (NSE), percent bias (PBIAS), and index of agreement ( d ) statistics. Model forecast success was evaluated using baseline-modified prime index of agreement (md) at the one, three, and five day predictions. All five models accurately predicted daily mean river temperature across the entire training dataset (RMSE = 0.58–1.311, NSE = 0.99–0.97, d = 0.98–0.99); ARIMA was most accurate (RMSE = 0.57, NSE = 0.99), but each model, other than ARIMA, showed short periods of under- or over-predicting observed warmer temperatures. For the training dataset, all models besides ARIMA had overestimation bias (PBIAS = −0.10 to −1.30). Validation analyses showed all models performed well; the HFM model was the most accurate compared other models (RMSE = 0.92, both NSE = 0.98, d = 0.99) and the ARIMA model was least accurate (RMSE = 2.06, NSE = 0.92, d = 0.98); however, all models had an overestimation bias (PBIAS = −4.1 to −10.20). Aside from the one day forecast ARIMA model (md = 0.53), all models forecasted fairly well at the one, three, and five day forecasts (md = 0.77–0.96). Overall, we were successful in developing models predicting daily mean temperature across a broad range of temperatures. These models, specifically the GLScos, ANN, and HFM, may serve as important tools for predicting conditions and managing thermal releases in regulated river systems such as the Delaware River. Further model development may be important in customizing predictions for particular biological or ecological needs, or for particular temporal or spatial scales.