Shape Operator Research Articles

Exploring slip flow and heat transfer of power-law fluid past an induced magnetic stretching regime subject to Cattaneo-Christov flux theory

This work investigates the heat transmission and boundary layer (BL) slip flow of a power-law fluid induced by stretching surfaces. The power-law fluid, induced magnetic field, and finite thermal relaxation have significant applications in a variety of industrial settings, including thin-layer growth, cooling systems, the extrusion process, and coating and shaping operations in a heat transfer mechanism. With these significant industrial applications, the current study explores BL flow and heat transfer in the context of the of the Cattaneo-Christov theory against the backdrop of an induced magnetic field over a stretching surface. The shear-thinning and thickening features are captured by the power-law fluid model, while the Cattaneo-Christov theory solves the deficiencies of Fourier's law. The BVP4c technique is used to construct and solve BL equations numerically. The surface drag and heat transmission rates at the wall are studied using statistical multi-regression analysis. The findings clarify that the magnetic and power law indices have a favorable effect on the Nusselt number, while their influence on skin friction is conflicting. A lower heat transmission is predicted with thermal relaxation as compared to Fourier's law in the energy equation. The accumulated thermal relaxation parameter produces a non-equilibrium state, delaying the internal thermal processes.

Managing resources for digital transformation in supply chain integration: The role of hybrid governance structures

Digital transformation (DT) plays a crucial role in shaping operations and supply chain management. Through real-time data sharing and automated decision-making systems, DT fosters supply chain integration (SCI), facilitated by key digital technologies like Internet of Things (IoT), cloud computing, big data, and artificial intelligence. Effective DT necessitates managing organizational digital resources encompassing technical domains such as software, hardware, and data science, alongside financial resources and managerial capabilities. Navigating the complexities of DT requires strategic decisions in supply chain governance regarding the management of these digital resources. While in-house development offers control and differentiation, it entails organizational and financial risks. Conversely, outsourcing digital activities reduces risks but increases technological dependence. Hybrid governance (concurrently sourcing in-house and outsourcing activities) presents a reconciliatory approach that can be valuable for DT in SCI. This study investigates the contribution of hybrid governance for DT, focusing on its effects on SCI and delivery performance. Through quantitative analysis of 379 manufacturing companies, our findings reveal that hybrid governance positively influences the digitalization of SCI and contributes to delivery performance through a digitalized SCI. Our research contributes to the theoretical understanding of hybrid governance in DT, offering insights into strategic digital resource management for SCI. It underscores the importance of balancing internal and external resources to optimize supply chain performance in the digital era.

Compilation of Shape Operators on Sparse Arrays

We show how to build a compiler for a sparse array language that supports shape operators such as reshaping or concatenating arrays, in addition to compute operators. Existing sparse array programming systems implement generic shape operators for only some sparse data structures, reduce shape operators on other data structures to those, and do not support fusion. Our system compiles sparse array expressions to code that efficiently iterates over reshaped views of irregular sparse data structures, without needing to materialize temporary storage for intermediates. Our evaluation shows that our approach generates sparse array code competitive with popular sparse array libraries: our generated shape operators achieve geometric mean speed-ups of 1.66×–15.3× when compared to hand-written kernels in scipy.sparse and 1.67×–651× when compared to generic implementations in pydata/sparse. For operators that require data structure conversions in these libraries, our generated code achieves geometric mean speed-ups of 7.29×–13.0× when compared to scipy.sparse and 21.3×–511× when compared to pydata/sparse. Finally, our evaluation demonstrates that fusing shape and compute operators improves the performance of several expressions by geometric mean speed-ups of 1.22×–2.23×.

Comprehensive Brand Analysis of the Telecommunication Industry in Delhi and Delhi NCR

The telecommunication sector in Delhi and the National Capital Region (NCR) is a crucial component of India's digital landscape, catering to a population exceeding 30 million and driving technological advancements in one of the country's most economically vibrant regions. In this dynamic environment, understanding the intricacies of brand strategies, market dynamics, and consumer behavior is paramount for industry stakeholders seeking to thrive amidst fierce competition and rapid technological evolution. This in-depth brand analysis embarks on a journey to unravel the complexities of the telecommunication sector in Delhi and the NCR. Through a meticulous blend of qualitative and quantitative methodologies, the research endeavors to shed light on the diverse array of factors shaping the regional telecommunications landscape. From the strategies adopted by industry contenders to the regulatory frameworks governing operations, this exploration aims to provide a comprehensive understanding of the opportunities and challenges inherent in the Delhi-NCR telecommunication market. The study delves into the strategies deployed by key players to navigate the competitive landscape. It illuminates how brands position themselves to capture market share, differentiate their offerings, and respond to evolving consumer demands. Additionally, the analysis dissects the regulatory context shaping operations within Delhi and the NCR, including licensing requirements, spectrum allocation policies, and consumer protection regulations. By examining the interplay between industry dynamics and regulatory frameworks, the research provides insights into the governance of the telecommunication sector in the region. As the telecommunication sector in Delhi-NCR continues to evolve, informed decision-making becomes imperative for industry participants, policymakers, and investors alike. By synthesizing insights gleaned from the analysis of market dynamics, consumer preferences, and regulatory frameworks, this examination serves as a strategic resource for navigating the complexities of the regional telecommunication market. Armed with actionable intelligence and a nuanced understanding of the telecommunication landscape, stakeholders can capitalize on emerging opportunities, address challenges, and contribute to the continued growth and innovation of the sector in Delhi and the NCR.

Mapping Digital Transformation of Municipalities through the Lens of Institutional Isomorphism

This paper examines the role of institutional isomorphism in influencing digital transformation (DT) within municipalities. It addresses the gap in understanding how coercive, mimetic, and normative pressures shape municipal strategies and operations as they adopt and implement digital technologies. Through a systematic literature review and thematic analysis, the study identifies key actors in municipal DT and maps out the domains of action in which institutional pressures are influential. The findings indicate that municipal DT can be seen as a bridging-issues field, where coercive pressures often stem from regulatory mandates requiring compliance with digital standards, where mimetic pressures arise from the need to emulate successful digital practices, and where normative pressures are related to professional standards and expectations within the administrative context. The study concludes that institutional pressures significantly dictate the pace and direction of digital innovation within municipalities. Understanding these pressures is crucial for municipal leaders to effectively manage and implement DT initiatives that are both compliant and innovative. Recommendations for future research include empirical studies to validate theoretical models and explore the variability in DT across different municipalities by considering their unique environments and challenges.

Purity and hybridness of two tensors on a real hypersurface in complex projective space

Abstract On a real hypersurface M M in complex projective space, we can define two tensor fields of type (1, 2), A F ( k ) {A}_{F}^{\left(k)} and A T ( k ) {A}_{T}^{\left(k)} , associated with the shape operator A A of the real hypersurface, for any nonnull real number k k . Following Tachibana [Analytic tensor and its generalization, Tohoku Math. J. 12 (1960), 208–221], we study the purity and hybridness of such tensors with respect to A A .

Right Conoids Demonstrating a Time-like Axis within Minkowski Four-Dimensional Space

In the four-dimensional Minkowski space, hypersurfaces classified as right conoids with a time-like axis are introduced and studied. The computation of matrices associated with the fundamental form, the Gauss map, and the shape operator specific to these hypersurfaces is included in our analysis. The intrinsic curvatures of these hypersurfaces are determined to provide a deeper understanding of their geometric properties. Additionally, the conditions required for these hypersurfaces to be minimal are established, and detailed calculations of the Laplace–Beltrami operator are performed. Illustrative examples are provided to enhance our comprehension of these concepts. Finally, the umbilical condition is examined to determine when these hypersurfaces become umbilic, and also the Willmore functional is explored.

Three-dimensional quasi-umbilical locally strongly convex homogeneous affine hypersurfaces

The study of strongly convex, locally homogeneous hypersurfaces in the affine space ℝn+1 has a rich history. In dimension 2, these hypersurfaces were first examined in Guggenheimer's 1977 book “Differential Geometry” [4], and the classification was completed by Nomizu and Sasaki in their 1991 paper “A new model of unimodular-affinely homogeneous surfaces” [6]. Apart from the work of Magid and Vrancken in their 1995 paper [5] and Ooguri’s 2013 paper [9], most studies have focused on locally strongly convex affine hypersurfaces. These are characterized by an induced affine metric that is positive definite, and have been extensively studied in Sasaki’s 1980 paper “Hyperbolic affine hyperspheres” [10]. When the hypersurface is an affine sphere, where the shape operator has all eigenvalues equal to zero, Dillen and Vrancken provided a complete classification in a series of papers. In dimension 3, their 1993 paper “The classification of 3-dimensional locally strongly convex homogeneous affine hypersurfaces” [3] offers a comprehensive classification for any dimensions of eigenvalues of the shape operator. In dimension 4, the quasi-umbilical case was explored by Dillen and Vrancken in their 1994 paper “Quasi-umbilical, locally strongly convex homogeneous affine hypersurfaces” [2]. The case where the affine shape operator has two distinct eigenvalues, each with a multiplicity of two, was investigated by Chikh-Salah and Vrancken in their 2017 paper “Four-dimensional locally strongly convex homogeneous affine hypersurfaces” [1]. In this paper, we provide a different proof of the final theorem in Dillen and Vrancken’s [3], utilizing Mathematica software to calculate all Christoffel symbol functions.

The role of shape operator in gauge theories

The role of shape operator in gauge theories

The Shape Operator of Real Hypersurfaces in S6(1)

The Shape Operator of Real Hypersurfaces in S6(1)

Rheological transition and mechanical properties of alumina–agar mixtures under temperature cycling

This study examined the gel formation behavior and temperature-dependent mechanical characteristics of gel-cast alumina–agar mixtures. The shift from viscoelastic to elastic behaviors, the influence of final agar content, the reversibility of the viscoelastic–elastic transition, and the relationship between complex modulus and temperature were all investigated. The complex viscosity of the mixtures was also investigated to determine their role in ceramic shaping operations. The findings are useful for academics and practitioners in materials science and engineering, especially those who work with alumina–agar mixtures.

Ricci Solitons on Spacelike Hypersurfaces of Generalized Robertson–Walker Spacetimes

Ricci Solitons on Spacelike Hypersurfaces of Generalized Robertson–Walker Spacetimes

Hypersurfaces in spaces of constant curvature satisfying a particular Roter type equation

Let M be a hypersurface isometrically immersed in an (n+1)-dimensional semi-Riemannian space of constant curvature, n>3, such that its shape operator A satisfies A3=ϕA2+ψA+ρId, where ϕ, ψ and ρ are some functions on M and Id is the identity operator. The main result of this paper states that on the set U of all points of M at which the square S2 of the Ricci operator S of M is not a linear combination of S and Id, the Riemann-Christoffel curvature tensor R of M is a linear combination of some Kulkarni-Nomizu products formed by the metric tensor g, the Ricci tensor S and the tensor S2 of M, i.e., the tensor R satisfies on U some Roter type equation. Moreover, the (0,4)-tensor R⋅S is on U a linear combination of some Tachibana tensors formed by the tensors g, S and S2. In particular, if M is a hypersurface isometrically immersed in the (n+1)-dimensional Riemannian space of constant curvature, n>3, with three distinct principal curvatures and the Ricci operator S with three distinct eigenvalues then the Riemann-Christoffel curvature tensor R of M also satisfies a Roter type equation of this kind.

New Results on Derivatives of the Shape Operator of Real Hypersurfaces in the Complex Quadric

A real hypersurface $M$ in the complex quadric $Q^{m}=SO_{m+2}/SO_mSO_2$ inherits an almost contact metric structure . This structure allows to define, for any nonnull real number $k$, the so called $k$-th generalized Tanaka-Webster connection on $M$, $\hat{\nabla}^{(k)}$. If $\nabla$ denotes the Levi-Civita connection on $M$, we introduce the concepts of $(\hat{\nabla}^{(k)},\nabla)$-Codazzi and $(\hat{\nabla}^{(k)},\nabla)$-Killing shape operator $S$ of the real hypersurface and classify real hypersurfaces in $Q$ satisfying any of these conditions.

Biconservative Riemannian Submanifolds in Minkowski 5-Space

In this study, we focus biconservative Riemannian submanifolds with parallel normalized mean curvature vector field (PNMCV) in $\mathbb{E}^5_1$. We obtain explicit classifications for these submanifolds with exactly two distinct principal curvatures of the shape operator along the mean curvature vector field. In particular, we investigate these submanifolds which have time-like and space-like mean curvature vector field in $\mathbb{E}^5_1$.

Approximating the Shape Operator with the Surface Hellan–Herrmann–Johnson Element

Approximating the Shape Operator with the Surface Hellan–Herrmann–Johnson Element

Characterizations of warped product pointwise semi-slant submanifolds of Sasakian manifold

A warped product submanifold, whose tangent bundle can be decomposed to two orthogonal distributions; invariant and pointwise slant, is called a warped product pointwise semi-slant submanifold. The objective of this paper is to classify warped product pointwise semi-slant submanifolds, isometrically immersed into a Sasakian manifold. Park [25] provided the (non)-existence of a warped product pointwise semi-slant submanifold in a Sasakian manifold such that the structure vector field is tangential to fibers. In contrast, we provide intriguing theorems on warped product pointwise semi-slant submanifolds in a Sasakian manifold in terms of the shape operator and tensor fields such that the structure vector field is tangential to a base manifold and each fiber is a pointwise slant submanifold.

Системный подход к обучению студентов возможностям современных систем автоматизированного проектирования

The article describes a systematic approach that is used at the Department of Engineering Graphics at Bauman Moscow State Technical University to teach students the possibilities of modern computer-aided design systems.
 
 A methodology for teaching the basics of creating solid-state geometric models of parts and drawings in the Compass-3D system based on a systematic approach is presented. The structure and content of classes are described. The educational materials are developed on the basis of the students' knowledge of stereometry acquired at school and the knowledge gained during the parallel study of the engineering graphics section "Projection drawing".
 
 Examples of practical tasks for students' independent work are given. The training begins with the construction of a flat contour, which is used as basis of a three-dimensional model. When constructing a contour, students practice to create the basic primitives that make up the contour, and superimposing geometric and dimensional dependencies on the primitives. The construction of solid-state models begins with the modeling of simple geometric bodies: a prism, a pyramid, a body of rotation. This allows students to focus on practicing shaping operations, and to better navigate the toolbars. Then, students consolidate their knowledge and skills in building models of more complex shapes, similar in design to mechanical engineering parts of two classes: "body of rotation" and "non-body of rotation". Students create electronic drawings based on the constructed models. At the same time, the following is being worked out: creating images in the drawing – views, sections, sections; applying dimensions while maintaining an associative connection with the part model; using drawing design elements.
 
 Examples of control tasks for editing created models and drawings are given, which are necessary for students to acquire skills important for engineering practice.
 
 It is noted that the acquired knowledge and skills can be used by students in further education. The proposed methodology can be recommended for use in the system of secondary and secondary vocational education.

Structure and its defects in additive manufacturing of stainless steels by laser melting and electric arc surfacing

Currently, there is an active development and study of additive technologies. Metal 3D printing makes it possible to obtain parts and structures of complex configuration using a minimum of shaping operations, which can lead to a reduction in overall cost of the resulting products. In this paper, we studied the structure formation in manufacture of products made of stainless steels 10Cr12Ni10Ti (analogue of AISI 321) and 08Cr18Ni9 (analogue of AISI 304) by additive methods – SLM (Selective Laser Melting) and WAAM (Wire Arc Additive Manufacturing). In the course of microstructural analysis, it was found that during the manufacture of products using SLM technology, small austenitic grains oriented in the direction of heat removal are formed, and with WAAM method, austenite is formed mainly in form of dendrites. It is shown that porosity is formed during manufacture of the samples by SLM method, which is associated with non-melting of individual powder particles. When implementing additive manufacturing by WAAM (electric arc surfacing), there is no increased porosity. In the course of the study, a new defect of the structure formed during the manufacture of products by both methods was revealed – formation of interface boundaries between layers, which is associated with the technology of additive manufacturing itself. When manufacturing a WAAM product, it manifests itself more clearly than when obtaining metal by SLM. Boundaries of the surfacing rollers in the manufacture of products by SLM accumulate various intermetallides and structural defects more intensively, relative to WAAM. As a result of the small relative volume of one surfacing roller, compared with WAAM, accumulation of these defects and intermetallides can act as an effective barrier during movement of dislocations, which can lead to an increase in the strength properties of products.

Features of the influence of working conditions on psychophysiological functions of unmanned aircraft systems operators

This study was conducted to determine the influence and assess the impact of specific factors of working conditions on the psychophysiological functions of Unmanned Aircraft Systems (UAS) operators. The research involved 41 military personnel (men aged 20-35 years old) who operated the I class “Light” UAS and were engaged in a varied range of professional tasks. The aim was to understand the complex impact of these distinct factors on operators during the execution of their duties. To examine their psychophysiological status, we employed modified methods using the PFI-2 hardware/software complex. The following indicators were determined: accuracy of reaction to a moving object, strength of nervous processes, functional mobility of nervous processes, simple visual-motor reaction, complex visual-motor reaction, orientation in space, and visual memory. The role of climatic and microclimatic factors in professional activity was studied using a questionnaire, where their influence on functional status was assessed on a 100-point scale. To facilitate further theoretical development and practical application, we determined the investigated factors integral impact on shaping operators’ subjective perception and specific psychophysiological qualities that are professionally significant for military personnel. The preliminary analysis showed the heterogeneity of feelings the influence of various components of the external environment factor. To correct this heterogeneity, we used the non-linear correction method (logarithmization of analyzed data, when large values of an analyzed parameter could be reduced due to the properties of logarithmic function). Then, a correlation (Spearman correlation coefficient) and regression analysis of studied parameters has been carried out with a preliminary check of the structure of operator perceptions for normality using the Shapiro-Wilk test. As a result, a list of psychophysiological qualities that change under the influence of the external environment factor in individuals with different perceptivity to its components has been selected.