Search Results (130)

The primary focus of this paper is to extend the concept of pseudospectrum from operators and matrices to elements of a unital complex Banach Jordan algebra, thereby moving from the associative to the non-associative setting. We introduce the notion of $\epsilon$-invertibility in a Banach Jordan algebra $\mathcal{J}$ and establish the invariance of pseudospectra with respect to full subalgebras of $\mathcal{J}$. We further investigate fundamental properties of the pseudospectrum of an element in a Banach Jordan algebra, including its relationship with level sets of analytic functions and pseudospectral bounds. The paper also examines linear maps that preserve pseudospectra in Banach Jordan algebras, as well as decomposition results for certain elements into simpler components within suitable localized subalgebras. Finally, we study an extension of the Roch–Silberman theorem in the setting of JB-algebras. Full article

We develop a function theory on a three-dimensional reduced quaternionic model endowed with a projected (and, therefore, non-associative) product, together with its natural dual extension generated by a nilpotent infinitesimal unit. After introducing the associated first-order Dirac-type system, we construct explicit Cauchy kernels and prove a Cauchy–Pompeiu representation for sufficiently smooth functions with values in the dual algebra. We derive a Teodorescu-type right inverse, Liouville- and uniqueness-type principles, and residue formulas for isolated singularities. For smooth hypersurfaces, we establish Plemelj–Sokhotski boundary limits for the Cauchy transform and its dual lift. Worked examples illustrate how the reduced product interacts with boundary geometry and provide a practical route to computation. Full article

Vertical shafts are key channels for underground energy storage, mineral exploitation, and related engineering fields. Yet in deeply buried complex strata and high ground stress environments, traditional passive supports are prone to lining failure, while linear yield criteria cannot accurately characterize rock masses’ nonlinear mechanical behavior, limiting their use in shaft analysis. The core mechanical process of shaft construction aligns with the cavity contraction–expansion mechanism: excavation induces cavity unloading and contraction, causing shaft deformation and plastic zone expansion in surrounding rock; support enables cavity reverse expansion via preset shaft wall counter loads to actively control surrounding rock deformation. Based on this, this study integrates the Hoek–Brown nonlinear yield criterion, large-strain theory, and non-associated flow rules; couples cavity contraction–expansion semi-analytical solutions with the composite shaft wall mechanical model; and establishes a composite shaft wall–surrounding rock interaction analysis method. This research clarifies excavation-induced surrounding rock mechanical responses, reveals shaft wall counter loads’ regulatory effect on surrounding rock, and develops a systematic excavation support calculation workflow. Parameter analysis shows that increasing lining thickness is the most direct way to reduce inner wall tensile stress and improve safety; composite linings optimize stress distribution and enhance structural collaborative performance; and safety assessment confirms the lining inner wall as a structural weak zone. The proposed method and findings fill the gap in applying cavity contraction–expansion theory to shaft construction, providing reliable theoretical and practical guidance for deep shaft design, construction, and safety evaluation. 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 skin of turtles, particularly aquatic species, can harbor a diverse range of bacteria, including Citrobacter species, which are recognized as causative agents of Septicemic Cutaneous Ulcerative Disease. Consequently, turtles may act as reservoirs of pathogenic and multidrug-resistant bacteria, posing a potential public health concern. This case-based study investigated the presence of Citrobacter spp. in a loggerhead sea turtle (Caretta caretta) housed at the Livorno Aquarium, Italy. Nine swabs were collected from skin lesions (plastron, carapace, nuchal mass), the oral cavity, and the cloaca. The isolated strains were identified by MALDI-TOF MS and tested for their susceptibility to 12 antimicrobials, belonging to eight antimicrobial classes, by the disc diffusion method. Isolates were investigated genotypically for extended-spectrum-β-lactamase (ESBL) bla_CTX−M, bla_TEM, bla_SHV, bla_PER, and metallo-β-lactamase (MBL) bla_IMP, bla_OXA−48, bla_VIM, bla_NDM, bla_GES genes. Biofilm production ability was also evaluated. Fifteen Citrobacter spp. strains were recovered from the analyzed samples. Complete resistance was recorded for ampicillin, followed by high levels of resistance to imipenem, tetracycline and piperacillin-tazobactam. Worryingly, 86.7% were classified as multidrug-resistant. The most common ESBL-genotype combination was bla_SHV and bla_PER genes (60%), while the most frequently detected MBL gene was bla_NDM (46.7%), followed by bla_GES (40%). Most isolates were classified as weak biofilm producers (80%). The findings of this study demonstrate the presence of Citrobacter spp., an opportunistic pathogen, with a notable prevalence of multidrug-resistant strains carrying beta-lactamase-encoding genes, in a loggerhead sea turtle in Italy, across both lesioned and healthy anatomical sites. Full article

Symmetric structures are key in non-associative algebras. A Mock-Lie algebra, defined by commutativity and the Jacobi identity, shows strong algebraic symmetry. This paper studies the quasi-centroid, which captures the symmetry of linear operators commuting with the algebra’s product. We define the quasi-centroid and set its condition for linear endomorphisms under the bracket operation. We classify matrix representations of quasi-centroids for all Mock-Lie algebras of dimensions 2 to 5 by computing matrices and analyzing coefficient relations. These results provide a foundation for further structural study. We also show that in each case, the centroid is strictly contained in the quasi-centroid, confirming proper containment for all these algebras. Full article

We develop detailed quaternionic and octonionic frameworks for quantum computation grounded on normed division algebras. Our central result is to prove the polynomial computational equivalence of quaternionic and complex quantum models: Computation over $\mathbb{H}$ is polynomially equivalent to the standard complex quantum circuit model and hence captures the same complexity class BQP up to polynomial reductions. Over $\mathbb{H}$, we construct a complete model—quaternionic qubits on right $\mathbb{H}$-modules with quaternion-valued inner products, unitary dynamics, associative tensor products, and universal gate sets—and establish polynomial equivalence with the standard complex model; routes for implementation at fidelities exceeding $99\%$ via pulse-level synthesis on current hardware are discussed. Over $\mathbb{O}$, non-associativity yields path-dependent evolution, ambiguous adjoints/inner products, non-associative tensor products, and possible failure of energy conservation outside associative sectors. We formalize these obstructions and systematize four mitigation strategies: Confinement to associative subalgebras, $G_2$-invariant codes, dynamical decoupling of associator terms, and a seven-factor algebraic decomposition for gate synthesis. The results delineate the feasible quaternionic regime from the constrained octonionic landscape and point to applications in symmetry-protected architectures, algebra-aware simulation, and hypercomplex learning. Full article

Habituation is a fundamental form of non-associative learning that allows organisms to filter out repetitive, non-salient stimuli but declines with age. While the kynurenine pathway (KP) of tryptophan metabolism is implicated in psychiatric and neurodegenerative diseases, its role in age-related habituation deficits has been overlooked. This review proposes a systems-level framework suggesting that age-related, chronic inflammation KP dysregulation is a key driver of habituation deficits. We present evidence showing that neurotoxic metabolites from the kynurenine-3-monooxygenase (KMO)-dependent branch drive a self-reinforcing cycle of oxidative stress, excitotoxicity, and glial reactivity that destabilizes the neural circuits required for habituation. This framework redefines KP modulation as context dependent: metabolites such as kynurenic acid (KYNA), which can be disruptive when elevated in youth, may become compensatory under the oxidative load of aging. Our findings that genetic KMO deletion preserves habituation in aged and old mice provide the first direct in vivo evidence supporting this model. We propose that inhibiting the KMO branch preserves habituation not by simply altering metabolite levels but by restoring homeostatic balance across neuroimmune, redox, and plasticity networks. KMO thus emerges as a critical node for maintaining cognitive resilience, offering a therapeutic target for preserving brain function during aging. Full article

Accurate forecasting of springback continues to pose a significant challenge in sheet metal forming processes. The present paper presents a numerical model designed for the precise prediction of springback, allowing for a deeper understanding of plasticity behavior during cold forming operations in sheet metals. The key contribution of this model is the introduction of a non-associated anisotropic constitutive model featuring nonlinear mixed isotropic–kinematic hardening. This model is derived from Hill’48 quadratic function and it was implemented into ABAQUS 6.13 software environment through the user defined UMAT subroutine. For improved precision, kinematic hardening parameters specific to 5083 aluminum sheet metal were meticulously derived from cyclic shear experiments. Our results demonstrate the model’s strong capability in predicting springback during the U-bending operation, achieving remarkable accuracy. The design of experiments DOE is used as a statistical method to optimize the number of experiments and analyze the effects of key input factors. In this study, sheet thickness, punch speed, and sampling angle relative to the rolling direction (RD) are examined at different levels to assess their impact on folding force and springback. The strong agreement between experimental results and theoretical predictions confirms the accuracy and reliability of the proposed models in estimating folding force and springback. Full article

Steel slag aggregate concrete (SAC) is widely recognized as a high-performance and sustainable construction material. However, its broader structural application has been impeded by the limited development of reliable constitutive models. Building upon the well-established non-uniform hardening plasticity theory, this study proposes a comprehensive theoretical framework to establish a stress–strain relationship model for SAC under complex stress states. To this end, a multiaxial elastoplastic constitutive model for SAC is developed through the following steps: (1) The Guo–Wang failure criterion is employed as the bounding surface, from which a yield criterion is formulated to capture the characteristic mechanical responses of SAC under multiaxial loading; (2) Based on fundamental plasticity theory, the stress–strain relationship is derived by integrating the proposed yield function with a non-associated flow rule using a Drucker–Prager-type plastic potential function, while ensuring consistency conditions are satisfied; (3) A parameter calibration methodology is introduced and applied using experimental data from uniaxial and multiaxial tests on SAC; (4) A numerical implementation scheme is developed in MATLAB 2024a, and the model is validated through computational simulations. The validation results confirm that the proposed model reliably captures the stress–strain behavior of SAC under complex loading conditions. Overall, this study not only delivers a robust multiaxial constitutive model for SAC, but also offers a systematic modeling approach that may serve as a reference for the further development of constitutive theories for steel slag-based concretes and their broader application in structural engineering. Full article

The integration of radar and Automatic Dependent Surveillance–Broadcast (ADS-B) surveillance data is critical for increasing the accuracy of air traffic monitoring; however, effective track associations remain challenging due to inherent sensor discrepancies and computational constraints. To achieve accurate identification and association between radar tracks and ADS-B tracks, this study proposes an adaptive feature extraction method based on the longest common subsequence (LCSS) combined with classification theory to address the limitations inherent in traditional machine learning-based track association approaches. These limitations encompass challenges in acquiring training samples, extended training times, and limited model generalization performance. The proposed method employs LCSS to measure the similarity between two types of trajectories and categorizes tracks into three groups—definite associations, definite nonassociations, and fuzzy associations—using a similarity matrix and an adaptive sample classification model (adaptive classification model). Fuzzy mathematical techniques are subsequently applied to extract discriminative features from both definite association and nonassociation sets, followed by training a support vector machine (SVM) model. Finally, the SVM performs classification and association of trajectories in the fuzzy association group. The computational results show that, compared with conventional statistical methods, the proposed methodology achieves both superior precision and recall rates while maintaining computational efficiency threefold that of traditional machine learning algorithms. Full article

The precise prediction of soil settlement under applied loads is of paramount importance in the field of geotechnical engineering. Conventional analytical approaches often lack the capacity to accurately represent the rate-dependent deformations exhibited by soft soils. Creep affects the integrity of geotechnical structures and can lead to loss of serviceability or even system failure. Over time, they deform, the soil structure can be weakened, and consequently, the risk of collapse increases. Despite extensive research, regarding the creep characteristics of soft soils, the prediction of creep deformation remains a substantial challenge. This study explores soil consolidation settlement by employing three different material models: the Soft Soil Creep (SSC) model implemented in PLAXIS 2D, alongside two user-defined elasto-viscoplastic models, specifically Creep-SCLAY1S and the non-associated creep model for Structured Anisotropic Clay (n-SAC). Through the simulation of laboratory experiments and the Lilla Mellösa test embankment situated in Sweden, the investigation evaluates the strengths and weaknesses of these models. The results demonstrate that the predictions produced by the SSC, n-SAC, and Creep-SCLAY1S models are in close correspondence with the field observations, in contrast to the more simplistic elastoplastic model. The n-SAC and Creep-SCLAY1S models adeptly represent the stress–strain response in CRS test simulations; however, they tend to over-predict horizontal deformations in field assessments. Further investigation is advisable to enhance the ease of use and relevance of these sophisticated models. Full article

Feline infectious peritonitis (FIP) is caused by mutated feline coronaviruses. Immune-mediated hemolytic anemia (IMHA) arises due to immune-mediated erythrocyte destruction and can be non-associative or associative with diseases such as FIP. Records of cats with FIP were reviewed to find those with associative IMHA based on exclusion of other causes of anemia and a positive saline agglutination test and/or Coombs test. The inclusion criteria were met for 45 cats (26 (58%) cats with effusive and 19 (42%) with non-effusive FIP). Median hematocrit was 18% (interquartile range [IQR] 13–20). Anemia was non-regenerative in 36 (80%) cats and regenerative in 5 (11%) cats; 4 (9%) cats had no reticulocyte count available. Concurrent thrombocytopenia was present in 18 (40%) cats. All 45 cats were treated with nucleoside analogs, and 44 (98%) cats with glucocorticoids; in 5 (11%) cats, glucocorticoids were added after starting antiviral treatment due to persistent anemia. Median follow-up was 72 days (IQR 14–246); at the time of last follow-up 33 (73%) cats had survived while 12 (27%) had died or were euthanized. Of the 33 surviving cats, 17 achieved remission of both FIP and IMHA. In three cats, FIP remission was achieved, but IMHA relapsed; in one of these, IMHA relapsed twice. FIP relapsed without IMHA in two cats, and both FIP and IMHA relapsed in one cat. In 9 cats the antiviral and glucocorticoid treatment is still ongoing at the time of the publication. Although FIP is likely an uncommon cause of associative IMHA, as more cats with FIP are treated with antiviral therapy, it is important to consider IMHA as a possible cause of anemia in cats with FIP. Full article

This paper comprehensively examines symmetric difference operators within logical systems generated by nilpotent t-norms and t-conorms, specifically addressing their behavior and applicability in bounded and Łukasiewicz fuzzy logic systems. We identify two distinct symmetric difference operators and analyze their fundamental properties, revealing their inherent non-associativity. Recognizing the limitations posed by non-associative behavior in practical multi-step logical operations, we introduce a novel aggregated symmetric difference operator constructed through the arithmetic mean of the previously defined operators. The primary theoretical contribution of our research is establishing the associativity of this new aggregated operator, significantly enhancing its effectiveness for consistent multi-stage computations. Moreover, this operator retains critical properties including symmetry, neutrality, antitonicity, and invariance under negation, thus making it particularly valuable for various computational and applied domains such as image processing, pattern recognition, fuzzy neural networks, cryptographic schemes, and medical data analysis. The demonstrated theoretical robustness and practical versatility of our associative operator provide a clear improvement over existing methodologies, laying a solid foundation for future research in fuzzy logic and interdisciplinary applications. Our broader aim is to derive and study symmetric difference operators in both bounded and Łukasiewicz systems, as this represents a new direction of research. Full article

To overcome the limitation of traditional elastic phase field models that neglect plastic deformation in rock compressive-shear failure, this study developed an elastoplastic phase field fracture model incorporating plastic strain energy and established a coupling framework for plastic deformation and crack evolution. By introducing the non-associated flow rule and plastic damage variable, an energy functional comprising elastic strain energy, plastic work, and crack surface energy was constructed. The phase field governing equation considering plastic-damage coupling was obtained, enabling the simulation of the energy evolution in rock from the elastic stage to plastic damage and unstable failure. Validation was carried out through single-edge notch tension tests and uniaxial compression tests with prefabricated cracks. Results demonstrate that the model accurately captures characteristics such as the linear propagation of tensile cracks, the initiation of wing-like cracks under compressive-shear conditions, and the evolution of mixed-mode failure modes, which are highly consistent with classical experimental observations. Specifically, the model provides a more detailed description of local damage evolution and residual strength caused by stress concentration in compressive-shear scenarios, thereby quantifying the influence of plastic deformation on crack driving force. These findings offer theoretical support for crack propagation analysis in rock engineering applications, including hydraulic fracturing and the construction of underground energy storage caverns. The proposed plastic phase field model can be effectively utilized to simulate rock failure processes under complex stress states. Full article