Search Results (2,365)

Let $\mathcal{Z}{\left(\mathcal{R}\right)}^{\prime }$ denote the set of all elements in the ring $\mathcal{R}$ that are neither zero nor units, where $\mathcal{R}$ is assumed to be a commutative ring with a multiplicative identity satisfying $1\ne 0.$ Two distinct vertices w and $\kappa$ are defined to be adjacent if and only if $\kappa$ does not lie in the ideal generated by w in $\mathcal{R},$ that is, $\kappa \notin w\mathcal{R},$ and simultaneously, w does not lie in the ideal generated by $\kappa$ in $\mathcal{R},$ that is, $w\notin \kappa \mathcal{R}.$ The cozero-divisor graph of $\mathcal{R},$ denoted by ${\Gamma }^{\prime }\left(\mathcal{R}\right),$ is an undirected graph in which the vertices are given by the set $\mathcal{Z}{\left(\mathcal{R}\right)}^{\prime }.$ This article presents a comprehensive evaluation of both the Euler Sombor index and the average Sombor index for the graphs ${\Gamma }^{\prime }\left({\mathbb{Z}}_n\right)$ corresponding to various values of $n.$ Full article

Background: The rising costs in the metropolitan real estate market are compelling individuals to relocate outside of the city. The anticipated financial savings, however, may be undermined by long and costly commutes; raising the question of whether this trade-off is a worthwhile proposition. This paper uses a digital model of workplace commutes, income levels and house prices in England as well as Wales, to evaluate the trade-off between (i) moving to the city centre and cycling to work versus (ii) continuing to commute by car from a residence on the periphery. Methods: An indicator has been introduced that unifies the transport and housing affordability by expanding the concept of the ‘effective speed’ to include housing costs. The effective speed itself is commonly defined as the travel distance divided by the time dedicated to the transport activity (i.e., travel duration and time given to earn the money to pay for the costs incurred). Results: If only the associated fuel and mortgage costs are considered, residing on the periphery can—for those already living there—be a cost-effective option specially in cities like Cambridge and Oxford. Yet, accounting for the total ownership costs of cars or external effects, this advantage shifts in favour of relocating to the city centre. Conclusion: This study does not negate the existence of an affordable housing crisis in urban environments, though it demonstrates that strategies to cut transport emissions can produce economic gains. Full article

In this paper, for any real number λ, we transform the complete max-plus semiring ${\mathbb{R}}_{\infty }$ into a commutative, complete, additively idempotent semiring ${\mathbb{R}}_{\infty }^{\lambda }$, called the lower λ-truncation of ${\mathbb{R}}_{\infty }$. It is obtained by removing from ${\mathbb{R}}_{\infty }$ all real numbers smaller than λ, inheriting the addition operation, shifting the original products by −λ, and appropriately modifying the residuum operation. The purpose of lower truncations is to transfer the iterative procedures for computing the greatest presimulations and prebisimulations between max-plus automata, in cases where they cannot be completed in a finite number of iterations over ${\mathbb{R}}_{\infty }$, to ${\mathbb{R}}_{\infty }^{\lambda }$, where they could terminate in a finite number of iterations. For instance, we prove that this necessarily happens when working with max-plus automata with integer weights. We also show how presimulations and prebisimulations computed over ${\mathbb{R}}_{\infty }^{\lambda }$ can be transformed into presimulations and prebisimulations between the original automata over ${\mathbb{R}}_{\infty }$. Although they do not play a significant role from the standpoint of computing presimulations and prebisimulations, for theoretical reasons we also introduce two types of upper truncations of the complete max-plus semiring ${\mathbb{R}}_{\infty }$. Full article

Postsocialist peri-urban spaces are characterized by a chaotic development as a result of the transition from communism to capitalism. Recent research has highlighted that liveability in peri-urban spaces encounters challenges of adaptation to the peri-urban areas. The aim of the present study is to identify and analyze patterns and contrasts that occur between age groups and gender in relation to the level of liveability as well as to better understand the daily mobility practices and commuting dependencies and how mobility shapes key contrasts and emerging tensions within Timișoara’s postsocialist peri-urban spaces. As liveability relates to local development, commuting, and accessibility to service facilities in the residential environment, the identification of patterns and differences is imperative when considering the perception of local residents on potential (un)sustainable liveability in peri-urban areas. This study utilizes a quantitative analysis, informed by a survey of considerable size (N = 954) conducted in peri-urban settlements of Timisoara, Romania, with a view to elucidating the distinctions and commonalities in the perceptions held by the local populace. The findings indicate that the elderly population exhibits a greater reluctance to adapt to the emerging peri-urban environment. In contrast, the younger and more educated demographic demonstrates a higher degree of adaptability to the contemporary challenges posed by peri-urban expansion and hazardous development. Daily mobility, including commuting, is directly influenced by the effects of dispersed and chaotic development (e.g., more than 79% of respondents rely on private cars for commuting), as well as the lack of facilities and services (e.g., 2.21 level of satisfaction regarding cultural events). This highlights Timisoara’s dependence on external services, as well as the significant role of personal vehicles in providing access to the city center and its neighborhoods. Therefore, we can observe the peri-urban area undergoing a transitional phase as it navigates the initial stages of sustainable urban development and pursues an enhanced quality of life. Finally, we propose several policy recommendations for local authorities, offering solutions for enhancing liveability in peri-urban areas. Full article

Previous research on subway stations has emphasized indexicality, functionality, comfort, aesthetics, etc., while cultural representation has been neglected. Notably, however, cultural representations in subway stations shape the city image and affects residents’ sense of identity and belonging. In particular, cultural representations on the decorative walls of subway stations play a crucial role. Therefore, the following questions can be asked: Do passengers perceive the representational culture in these subway stations? What is the relationship between the cultural representations on the decorative walls in subway stations and commuters’ spatial perception? Using a case study of the Ping’anli station in Beijing, in response to the research conducted by Xu Y.J. and other scholars, and adopting the method of data triangulation performed through content analysis, social media, and questionnaires, this paper analyses whether and how cultural representations on the decorative walls of subway stations affect commuters’ spatial perceptions. This study provides new insights into the influence of cultural representations in subway stations on commuters’ spatial perceptions. The findings reveal that cultural representations on decorative walls in subway stations do not fully align with commuters’ spatial perception. These findings can offer references for urban planning as well as the planning and design of decorative walls in subway stations. Full article

This paper introduces a generalized class of Weyl-type, Witt-type, and non-associative algebras constructed over an exponential–polynomial (expolynomial) framework. For fixed scalars ${\iota }_1,\dots ,{\iota }_r\in \mathcal{A}$ and for fixed integers $\mathbf{p}=(p_1,\dots ,p_n)\in {\mathbb{N}}^n$, we define the $\mathbb{F}$-algebra $\mathbb{F}\left[e^{\pm x^{\mathbf{p}}{e}^{\iota x}},e^{\mathcal{A}x},x^{\mathcal{A}}\right],$ an expolynomial ring over a field $\mathbb{F}$ of characteristic zero, where $\mathcal{A}$ is an additive subgroup of $\mathbb{F}$ containing $\mathbb{Z}$. This formulation extends the classical Weyl algebra through the integer power parameter $\mathbf{p}$, which generates a family of non-isomorphic simple algebras. The corresponding Weyl-type algebra $A\left(\mathbb{F}[e^{\pm x^{\mathbf{p}}{e}^{\iota x}},e^{\mathcal{A}x},x^{\mathcal{A}}]\right),$ the Witt-type Lie algebra $W\left(\mathbb{F}[e^{\pm x^{\mathbf{p}}{e}^{\iota x}},e^{\mathcal{A}x},x^{\mathcal{A}}]\right),$ and their non-associative variants are examined in detail. The simplicity, grading, and automorphism structures of these algebras are established, and the dependence of these properties on the deformation parameter $\mathbf{p}$ is analyzed. All the constructed Weyl-type algebras, the corresponding Witt-type Lie algebras, and the non-associative algebras are shown to be simple under derivation structures. Many naturally occurring subalgebras, such as the integer-coefficient subalgebra $A\left(\mathbb{Z}[e^{\pm x^{\mathbf{p}}{e}^{\iota x}},e^{\mathcal{A}x},x^{\mathcal{A}}]\right)$, are also proven to be simple. Our analysis reveals that different choices of $\mathbf{p}$ result in non-isomorphic algebraic structures while retaining non-commutativity. The results obtained generalize several existing constructions of Weyl-type algebras and lay the theoretical foundation for further developments in transcendental and non-commutative algebraic frameworks. Full article

The Ehrenfest theorem is a well-known theoretical result of quantum mechanics. It relates the dynamical evolution of the expectation value of a quantum operator to the expectation value of its corresponding commutator with the Hermitian Hamiltonian operator. However, the proof of validity of the Ehrenfest theorem for quantum gravity field theory has remained elusive, while its validation poses challenging conceptual questions. In fact, this presupposes a number of minimum requirements, which include the prescription of quantum Hamiltonian operator, the definition of scalar product, and the identification of dynamical evolution parameter. In this paper, it is proven that the target can be established in the framework of the manifestly covariant quantum gravity theory (CQG theory). This follows as a consequence of its peculiar canonical Hamiltonian structure and the commutator-bracket algebra that characterizes its representation and probabilistic interpretation. The theoretical proof of the theorem for CQG theory permits to elucidate the connection existing between quantum operator variables of gravitational field and the corresponding expectation values to be interpreted as dynamical physical observables set in the background metric space-time. Full article

Higher education institutions face a critical methodological challenge in pursuing net-zero commitments: Within the amount ofhe emissions related to Scope 3, including indirect emissions from water consumption, waste disposal, business travel, and mobility, employees commuting represents 50–92% of campus carbon footprints, yet reliable quantification remains elusive due to fragmented data collection and governance silos. The present research investigates how purposeful integration of the Home-to-Work Commuting Plan (HtWCP)—mandatory under Italian Decree 179/2021—into the Climate Neutrality Plan (CNP) could constitute an innovative strategy to enhance emissions accounting rigor while strengthening institutional governance. Stemming from the University of Genoa case study, we show how leveraging mandatory HtWCP survey infrastructure to collect granular mobility behavioral data (transportation mode, commuting distance, and travel frequency) directly addresses the GHG Protocol-specified distance-based methodology for Scope 3 accounting. In turn, the CNP could support the HtWCP in framing mobility actions into a wider long-term perspective, as well as suggesting a compensation mechanism and paradigm for mobility actions that are currently not included. We therefore establish a replicable model that simultaneously advances three institutional dimensions, through the operationalization of the Avoid–Shift–Improve framework within an integrated workflow: (1) methodological rigor—replacing proxy methodologies with actual behavioral data to eliminate the notorious Scope 3 data gap; (2) governance coherence—aligning voluntary and regulatory instruments to reduce fragmentation and enhance cross-functional collaboration; and (3) adaptive management—embedding biennial feedback cycles that enable continuous validation and iterative refinement of emissions reduction strategies. This framework positions universities as institutional innovators capable of modeling integrated governance approaches with potential transferability to municipal, corporate, and public administration contexts. The findings contribute novel evidence to scholarly literature on institutional sustainability, policy integration, and climate governance, whilst establishing methodological standards relevant to international harmonization efforts in carbon accounting. Full article

Excess commuting reflects the inefficiency of urban land resource allocation, generating additional greenhouse gas emissions and social costs, and has therefore become a central concern in the pursuit of sustainable cities. While exogenous shocks inevitably alter the efficiency of land resource allocation, it remains unclear how such shocks affect overall urban efficiency. To address this gap, this paper proposes a generalized framework for measuring excess commuting that accounts for imbalances between the numbers of jobs and residences. Drawing on mobile signaling big data, we trace the daily commuting patterns of more than 900,000 residents in Beijing, comparing the pre-pandemic period (March–October 2019) with the pandemic period (March–October 2020). The results show that: (1) Excess commuting increased significantly after the outbreak of COVID-19, with the observed average commuting distance (Tact) of the full sample rising from 6267 m to 10,058 m (an increase of 59%), indicating a decline in urban land resource allocation efficiency; (2) A more pronounced center-periphery pattern emerged at the metropolitan scale: the average Jobs–Housing Ratio (JHR) increased from 1.08 to 1.11, and its standard deviation rose from 0.54 to 0.70, with the JHR of central urban areas decreasing by 3% and that of suburban areas increasing by 20%—suggesting a marked increase in commuting distances; (3) Heterogeneous impacts were observed across age groups: the Difference-in-Differences (DID) regression confirmed a significant negative interaction term (Group × COVID-19 = −0.2991 **, p < 0.05), indicating that older adults experienced a greater increase in commuting inefficiency than younger adults. These findings reveal the dynamic mechanisms linking exogenous shocks, jobs–housing mismatch, and urban land resource allocation efficiency and provide policy implications for improving spatial resource allocation in the post-pandemic era. Full article

Vulnerability to heat and cold is influenced by many characteristics. This study analyzed determinants of vulnerability at the district level in the whole of Austria. Daily deaths (1970–2020) and daily temperatures per district were entered into time series models using negative binomial General Additive Models controlling for long-term and seasonal trends and for the day of the week. District-wise effect estimates of 111 districts in total were entered into linear meta-regression models seeking determinants of inter-district variation in heat and cold vulnerability. Generally, temperature effects on the daily number of deaths were highly significant in all districts, with higher death rates occurring when the same-day temperature exceeded a clear threshold and higher death rates with declining temperature averaged over the previous 14 days, in that case not showing any clear threshold effect. A higher heat vulnerability was observed for more densely populated areas, especially for the city of Vienna, for districts with a higher percentage of singles, of homeless people, of unemployed, and of migrants. Surprisingly, a higher percentage of outdoor workers seemed to be protective. Higher cold vulnerability was found for an increasingly autochthonous population, for districts with a higher employment rate, with more commuters, more agricultural workers, and more green spaces. Full article

The Finite State Model Predictive Control (FSMPC) of variable speed drives is the subject of many works in the recent literature. Many variants of FSMPC exist, each aiming at an aspect such as the complexity of the cost function, switching frequency, current quality, etc. In the case of multiphase drives, two popular variants are the monovector and multivector techniques. Despite past efforts to compare different techniques, the field must still reach a consensus regarding the relative merits of each one. This paper presents a new method to compare two families of FSMPC. The method is based on a reduced set of figures of merit using the current modulation index as the variable. The comparison is made for the equal usage of the power converter in terms of commutations. The results point to better values for the figures of merit for the monovector that, in addition, portrays more flexibility and better DC link usage. Full article

The main subject of this paper is the theme of differential operators defined for symmetric tensors on a Riemannian manifold and introduced in several new contexts. Some examples for 2-tensors are given and then the grad div operator for symmetric vector forms is defined. A few original operators in ${\mathbb{R}}^n$ related with grad div operator are discussed. Finally, important notions such as the Kenmotsu manifold, with some interesting examples, are also presented. Full article

The overlapping circulation of influenza (Flu), severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2; SC2), and respiratory syncytial virus (RSV) continues to challenge clinical laboratories, particularly in settings with limited automation and fragmented healthcare coverage. This study expanded the CDC Flu-SC2 assay by incorporating a laboratory-developed test (LDT) for RSV A/B detection into a fully automated quadruplex RT-qPCR (LDRA) on the Panther Fusion^® Open Access™ system. The design, based on more than 8000 RSV genomic sequences targeting the conserved M gene, achieved optimal amplification efficiencies (97–105%) and full multiplex compatibility. Analytical assessment established limits of detection between 9.6 and 37.8 copies per reaction, absence of cross-reactivity with 30 respiratory pathogens, and inclusivity for 32 viral variants. Commutability and diagnostic performance among the LDRA, CE IVD-marked Allplex™ SARS-CoV-2/FluA/FluB/RSV, and US IVD-marked Panther Fusion^® SARS-CoV-2/Flu A/B/RSV Assays were evaluated using 405 nasopharyngeal UTM-preserved swabs. The LDRA demonstrated excellent concordance (overall agreement ≥ 98%, κ > 0.95), strong diagnostic accuracy, and reliable detection of mixed infections. This quadruplex provides a fully automated, rapid, and accurate solution for the simultaneous detection of influenza A, influenza B, SARS-CoV-2, and RSV viruses, enhancing molecular diagnostic capacity and supporting equitable, timely clinical decision-making in middle-income healthcare systems such as that of the Dominican Republic. Full article

The q-Heisenberg algebra ${\mathfrak{h}}_n\left(q\right)$ is a significant class of solvable polynomial algebras, and it unifies the canonical commutation relations of Heisenberg algebras and the deformation theory of quantum groups. In this paper, we employ Gröbner-Shirshov basis theory and PBW (Poincar$\acute{e}$-Birkhoff-Witt) basis techniques to systematically investigate ${\mathfrak{h}}_n\left(q\right)$. Our main results establish that: ${\mathfrak{h}}_n\left(q\right)$ possesses an iterated skew-polynomial algebra structure, and it satisfies the important homological regularity properties of being Auslander regular, Artin-Schelter regular, and Cohen-Macaulay. These findings provide deep insights into the algebraic structure of ${\mathfrak{h}}_n\left(q\right)$, while simultaneously bridging the gap between noncommutative algebra and quantum representation theory. Furthermore, our constructive approach yields computable methods for studying modules over ${\mathfrak{h}}_n\left(q\right)$, opening new avenues for further research in deformation quantization and quantum algebra. Full article