Subcategories Research Articles

FELA evaluation of undrained bearing capacity of cutting edge of circular open caisson

ABSTRACT Circular open caissons are deep foundations sunk into the ground utilising the self-weight of cutting edge and steining as driving force along with the subsequent failure of soil in bearing. During the sinking of the caisson, the clay in contact with the cutting edge is subjected to undrained loading and the controlled sinking of the caisson can be achieved by evaluating the undrained bearing capacity of the cutting edge. In the study, the undrained bearing capacity factor (N) of the cutting edge for varying cutting angle (b), radius ratio of the caisson (r i /r o ), full embedment of the caisson (d), removal of soil within the caisson (d'), and different roughness (α) conditions of the steining are evaluated using finite element limit analysis (FELA). The factors affecting the undrained stability of caisson considering all practical scenarios are addressed and presented as charts to be used in practice.

The uniform homotopy category

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the respective Lipschitz and uniform settings. Cubical sets and uniform spaces admit the additional compatible structures of categories of (co)fibrant objects. A categorical equivalence between classical homotopy categories of cubical sets and spaces lifts to a full and faithful embedding from an associated Lipschitz homotopy category of cubical sets into an associated uniform homotopy category of uniform spaces. Bounded cubical cohomology generalizes to a representable theory on the Lipschitz homotopy category. Bounded singular cohomology on path-connected spaces generalizes to a representable theory on the uniform homotopy category. Along the way, this paper develops a cubical analogue of Kan's Ex∞ functor and proves a cubical approximation theorem for uniform maps.

Skew category algebras and modules on ringed finite sites

Let C be a small category. We investigate ringed sites (C,R) on C and the resulting module categories Mod-R. When C is finite, based on Grothendieck and Verdier's classification of finite topoi, we prove that each Mod-R is equivalent to Mod-R|D[D], where R|D[D] is the skew category algebra, canonically defined on (C,R), for a uniquely determined full subcategory D⊂C and the restriction R|D of R to D.

MODEL CATEGORIES AND PRO-p IWAHORI–HECKE MODULES

AbstractLet G denote a possibly discrete topological group admitting an open subgroup I which is pro-p. If H denotes the corresponding Hecke algebra over a field k of characteristic p, then we study the adjunction between H-modules and k-linear smooth G-representations in terms of various model structures. If H is a Gorenstein ring, we single out a full subcategory of smooth G-representations which is equivalent to the category of all Gorenstein projective H-modules via the functor of I-invariants. This applies to groups of rational points of split connected reductive groups over finite and over non-Archimedean local fields, thus generalizing a theorem of Cabanes. Moreover, we show that the Gorenstein projective model structure on the category of H-modules admits a right transfer. On the homotopy level, the right derived functor of I-invariants then admits a right inverse and becomes an equivalence when restricted to a suitable subcategory.

THE EMBEDDING PROPERTY FOR SORTED PROFINITE GROUPS

AbstractWe study the embedding property in the category of sorted profinite groups. We introduce a notion of the sorted embedding property (SEP), analogous to the embedding property for profinite groups. We show that any sorted profinite group has a universal SEP-cover. Our proof gives an alternative proof for the existence of a universal embedding cover of a profinite group. Also our proof works for any full subcategory of the sorted profinite groups, which is closed under taking finite quotients, fibre products, and inverse limits. We also show that any sorted profinite group having SEP has a sorted complete system whose theory is $\omega $ -categorical and $\omega $ -stable under the assumption that the set of sorts is countable.

English

We investigate the triangulated hull of the orbit categories of the perfect derived category and the bounded derived category of a ring concerning the power of the suspension functor. It turns out that the triangulated hull will correspond to the full subcategory of compact objects of certain triangulated categories of periodic complexes. This specializes to Stai and Zhao's result when the ring is a finite dimensional algebra with finite global dimension over a field. As the first application, if $A,B$ are flat algebras over a commutative ring and they are derived equivalent, then the corresponding derived categories of $n$-periodic complexes are triangle equivalent. As the second application, we get the periodic version of the Koszul duality.

Geometrical isomorphisms between categories of fuzzy coverings and fuzzy partitions

Let Covering be the category of the category of fuzzy coverings, and Partition, the category of fuzzy partitions. We geometrically construct an isomorphism of categories between Partition and a full subcategory of Covering, which can be used to derive bijections between fuzzy partitions and fuzzy coverings with finitely many fuzzy sets. Also, we establish an isomorphism between Covering[n], the category of coverings with n fuzzy sets, and a subcategory of Partition, whose objects are partitions with n fuzzy sets which satisfy certain conditions.

HS-Vectors: Heart Sound Embeddings for Abnormal Heart Sound Detection Based on Time-Compressed and Frequency-Expanded TDNN With Dynamic Mask Encoder.

In recent years, auxiliary diagnosis technology for cardiovascular disease based on abnormal heart sound detection has become a research hotspot. Heart sound signals are promising in the preliminary diagnosis of cardiovascular diseases. Previous studies have focused on capturing the local characteristics of heart sounds. In this paper, we investigate a method for mapping heart sound signals with complex patterns to fixed-length feature embedding called HS-Vectors for abnormal heart sound detection. To get the full embedding of the complex heart sound, HS-Vectors are obtained through the Time-Compressed and Frequency-Expanded Time-Delay Neural Network(TCFE-TDNN) and the Dynamic Masked-Attention (DMA) module. HS-Vectors extract and utilize the global and critical heart sound characteristics by masking out irreverent information. Based on the TCFE-TDNN module, the heart sound signal within a certain time is projected into fixed-length embedding. Then, with a learnable mask attention matrix, DMA stats pooling aggregates multi-scale hidden features from different TCFE-TDNN layers and masks out irrelevant frame-level features. Experimental evaluations are performed on a 10-fold cross-validation task using the 2016 PhysioNet/CinC Challenge dataset and the new publicly available pediatric heart sound dataset we collected. Experimental results demonstrate that the proposed method excels the state-of-the-art models in abnormality detection.

Higher Auslander-Reiten sequences via morphisms determined by objects

Let be an Ext-finite, Krull-Schmidt and k-linear n-exangulated category with k a commutative artinian ring. In this note, we define two additive subcategories and of in terms of the representable functors from the stable category of to the category of finitely generated k-modules. Moreover, we show that there exists an equivalence between the stable categories of these two full subcategories. Finally, we give some equivalent characterizations on the existence of Auslander-Reiten n-exangles via determined morphisms. These results unify and extend their works by Jiao–Le for exact categories, Zhao–Tan–Huang for extriangulated categories, Xie–Liu–Yang for n-abelian categories.

Actions and semi-direct products in categories of groups with action

Derived actions in the category of groups with action on itself $\mathbf{Gr}^{\bullet}$ are defined and described. This category plays a crucial role in the solution of two problems of Loday stated in the literature. A full subcategory of reduced groups with action $\mathbf{rGr}^{\bullet}$ of $\mathbf{Gr}^{\bullet}$ is introduced, which is not a category of interest but has some properties, which can be applied in the investigation of action representability in this category; these properties are similar to those, which were used in the construction of universal strict general actors in the category of interest. Semi-direct product constructions are given in $\mathbf{Gr}^{\bullet}$ and $\mathbf{rGr}^{\bullet}$ and it is proved that an action is a derived action in $\mathbf{Gr}^{\bullet}$ (resp. $\mathbf{rGr}^{\bullet}$) if and only if the corresponding semi-direct product is an object of $\mathbf{Gr}^{\bullet}$ (resp. $\mathbf{rGr}^{\bullet}$). The results obtained in this paper will be applied in the forthcoming paper on the representability of actions in the category $\mathbf{rGr}^{\bullet}$.

Limits and colimits, generators and relations of partial groups

We analyze limits and colimits in the category Part of partial groups, algebraic structures introduced by A. Chermak. We will prove that Part is both complete and cocomplete and, in addition, that the full subcategory of finite partial groups is both finitely complete and finitely cocomplete.Cocompleteness is then used in order to define quotients of partial groups. We will also identify a category richer than Set (the category of sets and set-maps) and build the free partial groups over objects is such category; this yields a larger class of free partial groups, eventually allowing to prove that every partial group is the quotient of a free partial group.

Embedding ceramic components in metal structures with hybrid directed energy deposition

The combined benefit of both additive and subtractive manufacturing within the same gantry system enables hybrid directed energy deposition to create complex geometries with smooth surface finish and superior dimensional accuracy. Moreover, with layer-by-layer access to the structure during both the addition and subtraction of material, the insertion of components is now possible, assuming the components can survive the high temperatures associated with the subsequent metal deposition. Ceramic inserts are of interest for a variety of reasons including (1) to create complex interwoven ductile/brittle composites for ballistics or high-temperature applications or (2) to integrate high-temperature strain or temperature sensors protected within ceramic substrate subsumed into a larger metal structure. In this work, stainless steel substrates were machined to create an internal cavity for the insertion of a ceramic component. During the investigation of several different over-the-ceramic deposition strategies, components were inserted, and different process sequences were allowed to continue to envelop the inserted ceramic with varying success. Unmelted powder was used to serve both as a thermal buffer and to provide a flush surface upon which the laser cladding could continue. Subsequent depositions were attempted with both dry and wet powder (addition of machining coolant to wet). The wet powder has previously been demonstrated to not significantly impact the mechanical properties of a final structure and provided a thermal barrier to protect the ceramic piece from the extreme temperatures of the final metal deposition. The wetting of the powder provided stability and minimized displacement caused by the powder flow from the laser cladding head. Finally, the use of an oblique angle for laser cladding allowed for the redirection of some fraction of the introduced thermal energy away from the ceramic component and, consequently, improved the survival of the ceramic inserts. With this combination of techniques, ceramic inserts survived full embedding within a 3D-printed stainless steel structure.

Defining an Affine Partition Algebra

We define an affine partition algebra by generators and relations and prove a variety of basic results regarding this new algebra analogous to those of other affine diagram algebras. In particular we show that it extends the Schur-Weyl duality between the symmetric group and the partition algebra. We also relate it to the affine partition category recently defined by J. Brundan and M. Vargas. Moreover, we show that this affine partition category is a full monoidal subcategory of the Heisenberg category.

A pointfree theory of Pervin spaces

We lay down the foundations for a pointfree theory of Pervin spaces. A Pervin space is a set equipped with a bounded sublattice of its powerset, and it is known that these objects characterize those quasi-uniform spaces that are transitive and totally bounded. The pointfree notion of a Pervin space, which we call Frith frame, consists of a frame equipped with a generating bounded sublattice. In this paper we introduce and study the category of Frith frames and show that the classical dual adjunction between topological spaces and frames extends to a dual adjunction between Pervin spaces and Frith frames. Unlike what happens for Pervin spaces, we do not have an equivalence between the categories of transitive and totally bounded quasi-uniform frames and of Frith frames, but we show that the latter is a full coreflective subcategory of the former. We also explore the notion of completeness of Frith frames inherited from quasi-uniform frames, providing a characterization of those Frith frames that are complete and a description of the completion of an arbitrary Frith frame.

Cohen–Macaulay Noetherian algebras

Let (R,m) be a d-dimensional commutative complete Noetherian local ring and Λ be a Noetherian R-algebra. Motivated by the notion of Cohen–Macaulay Artin algebras of Auslander and Reiten, we say that Λ is Cohen–Macaulay if there is a finitely generated Λ-bimodule ω that is maximal Cohen–Macaulay over R such that the adjoint pair of functors (ω⊗Λ′−,HomΛ′(ω,−)) induces quasi-inverse equivalences between the full subcategories of finitely generated Λ′-modules consisting of modules of finite projective dimension, P∞(Λ′), and the modules of finite injective dimension, I∞(Λ′), whenever Λ′=Λ,Λop. It is proved that such a module ω is unique, up to isomorphism, as a Λ′-module. It is also shown that Λ is a Cohen–Macaulay algebra if and only if there is a semidualizing Λ-bimodule ω of finite injective dimension and P∞(Λ′) and I∞(Λ′) are contained in the Auslander and Bass classes, respectively. We prove that Cohen–Macaulayness behaves well under reduction modulo system of parameters of R. Indeed, it will be observed that if Λ is a Cohen–Macaulay algebra, then for any system of parameters x=x1,…,xd of R, the Artin algebra Λ∕xΛ is Cohen–Macaulay as well. Assume that ω is a semidualizing Λ-bimodule of finite injective dimension that is maximal Cohen–Macaulay as an R-module. It will turn out that Λ being a Cohen–Macaulay algebra is equivalent to saying that the pair (CM(Λ′),I∞(Λ′)) forms a hereditary complete cotorsion theory and the pair (CM(Λ′op),P∞(Λ′)) forms a Tor-torsion theory, where CM(Λ′) is the class of all finitely generated Λ′-modules admitting a right resolution by modules in addω. Finally, it is shown that Cohen–Macaulayness ascends from R to RΓ and RQ, where Γ is a finite group and Q is a finite acyclic quiver.

HOPF CO-BRACE, BRAID EQUATION AND BICROSSED

In this paper, we mainly give some equivalent characterisations of Hopf cobraces, show that the full subcategory HCB(A) of Hopf co-braces is equivalent to the full subcategory C(A) of bijective 1-cocycles, and prove that the full subcategory HCB(A) is also equivalent to the category M(A) of Hopf matched pairs. Moreover, we construct many Hopf co-braces on polynomial Hopf algebras, Long copaired Hopf algebras and Drinfel’d doubles of finite dimensional Hopf algebras. And we also give a sufficient and necessary condition for a given bicrossed coproduct A ▷◁ H to be a Hopf co-brace if A or H is a Hopf co-brace

Localization for affine [formula omitted]-algebras

We prove a localization theorem for affine W-algebras in the spirit of Beilinson–Bernstein and Kashiwara–Tanisaki. More precisely, for any non-critical regular weight λ, we identify λ-monodromic Whittaker D-modules on the enhanced affine flag variety with a full subcategory of Category O for the W-algebra.To identify the essential image of our functor, we provide a new realization of Category O for affine W-algebras using Iwahori–Whittaker modules for the corresponding Kac–Moody algebra. Using these methods, we also obtain a new proof of Arakawa's character formulae for simple positive energy representations of the W-algebra.

Finite torsors on projective schemes defined over a discrete valuation ring

Given a Henselian and Japanese discrete valuation ring $A$ and a flat and projective $A$-scheme $X$, we follow the approach of Biswas-dos Santos to introduce a full subcategory of coherent modules on $X$ which is then shown to be Tannakian. We then prove that, under normality of the generic fibre, the associated affine and flat group is pro-finite in a strong sense (so that its ring of functions is a Mittag-Leffler $A$-module) and that it classifies finite torsors $Q\to X$. This establishes an analogy to Nori's theory of the essentially finite fundamental group. In addition, we compare our theory with the ones recently developed by Mehta-Subramanian and Antei-Emsalem-Gasbarri. Using the comparison with the former, we show that any quasi-finite torsor $Q\to X$ has a reduction of structure group to a finite one.

Curvature Invariants of Equivariant Isometric Minimal Immersions into Grassmannian Manifolds

Using theories of principal fibre bundles and connections in [11], we study curvature invariants as Riemannian submanifolds for equivariant isometric minimal immersions from Riemannian or Hermitian symmetric spaces of compact type into Grassmannian manifolds. First we calculate principal curvatures of all equivariant full isometric minimal immersions from the complex projective line to complex quadrics. It is shown that they do not depend on the parameter of the moduli space. According to the preceding research, it is important for the study of curvature invariants to examine the behavior of higher order covariant derivative of the second fundamental form. It also enables us to distinguish those maps by curvature invariants in the moduli space. In addition, we calculate principal curvatures of all equivariant full holomorphic isometric embeddings between the complex projective spaces.

On periodic stable Auslander–Reiten components containing Heller lattices over the symmetric Kronecker algebra

Let O be a complete discrete valuation ring, K its quotient field, and A the symmetric Kronecker algebra over O. We consider the full subcategory of the category of A-lattices whose objects are A-lattices M such that M⊗OK is projective A⊗OK-modules. In this paper, we study Heller lattices of indecomposable periodic modules over A. As a main result, we determine the shapes of stable Auslander–Reiten components containing Heller lattices of indecomposable periodic modules over A.