Numerical Quantities Research Articles

Teaching & learning guide for: Risky‐choice framing and rational decision‐making

Teaching & learning guide for: Risky‐choice framing and rational decision‐making

The Second Hyper-Zagreb Index of Complement Graphs and Its Applications of Some Nano Structures

In chemical graph theory, a topological descriptor is a numerical quantity that is based on the chemical structure of underlying chemical compound. Topological indices play an important role in chemical graph theory especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). In this paper, we present explicit formulae for some basic mathematical operations for the second hyper-Zagreb index of complement graph containing the join G1 + G2, tensor product G1 \(\otimes\) G2, Cartesian product G1 x G2, composition G1 \(\circ\) G2, strong product G1 * G2, disjunction G1 V G2 and symmetric difference G1 \(\oplus\) G2. Moreover, we studied the second hyper-Zagreb index for some certain important physicochemical structures such as molecular complement graphs of V-Phenylenic Nanotube V PHX[q, p], V-Phenylenic Nanotorus V PHY [m, n] and Titania Nanotubes TiO2.

Study of Carbon Nanbotubes and Boron Nanotubes Using Degree Based Topological Indices

The numerical quantity that correlates chemical structure of a molecule with its physico–chemical properties is known as topological index. Topological indices are widely used to investigate the characteristics of molecular structres. Boron and carbon nanostructures are widely studied by researchers due to their novel properties. In this paper, the first extended first–order connectivity index and neighborhood second Zagreb index are calculated due to their better correlation ability among existing indices. In addition to this, closed formulae of these topological indices are also presented for the above mentioned nanostructure networks.

СВИНЦОВАЯ ЭКСПОЗИЦИЯ КАК ПРЕДПОСЫЛКА ОГРАНИЧЕНИЯ РЕАЛИЗАЦИИ МАКСИМАЛЬНОЙ ФИЗИЧЕСКОЙ АКТИВНОСТИ

As a result of man’s technological activities, numerous quantities of lead and its compounds are spread into the environment annually. The long-term effects of low doses of lead on the lungs, heart muscle and the transport function of erythrocytes were investigated. The study results indicate that long-term intake of small doses of lead, even in the absence of visible clinical manifestations, causes distinct structural changes and therefore, functional changes in the heart muscle, respiratory system, reduces the transport function of erythrocytes, and also possibly limiting the oxygen transport in myocytes and its deposition in tissues and diffusion into cells. There is no doubt that these changes will limit the ability to maximize the realization of physical activity.

On Degree Based Topological Indices of Polycyclic Certain Interconnection Networks

Topological indices are the significant numerical quantities in the fields of chemical graph theory. Quantitative structure-property and structure-activity relationships of the Honeycomb Network, Hexagonal Network and Silicate Network SiO4 necessitate expressions for the molecular topological features of these networks. ev-degree and ve-degree established topological indices demarcated as analogous to their relating spouses. In this paper, we have computed topological indices based on ev-degree and ve-degree for the Honeycomb Network, Hexagonal Network and Silicate Network.

EXPLORING THE IMPLEMENTATION OF AN INTERVENTION FOR A PUPIL WITH MATHEMATICAL LEARNING DIFFICULTIES: A CASE STUDY

This study presents a single case study of how a remedial mathematics teacher incorporated an instructional intervention into her teaching practices in order to teach counting to a pupil with mathematical learning difficulties. This new theory-driven intervention was developed by the authors of this study. Dyscalculia is a term which refers to a wide range of mathematical learning difficulties or disabilities. Dyscalculic pupils have a specific mathematics learning disorder with a core deficit in representing and processing of numerosity. They might not be able to recognise numerical quantities, performing counting and so on. Early supports such as interventions have a great potential in helping dyscalculic pupils to improve mathematical skills. However, there remains a lack of appropriate instructional scaffolds to help dyscalculic pupils to organise their learning structures by addressing both cognitive deficits and mathematical skills. The present study involves a primary school remedial teacher, Daisy, and an at-risk dyscalculic pupil, David, both pseudonyms. Data were collected through interviews, lesson observations, and reflective journals. The findings revealed that the proposed intervention improved the counting ability of the pupil.

Topological Descriptors on Some Families of Graphs

In view of the successful applications of graph theory, relationships between the biological activity and chemical structure have been developed. One of the popular topics in graph theory is problems relating to topological indices. Degree-based topological indices, distance-based topological indices, and counting-related topological indices are various types of topological indices. Physiochemical properties such as boiling point and stability of chemical compounds are correlated by these topological indices. A topological index of a graph is a numerical quantity obtained from the graph mathematically. A cactus graph is a connected graph in which no edge lies in more than one cycle. In this study, we have derived certain degree-based topological indices for some families of graphs consisting of graph obtained by the rooted product of paths and cycles and two types of cactus graph (paracactus and orthocactus) with the help of the generalized Zagreb index.

Numerical investigation of chemical reaction, Soret and Dufour impacts on MHD free convective gyrating flow through a vertical porous channel

The extensive variety of issues include reactions kinetics, simulations and optimizations of different models of reactors including basic explorations of the processes of temperature, mass and momentum transfer that taken places with chemical reaction. Based on this criteria, it is discussed the impacts of the Soret and Dufour consequences on natural convective heat and mass transfer for the unsteady two dimensional boundary layer flow through a vertical channel/duct with the influence of viscous dissipation, invariable suction into the description. The governing dimensionless partial differential equations are solved digitally making use of the implicit Crank-Nicolson method. The velocity, temperature, and concentration dispensations are addressed computationally and demonstrated by the graphs. Numerical quantities of the skin-friction, Nusselt number and Sherwood number at the plate are found for a choice of assessments of substantial parameters and which are displayed by tabular manner. It is significant to notice that, Soret impacts emerge in suspended mixture of particles and fluids. These phenomenons are reasoned with the temperature gradients; hence, the movements of fluid molecules in the hottest zone and highest energy level in this region transfer the particles towards the coldest region. It is also most useful in chemical engineering.

Spontaneous representation of numerosity zero in a deep neural network for visual object recognition

SummaryConceiving “nothing” as a numerical value zero is considered a sophisticated numerical capability that humans share with cognitively advanced animals. We demonstrate that representation of zero spontaneously emerges in a deep learning neural network without any number training. As a signature of numerical quantity representation, and similar to real neurons from animals, numerosity zero network units show maximum activity to empty sets and a gradual decrease in activity with increasing countable numerosities. This indicates that the network spontaneously ordered numerosity zero as the smallest numerical value along the number line. Removal of empty-set network units caused specific deficits in the network's judgment of numerosity zero, thus reflecting these units' functional relevance. These findings suggest that processing visual information is sufficient for a visual number sense that includes zero to emerge and explains why cognitively advanced animals with whom we share a nonverbal number system exhibit rudiments of numerosity zero.

M-polynomials and degree-based topological indices of tadpole graph

Chemical graph theory is a branch of mathematical chemistry which has an important outcome on the development of the chemical sciences. A chemical graph is a graph which is produced from some molecular structure by applying some graphical operations. The demonstration of chemical compounds and chemical networks with M-polynomials is a new idea and the M-polynomial of different molecular structures supports us to calculate many topological indices. A topological index is a numeric quantity that describes the whole structure of a molecular graph of the chemical compound and supports to understand its physical features, chemical reactivates and boiling activities. In this paper, we compute M-polynomial and topological indices of tadpole graph, then we recover numerous topological indices using the M-polynomial.

On Topological Indices and QSPR Analysis of Drugs Used for the Treatment of Breast Cancer

A topological index of graph G is a numerical quantity which describes its topology. If it is applied to molecular structure of a chemical compounds then it reflects the theoretical properties of the chemical compounds. In this article, well-known degree based topological indices are applied on chemical structures of medicine used for treatment of breast cancer. Chemical structure is considered as graph, where elements are taken as vertices and bounds between them are taken as edges. Further, QSPR analysis of said topological indices are discussed and it is shown that these topological indices are highly correlated with the physical properties of chemical compounds used for the treatment of breast cancer.

Causal analyses of existing databases: no power calculations required

Observational databases are often used to study causal questions. Before being granted access to data or funding, researchers may need to prove that “the statistical power of their analysis will be high.” Analyses expected to have low power, and hence result in imprecise estimates, will not be approved. This restrictive attitude towards observational analyses is misguided.A key misunderstanding is the belief that the goal of a causal analysis is to “detect” an effect. Causal effects are not binary signals that are either detected or undetected; causal effects are numerical quantities that need to be estimated. Because the goal is to quantify the effect as unbiasedly and precisely as possible, the solution to observational analyses with imprecise effect estimates is not avoiding observational analyses with imprecise estimates, but rather encouraging the conduct of many observational analyses. It is preferable to have multiple studies with imprecise estimates than having no study at all. After several studies become available, we will meta-analyze them and provide a more precise pooled effect estimate. Therefore, the justification to withhold an observational analysis of preexisting data cannot be that our estimates will be imprecise. Ethical arguments for power calculations before conducting a randomized trial which place individuals at risk are not transferable to observational analyses of existing databases.If a causal question is important, analyze your data, publish your estimates, encourage others to do the same, and then meta-analyze. The alternative is an unanswered question.

Implicit visuospatial attention shapes numerosity adaptation and perception

The perception of numerical quantities is susceptible to adaptation: after inspecting a numerous dot array for a few seconds a subsequent dot array is grossly underestimated. In a recent work we showed that the mere appearance of an additional numerically neutral stimulus significantly reduces the adaptation magnitude. Here we demonstrate that this reduction is likely due to a numerosity underestimation of the adaptor caused by a change of numerosity-related attentional resources deployed on the adapting stimulus. In Experiment 1 we replicated previous findings revealing a robust reduction of numerosity adaptation when an additional adaptor (even if neutral) was displayed. In Experiment 2 we used the method of magnitude estimation to demonstrate that numerosity is underestimated whenever a second task-irrelevant numerical stimulus appears on screen. Furthermore we demonstrated that the same experimental manipulations were not effective in modulating orientation adaptation magnitude as well as orientation estimation accuracy. Our results support the hypothesis of a tight relationship between numerosity perception and implicit visuospatial attention and corroborate the notion that numerosity adaptation depends on perceived rather than physical numerosity. However the lack of an effect of visuospatial attentional deployment for orientation perception suggests that attention might differently shape adaptation aftereffects for different features along the visual hierarchy.

The emergence of children’s natural number concepts: Current theoretical challenges

AbstractLearning the meaning of number words is a lengthy and error‐prone process. In this review, we highlight outstanding issues related to current accounts of children’s acquisition of symbolic number knowledge. We maintain that, despite the ability to identify and label small numerical quantities, children do not understand initially that number words refer only to sets of discrete countable items, not to other nonnumerical dimensions. We question the presence of a sudden change in children’s understanding of cardinality, and we report the limits of the give‐a‐number task. We also highlight that children are still learning the directional property of the counting list, even after acquiring the cardinality principle. Finally, we discuss the role that the Approximate Number System may have in supporting the acquisition of symbolic numbers. We call for improvements in methodological tools and refinement in theoretical understanding of how children learn natural numbers.

Molecular Descriptor Analysis of Certain Isomeric Natural Polymers

Polymers, drugs, and almost all chemical or biochemical compounds are frequently modeled as diverse ω -cyclic, acyclic, bipartite, and polygonal shapes and regular graphs. Molecular descriptors (topological indices) are the numerical quantities and computed from the molecular graph Γ (2D lattice). These descriptors are highly significant in quantitative structure-property or activity relationship (QSPR and QSAR) modeling that provides the theoretical and the optimal basis to expensive experimental drug design. In this paper, we study three isomeric natural polymers of glucose (polysaccharides), namely, cellulose, glycogen, and amylopectin (starch), having promising pharmaceutical applications, exceptional properties, and fascinating molecular structures. We intend to investigate and compute various closed-form formulas such as ABC , GA , sum-connectivity χ − 1 / 2 , ABC 4 , GA 5 , and Sanskruti indices for the aforementioned macromolecules. Also, we present the closed-form formulas for the first, second, modified, and augmented Zagreb indices, inverse and general Randić indices, and symmetric division deg, harmonic, and inverse sum indices. Furthermore, we provide a comparative analysis using 3D graphs for these families of macromolecules to clarify their nature.

Nonlinear usual convection flow of couple stress micropolar nanofluids over isothermal sphere with non‐Fourier's heat and non‐Fick's mass fluxes under high classify slip states

AbstractThe goal of this study is to examine the influences of couple stress, the ratio of buoyancy forces, and thermal and solutal relaxation time constraints on two state line sheet flow of nonlinear movement flow of couple stress micropolar nanofluid past the isothermal ball. The mathematical modeling for the flow problem has been made with appropriate likeness change with nondimensional variables. The goal of nonlinear state line value problems were implied in combined high classifies nonlinear ordinary degree of difference equations. The equations were calculated by using the technique bvp4c from Matlab software for numerous quantities of main constraints. Influences of constraints on velocities, thermal, and solutal profiles are displayed from side to side of the charts. The junction test has been continued; for spots larger than apposite web spots, the meticulousness is not affected. Moreover, a comparison with previous papers reachable in the literature has been reported as well as an excellent agreement is presented. The results show that enhancing thermal relaxation time parameter Fo agree to reduce micro‐inertia density that improve velocity profile f'(η), temperature distribution , Nusselt number −θ'(η) and Sherwood number −, and reduce concentration distribution , coefficient of skin friction and wall couple stress and respectively.

Study of Generalized Hourglass Section in Carbon Nanocone via Connection Number

In 1972, Gutman and Trinajstic showed that total π -energy of a molecule depends upon a numeric quantity which is often called as Zagreb index. In the same report, they also discussed another numeric quantity depending on the number of atoms at a distance two from a particular atom and proved influencing results on π -energy of a molecule. In modern literature, this quantity is named as connection number. In this article, we will describe some Zagreb connection numbers for hourglass section in carbon nanocone network with different lengths of cycle in the central core.

Magnitude integration in the Archerfish

We make magnitude-related decisions every day, for example, to choose the shortest queue at the grocery store. When making such decisions, which magnitudes do we consider? The dominant theory suggests that our focus is on numerical quantity, i.e., the number of items in a set. This theory leads to quantity-focused research suggesting that discriminating quantities is automatic, innate, and is the basis for mathematical abilities in humans. Another theory suggests, instead, that non-numerical magnitudes, such as the total area of the compared items, are usually what humans rely on, and numerical quantity is used only when required. Since wild animals must make quick magnitude-related decisions to eat, seek shelter, survive, and procreate, studying which magnitudes animals spontaneously use in magnitude-related decisions is a good way to study the relative primacy of numerical quantity versus non-numerical magnitudes. We asked whether, in an animal model, the influence of non-numerical magnitudes on performance in a spontaneous magnitude comparison task is modulated by the number of non-numerical magnitudes that positively correlate with numerical quantity. Our animal model was the Archerfish, a fish that, in the wild, hunts insects by shooting a jet of water at them. These fish were trained to shoot water at artificial targets presented on a computer screen above the water tank. We tested the Archerfish's performance in spontaneous, untrained two-choice magnitude decisions. We found that the fish tended to select the group containing larger non-numerical magnitudes and smaller quantities of dots. The fish selected the group containing more dots mostly when the quantity of the dots was positively correlated with all five different non-numerical magnitudes. The current study adds to the body of studies providing direct evidence that in some cases animals’ magnitude-related decisions are more affected by non-numerical magnitudes than by numerical quantity, putting doubt on the claims that numerical quantity perception is the most basic building block of mathematical abilities.

On the dissipation of H(div)-conforming schemes for incompressible flows

In this paper, we present a systematic construction of a H(div)-conforming numerical dissipation for time-dependent incompressible Euler and Navier–Stokes equations. The goal is to improve the performance of the central flux scheme. The construction is a generalization of the upwind flux scheme from the dissipation point of view and makes use of the discontinuity of numerical quantities across interior edges. It is physically connected to the implicit large eddy simulation used in turbulent flow simulations. Examples are constructed when the jump of the gradient or curl of numerical velocity is used, and their performance is tested through numerical experiments. Numerical results show that the added dissipation does a good job in reducing numerical errors and in preserving the right physics.

Linear and nonlinear profiles of weak behavioral and neural differentiation between numerical operations in children with math learning difficulties

Mathematical knowledge is constructed hierarchically during development from a basic understanding of addition and subtraction, two foundational and inter-related, but semantically distinct, numerical operations. Early in development, children show remarkable variability in their numerical problem-solving skills and difficulties in solving even simple addition and subtraction problems are a hallmark of math learning difficulties. Here, we use novel quantitative analyses to investigate whether less distinct representations are associated with poor problem-solving abilities in children during the early stages of math-skill acquisition. Crucially, we leverage dimensional and categorical analyses to identify linear and nonlinear neurobehavioral profiles of individual differences in math skills. Behaviorally, performance on the two different numerical operations was less differentiated in children with low math abilities, and lower problem-solving efficiency stemmed from weak evidence-accumulation during problem-solving. Children with low numerical abilities also showed less differentiated neural representations between addition and subtraction operations in multiple cortical areas, including the fusiform gyrus, intraparietal sulcus, anterior temporal cortex and insula. Furthermore, analysis of multi-regional neural representation patterns revealed significantly higher network similarity and aberrant integration of representations within a fusiform gyrus-intraparietal sulcus pathway important for manipulation of numerical quantity. These findings identify the lack of distinct neural representations as a novel neurobiological feature of individual differences in children's numerical problem-solving abilities, and an early developmental biomarker of low math skills. More generally, our approach combining dimensional and categorical analyses overcomes pitfalls associated with the use of arbitrary cutoffs for probing neurobehavioral profiles of individual differences in math abilities.