This paper presents the prelaunch radiometric calibration of the Ozone Monitor Suite - Nadir (OMS-N) instrument, a vital payload on the FY-3F satellite. FY-3F achieved a successful launch on August 3, 2023. The radiance calibration of the OMS-N instrument was achieved using an integrating sphere, with known exit radiance ascertained through a transferring radiometer. The calibration model incorporates six energy levels. The Solar Simulator Standard System was employed to validate the calibration results, selecting specific rows to represent varying spatial dimensions. Considering the influence of xenon lamp characteristic peaks and transmission errors during the calibration process, the average deviation remained within 2.3% for the UVIS channel, 3% for the UV1 channel, and 2.2% for the UV2 channel. Furthermore, this study analyzed the uncertainty of the radiometric calibration. The results indicated an absolute uncertainty of 2.32% for both UV1 and UV2 channels, while the VIS channel exhibited an uncertainty of 1.67%. The relative uncertainty was 1.84% for both UV1 and UV2 channels, with the VIS channel exhibiting an uncertainty of 1.45%. The obtained calibration coefficients are accurate and reliable and can be used for the inversion of product parameters, which is of great significance to the quantitative application of satellite data and the advancement of scientific research on quantitative remote sensing.

Abstract: Cell-based neural regeneration is challenging due to the difficulty in obtaining sufficient neural stem cells with clinical applicability. SCAPs originating from embryonic neural crest with high neurogenic potential could be a promising cell source for neural regeneration. This study aimed to investigate whether the formation of 3D spheres can promote SCAPs neurogenic potential. Material and methods: 3D SCAPs spheres were first generated in 256-well agarose microtissue mold. The spheres and single cells were individually cultured on collagen I coated μ-Slide for 4 and 7 days. Cell morphological changes, neural marker expression, and neurite outgrowth were evaluated under a confocal microscope. Secretion of BDNF and NGF-β was measured by ELISA kits. Results: Pronounced morphological changes were noticed in a time-dependent manner. The migrating cells’ morphology changed from fibroblast-like cells to neuron-like cells. Compared to the 2D culture, neurite length, number, and the expression of neural markers, including Nestin, β-tubulin III, NeuN, and MAP-2 were significantly increased in the 3D spheres, while the secretion of BDNF and NGF-β was markedly downregulated at day 7. Conclusion: The formation of 3D spheres enhanced the neurogenic potential of SCAPs, suggesting the advantage of using the 3D spheres of SCAPs for the treatment of neural diseases.

The combined ecological, geophysical, climatic, and social factors of the Northeast of Russia influence the organism from the early childhood being too intense for the functional systems. The purpose of the research is to study the emotional characteristics of adolescents of different ethnic groups in the northeast of Russia. Presented in the paper are results of the study that covered 826 adolescents (445 females and 381 males) at the age of 15–17, different by ethnic origin. We used standard methods of psycho-diagnostics. Our study has showed that the formation of the adolescents’ emotional sphere in the North is undoubtedly influenced not only by the climatic and socio-economic environmental factors but also by ethnic features. There are intergroup differences in the aggressiveness profile of older adolescents living in the remote settlement vs. the regional center. It is shown that high school students in the remote settlement of Evensk, compared to their peers in Magadan, regardless of gender and ethnicity, are characterized by more pronounced hostile and auto-aggressive reactions. In adolescents of the Aboriginal population, as compared with their age mate Caucasians, the indicators of impairment in the field of Neuro Psychic Adaptation, Situational and Personal Anxiety, and Social Frustration are significantly more pronounced.

We demonstrate, in the context of Loop Quantum Gravity, the Quantum Holographic Principle, according to which the area of the boundary surface enclosing a region of space encodes a qubit per Planck unit. To this aim, we introduce fermion fields in the bulk, whose boundary surface is the two-dimensional sphere. The doubling of the fermionic degrees of freedom and the use of the Bogoliubov transformations lead to pairs of spin network’s edges piercing the boundary surface with double punctures, giving rise to pixels of area encoding a qubit. The proof is also valid in the case of a fuzzy sphere.

Collective spread of aggregated viral particles may have beneficial effects on viral capability to survive in the external environment, to counteract immune responses, and to successfully colonize host cells. Here we ask whether SARS-Cov-2 particles, responsible for COVID-19, display collective clustering behavior. Looking at microphotographs and movies of SARS-Cov-2 particles emerging from the surface of cultured cells, we describe single virions that tend to aggregate in progressively larger globular assemblies, until a network-like appearance is achieved. When SARS-Cov-2 particles stick into each other, the squeezing of single virions leads to improved viral package in host’s fluids. We discuss how these findings might explain both the ability to spread of SARS-Cov-2 and the clinical severity of COVID-19 in humans, paving the way to novel therapeutic strategies to mechanically disrupt collective clustering.

Abstract: The chemical mechanical polishing (CMP) has been widely used for surface modification of critical materials and components and provided global planarization of topography with a low post-planarization slope high quality and efficiency. The colloidal silica slurries play an important role in the finishing processes of optical components. Monodisperse mesoporous silica nanospheres were synthesized with different surfactant by Stöber method. Their architectural features and texture parameters were characterized by XRD, FTIR, N2 adsorption–desorption isotherms, SEM, XPS, and TGA techniques. The spherical SiO2 products presented with the controllable 50-150 nm particle size and distribution. The AFM micrographs reveal that flat and smooth surfaces without distinct scratches residual particles are achieved by using the as-obtained composite particles as abrasives[The particle size of SiO2 slurry plays a critical role in the chemical-mechanical polishing process.

Physical measurements might display range values extending towards infinite. The occurrence of infinity in physical equations, such as the black hole singularities, is a troublesome issue that causes many theories to break down when assessing extreme events. Different methods, such as re-normalization, have been proposed to avoid detrimental infinity. Here a novel technique is proposed, based on physical geometrical considerations and the Alexander Horned sphere, that permits to undermine infinity in physical equations. In this unconventional approach, a continuous monodimensional line becomes an assembly of countless bidimensional lines that superimpose in quantifiable knots and bifurcations.

We introduce a special vector field ω on a Riemannian manifold (N^m, g), such that the Lie derivative of the metric g with respect to ω is equal to ρRic, where Ric is the Ricci curvature of (N^m, g) and ρ is a smooth function on N^{m} and call this vector field a ρ-Ricci vector field. We use ρ-Ricci vector field on a Riemannian manifold (N^m, g) and find two characterizations of m-sphere S^m(α). In first result, we show that an m-dimensional compact and connected Riemannian manifold (N^m, g) with nonzero scalar curvature admits a ρ-Ricci vector field ω such that ρ is nonconstant function and the integral of Ric(ω,ω) has a suitable lower bound is necessary and sufficient for (N^m, g) to be isometric to m-sphere S^m(α). In second result, we show that an m-dimensional complete and simply connected Riemannian manifold (N^m, g) of positive scalar curvature admits a ρ-Ricci vector field ω such that ρ is a nontrivial solution of Fischer-Marsden equation and the squared length of the covariant derivative of ω has an appropriate upper bound, if and only if, (N^m, g) to be isometric to m-sphere S^m(α).

This research explores the intricate relationship between gravitational and cosmic redshift phenomena, unveiling a profound understanding of how light behaves as it traverses the cosmos. The study begins with an examination of gravitational redshift, a well-established concept occurring when photons move away from massive gravitational sources, such as stars within galaxies. Gravitational redshift, expressed as λ/λ₀, manifests within the gravitational influence and extends to the boundary of the observed "zero-gravity sphere" enveloping galaxies. Within this remarkable zero-gravity sphere, gravitational effects persist, while the antigravity influence of dark energy remains negligible. As a result, gravitational redshift dominates, and cosmic redshift is notably absent within the sphere. Photons within this sphere maintain their constant speed 'c' and undergo gravitational redshift exclusively. However, as photons exit the zero-gravity sphere at a distance 'r' equivalent to the source star's radius, they encounter the onset of cosmic redshift, quantified as {(λ_obs - λ_emit)/ λ_emit}. Cosmic redshift blends with gravitational redshift, forming the effective redshift of the photon. Critically, the effective cosmic redshift surpasses gravitational redshift, illuminating a profound revelation: photons traverse a greater "light-traveled distance" than their proper distance from the source. In essence, cosmic redshift signifies that photons move across their intended distances at their intrinsic speed c, while the expanding universe introduces a relative distance expansion, influenced by antigravity. This research delves into the intricate dance between gravitational and cosmic redshift, shedding light on their remarkable implications for our comprehension of the expanding universe.

The issue of being pro-gender is still a controversial topic to be debated in Indonesian society. However, in the 21st Century, many women have been able to break through barriers and participate in the public sphere. It is a form of self-existence as proposed by Simone de Beauvoir on existentialist feminism. Based on these problems, this study aims to find out and answer questions about how Indonesian women exist in the public sphere in the 21st Century and find out how Indonesian women exist in the public sphere through Simone de Beauvoir's existentialist feminism paradigm. The research method used is descriptive-qualitative through a literature review of 23 journal articles, websites, and data reports with a range of 2019-2021. This study found that based on Simone de Beauvoir's feminist paradigm, Indonesian women in the 21st Century are no longer a figure other than complete. Furthermore, the data collected by the researcher shows that several gender indicators have shown that Indonesian women have been able to occupy public spaces in various aspects. Based on these results, it is hoped that it can provide information about Simone de Beauvoir's existentialist feminism thought and its relevance to the existence of Indonesian women in the public sphere in the 21st Century. However, this research has limitations, those are only about women in Indonesia, and the paradigm of feminism is limited to Simone de Beauvoir's existentialist feminism.

Here, we propose a novel scheme based on advanced techniques of digital modulation in optical communications to achieve a single-channel transmission rate above 100 Gb/s. We utilize a hybrid scheme amplitude/phase/frequency/dual polarization, combined with multidimensional dual lattice and a low-density parity-check-coded modulation. The Stokes parameters are applied to the proposed scheme to map the four-dimensional classical polarization \({I_X},{Q_X},{I_Y},{Q_Y}\) in a three-dimensional space. In addition, in the proposed system, the packing theory is applied to the bit interleaver process, three wavelengths are packaged before being transmitted over a wavelength-division multiplexing optical channel. This modulation process is carried out using symmetrical geometric shapes, such as a hypercube or a polyhedron, based on the molecular links theory using a grouping of 12 and 13/15 bits for the cubic and spherical lattices, respectively. The proposed technique is evaluated in the context of long distance communications over distances up to 100 km. The bit error rate results showed that the optical signal-to-noise ratio was approximately 4 dB over a distance of 50 km. In addition, the power spectral efficiency was found to be 3 lambda, which is considered good performance considering the effects of distance and the non-linear effects influencing the number of lambdas. Also, we use an optical time division multiplexing scheme (OTDM) in order to achieve a transmission rate beyond 1Tbit/s, where the speed effect is evaluated, taking into consideration that the power spectral efficiency is degraded. Furthermore, the average noise floor is -60dBm for all transmission distances. These findings are expected to contribute to the future implementation of robust long-distance optical communication infrastructure.

The Casimir effect can either work over very short distances or at very low temperatures. At the cosmic scale, we naturally deal with long distances, but at the same time, we encounter extraordinarily low temperatures, namely the CMB (Cosmic Microwave Background) tem- perature. Recently, there has been increased interest in the Casimir effect and its implications in cosmology. Here, we briefly demonstrate that the luminosity and radiation pressure of the CMB is mathematical identical to a theoretical Casimir effect within the Hubble sphere, or actually our solution seems to be valid for any Schwarzschild black hole. The Casimir effect forevery Schwarzschild black hole is identical. This also include the Hubble sphere if we treat it as a Schwarzschild black hole that is related to increased interest in black hole cosmology.

\abstract{The existence of vorticies is well known in fluid mechanics and particularly in turbulence theory. In the context of the millennium problem of the Clay Institute on the existence (or not) of Global solutions in time of the Periodic Navier Stokes equations (PNS) results are now proposed to confirm that Global solutions do not exist in the general case of PNS defined on $\mathbb{T}^3$. This corresponds to part ($D$) proposition in the Navier Stokes problem as posted by C.Fefferman. Recent work has shown that for the Euler equations defined on the 3-Torus there exists a H\"older continuous solution for the third component of velocity $v_3$ at the center of each cell or cube of the 3-Torus Lattice. It has also been determined that as the kinematic viscosity changes from the corresponding value at $\nu=0$ to the fully viscous case for the Periodic Navier Stokes equations (PNS) at the value $\nu=1$ the solution reaches a peak ($\frac{\partial v_3}{\partial y_3} = 0$ ) in $y_3$. (third component of $\vec{r}=(y_1,y_2,y_3)$ in Cartesian co-ordinates) Here in the viscous case there exists a dipole which is not centered at the center of the cell of the Lattice. This immediately implies that since the dipole by definition has an equal in magnitude positive and negative peak in the third component of velocity, then the dipole Riemann cut-off surface is covered by a closed surface which is the sphere $\|\vec{r}\|=1$ and where a given cell of dimensions $[-1,1]^3$ is circumscribed on a sphere of radius $1$. For such a closed surface containing a dipole it necessarily follows that the flux at the surface of the sphere of $v_3$ wrt to surface normal $\vec{n}$ is zero including at $y_i, i=1\dots 3$ is zero at the points where the surface of sphere touches the cube walls. At the finite time singularity on the sphere a rotation boundary condition is deduced. Here $\frac{\partial v_3}{\partial \vec{n}}= \vec{n}\cdot \nabla v_3$. Also a boundary condition on the sphere shows rotation of sphere. Finally as a result, on the sphere a solution for $v_3$ is obtained which is proven to be H\"older continuous and it is proven that it is possible to extend H\"older continuity on the sphere uniquely to all of the interior of the ball.}

The bulk backscattering ratio ($\tilde{b_{bp}}$) is commonly used as a descriptor of the bulk real refractive index of the particulate assemblage in natural waters. Based on numerical simulations, we analyze the impact of heterogeneity of phytoplankton cells on $\tilde{b_{bp}}$. $\tilde{b_{bp}}$ is modeled considering viruses, heterotrophic bacteria, phytoplankton, detritus, and minerals. Three study cases are defined according to the relative abundance of these different components. Two study cases represent typical situations in open ocean, outside (No-B/No-M) and inside bloom (B/No-M). The third study case is typical of coastal waters with the presence of minerals. Phytoplankton cells are modeled by a two-layered spherical geometry representing a chloroplast surrounding the cytoplasm. The $\tilde{b_{bp}}$ values are higher when heterogeneity is considered because the contribution of coated spheres to backscattering is higher than homogeneous spheres. The impact of heterogeneity is however strongly conditioned by the hyperbolic slope $\xi$ of the particle size distribution. Even if the relative concentration of phytoplankton is small (<1%), $\tilde{b_{bp}}$ increases by about 60% (for $\xi=4.3$ and for the No-B/No-M water body), when the heterogeneity is taken into account, in comparison with a particulate population only composed by homogeneous spheres. As expected, heterogeneity has a much smaller impact (about 5$\%$ for $\xi=4.3$) on $\tilde{b_{bp}}$ when minerals are added.

We will apply Pascal’s hydrostatic pressure law to black holes and also to the Hubble sphere. Haug has recently demonstrated how hydrostatic pressure in water can be utilized to determine the Planck length. One can conceptualize the energy in the Hubble sphere as a type of superfluid, and if this is correct, then Blaise Pascal’s hydrostatic pressure formula may also be applicable to such a superfluid, even within the Hubble sphere. By employing the same method on the Hubble sphere and considering it as a Schwarzschild black hole with the critical Friedmann mass, we can estimate the Planck length based on its hypothetical hydrostatic pressure.

Particle-mediated elasticity/viscoelasticity imaging has potential to expand the elasticity imaging field, as it can provide accurate and local tissue elastic properties as well as density, Poisson’s ratio, and viscosity. Here, we investigated elasticity imaging based on the use of small particles located within the tissue and at the tissue interface exposed to a static and dynamic external load. First, we discuss elasticity/viscoelasticity imaging methods based on the use of particles (bubbles and rigid spheres) located within the tissue. Elasticity/viscoelasticity imaging techniques based on the use of particles (bubbles, rigid and soft spheres) located at the tissue interface are then presented. Based on new advances, we updated some of the models for the responses of the particles located within the tissue and at the tissue interface available in the literature. Finally, we compared the mathematical models for the particles located within the tissue and at the tissue interface and evaluated the elasticity/viscoelasticity imaging methods based on the use of small particles. Therefore, instead of the use of the term elasticity imaging, we suggest the use of the term viscoelasticity imaging.

Coronavirus disease 2019 (COVID-19) affected not only individuals but also families. The purpose of this study was to clarify the temporal changes in the impact of the COVID-19 pandemic on entire families with older adults susceptible to infection living on small islands in Japan over the duration of the pandemic. Family ethnographic research was conducted from 2021 to 2023, using the Concentric Sphere Family Environment Theory as the theoretical framework. Formal interviews were conducted with 20 families. In addition, data from informal interviews, participant observation and other sources were compiled into field notes. All data on the impact on the entire family were extracted and content analysis was conducted. Five categories and a total of 85 subcategories were extracted. The results show that COVID-19 exerted not only negative but also positive impacts on the entire family, and their temporal changes are clarified. The impact on families is believed to have been influenced by the family external environment, such as increases and decreases of infection cases or events that occurred outside the family. The knowledge acquired from these studies will help healthcare professionals in providing appropriate family support.

We study the tight focusing properties of generic bright and dark HyOPS beams in the presence of primary coma. The role of the polarization singularity index and handedness of the polarization of the HyOPS beams on the focused structure has been discussed. Results have been presented for the total intensity, component intensities, and component phase distributions for left-, and right-handed bright and dark star and lemon types singularities. The presence of primary coma distorted the focal plane intensity distributions for both positive and negative index generic C-points. Coma is known to disturb the circular symmetry of the focal plane intensity distribution. Similarly in tight focusing polarization is known to disturb the symmetry. Therefore, a beam with structured and inhomogeneous polarization distribution tightly focused under the influence of coma is a fit case to study. It is found that the presence of primary coma aberration in the focusing system produces a positional shift of the high-intensity peaks and a reduction of the intensity on one side of the center. As the strength of the primary coma increases, the focal plane intensity distributions shift more and more toward the right from the initial position. Unlike the scalar vortex case, in the case of HyOPS beams, the focal plane intensity distribution undergoes rotation, as the helicity of the HyOPS beams is inverted, in addition to shifting. All the component phase distributions are found to be embedded with phase vortices of charge ±1.

Primate vision is an active process that constructs a stable internal representation of the 3D world based on 2D sensory inputs that are inherently unstable due to incessant eye movements. We present here a mathematical framework for processing visual information for a biologically-mediated active vision stereo system with asymmetric conformal cameras. This model utilizes the geometric analysis on the Riemann sphere developed in the group-theoretic framework of the conformal camera, thus far only applicable in modeling monocular vision. The asymmetric conformal camera model constructed here includes the fovea’s asymmetric displacement on the retina and the eye’s natural crystalline lens tilt and decentration, as observed in ophthalmological diagnostics. We extend the group-theoretic framework underlying the conformal camera to the stereo system with asymmetric conformal cameras. Our numerical simulation shows that the 1 theoretical horopter curves in this stereo system are conics that well approximate the empirical longitudinal horopters of the primate vision system.

The objective of this paper is to investigate the convergence of coupling-parameter expansion-based solutions to Ornstein-Zernike equation in liquid state theory. The analytically solved Baxter's adhesive hard sphere model is analyzed first using coupling-parameter expansion. It is found that the expansion provides accurate approximations to solutions - including the liquid-vapor phase diagram - in most parts of the phase plane. However, it fails to converge in the region where the model has only complex solutions. Similar analysis and results are, then, obtained using analytical solutions within the mean spherical approximation for the hard-core Yukawa potential. Next, convergence of the expansion is analyzed for the Lennard-Jonnes potential using an accurate density-dependent bridge function in the closure relation. Numerical results are presented which show convergence of correlation functions, compressibility versus density profiles, etc., in the single as well as two phase regions. Computed liquid-vapor phase diagrams, using two independent schemes employing the converged profiles, compare excellently with simulation data. Results obtained for the generalized Lennard-Jonnes potential, with varying repulsive exponent, also compare well with simulation data. All these results together establish the coupling-parameter expansion as a practical tool for studying single component fluid phases modeled via general pair-potentials.

We present results on the spontaneous crystallization of freely-jointed polymers of hard spheres obtained in an unprecedentedly long Monte Carlo (MC) simulation on a system of 54 chains of 1000 monomers. Starting from a purely amorphous configuration and after a transitory dominance of the hexagonal closed packed (HCP) polymorph, the system crystallizes in a final, stable, face centered cubic (FCC) crystal of very high perfection. Through refined metrics we gauge the degree of ordering and identify the regions of the phase transition and the corresponding morphologies. An analysis of chain conformational characteristics, of the spatial distribution of monomers and of the volume accessible to them shows that the phase transition is caused by an increase in translational entropy that is larger than the loss of conformational entropy of the chains in the crystal compared to the amorphous state. Polymer chains in the crystal adopt ideal random walk statistics as their great length renders local conformational details, imposed by the geometry of the FCC crystal, irrelevant.

Imaginary dimensions in physics require an imaginary set of base Planck units and some negative parameter $c_n$ corresponding to the speed of light in vacuum $c$. The second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$ present in Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene leads to the imaginary Planck units. Furthermore, it sets $c_n \approx -3.06 \times 10^8~\text{[m/s]}$. It follows that electric charges are the same in real and imaginary dimensions. Neutron stars and white dwarfs, objects emitting perfect black-body radiation, need energy exceeding their mass-energy equivalence ratios. Complex energies are defined in terms of real and imaginary Planck units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It follows that black holes are fundamentally uncharged, charged micro neutron stars and white dwarfs with masses lower than $5.7275 \times 10^{-10}~[\text{kg}]$ are unphysical, and the radii of white dwarfs' cores are limited to $R_{\text{WD}} < 6.7933~G M_{\text{WD}}/c^2$. It is conjectured that the maximum atomic number $Z=238$. A black-body object is in the equilibrium of complex energies of masses, charges, and wavelengths if its radius $R_\text{eq} \approx 2.7665~G M_{\text{BBO}}/c^2$, which corrects the value of the photon sphere radius $R_{\text{ps}}=3G M/c^2$, taking into account the value(s) of the fine-structure constant(s), which is otherwise neglected in general relativity.

The local and global order in dense packings of linear, semi-flexible polymers of tangent hard spheres are studied by employing extensive Monte Carlo simulations at increasing volume fractions. Chain stiffness is controlled by a tunable harmonic potential for the bending angle whose intensity dictates the rigidity of the polymer backbone as a function of the bending constant and equilibrium angle. The studied angles range from acute to obtuse ones, reaching the limit of rod-like polymers. We analyze how packing density and chain stiffness affect the ability of chains to self-organize at the local and global levels. The former corresponds to crystallinity as quantified by the Characteristic Crystallographic Element (CCE) norm descriptor, while the latter is computed through the scalar orientational order parameter. In all cases, we identify the critical volume fraction for the phase transition and gauge the established crystal morphologies, developing a complete phase diagram as a function of packing density and equilibrium bending angle. A plethora of structures is obtained, ranging from random hexagonal closed packed morphologies of mixed character and almost perfect face centered cubic (FCC) and hexagonal close-packed (HCP) crystals at the level of monomers, to nematic mesophases, with prolate and oblate mesogens at the level of chains. For rod-like chains, hysteresis is observed between the establishment of long-range nematic order and crystallization, while for right-angle chains both transitions are synchronized. A comparison is also provided against the analogous packings of monomeric and fully flexible chains of hard spheres.

In the present work we revise and extend the Characteristic Crystallographic Element (CCE) norm, an algorithm used to simultaneously detect radial and orientational similarity of computer-generated structures with respect to specific reference crystals and local symmetries. Based on the identification of point group symmetry elements, the CCE descriptor is able to gauge local structure with high precision and finely distinguish between competing morphologies. As test cases we use computer-generated monomeric and polymer systems of spherical particles interacting with the hard-sphere and square-well attractive potentials. We demonstrate that the CCE norm is able to detect and differentiate, between others, among: hexagonal close packed (HCP), face centered cubic (FCC), hexagonal (HEX) and body centered cubic (BCC) crystals as well as non-crystallographic fivefold (FIV) local symmetry in bulk 3-D systems; triangular (TRI), square (SQU) and honeycomb (HON) crystals, as well as pentagonal (PEN) local symmetry in thin films of one-layer thickness (2-D systems). The descriptor is general and can be applied to identify the symmetry elements of any point group for arbitrary atomic or particulate system in two or three dimensions, in the bulk or under confinement.

Spinors are used for the computation of probability in quantum mechanics. They are treated as elements of a complex vector space in contrast to a real vector space. Spinor theory is abstract mathematics with an ambiguous interpretation. The overall phase of spinors does not affect the computation of probability in quantum mechanics. If two spinors have an overall phase of imaginary number i, then they can be treated like vectors in a real vector space. The square of the magnitude of the number, which is the sum of dot product and the term having basis vector i of cross product of two such vectors, is equal to the probability computed using the corresponding spinors. Therefore, the geometry of such spinors can be easily depicted in a three-dimensional space like vectors in a real vector space. Spinors are not isotropic vectors in Hilbert space. The sum of dot product and cross product of two complex numbers is equivalent to the quotient of the division of one complex number by another. Similarly, the sum of dot product and cross product of two vectors is the quotient of the division of one vector by another. Using the rules of division of vectors, we can find the rules of multiplication of vectors. The rules of multiplication and division of basis vector i match the rules of multiplication and division of imaginary number i. Therefore, basis vector i is nothing but imaginary number i. Multiplication of dot and cross product of two vectors to the second vector will give us the components of the first vector that are parallel and orthogonal to the second vector. Vectors are also made up of complex numbers like spinors. The reason for finding dot product of complex numbers in the process of computing the probability is to ignore the overall phase in contrast to the phase difference. This is misconstrued as complex vector space in quantum mechanics. 3-D number which is nothing but a spinor with new notation is an extension of vector algebra. It can have a real number as a term in addition to the terms i, j and k. In all other respects, it is a vector. 3-D numbers are part of the number system like real numbers and complex numbers. The real numbers are one dimensional numbers, the complex numbers are two-dimensional numbers and the 3-D numbers as well as vectors and spinors are three-dimensional numbers. As polarisation and spin are one and the same, we can straight away apply 3-D numbers to polarisation of light. 3-D numbers will greatly simplify the study of areas of science where three-dimensional space is involved.