Projective Space Research Articles

Fly-around-the-World Near-Space Picosatellite for Cost-Effective School Space Projects

This research presents the design and development of a near-space picosatellite platform intended to operate at high altitudes between 20–40 km above sea level. These picosatellites function similarly to orbital satellites but float and travel with the wind in the atmosphere instead of orbiting the Earth. The platform utilizes a super-pressure balloon to provide buoyancy, allowing the picosatellite to remain airborne and operational for several days to months, capable of flying around the world multiple times. This study focuses on the cost-effective design of high-altitude platforms, telecommunication systems, and energy consumption for the picosatellite, enabling it to communicate with ground stations from anywhere in the world while consuming low power. The use of common COTS (Commercial Off-The-Shelf) equipment aims to enhance accessibility for educational applications. This research gathered data from our previous studies for over 20 high-altitude platform flights, analyzed the necessary factors for whole system design, and developed a new prototype that has been successfully built and tested.

On the Algebraic Geometry of Multiview

We study the multiviews of algebraic space curves X from n pin-hole cameras of a real or complex projective space. We assume the pin-hole centers to be known, i.e., we do not reconstruct them. Our tools are algebro-geometric. We give some general theorems, e.g., we prove that a projective curve (over complex or real numbers) may be reconstructed using four general cameras. Several examples show that no number of badly placed cameras can make a reconstruction possible. The tools are powerful, but we warn the reader (with examples) that over real numbers, just using them correctly, but in a bad way, may give ghosts: real curves which are images of the emptyset. We prove that ghosts do not occur if the cameras are general. Most of this paper is devoted to three important cases of space curves: unions of a prescribed number of lines (using the Grassmannian of all lines in a 3-dimensional projective space), plane curves, and curves of low degree. In these cases, we also see when two cameras may reconstruct the curve, but different curves need different pairs of cameras.

On the subalgebra of invariant elements: Finiteness and immersions

Given the n-dimensional affine space over an arbitrary commutative ring k, G a group scheme flat and finitely presented over k and X⊂Akn a G-invariant affine and closed subscheme, we prove that the GIT quotient ▪ is of finite type over k, even if k is not noetherian, provided G is linearly reductive. This is well-known if ▪ is faithfully flat, which does not hold in general. We also explore the infinite-dimensional case. Concretely, we consider a G−k finitely presented projective module M and an arbitrary k-module N. We prove, under certain conditions on k and G, that the degrees of the generators of (S•(M∨⊗N))G and the degrees of the generators of the ideal of relations are bounded. We encode this property into the notion of partially generated graded (pgg) algebra and we give their main properties. In particular, we prove the existence of canonical equivariant immersions of spectra of pgg algebras in certain projective spaces.

Gluing theory for slc surfaces and threefolds in positive characteristic

We develop a gluing theory in the sense of Kollar for slc surfaces and threefolds in positive characteristic. For surfaces we are able to deal with every positive characteristic $p$, while for threefolds we assume that $p>5$. Along the way we study nodes in characteristic $2$ and establish a theory of sources and springs a la Kollar for threefolds. We also give applications to the topology of lc centers on slc threefolds, and to the projectivity of the moduli space of stable surfaces in characteristic $p>5$.

The European Space Agency MBSE Methodology

AbstractThe European Space Agency (ESA) has been developing an MBSE Methodology to address the increased digitalization of systems engineering and facilitate the complex system development in ESA projects and other European space projects. The methodology is based on the European Cooperation for Space Standardization (ECSS) standards for Systems Engineering, and feedback from projects using the methodology. By using the ECSS standards as the starting point, the processes, terminology and expected outputs are familiar to the engineers, lowering the usage barrier within the Agency. This paper describes the background of and effort for establishing the MBSE methodology and a description of the methodology. The paper also reports on the current efforts at ESA for deploying MBSE and the way forward regarding the methodology.

장 이론(Field theory)을 이용한 청년아파트 입주자 커뮤니케이션 방법에 관한 연구

This study analyzes Chinese representative rental youth apartments based on Field theory, examining the correlation between these apartments and their fields. The purpose of this study is to analyze the influence of spatial design of projects on interaction patterns and communication modes among tenants through the field theory. First, it explores the relationship between Field theory's concepts and characteristics, applying the relationship between field capital and practice to rental youth apartments. It then examines how project background, space structure, and field relationships impact residents' social behavior. Findings indicate that the rules of the field in rental youth apartments influence social methods, with functional diversity, shared spaces, and enhanced transitions between areas increasing residents' social willingness.

A Simons-type Integral Inequality for Minimal Surfaces with Constant Kähler Angle in Complex Projective Spaces

A Simons-type Integral Inequality for Minimal Surfaces with Constant Kähler Angle in Complex Projective Spaces

Cohomology-developed matrices: constructing families of weighing matrices and automorphism actions

The aim of this work is to construct families of weighing matrices via their automorphism group action. The matrices can be reconstructed from the 0, 1, 2-cohomology groups of the underlying automorphism group. We use this mechanism to (re)construct the matrices out of abstract group datum. As a consequence, some old and new families of weighing matrices are constructed. These include the Paley conference, the projective space, the Grassmannian, and the flag variety weighing matrices. We develop a general theory relying on low-dimensional group cohomology for constructing automorphism group actions and in turn obtain structured matrices that we call cohomology-developed matrices. This ‘cohomology development’ generalizes the cocyclic and group developments. The algebraic structure of modules of cohomology-developed matrices is discussed, and an orthogonality result is deduced. We also use this algebraic structure to define the notion of quasiproducts, which is a generalization of the Kronecker product.

Connection of BRICS and EAEU integration projects in the context of Russian economic development

The ongoing transformation of the Russian economy under external sanctions pressure determines the development of integration projects in the post-Soviet space, which differ in the form and depth of economic cooperation. The expansion of BRICS, as well as the strengthening of mutual trade with Asia and the search for new trading partners, is of great relevance in the context of studying trade and economic connectivity between the BRICS members, Russia and the EAEU countries. The article is devoted to the analysis of promising areas of cooperation between the BRICS countries and the EAEU. The purpose is to identify the most promising trading partners among the BRICS countries in the context of the expansion of the organization and the accession of five new members. The study highlights optimal models of cooperation between the EAEU and BRICS countries in the context of reorientation of trade flows. The conclusion of the article is the need to strengthen horizontal interaction between companies of the EAEU and BRICS jurisdictions in the context of increasing the volume of parallel imports of high-tech products and developing infrastructure projects that affect the interests of Russia and partner countries.

Equivariant harmonic maps of the complex projective spaces into the quaternion projective spaces

We classify equivariant harmonic maps of the complex projective spaces CPm into the quaternion projective spaces. To do this, we employ differential geometry of vector bundles and connections. When the domain is the complex projective line, we have one parameter family of those maps. (This result is already shown in [2] and [4] in other ways). However, when m≧2, we will obtain the rigidity results.

Hofer–Zehnder capacity of disc tangent bundles of projective spaces

AbstractWe compute the Hofer–Zehnder capacity of disc tangent bundles of the complex and real projective spaces of any dimension. The disc bundle is taken with respect to the Fubini–Study resp. round metric, but we can obtain explicit bounds for any other metric. In the case of the complex projective space, we also compute the Hofer–Zehnder capacity for the magnetically twisted case, where the twist is proportional to the Fubini–Study form. For arbitrary twists, we can still give explicit upper bounds.

Modified defect relation for Gauss maps of minimal surfaces with hypersurfaces of projective varieties in the subgeneral position

AbstractIn this paper, we establish some modified defect relations for the Gauss map of a complete minimal surface into a ‐dimension projective subvariety with hypersurfaces of in ‐subgeneral position with respect to . In particular, we give the upper bound for the number if the image intersects each hypersurface a finite number of times and is nondegenerate over , where , that is, the image of is not contained in any hypersurface of degree with . Our results extend and generalize the previous results for the case of the Gauss map and hyperplanes in a projective space. The results and the method of this paper have been applied by some authors to study the unicity problem of the Gauss maps sharing families of hypersurfaces.

Dynamical branes on expanding orbifold and complex projective space

We construct some new dynamical p-brane solutions to gravity theories on curved backgrounds. We discuss the relations between dynamical branes, a new time-dependent solution on complex projective space CPn, and the static p-branes on the orbifold Cn/Zn. Published by the American Physical Society 2024

Data oversampling and feature selection for class imbalanced datasets

Introduction: Significant advancements and modifications have been implemented in data classification (DC) in the past few decades. Due to their infinite quantity and imbalance, data becomes challenging for classification. The biggest concern in DM (Data Mining) is Class Imbalance (CI). To avoid these issues in recent work proposed map reduce based data parallelization of class imbalanced datasets. Methods: A novel Over Sampling (OS) technique called Minority Oversampling in Kernel Canonical Correlation Adaptive Subspaces (MOKCCAS) has been suggested with the objective to minimize data loss throughout (FSP) Feature Space Projections. This technique takes advantage of the constant Feature Extraction (FE) capability of a version of the ASSOM (Adaptive Subspace Self-Organizing Maps) that is derived from Kernel Canonical Correlation Analysis (KCCA). And in classification, Feature Selection (FS) plays an important role because the acquired dataset might contain large volume of samples, utilizing all features of samples from the dataset for classification will decrease the classifier performance. And then data parallelization will be done by using map reduce framework to solve this computation requirement problem.Result: Then proposes a feature selection model using Mutated whale optimization (MWO) methods and produces features and reduces the time consumption. Finally proposed class balancing model will be tested using uniform distribution based enhanced adaptive neuro fuzzy inference system (UDANFIS). Test outcomes validate the efficiency of the suggested technique by precision, recall, accuracy and Error Rate (ER).Conclusion: The study subsequently suggests a novel OS approach called MOKCCAS to lessen the loss of data throughout feature space projection.

The third space, student and staff co-creation of gamified informal learning: an emerging model of co-design

This article draws from the authors’ exploration of an innovative third space approach to engaging students with informal learning through the use of co-design and co-creation, which sits outside traditional subject delivery spaces. The third space project, the Digital Citizenship Programme, centres on the transformative experience and dialogic encounter for participants. The third space in this context was constituted by co-design and co-production involving students, alumni, academics and professional service staff. The project evaluated third space activity in terms of co-design, through its development process and in what is achieved by participants’ engagement with it. The aims were to analyse the mutuality and relational aspects of the innovative pedagogic intervention; the development of transferable skills and agentic development in the third space; and the dialogic experience for participants. The research data were collected over a period of three years, using focus groups, co-creation workshop observations and field notes. This project builds on the body of research that focuses on partnerships with students that fall under the umbrella of the third space. The article underlines the importance of co-creation approaches in building the relational and dialogic dynamic in higher education spaces.

Surface counterexamples to the Eisenbud-Goto conjecture

It is well known that the Eisenbud-Goto regularity conjecture is true for arithmetically Cohen-Macaulay varieties, projective curves, smooth surfaces, smooth threefolds in P 5 \mathbb {P}^5 , and toric varieties of codimension two. After J. McCullough and I. Peeva constructed counterexamples in 2018, it has been an interesting question to find the categories such that the Eisenbud-Goto conjecture holds. So far, surface counterexamples have not been found while counterexamples of any dimension greater or equal to 3 are known. In this paper, we construct counterexamples to the Eisenbud-Goto conjecture for projective surfaces in P 4 \mathbb {P}^4 and investigate projective invariants, cohomological properties, and geometric properties. The counterexamples are constructed via binomial rational maps between projective spaces.

The Witt rings of many flag varieties are exterior algebras

The Witt ring of a complex flag variety describes the interesting – i.e. torsion – part of its topological KO-theory. We show that for a large class of flag varieties, these Witt rings are exterior algebras, and that the degrees of the generators can be determined by Dynkin diagram combinatorics. Besides a few well-studied examples such as full flag varieties and projective spaces, this class includes many flag varieties whose Witt rings were previously unknown, including many flag varieties of exceptional types. In particular, it includes all flag varieties of types G 2 G_2 and F 4 F_4 . The results also extend to flag varieties over other algebraically closed fields.

Orthodontic maxillary molar movement-induced zygomatic pillar remodeling and its consequences on occlusal characteristics and stress distribution

ObjectiveWe aimed to evaluate changes in the zygomatic pillar during orthodontic treatment involving premolar extraction, analyze the effects of maxillary first molar movement on zygomatic pillar remodeling, and examine occlusal characteristics and stress distribution after remodeling.MethodsTwenty-five patients who underwent premolar extraction were included in the study. The zygomatic pillar measurement range was defined, and cross-sectional areas, surface landmark coordinates, alveolar and cortical bone thicknesses, and density changes were assessed using Mimics software based on the cone-beam computed tomography scans taken before (T0) and after the treatment (T1). Multiple linear regression analysis was performed to determine the correlation between changes in the zygomatic pillar and maxillary first molar three-dimensional (3D) movement and rotation. Additionally, the correlation between pillar remodeling and occlusal characteristics was analyzed by Teetester. Pre- and post-reconstruction 3D finite element models were constructed and loaded with an average occlusal force of two periods.ResultsThe morphological and structural remodeling of the zygomatic pillar after orthodontic treatment involving premolar extraction showed a decreased cross-sectional area of the lower segment of the zygomatic pillar. The zygomatic process point moved inward and backward, whereas the zygomatico-maxillary suture point moved backward. The thicknesses of the zygomatic pillar alveolar and cortical bones were thinner, and reduced alveolar bone density was observed. Simultaneously, the movement and angle change of the maxillary first molar could predict zygomatic pillar reconstruction to a certain extent. With decreasing the total occlusal force and the occlusal force of the first molar, occlusal force distribution was more uniform. With zygomatic pillar remodeling, occlusal stress distribution in the zygomatic alveolar ridge decreased, and occlusal stress was concentrated at the junction of the vertical and horizontal parts of the zygomatic bone and the posterior part of the zygomatic arch.ConclusionsOrthodontic treatment involving premolar extraction led to zygomatic pillar remodeling, making it more fragile than before and reducing the occlusal force of the maxillary first molar and the entire dentition with stress concentrated in weak areas.Clinical relevanceNo other study has focused on the effects of orthodontics on pillar structures. The present study indicates that the mesial movement of the maxillary first molar weakened the zygomatic pillar and reduced occlusal function, thereby providing insights for inserting anchorage screws and facial esthetics.

Circle Actions on Oriented Manifolds With 3 Fixed Points

Abstract Let the circle group act on a compact oriented manifold $M$ with a non-empty discrete fixed point set. Then the dimension of $M$ is even. If $M$ has one fixed point, $M$ is the point. In any even dimension, such a manifold $M$ with two fixed points exists, a rotation of an even dimensional sphere. Suppose that $M$ has three fixed points. Then the dimension of $M$ is a multiple of 4. Under the assumption that each isotropy submanifold is orientable, we show that if $\dim M=8$, then the weights at the fixed points agree with those of an action on the quaternionic projective space $\mathbb{H}\mathbb{P}^{2}$, and show that there is no such 12-dimensional manifold $M$.

Strong blocking sets and minimal codes from expander graphs

A strong blocking set in a finite projective space is a set of points that intersects each hyperplane in a spanning set. We provide a new graph theoretic construction of such sets: combining constant-degree expanders with asymptotically good codes, we explicitly construct strong blocking sets in the ( k − 1 ) (k-1) -dimensional projective space over F q \mathbb {F}_q that have size at most c q k c q k for some universal constant c c . Since strong blocking sets have recently been shown to be equivalent to minimal linear codes, our construction gives the first explicit construction of F q \mathbb {F}_q -linear minimal codes of length n n and dimension k k , for every prime power q q , for which n ≤ c q k n \leq c q k . This solves one of the main open problems on minimal codes.