Numerical Quantities Research Articles

The link between number and action in human infants

Humans' inborn ability to represent and manipulate numerical quantities is supported by the parietal cortex, which is also involved in a variety of spatial and motor abilities. While the behavioral links between numerical and spatial information have been extensively studied, little is known about the connection between number and action. Some studies in adults have shown a series of interference effects when simultaneously processing numerical and action information. We investigated the origins of this link by testing forty infants (7- to 9-month-old) in one of two experimental conditions: one group was habituated to congruent number-hand pairings, where the larger the number, the more open the hand-shape associated; the second group was habituated to incongruent number-hand pairings, where the larger the number, the more close the hand-shape associated. In test trials, both groups of infants were presented with congruent and incongruent pairings. We found that only infants habituated to congruency showed a significantly higher looking time to the test trial depicting incongruent pairings. These findings show for the first time that infants spontaneously associate magnitude-related changes across the dimensions of number and action-related information, thus offering support to the existence of an early, preverbal number-action link in the human mind.

Degree-Based Topological Indices and QSPR Analysis of Antituberculosis Drugs

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 paper, well-known degree-based topological indices are applied on chemical structures of antituberculosis drugs. Chemical structure is considered as graph, where elements are taken as vertices and bounds between them are taken as edges. Furthermore, QSPR analysis of the said topological indices are discussed, and it is shown that these topological indices are highly correlated with the physical properties of antituberculosis drugs. This theocratical analysis may help the chemist and people working in pharmaceutical industry to predict properties of antituberculosis drugs without experimenting.

Numerical estrangement and integration between symbolic and non-symbolic numerical information: Task-dependence and its link to math abilities in adults

Most adults have access to two different number systems to represent numerical information: an exact number system, which relies on different forms of number symbols to represent exact numerical information, and an approximate number system, which allows for approximate estimates of numerical quantities. Here we investigate the integration between the symbolic and non-symbolic numerical information (i.e., “numerical integration”), and how numerical integration relates to adults' formal math abilities. We administered two tasks to measure numerical integration. For a number comparison task with non-symbolic dot arrays and Arabic numerals, participants indicated the larger of two sequentially presented stimuli that were same-format (dot-dot or numeral-numeral), or mixed-format (dot-numeral or numeral-dot). For a number-letter discrimination task, participants identified Arabic numerals or letter pairs that co-occurred with dot arrays (matching or mismatching the quantity represented by the numeral). In the number comparison task, participants were significantly slower when comparing mixed-format stimuli, especially when Arabic numerals were presented first and dot arrays second, suggesting estrangement between symbolic and non-symbolic numerical information and an asymmetry depending on the order in which the numerical information is presented. In contrast, in the number-letter discrimination task, participants were significantly faster in number-letter discrimination for matching dot arrays and numerals, suggesting integration between symbolic and non-symbolic numerical information. Surprisingly, some measures of numerical estrangement derived from the number comparison task significantly correlated with adults' performance on a standardized math assessment. Thus, we conclude that numerical integration or estrangement is task-dependent, and adults with greater levels of symbolic estrangement tend to have higher math skills.

Understanding Estimations of Magnitudes: An fMRI Investigation.

The current study examined whether discrete numerical estimation is based on the same cognitive process as estimation of continuous magnitudes such as weight and time. While the verbal estimation of numerical quantities has a contingent unit of measurement (e.g., how many cookies fit in a cookie jar? _X_ cookies), estimation of time and weight does not (e.g., how much time does it take to fill a bath with water? _X_ minutes/hours/seconds). Therefore, estimation of the latter categories has another level of difficulty, requiring extensive involvement of cognitive control. During a functional magnetic resonance imaging (fMRI) scan, 18 students performed estimations with three estimation categories: number, time, and weight. Estimations elicited activity in multiple brain regions, mainly: (1) visual regions including bilateral lingual gyrus), (2) parietal regions including the left angular gyrus and right supramarginal gyrus, and (3) the frontal regions (cingulate gyrus and the inferior frontal cortex). Continuous magnitude estimations (mostly time) produced different frontal activity than discrete numerical estimations did, demonstrating different profiles of brain activations between discrete numerical estimations and estimations of continuous magnitudes. The activity level in the right middle and inferior frontal gyrus correlated with the tendency to give extreme responses, signifying the importance of the right prefrontal lobe in estimations.

Computing Some Degree-Based Topological Indices of Honeycomb Networks

A topological index is a numeric quantity related with the chemical composition claiming to correlate the chemical structure with different chemical properties. Topological indices serve to predict physicochemical properties of chemical substance. Among different topological indices, degree-based topological indices would be helpful in investigating the anti-inflammatory activities of certain chemical networks. In the current study, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for oxide network O X n , silicate network S L n , chain silicate network C S n , and hexagonal network H X n . Also, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for honeycomb network H C n .

Topological indices relating some nanostructures

The application of mathematics mainly graph theory has a significant role in the development of chemistry. Topological indices act as a bridge between mathematics and chemistry. The topological index is nothing but a numerical quantity that has yielded valuable insights in terms of molecular structure. In nanotechnology, the structural characterization of the molecular species and the nanoparticles are indicated by the indices. These indices identify the symmetry of molecular structures and provide them a scientific terminology to predict qualities like boiling temperatures, viscosity, and gyrating radius. The main objective of the current paper is to compute topological indices with the corresponding formulae, moreover, these indices help in predicting physicochemical properties without the involvement of the laboratory. The current research paper investigated the computation of degree-based topological indices for the nanotubes HAC5C6C7[a,b] and TU(C4C6C8[a,b].

Ve‐Degree, Ev‐Degree, and Degree‐Based Topological Indices of Fenofibrate

The molecular topology of a graph is described by topological indices, which are numerical measures. In theoretical chemistry, topological indices are numerical quantities that are used to represent the molecular topology of networks. These topological indices can be used to calculate several physical and chemical properties of chemical compounds, such as boiling point, entropy, heat generation, and vaporization enthalpy. Graph theory comes in handy when looking at the link between certain topological indices of some derived graphs. In the ongoing research, we determine ve‐degree, ev‐degree, and degree‐based (D‐based) topological indices of fenofibrate’s chemical structure. These topological indices are the Zagreb index, general Randić index, modified Zagreb index, and forgotten topological index. These indices are very helpful to study the characterization of the given structure.

On oscillation of solutions of scalar delay differential equation in critical case

In this paper we study the oscillation problem for the known scalar delay differential equation. We assume that the coefficients of this equation have an oscillatory behaviour with an amplitude of oscillation tending to zero at infinity. The asymptotic formulae for the solutions of the considered equation in the so-called critical case are constructed. We give the conditions for existence of oscillatory or nonoscillatory solutions in terms of certain numerical quantities. The obtained results are illustrated by a number of examples.

A novel analytical Aboodh residual power series method for solving linear and nonlinear time-fractional partial differential equations with variable coefficients

<abstract><p>The goal of this research is to develop a novel analytic technique for obtaining the approximate and exact solutions of the Caputo time-fractional partial differential equations (PDEs) with variable coefficients. We call this technique as the Aboodh residual power series method (ARPSM), because it apply the Aboodh transform along with the residual power series method (RPSM). It is based on a new version of Taylor's series that generates a convergent series as a solution. Establishing the coefficients for a series, like the RPSM, necessitates the computation of the fractional derivatives each time. As ARPSM just requires the idea of an infinite limit, we simply need a few computations to get the coefficients. This technique solves nonlinear problems without the He's polynomials and Adomian polynomials, so the small size of computation of this technique is the strength of the scheme, which is an advantage over the homotopy perturbation method and the Adomian decomposition method. The absolute and relative errors of five linear and non-linear problems are numerically examined to determine the efficacy and accuracy of ARPSM for time-fractional PDEs with variable coefficients. In addition, numerical results are also compared with other methods such as the RPSM and the natural transform decomposition method (NTDM). Some graphs are also plotted for various values of fractional orders. The results show that our technique is easy to use, accurate, and effective. Mathematica software is used to calculate the numerical and symbolic quantities in the paper.</p></abstract>

The number sense: a comparison between normal and adapted curriculum pupils in terms of subitization ability, the distance and magnitude effects

Number sense refers to the ability to easily understand, approximate and manipulate numerical quantities. In solving numerical problems, children use exact, respectively approximate calculation strategies. Unfortunately, some persons encounter difficulties in acquiring basic mathematical skills, and this condition represent a specific learning disability called developmental discalculia. The aim of the present study was to compare normal and adapted curriculum pupils in terms of subitization ability and efectiveness of number sense. The presence of magnitude and distance effects was tested in four distinct formats: 3D objects, 2D figures, verbal and visual Arabic numerical representation. The sample consisted of 111 normal and adapted curriculum pupils. Both number of errors and reaction times were registered. Adapted curriculum pupils registered more erroneous answers in the 2D, verbal, and arabic tasks and bigger reaction times in the 3D, tasks with Arabic or verbal numerals. Both normal and adapted curriculum pupils registered the best performances in the visual Arabic numerical representation task. Contrary to the expectations, the magnitude effect was not outlined in terms of reaction times, perhaps due to the calculation strategies which pupils adopted in different tasks.

Structure, mechanical stability, lattice dynamics and thermodynamic properties of C15-Laves phase Mg2Ce

A systematic study of the structure, mechanical properties, lattice dynamics and thermo-physical properties of C15-Laves phase Mg2Ce is performed through density functional theory (DFT) and density functional perturbation theory (DFPT). The optimized equilibrium lattice constant, equilibrium cell volume, bulk modulus and its pressure derivative reproduce perfectly the available experimental data and other calculated values. The individual crystal elastic constants and polycrystalline aggregates including the isotropic bulk modulus, shear modulus, Young's modulus, brittle/ductile characteristics, Poisson's ratio, Debye temperature and the integration of elastic wave velocities over different directions for C15-Laves phase Mg2Ce have also been evaluated up to 15 GPa using “energy-strain” method, the results indicate that C15–Mg2Ce is mechanically stable up to 15 GPa. Ideal tensile strengths (ITS) along three typical crystallographic orientations, and ideal shear strengths (ISS) in the (010)[101] slip direction of Mg2Ce have been explored by virtue of first principles total energy method. Additionally, both the density functional perturbation theory and the small displacement method are applied to determine the lattice dynamical stability and vibrational modes of Mg2Ce, it is predicted that C15-Laves Mg2Ce system is also dynamically stable up to 15 GPa. The microscopic symmetry properties of optical modes of Mg2Ce at the center of the Brillouin zone have also been analyzed with the combination of group theory. Numerous thermodynamic quantities in the temperature range 0–1000 K and the pressure range 0–15 GPa are obtained further based on quasi-harmonic approximation (QHA) and Debye model.

Children's attention to numerical quantities relates to verbal number knowledge: An introduction to the Build-A-Train task.

Which dimension of a set of objects is more salient to young children: number or size? The 'Build-A-Train' task was developed and used to examine whether children spontaneously use a number or physical size approach on an un-cued matching task. In the Build-A-Train task, an experimenter assembles a train using one to five blocks of a particular length and asks the child to build the same train. The child's blocks differ in length from the experimenter's blocks, causing the child to build a train that matches based on either the number of blocks or length of the train, as it is not possible to match on both. One hundred and nineteen children between 2 years 2 months and 6 years 0months of age (M=4.05, SD=0.84) completed the Build-A-Train task, and the Give-a-Number task, a classic task used to assess children's conceptual knowledge of verbal number words. Across train lengths and verbal number knowledge levels, children used a number approach more than a size approach on the Build-A-Train task. However, children were especially likely to use a number approach over a size approach when they knew the verbal number word that corresponded to the quantity of blocks in the train, particularly for quantities smaller than four. Therefore, children's attention to number relates to their knowledge of verbal number words. The Build-A-Train task and findings from the current study set a foundation for future longitudinal research to investigate the causal relationship between children's acquisition of symbolic mathematical concepts and attention to number.

Topological Characterization of the Third Type of Triangular Hex-derived Networks

A topological index is a numerical quantity that defines a chemical descriptor to report several physical, biological and chemical properties of a chemical structure. In recent literature, various degree-based topological indices of a molecular structure are easily calculated by deriving a M-polynomial of that structure. In this paper, we first determine the expression of a M-polynomial of the triangular Hex-derived network of type three of dimension n and then obtain the corresponding degree-based topological indices from the closed form of M-polynomial. In addition, we use Maple software to represent the M-polynomial and the concerned degree-based topological indices pictorially for different dimensions.

On Wiener Polarity Index and Wiener Index of Certain Triangular Networks

A topological index of graph G is a numerical quantity which describes its topology. If it is applied to the molecular structure of chemical compounds, it reflects the theoretical properties of the chemical compounds. A number of topological indices have been introduced so far by different researchers. The Wiener index is one of the oldest molecular topological indices defined by Wiener. The Wiener index number reflects the index boiling points of alkane molecules. Quantitative structure activity relationships (QSAR) showed that they also describe other quantities including the parameters of its critical point, density, surface tension, viscosity of its liquid phase, and the van der Waals surface area of the molecule. The Wiener polarity index has been introduced by Wiener and known to be related to the cluster coefficient of networks. In this paper, the Wiener polarity index W p G and Wiener index W G of certain triangular networks are computed by using graph-theoretic analysis, combinatorial computing, and vertex-dividing technology.

On Reverse Valency Based Topological Indices of Metal–Organic Framework

Metal–organic frameworks (MOFs) are penetrable materials created by very strong bonds between metal ions and organic ligands to perform very high surface area, large pore volume, attractive chemical stability, and erratic morphology. Work on characteristics, synthesis, and structures of many MOFs manifest the significance of these frameworks with adaptable applications, such as energy storage devices of excellent electrode materials, gas storage, heterogeneous catalysis, environmental hazard, evaluation of chemicals, sensing of distinct gases, conducting solids, and super-capacitors. Topological descriptors are numerical quantity that are used to design various physical, medical, chemical, and pharmacological properties of molecular compounds. It is very fascinating to study the molecular topology that contributes a basis for correlation of physicochemical property of a well-defined molecule. Reverse degree-based topological indices play important role for calculation of topological descriptor. In this article, we give explicit expression of the reverse general Randic index, the reverse atom bond connectivity index, the reverse geometric arithmetic index, the reverse forgotten index, the reverse augmented index, and different types of reverse Zagreb indices of the MOF butylated hydroxytoluene (BHT)- based metal–organic (M = Co, Fe, Mn, and Cr) (MBHT) frameworks. A comparison between the calculated different types of the reverse degree-based topological indices with the aid of the numerical values and their graphs is also included.

Wannier Function Perturbation Theory: Localized Representation and Interpolation of Wave Function Perturbation

Thanks to the nearsightedness principle, the low-energy electronic structure of solids can be represented by localized states such as the Wannier functions. Wannier functions are actively being applied to a wide range of phenomena in condensed matter systems. However, the Wannier-functionbased representation is limited to a small number of bands and thus cannot describe the change of wavefunctions due to various kinds of perturbations, which require sums over an infinite number of bands. Here, we introduce the concept of the Wannier function perturbation, which provides a localized representation of wavefunction perturbations. Wannier function perturbation theory allows efficient calculation of numerous quantities involving wavefunction perturbation, among which we provide three applications. First, we calculate the temperature-dependent indirect optical absorption spectra of silicon near the absorption edge nonadiabatically, i.e., differentiating phonon-absorption and phonon-emission processes, and without arbitrary temperature-dependent shifts in energy. Second, we establish a theory to calculate the shift spin conductivity without any band-truncation error. Unlike the shift charge conductivity, an exact calculation of the shift spin conductivity is not possible within the conventional Wannier function methods because it cannot be obtained from geometric quantities for low-energy bands. We apply the theory to monolayer WTe$_2$. Third, we calculate the spin Hall conductivity of the same material again without any band-truncation error. Wannier function perturbation theory is a versatile method that can be readily applied to calculate a wide range of quantities related to various kinds of perturbations.

VDB Entropy Measures and Irregularity-Based Indices for the Rectangular Kekulene System

Theoretical chemists are fascinated by polycyclic aromatic hydrocarbons (PAHs) because of their unique electromagnetic and other significant properties, such as superaromaticity. The study of PAHs has been steadily increasing because of their wide-ranging applications in several fields, like steel manufacturing, shale oil extraction, coal gasification, production of coke, tar distillation, and nanosciences. Topological indices (TIs) are numerical quantities that give a mathematical expression for the chemical structures. They are useful and cost-effective tools for predicting the properties of chemical compounds theoretically. Entropic network measures are a type of TIs with a broad array of applications, involving quantitative characterization of molecular structures and the investigation of some specific chemical properties of molecular graphs. Irregularity indices are numerical parameters that quantify the irregularity of a molecular graph and are used to predict some of the chemical properties, including boiling points, resistance, enthalpy of vaporization, entropy, melting points, and toxicity. This study aims to determine analytical expressions for the VDB entropy and irregularity-based indices in the rectangular Kekulene system.

Gourava and Hyper-Gourava Indices of Some Cactus Chains

The mathematical chemistry deals with applications of graph theory to study the physicochemical properties of molecules theoretically. A topological index of a graph is a numeric quantity obtained from the graph mathematically. A cactus graph is a connected graph in which no edges lie in more than one cycle. In this paper, we compute Gourava and hyper-Gourava indices of some cactus chains.

Topological Properties of Curcumin and Hyaluronic Acid Conjugated Molecular Structure: An Anti-Cancer Drug

Curcumin is well known for its anti-cancer effectiveness, and its herbal properties. The low water solubility that contributes to decreased bioavailability is one of the significant disadvantages of curcumin. Much emphasis has been focused on polymer-drug conjugates, mainly to bypass the lower solubility of drugs and improve the stability of drugs. This paper discusses the topological research findings on the wound healing efficacy of curcumin conjugated with hyaluronic acid (HA), a natural polysaccharide believed to influence the healing process. Topological indices are critical tools for the analysis of these chemical substances to consider the essential topology. Topological descriptors are the significant numerical quantities or invariant in the fields of chemical graph theory. In this paper, we give explicit expressions of two recently defined novel ev-degrees and ve-degrees and retrieved the quantitative closed formulations for the Zagreb, Randic, geometric-arithmetic and atom-bond connectivity (ABC) indices for the curcumin and hyaluronic acid conjugated molecular structure graph based on ev-degrees and ve-degrees. These kinds of studies may be useful for understanding the biological behavior of drugs.

Gluconic acid content is negatively correlated with total sugar content in honey

Honey contains numerous sugars and small quantities of gluconic acid (GA), which is the major organic acid in honey. To examine the correlation between GA and total sugar contents in honey, GA and total sugar contents were determined in 21 honey samples. The GA content was shown to be negatively correlated with the total sugar content (r = −0.788).