NEW APPROACHES ON DUAL SPACE

In this paper, we give how to define the basic concepts of differential geometry on Dual space. For this, dual tangent vectors that have p as dual point of application are defined. Then, the dual analytic functions defined by Dimentberg are examined in detail, and by using the derivative of the these functions, dual directional derivatives and dual tangent maps are introduced

Notes concerning K\"ahler and anti-K\"ahler structures on quasi-statistical manifolds

Let $(\acute{N},g,\nabla )$\ be a $2n$-dimensional quasi-statistical manifold that admits a pseudo-Riemannian metric $g$ (or $h)$ and a linear connection $\nabla$ with torsion. This paper aims to study an almost Hermitian structure $(g,L)$ and an almost anti-Hermitian structure $(h,L)$ on a quasi-statistical manifold that admit an almost complex structure $L$. Firstly, under certain conditions, we present the integrability of the almost complex structure $L$. We show that when $d^\nabla L =0$ and the condition of torsion-compatibility are satisfied, $(\acute{N},g,\nabla ,$ $L)$ turns into a K\"{a}hler manifold. Secondly, we give necessary and sufficient conditions under which $(\acute{N},h,\nabla ,L)$ is an anti-K\"{a}% hler manifold, where $h$ is an anti-Hermitian metric. Moreover, we search the necessary conditions for $(\acute{N},h,\nabla ,L)$ to be a quasi-K\"{a}hler-Norden manifold

Developmental Hints of Fairness Sensitivity: Current Investigations on Inequity Avoidance Inequity Avoidance

Fairness-based decision-making is considered one of the most crucial topics in the literature on moral psychology. Previous findings have demonstrated that people make costly irrational decisions according to their level of fairness sensitivity. Moreover, individuals display inequity avoidance behavior by rejecting inequity favoring others (disadvantageous inequity) or themselves (advantageous inequity). According to developmental investigations, different mechanisms may underlie the display of advantageous or disadvantageous inequity avoidance. Previous studies have indicated that in various cultures, disadvantageous inequity avoidance follows a similar path, whereas advantageous inequity avoidance emerges at different ages. These findings have pointed out that socialization practices and cultural factors may be dominant in terms of the age of onset of advantageous inequity avoidance. In parallel, this review first presents the pioneer approaches to fairness in the recent literature on moral psychology and provides a summary of developmental studies that investigated inequity avoidance behavior by considering cultural differences. In summary, the literature has proposed that social context and reputational concerns may encourage children to adopt better strategies for displaying inequity avoidance with the increasing age. From this perspective, this notion was considered to lead to crosscultural differences in the developmental spectrum of behaviors particularly linked to advantageous inequity avoidance. This finding may be attributed to different social practices across cultures that are considered to play a functional role in reducing reputational concerns. Moreover. explanations based on collectivistic versus individualistic dual perspective are unable to explicate various specific dynamics for understanding the age of onset of the display of inequity avoidance behavior. Therefore, further studies are required to reveal the roles of specific socialization dynamics in the community, parental expectations, and widely accepted social interaction practices with relatives, which would largely contribute to the relevant literature

Does training analytical thinking decrease superstitious beliefs? Relationship between analytical thinking, intrinsic religiosity, and superstitious beliefs

The associations between cognitive thinking style, religiosity, and superstitious beliefs were presented in the previous research. Still, the role of intrinsic religiosity on the link between analytical thinking and belief in superstitions was not examined specifically. In the first study, we explored the intrinsic type of religiosity's moderating role in the association between individuals' analytical thinking tendency and belief in superstitions after controlling for gender, age, education, and political ideology. Findings showed that participants having lower analytical thinking tendencies were more likely to engage beliefs in superstitions. There was no significant relationship between intrinsic religiosity and belief in superstitions. The negative relationship between analytical thinking and belief in superstitions was more evident for participants with a low and moderate intrinsic religiosity degree. In the second study, we primed the participants' analytical thinking tendency and looked into superstitious beliefs. As expected, enhancing analytical thinking led to decreased reporting of superstitious beliefs, but contrary to our hypothesis, the moderating role of intrinsic religiosity was not evident. The present findings were consistent with the idea that analytical thinking tendency would lead people to be less superstitious. Still, the role of intrinsic religiosity needs to be clarified in future research

Gut-lung axis and dysbiosis in COVID-19

COVID-19, a novel infectious disease, caused by SARS-CoV-2, affected millions of people around the world with a high mortality rate. Although SARS-CoV-2 mainly causes lung infection, gastrointestinal symptoms described in COVID-19 patients and detection of the viral RNA in feces of infected patients drove attentions to a possible fecal-oral transmission route of SARS-CoV-2. However, not only the viral RNA but also the infectious viral particles are required for the viral infection and no proof has been demonstrated the transmission of the infectious virus particles via the fecal-oral route yet. Growing evidence indicates the crosstalk between gut microbiota and lung, that maintains host homeostasis and disease development with the association of immune system. This gut-lung interaction may influence the COVID-19 severity in patients with extrapulmonary conditions. Severity of COVID-19 has mostly associated with old ages and underlying medical conditions. Since the diversity in the gut microbiota decreases during aging, dysbiosis could be the reason for older adults being at high risk for severe illness from COVID-19. We believe that gut microbiota contributes to the course of COVID-19 due to its bidirectional relationship with immune system and lung. Dysbiosis in gut microbiota results in gut permeability leading to secondary infection and multiple organ failure. Conversely, disruption of the gut barrier integrity due to dysbiosis may lead to translocation of SARS-CoV-2 from the lung into the intestinal lumen via circulatory and lymphatic system. This review points out the role of dysbiosis of the gut microbiota involving in sepsis, on the severity of SARS-CoV-2 infection. Additionally, this review aims to clarify the ambiguity in fecal-oral transmission of SARS- CoV-2

The derivative and tangent operators of a motion in Lorentzian space

WOS: 000397608400011In this paper, by using Lorentzian matrix multiplication, L-Tangent operator is obtained in Lorentzian space. The L-Tangent operators related with planar, spherical and spatial motion are computed via special matrix groups. L-Tangent operators are related to vectors. Some illustrative examples for applications of L-Tangent operators are also presented.TUBITAK (The Scientific and Technological Research Council of Turkey)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK)The second author would like to thank TUBITAK (The Scientific and Technological Research Council of Turkey) for their financial supports during her PhD studies

On Interpretation of Hyperbolic Angle

WOS:000558410100012Minkowski spaces have long been investigated with respect to certain properties and substructues such as hyperbolic curves, hyperbolic angles and hyperbolic arc length. In 2009, based on these properties, Chung et al. [3] defined the basic concepts of special relativity, and thus; they interpreted the geometry of the Minkowski spaces. Then, in 2017, E. Nesovic [6] showed the geometric meaning of pseudo angles by interpreting the angle among the unit timelike, spacelike and null vectors on the Minkowski plane. In this study, we show that hyperbolic angle depends on time, t. Moreover, using this fact, we investigate the angles between the unit timelike and spacelike vectors.TUBITAK (The Scientific and Technological Research Council of Turkey)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK); Kirikkale University, BAP, (Turkey)Kirikkale University [2018/015]The first and second authors would like to thank TUBITAK (The Scientific and Technological Research Council of Turkey) for their financial supports during their Ph.D. studies. The authors are partially supported by the Research Project of Kirikkale University, BAP, 2018/015 (Turkey)

On Parallelizable Spheres in Semi Euclidean Space

WOS:000544809000004In Euclidean space, there exist four theorems which show that S-n sphere is not parallelizable for n not equal 1, 3, 7. While three of them are shown by using Bott theorem, the last one is shown by using Hurwitz-Radon numbers. In this paper, a theorem and the proof of this theorem about parallelization of spheres in semi-Euclidean space is given. It is presented that some spheres are parallelizable with respect to specific number systems.TUBITAK (The Scientific and Technological Research Council of Turkey)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK)The first and second authors would like to thank TUBITAK (The Scientific and Technological Research Council of Turkey) for their financial supports during his and her Ph.D. studies