arXiv subjects

Richard Pincak

Publications and source records attributed to Richard Pincak.

At least 19 recordsLinked to original sources

arXiv2025

A note on the theoretical approach to Grassmannians and Plücker coordinates for additive skew-symmetric pairwise comparisons matrices

Symmetry and antisymmetry are fundamental concepts in many strict sciences. Pairwise comparisons (PC) matrices are fundamental tools for representing pairwise relations in decision making. In this theoretical study, we present a novel framework that embeds additive skew-symmetric PC matrices into the Grassmannian manifold $G(2, n)$. This framework leverages Plücker coordinates to provide a rigorous geometric interpretation of their structure. Our key result demonstrates that the algebraic consistency condition $a_{ij} + a_{jk} - a_{ki} = 0$ is equivalent to the geometric consistency of $2$-planes in $G(2, n)$, satisfying the Plücker relations. This connection reveals that the algebraic properties of PC matrices can be naturally understood through their geometric representation. Additionally, we extend this framework by interpreting PC matrices as differential $2$-forms, providing a new perspective on their consistency as a closedness condition. Our framework of linear algebra, differential geometry, and algebraic geometry, placing PC matrices in a broader mathematical context. Rather than proposing a practical alternative to existing methods, our study aims to offer a theoretical foundation for future research by exploring new insights into higher-dimensional geometry and the geometric modeling of pairwise comparisons.

math.DG↗

arXiv2024

Analysis of a special type of soliton on Kenmotsu manifolds

In this paper, we aim to investigate the properties of an almost $*$-Ricci-Bourguignon soliton (almost $*-$R-B-S for short) on a Kenmotsu manifold (K-M). We start by proving that if a Kenmotsu manifold (K-M) obeys an almost $*-$R-B-S, then the manifold is $η$-Einstein. Furthermore, we establish that if a $(κ, -2)'$-nullity distribution, where $κ<-1$, has an almost $*$-Ricci-Bourguignon soliton (almost $*-$R-B-S), then the manifold is Ricci flat. Moreover, we establish that if a K-M has almost $*$-Ricci-Bourguignon soliton gradient and the vector field $ξ$ preserves the scalar curvature $r$, then the manifold is an Einstein manifold with a constant scalar curvature given by $r=-n(2n-1)$. Finaly, we have given en example of a almost $*-$R-B-S gradient on the Kenmotsu manifold.

physics.gen-ph↗

arXiv2023

A K-Theory approach to characterize admissible physical manifolds

We will classify physically admissible manifold structures by the use of Waldhausen categories. These categories give rise to algebraic K-Theory. Moreover, we will show that a universal K-spectrum is necessary for a physical manifold being admissible. Application to the generalized structure of D-branes are also provided. This might give novel insights in how the manifold structure in String and M-Theory looks like.

math.GN↗

arXiv2022

A family of special case of sequential warped product manifolds with semi-Riemannian Einstein metrics

We derive the general formulas for a special configuration of the sequential warped product semi-Riemannian manifold to be Einstein, where the base-manifold is the product of two manifolds both equipped with a conformal metrics. Subsequently we study the case in which these two manifolds are conformal to a $n_1$-dimensional and $n_2$-dimensional pseudo-Euclidean space, respectively. For the latter case, we prove the existence of a family of solutions that are invariant under the action of a $(n_1-1)$-dimensional group of transformations to the case of positive constant Ricci curvature ($λ>0$).

math.DG↗

arXiv2022

Existence and Nonexistence of Warped Product Submanifolds of Almost Contact Manifolds

This paper has two goals; the first is to generalize results for the existence and nonexistence of warped product submanifolds of almost contact manifolds, accordingly a self-contained reference of such submanifolds is offered to save efforts of potential research. Most of the results of this paper are general and decisive enough to generalize both discovered and not discovered results. Moreover, a discrete example of contact CR-warped product submanifold in Kenmotsu manifold is constructed. For further research direction, we addressed a couple of open problems arose from the results of this paper.

math.DG↗

arXiv2021

A topological approach for emerging D-branes and its implications for gravity

We introduce a new geometric/topological approach to the emerging braneworld scenario in the context of D-branes using partially negative dimensional product (PNDP) manifolds. The working hypothesis is based on the fact that the orientability of PNDP manifolds can be arbitrary, and starting from this, we propose that gravitational interaction can derive naturally from the non-orientability. According to this hypothesis, we show that topological defects can emerge from non-orientability and they can be identified as gravitational interaction at macroscopic level. In other words, the orientability of fundamental PNDPs can be related to the appearance of curvature at low energy scales.

physics.gen-ph↗

arXiv2018

GARCH(1,1) model of the financial market with the Minkowski metric

We solved a stylized fact on a long memory process of volatility cluster phenomena by using Minkowski metric for GARCH(1,1) under assumption that price and time can not be separated. We provide a Yang-Mills equation in financial market and anomaly on superspace of time series data as a consequence of the proof from the general relativity theory. We used an original idea in Minkowski spacetime embedded in Kolmogorov space in time series data with behavior of traders.The result of this work is equivalent to the dark volatility or the hidden risk fear field induced by the interaction of the behavior of the trader in the financial market panic when the market crashed.

q-fin.ST↗

arXiv2018

The Chern-Simons Current in Time Series of Knots and Links in Proteins

A superspace model of knots and links for DNA time series data is proposed to take into account the feedback loop from docking to undocking state of protein-protein interactions. In particular, the direction of interactions between the 8 hidden states of DNA is considered. It is a $E_{8}\times E_{8}$ unified spin model where the genotype, from active and inactive side of DNA time data series, can be considered for any living organism. The mathematical model is borrowed from loop-quantum gravity and adapted to biology. It is used to derive equations for gene expression describing transitions from ground to excited states, and for the 8 coupling states between geneon and anti-geneon transposon and retrotransposon in trash DNA. Specifically, we adopt a modified Grothendieck cohomology and a modified Khovanov cohomology for biology. The result is a Chern-Simons current in $(8+3)$ extradimensions of a given unoriented super manifold with ghost fields of protein structures. The $8$ dimensions come from the 8 hidden states of spinor field of genetic code. The extradimensions come from the 3 types of principle fiber bundle in the secondary protein.

physics.gen-ph↗

arXiv2018

Cosmic acceleration in non-flat $f(T)$ cosmology

We study $f(T)$ cosmological models inserting a non-vanishing spatial curvature and discuss its consequences on cosmological dynamics. To figure this out, a polynomial $f(T)$ model and a double torsion model are considered. We first analyze those models with cosmic data, employing the recent surveys of Union 2.1, baryonic acoustic oscillation and cosmic microwave background measurements. We then emphasize that the two popular $f(T)$ models enable the crossing of the phantom divide line due to dark torsion. Afterwards, we compute numerical bounds up to 3-$σ$ confidence level, emphasizing the fact that $Ω_{k0}$ turns out to be non-compatible with zero at least at 1$σ$. Moreover, we underline that, even increasing the accuracy, one cannot remove the degeneracy between our models and the $Λ$CDM paradigm. So that, we show that our treatments contain the concordance paradigm and we analyze the equation of state behaviors at different redshift domains. We also take into account gamma ray bursts and we describe the evolution of both the $f(T)$ models with high redshift data. We calibrate the gamma ray burst measurements through small redshift surveys of data and we thus compare the main differences between non-flat and flat $f(T)$ cosmology at different redshift ranges. We finally match the corresponding outcomes with small redshift bounds provided by cosmography. To do so, we analyze the deceleration parameters and their variations, proportional to the jerk term. Even though the two models well fit late-time data, we notice that the polynomial $f(T)$ approach provides an effective de-Sitter phase, whereas the second $f(T)$ framework shows analogous results compared with the $Λ$CDM predictions.

gr-qc↗

arXiv2018

Electronic properties of phosphorene and graphene nanoribbons with edge vacancies in magnetic field

The graphene and phosphorene nanostructures have a big potential application in a large area of actuals research in physics. However, their methods of synthesis still do not allow the production of perfect materials with an intact molecular structure. In this paper, the occurrence of atomic vacancies was considered in the edge structure of the zigzag phosphorene and graphene nanoribbons. For different concentrations of these edge vacancies, their influence on the metallic properties was investigated. The calculations were performed for different sizes of the unit cell. Furthermore, for a smaller size, the influence of a uniform magnetic field was added.

cond-mat.mes-hall↗

arXiv2017

Anomaly on Superspace of Time Series Data

We apply the G-Theory and anomaly of ghost and anti-ghost fields in the theory of supersymmetry to study a superspace over time series data for the detection of hidden general supply and demand equilibrium in the financial market. We provide a proof of the existence of the general equilibrium point over 14-extradimensions of the new G-theory compared to M-theory of 11 dimensions model of Edward Witten. We found that the process of coupling between nonequilibrium and equilibrium spinor fields of expectation ghost fields in the superspace of time series data induces an infinitely long exact sequence of cohomology from a short exact sequence of moduli state space model. If we assume that the financial market is separated into $2$ topological spaces of supply and demand as the D-brane and anti-D-brane model, then we can use a cohomology group to compute the stability of the market as a stable point of the general equilibrium of the interaction between D-branes of the market. We obtain the result that the general equilibrium will exist if and only if the 14-th-Batalin-Vilkovisky cohomology group with the negative dimensions underlying major 14 hidden factors influencing the market is zero.

physics.gen-ph↗

arXiv2017

The Chern-Simons current in systems of DNA-RNA transcriptions

A Chern-Simons current, coming from ghost and anti-ghost fields of supersymmetry theory, can be used to define a spectrum of gene expression in new time series data where a spinor field, as alternative representation of a gene, is adopted instead of using the standard alphabet sequence of bases $A, T, C, G, U$. After a general discussion on the use of supersymmetry in biological systems, we give examples of the use of supersymmetry for living organism, discuss the codon and anti-codon ghost fields and develop an algebraic construction for the trash DNA, the DNA area which does not seem active in biological systems. As a general result, all hidden states of codon can be computed by Chern-Simons 3 forms. Finally, we plot a time series of genetic variations of viral glycoprotein gene and host T-cell receptor gene by using a gene tensor correlation network related to the Chern-Simons current. An empirical analysis of genetic shift, in host cell receptor genes with separated cluster of gene and genetic drift in viral gene, is obtained by using a tensor correlation plot over time series data derived as the empirical mode decomposition of Chern-Simons current.

physics.gen-ph↗

arXiv2017

Quarkonium in a thermal BIon

In the present article, the authors intend to propose a new theory which potentially allows the propagation of the formation and the evolution of quarkonium in a thermal BIon. When quarks are close to each other, quarkonium behaves like a scalar and by their getting away, it transits to a fermionic system. In order to analyze this particular behaviour, a new outlook approach needs to be adopted as the concurrent view is found deficient to analyse the aforesaid behaviour. Therefore, the authors' post deliberation accept the fermions and fermionic being cognate. We need to accept a theory that the origin of fermions and bosons be the same. However, in $M$-theory, these particles are independent and for this reason, \textbf{we use a new broader theory based on Lie-$N$-Algebra and we call it BLNA (Broad Lie-$N$-Algebra)} theory. Thus, the BLNA in a way the $M$-theory with $11$ dimensions. In this model, two types of energies with opposite signs emerge from nothing such as the sum over them becomes zero. They produce two types of branes with opposite quantum numbers and bosonic fields, which interact with each other and get compact. By compacting branes, the quarks and anti-quarks are produced on branes and exchange the graviton and the gravitino. These particles produce two types of wormholes which act opposite to each other. They preclude from closing or getting away of branes from each other and also occurrence of confinement. This confined potential which emerges from these wormholes depends on the separation distance between quarks and anti-quarks and also on temperature of system and is reduced to predicted potential in experiments and QCD. Also, total entropy of this system grows with increasing temperature and produces a repulsive force which leads to the separation of quarks and anti-quarks and also to the emergence of deconfinement.

hep-th↗

arXiv2017

Effects of ultrasound waves intensity on the removal of Congo red color from the textile industry wastewater by Fe3O4@TiO2 core-shell nanospheres

Environmental pollutants, such as colors from the textile industry, affect water quality indicators like color, smell, and taste. These substances in the water cause the obstruction of filters and membranes and thereby reduce the efficiency of advanced water treatment processes. In addition, they are harmful to human health because of reaction with disinfectants and production of by-products. Iron oxide nanoparticles are considered effective absorbents for the removal of pollutants from aqueous environments. In order to increase the stability and dispersion, nanospheres with iron oxide core and titanium dioxide coating were used in this research and their ability to absorb Congo red color was evaluated. Iron oxide-titanium oxide nanospheres were prepared based on the coprecipitation method and then their physical properties were determined using a tunneling electron microscope (TEM) and an X-ray diffraction device. Morphological investigation of the absorbent surface showed that iron oxide-titanium oxide nanospheres sized about 5 to 10 nm. X-ray dispersion survey also suggested the high purity of the sample. In addition, the absorption rate was measured in the presence of ultrasound waves and the results indicated that the capacity of the synthesized sample to absorb Congo red is greatly dependent on the intensity power of ultrasound waves, as the absorption rate reaches 100% at powers above 30 watts.

physics.app-ph↗

arXiv2017

Birth of the GUP and its effect on the entropy of the Universe in Lie-$N$-algebra

In this paper, the origin of the generalized uncertainty principle (GUP) in an $M$-dimensional theory with Lie-$N$-algebra is considered. This theory which we name GLNA(Generalized Lie-$N$-Algebra)-theory can be reduced to $M$-theory with $M=11$ and $N=3$. In this theory, at the beginning, two energies with positive and negative signs are created from nothing and produce two types of branes with opposite quantum numbers and different numbers of timing dimensions. Coincidence with the birth of these branes, various derivatives of bosonic fields emerge in the action of the system which produce the $r$ GUP for bosons. These branes interact with each other, compact and various derivatives of spinor fields appear in the action of the system which leads to the creation of the GUP for fermions. The previous predicted entropy of branes in the GUP is corrected as due to the emergence of higher orders of derivatives and different number of timing dimensions.

physics.gen-ph↗

arXiv2017

Current density and conductivity through modified gravity in the graphene with defects

We propose a model describing the evolution of the free electron current density in graphene. Based on the concept of Mp-branes, we perform the analysis using the difference between curvatures of parallel and antiparallel spins. In such a framework an effective graviton emerges in the form of gauge field exchange between electrons. In a plain graphene system, the curvatures produced by both kinds of spins neutralize each other. However, in the presence of defects, the inequality between curvatures leads to the emergence of current density, modified gravity and conductivity. Depending on the type of the defects, the resulting current density can be negative or positive.

gr-qc↗

arXiv2017

The birth of the universe in a new G-Theory approach

Recently, Padmanabhan has discussed that the expansion of the cosmic space is due to the difference between the number of degrees of freedom on the boundary surface and the number of degrees of freedom in a bulk region. Now, a natural question arises that how these degrees of freedom are emerged from nothing? We try to address this issue in a new theory which is more complete than M-theory and reduces to it with some limitations. In M-theory, there isn't any stable object like stable M3-branes that our universe is formed on it and for this reason can't help us to explain cosmological events. In this research, we propose a new theory, named G -theory which could be the mother of M-theory and superstring theory. In G-theory, at the beginning, two types of G0-branes, one with positive energy and one with negative energy are produced from nothing in fourteen dimensions. Then, these branes are compactified on three circles via two different ways (symmetrically and anti-symmetrically), and two bosonic and fermionic parts of action for M0-branes are produced. By joining M0-branes, supersymmetric Mp-branes are created which contain the equal number of degrees of freedom for fermions and bosons. Our universe is constructed on one of Mp-branes and other Mp-brane and extra energy play the role of bulk. By dissolving extra energy which is produced by compacting actions of Gp-branes, into our universe, the number of degrees of freedom on it and also it's scale factor increase and universe expands. We test G-theory with observations and find that the the magnitude of the slow-roll parameters and the tensor-to-scalar ratio in this model are very smaller than one which are in agreement with predictions of experimental data. Finally, we consider the origin of the extended theories of gravity in G-theory and show that these theories could be anomaly free.

physics.gen-ph↗

arXiv2016

Emergence of the world with Lie-N-algebra and M-dimensions from nothing

In this paper, we propose a new model in Lie-N-algebra that removes big bang singularity and produces the world with all it's objects and dimensions from nothing. We name this theory as G-theory. In this model, first, two types of energies with opposite signs are produced from nothing such as the sum over them be zero. They create two types of branes with opposite quantum numbers which interact with each other by exchanging bosonic tensor fields like graviton and compact. By compacting branes, fermionic tensor fields are emerged which some of them play the role of the gravitinos. Also, some dimensions take extra (i) factors, their properties become different and they behave like time dimensions. Gravitons and gravitinos create two types of wormholes which lead to the oscillation of branes between expansion and contracting branches. These wormholes produce a repulsive gravity in compacted branes and cause that their particles get away from each other and expansion branch begin. Also, they create an attractive gravity in opening branes and lead to closing their particles and starting the contraction epoch. Our universe is born on one of these branes and oscillates between contraction and expansion branch.

physics.gen-ph↗