Arithmetic Relations Research Articles

Retrieval of aerosol parameters from multiwavelength lidar: investigation of the underlying inverse mathematical problem

We present an investigation of some important mathematical and numerical features related to the retrieval of microphysical parameters [complex refractive index, single-scattering albedo, effective radius, total number, surface area, and volume concentrations] of ambient aerosol particles using multiwavelength Raman or high-spectral-resolution lidar. Using simple examples, we prove the non-uniqueness of an inverse solution to be the major source of the retrieval difficulties. Some theoretically possible ways of partially compensating for these difficulties are offered. For instance, an increase in the variety of input data via combination of lidar and certain passive remote sensing instruments will be helpful to reduce the error of estimation of the complex refractive index. We also demonstrate a significant interference between Aitken and accumulation aerosol modes in our inversion algorithm, and confirm that the solutions can be better constrained by limiting the particle radii. Applying a combination of an analytical approach and numerical simulations, we explain the statistical behavior of the microphysical size parameters. We reveal and clarify why the total surface area concentration is consistent even in the presence of non-unique solution sets and is on average the most stable parameter to be estimated, as long as at least one extinction optical coefficient is employed. We find that for selected particle size distributions, the total surface area and volume concentrations can be quickly retrieved with fair precision using only single extinction coefficients in a simple arithmetical relationship.

Adaptive number knowledge: Exploring the foundations of adaptivity with whole-number arithmetic

Adaptivity with arithmetic problem solving is a key aspect in the long-term development of mathematical skills, and the knowledge of numerical characteristics and relations is a core component of adaptivity with whole-number arithmetic. The present studies represent the first attempt to investigate the nature of the adaptive number knowledge, referring to the well-connected knowledge of numerical characteristics and arithmetic relations between numbers, which underlies adaptivity with arithmetic. A new measurement tool, the Adaptive Number Knowledge Task, was developed to capture individual differences in primary school students' and adults' number knowledge. Three groups of participants – 3rd to 5th graders, university students, and 6th graders – completed the measure, which required participants to produce arithmetic sentences equaling a target number by using any combination of four to five given numbers and arithmetic operations. These studies revealed substantial individual differences in the quantity and quality of participants' adaptive number knowledge. Adaptive number knowledge was found to be related to arithmetic fluency and knowledge of arithmetic concepts in 6th graders. Results suggest that the Adaptive Number Knowledge Task was able to capture individual differences in recognizing and using numerical relations in whole-number arithmetic problem solving, and that these differences may help explain differences in adaptivity with arithmetic.

Structural chemistry and number theory amalgamized: crystal structure of Na11Hg52.

The recently elucidated crystal structure of the technologically important amalgam Na11Hg52 is described by means of a method employing some fundamental concept of number theory, namely modular arithmetical (congruence) relations observed between a slightly idealized set of atomic coordinates. In combination with well known ideas from group theory, regarding lattice-sublattice transformations, these allow for a deeper mutual understanding of both and provide the structural chemist with a slightly different kind of spectacles, thus enabling a distinct viw on complex crystal structures in general.

Pollen limitation and its influence on natural selection through seed set

Stronger pollen limitation should increase competition among plants, leading to stronger selection on traits important for pollen receipt. The few explicit tests of this hypothesis, however, have provided conflicting support. Using the arithmetic relationship between these two quantities, we show that increased pollen limitation will automatically result in stronger selection (all else equal) although other factors can alter selection independently of pollen limitation. We then tested the hypothesis using two approaches. First, we analysed the published studies containing information on both pollen limitation and selection. Second, we explored how natural selection measured in one Ontario population of Lobelia cardinalis over 3years and two Michigan populations in 1year relates to pollen limitation. For the Ontario population, we also explored whether pollinator-mediated selection is related to pollen limitation. Consistent with the hypothesis, we found an overall positive relationship between selection strength and pollen limitation both among species and within L.cardinalis. Unexpectedly, this relationship was found even for vegetative traits among species, and was not found in L.cardinalis for pollinator-mediated selection on nearly all trait types.

Arithmetic properties of partition triples with odd parts distinct

Let pod -3(n) denote the number of partition triples of n where the odd parts in each partition are distinct. We find many arithmetic properties of pod -3(n) involving the following infinite family of congruences: for any integers α ≥ 1 and n ≥ 0, [Formula: see text] We also establish some arithmetic relations between pod (n) and pod -3(n), as well as some congruences for pod -3(n) modulo 7 and 11.

Efficient radix-r adders for nanoelectronics

In this study, a new design method and efficient designs for radix-r adders are proposed for carbon nanotube field effect transistor (CNFET) FET nanotechnology. This application also investigates the capability of the nanoscale device for designing high-performance analogue circuits. The proposed designs benefit from the unique electrical properties of CNFET, such as near-ideal current voltage characteristics, very high transconductance, high-performance switches and very high-performance and high-gain binary inverters, at nanoscale. Moreover, adjustable threshold voltage and the same mobility of electrons and holes in a CNFET facilitate the design and modification procedures. The proposed design can be considered as an instance of a general adder, capable of adding radix-r digits with high precision. It is noteworthy that a very limited number of carbon nanotube diameters for designing the proposed adder are needed, which enhance the manufacturability. The proposed circuits are designed based on arithmetic relations and are also verified at 32 nm feature size using HSPICE and the Stanford standard SPICE model.

Anisotropy Influence in Obtaining Stiffness Property in Bending of Brazilian Wood Species

The design of timber structures, and other materials, must follow the procedures and methods of calculation of normative standards. Some normative documents in the design of timber structures adopt quite simple arithmetical relationships to relate wood properties in order to make it simple and quick evaluation of the behavior of structural elements, as is the specific case of Brazilian standard ABNT NBR 7190:1997, establishing a single relation for the shear (G) and the longitudinal (E) modulus of elasticity [E=G/20], which implies taking statistical equivalence to the values of the elastic moduli in the longitudinal-radial (G<SUB>LR</SUB>) and longitudinal-tangential (G<SUB>LT</SUB>) directions, which are important properties in relation to the requirements of structural projects. In this context, this study aimed to investigate, with the aid of four and three points static bending tests performed on the of dicotyledonous wood species grown in Brazil, the determination of the values of E<SUB>LR</SUB>, E<SUB>LT</SUB>, G<SUB>LR</SUB> and G<SUB>LT</SUB> to confirm the possibility of its equivalence (E<SUB>LR</SUB> and E<SUB>LT</SUB>, G<SUB>LR</SUB> and G<SUB>LT</SUB>), and for establishing correlations among them. The results of the hypothesis testing between the shear and longitudinal modulus of elasticity exhibited equivalent by species and simultaneously for all species, and the results of the linear regression model showed not possible to estimate the shear modulus of elasticity with knowledge of the longitudinal modulus of elasticity, and the optimal coefficient found by least squares method to the relation between the modulus of elasticity was equal to 35 (E=G/35), suggesting the need for an adjustment of the coefficient for this scale more safe wooden structures.

Predicting enthalpy of vaporization for Persistent Organic Pollutants with Quantitative Structure–Property Relationship (QSPR) incorporating the influence of temperature on volatility

Enthalpy of vaporization (ΔHvap) is a thermodynamic property associated with the dispersal of Persistent Organic Pollutants (POPs) in the environment. Common problem in the environmental risk assessment studies is the lack of experimentally measured ΔHvap data. This problem can be solved by employing computational techniques, including QSPR (Quantitative Structure–Property Relationship) modelling to predict properties of interest. Majority of the published QSPR models can be applied to predict the enthalpy of vaporization of compounds from only one, particular group of POPs (i.e., polychlorinated biphenyls, PCBs). We have developed a more general QSPR model to estimate the ΔHvap values for 1436 polychlorinated and polybrominated benzenes, biphenyls, dibenzo-p-dioxins, dibenzofurans, diphenyl ethers, and naphthalenes. The QSPR model developed with Multiple Linear Regression analysis was characterized by satisfactory goodness-of-fit, robustness and the external predictive performance (R2 = 0.888, QCV2=0.878, QExt2=0.842, RMSEC = 5.11, RMSECV = 5.34, RMSEP = 5.74). Moreover, we quantified the temperature dependencies of vapour pressure for twelve groups of POPs based on the predictions at six different temperatures (logPL(T)). In addition, we found a simple arithmetic relationship between the logarithmic values of vapour pressure in pairs of chloro- and bromo-analogues. By employing this relationship it is possible to estimate logPL(T) for any brominated POP at any temperature utilizing only the logPL(T) value for its chlorinated analogues.

Qumran Calendars and the Creation

This paper re-examines 4QcryptA Lunisolar Calendar (4Q317), a scroll from Qumran in an esoteric Hebrew script with many emendations that aligns the moon’s daily waxing and waning to a 364-day calendar. It seeks to ascertain whether the calendar may be exegetically related to the Creation and also discusses the text’s arithmetical relationships with the cycles of the priestly courses from Qumran, possible intertextual allusions to other lunar calendars in the Dead Sea Scrolls (4QDaily Prayers [4Q503], 4QAstronomical Enocha–bar [4Q208–4Q209]), biblical passages, and parallels with another Mesopotamian calendar text. The first transcription of the largest fragments using a Cryptic A font is here published with a commentary (in the Appendix), focusing on the text’s unusual scribal features. A reconsideration of the calendar’s structure with a new arrangement of its dates is presented.

Low-Complexity Parallel QPP Interleaver Based on Permutation Patterns

In this brief, we present how parallel-interleaved addresses generated by a quadratic permutation polynomial (QPP) interleaver are related to each other and propose a low-complexity parallel QPP interleaver based on the relationship. While a conventional parallel turbo decoder employs a number of interleavers as many as the parallel factor, the proposed method, which benefits from the arithmetic relationship denoted as the permutation pattern (PP), supports the parallel interleaving using only a single interleaver, resulting in a notable reduction of complexity. The strength of the proposed method stems from the fact that the PP is fully determined by only the decoding parameters, such as block size, parallel factor, and QPP coefficients. Experiment results on the Long Term Evolution turbo codes show that the proposed interleaver can significantly reduce the hardware complexity compared with conventional implementations.

Complete characterization by multistationarity of fully open networks with one non-flow reaction

This article characterizes certain small multistationary chemical reaction networks. We consider the set of fully open networks, those for which all chemical species participate in inflow and outflow, containing one non-flow (reversible or irreversible) reaction. We show that such a network admits multiple positive mass-action steady states if and only if the stoichiometric coefficients in the non-flow reaction satisfy a certain simple arithmetic relation. The multistationary fully open one-reaction networks are identified with the chemical process of autocatalysis. Using the notion of ‘embedded network’ defined recently by Joshi and Shiu, we provide new sufficient conditions for establishing multistationarity of fully open networks, applicable well beyond the one-reaction setting.

Crunch Time: how did the students perform?

Two newspaper numbers games based on simple arithmetic relationships are discussed. One is rather trivial, but very useful as an introduction to the second, whose potential to give students of elementary algebra practice in semi-ad hoc reasoning and to build general arithmetic reasoning skills was explored theoretically in an earlier paper. Preliminary results on the effectiveness of this general approach are presented, with student performance and feedback on an assignment task and formal examination included, and recommendations for future work.

Evolution of genome size in Carex (Cyperaceae) in relation to chromosome number and genomic base composition.

The genus Carex exhibits karyological peculiarities related to holocentrism, specifically extremely broad and almost continual variation in chromosome number. However, the effect of these peculiarities on the evolution of the genome (genome size, base composition) remains unknown. While in monocentrics, determining the arithmetic relationship between the chromosome numbers of related species is usually sufficient for the detection of particular modes of karyotype evolution (i.e. polyploidy and dysploidy), in holocentrics where chromosomal fission and fusion occur such detection requires knowledge of the DNA content. The genome size and GC content were estimated in 157 taxa using flow cytometry. The exact chromosome numbers were known for 96 measured samples and were taken from the available literature for other taxa. All relationships were tested in a phylogenetic framework using the ITS tree of 105 species. The 1C genome size varied between 0·24 and 1·64 pg in Carex secalina and C. cuspidata, respectively. The genomic GC content varied from 34·8 % to 40·6 % from C. secalina to C. firma. Both genomic parameters were positively correlated. Seven polyploid and two potentially polyploid taxa were detected in the core Carex clade. A strong negative correlation between genome size and chromosome number was documented in non-polyploid taxa. Non-polyploid taxa of the core Carex clade exhibited a higher rate of genome-size evolution compared with the Vignea clade. Three dioecious taxa exhibited larger genomes, larger chromosomes, and a higher GC content than their hermaphrodite relatives. Genomes of Carex are relatively small and very GC-poor compared with other angiosperms. We conclude that the evolution of genome and karyotype in Carex is promoted by frequent chromosomal fissions/fusions, rare polyploidy and common repetitive DNA proliferation/removal.

Is there teleological order in nature? is there teleological explanation in science?

The paper will be divided into two parts. In the first part concerning teleological order in nature, different types of order will be distinguished: beginning with order as structure and then proceeding to higher and stronger types of order, which include special arithmetical and geometrical relations and eventually also negentropy. It will be shown that certain processes of becoming can possess higher order in such a way that they can have teleological order. In the second part a definition of teleological explanation will be given and the following two questions will be answered: (1) Are there teleological explanations which are logically valid? (2) Are there teleological explanations which are used by scientists?

INFINITE FAMILIES OF ARITHMETIC IDENTITIES FOR 4-CORES

AbstractLetu(n) andv(n) be the number of representations of a nonnegative integernin the formsx2+4y2+4z2andx2+2y2+2z2, respectively, withx,y,z∈ℤ, and leta4(n) andr3(n) be the number of 4-cores ofnand the number of representations ofnas a sum of three squares, respectively. By employing simple theta-function identities of Ramanujan, we prove that$u(8n+5)=8a_4(n)=v(8n+5)=\frac {1}{3}r_3(8n+5)$. With the help of this and a classical result of Gauss, we find a simple proof of a result ona4(n) proved earlier by K. Ono and L. Sze [‘4-core partitions and class numbers’,Acta Arith.80(1997), 249–272]. We also find some new infinite families of arithmetic relations involvinga4(n) .

RAPD marker evaluation of phylogenetic relationships in species of genus Beta L.

RAPD markers are used for establishing phylogenetic relationships between and within various beet species. On the basis of the electrophoretic profiles obtained, phylogenetic trees are constructed by the unweighted pair group with arithmetic mean (UPGMA) method and relationships between wild and cultivated beet accessions stored in the world collection at the Vavilov Plant Industry Research Institute (VIR)are determined.

On constrained optimization by interval arithmetic and interval order relations

The goal of this article is to develop an optimization technique based on the splitting criterion of search region into several equal and disjoint subregions for solving the constrained optimization problems by finite interval arithmetic and interval order relations in the context of a decision maker’s point of view. This method has been applied for solving some benchmark test problems taken from the literature and the results are compared with those obtained from several existing different heuristic or meta-heuristic methods.

Muscovite Arithmetic in Seventeenth-Century Russian Civilization: Is It Not Time to Discard the “Backwardness” Label?

Muscovite civilization utilized Byzantine-Greek alphanumerals for its mathematical symbols. Occasionally derided by historians for being retrograde in comparison to the Hindu-Arabic numerals sixteenth- and seventeenth-century Europe adopted, Muscovy’s alphanumerals were versatile and suitably contoured to perform a variety of computational tasks. Muscovite alphanumerals were an integral part of early Moderen Russia’s administrative culture, and played a prominent role in fostering the experiential knowledge underlying the educational achievements of the Imperial Period. Though they lacked the zero and the decimal, Muscovites still had a reasonable grasp of the base-ten system, and comprehended well basic arithmetical skills and relationship properties, less so equational ones. The Russians developed complex abaci well suited for commercial transactions, large-scale construction, military inventories and payrolls, and the land registry, to name a few. These instruments manipulated an extensive variety of weights, measures, linear distances, area dimensions, volume measurements, and currency. Muscovite arithmetic was a prominent factor assisting in the advancement of critical thinking skills in 1600’s Russia. Nonetheless, as the seventeenth century wore on, sociological, educational or pedagogical, military scientific, administrative, and cultural arguments or interactive phenomena came to bear and increasingly found the Muscovite algorithmic symbols wanting. In 1699 the government decreed that Hindu-Arabic numerals henceforth were to be used in official documents throughout the country. Directly and indirectly, the complex thought processes bound up when operating with Muscovite alphanumerals were one impetus for the further unfolding of Russian civilization after 1700.

Sequential Processing of Two-Digit Numbers

Two experiments using a number matching task (NMT) explored whether two-digit numbers are processed holistically or in a compositional fashion. In the NMT participants are required to decide whether one of the two numbers initially provided (cues) is presented some milliseconds later or not (probe). Probes which have some arithmetic relationship to the cues (e.g., cues: 2 3, probe: 6) are rejected more slowy than probes unrelated to their cues (e.g., cues: 2 3, probe: 7) – interference effect –, and this is considered as evidence of the automatic activation of that arithmetic relationship. Participants were presented with two-digit cues and probes which had an arithmetic progression relationship only detectable once the numbers were decomposed (Experiment 1: cues: 56 7, probe: 89; Experiment 2: cues: 45 67, probe: 89). Results showed longer response times in these conditions compared to unrelated conditions. Data support componential processing even when the numbers to be matched are presented serially.

The Number Crunch game: a simple vehicle for building algebraic reasoning skills

A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-ad hoc reasoning and to build general arithmetic reasoning skills is explored.