Category Of Functors Research Articles

On simultaneously reflective and coreflective subcategories of functor categories

On simultaneously reflective and coreflective subcategories of functor categories

Krull–Gabriel dimension of Cohen–Macaulay modules over hypersurfaces of countable Cohen-Macaulay representation type

We calculate the Krull–Gabriel dimension of the functor category of the (stable) category of maximal Cohen–Macaulay modules over complete Cohen-Macaulay local rings of countable Cohen-Macaulay representation type. We show that the Krull–Gabriel dimension is 0 if and only if the ring is of finite Cohen–Macaulay representation type and that is 2 if the ring is a hypersurface of countable but not finite Cohen–Macaulay representation type.

Galois theory and homology in quasi-abelian functor categories

Given a finite category T, we consider the functor category AT, where A can be any quasi-abelian category. Examples of quasi-abelian categories are given by any abelian category but also by non-exact additive categories as the categories of torsion(-free) abelian groups, topological abelian groups, locally compact abelian groups, Banach spaces and Fréchet spaces. In this situation, the categories of various internal categorical structures in A, such as the categories of internal n-fold groupoids, are equivalent to functor categories AT for a suitable category T. For a replete full subcategory S of T, we define F to be the full subcategory of AT whose objects are given by the functors F:T→A with F(T)=0 for all T∉S. We prove that F is a torsion-free Birkhoff subcategory of AT. This allows us to study (higher) central extensions from categorical Galois theory in AT with respect to F and generalized Hopf formulae for homology.

A Specific Class of Harmonic Meromorphic Functions Associated with the Mittag-Leffler Transformation

This article uses the Mittag-Leffler transformation to explore a specific category of harmonic meromorphic functions. The Mittag-Leffler transformation is a crucial tool for analysing meromorphic functions and provides essential properties and insights into their behavior. The main focus of this study is on harmonic meromorphic functions that can be represented by the Mittag-Leffler transformation. Furthermore, this research introduces an innovative derivative operator that incorporates this transformation into the domain of harmonic meromorphic functions. The Mittag-Leffler transformation is widely recognised as a powerful technique for analysing various mathematical functions, especially those with fractional order derivatives. It improves our understanding of harmonic meromorphic functions and their inherent characteristics. The research findings highlight the effectiveness of this new derivative operator in unraveling the complexities of these functions. They provide valuable insights into their behavior and fundamental traits. Additionally, the study offers coefficient inequalities, the distortion theorem, distortion bounds, extreme points, convex combinations, and convolution analyses specifically tailored to functions within this particular class.

About one strengthening of the Massera’s existence theorem of periodic solutions of linear differential periodic systems

According to Massera’s theorem, an ordinary differential linear nonhomogeneous periodic system has a periodic solution with a period coinciding with that of the system if and only if this system has a bounded solution. We introduce the class L of vector functions called growing slower than a linear function. This class contains the class B of bounded vector functions in as its own subclass. It has been proved that Massera’s above-mentioned theorem will remain true if in its formulation a bounded solution is replaced by a slower growing solution than a linear function. It is shown that the set B in the metric space (L, distc ), where distc is the uniform convergence metric vector functions on intervals, has Baer’s first category, i. e. almost everything in the sense of the category of space vector functions (L, distc ) are not bounded. This fact shows the significance of the obtained strengthening of Massera’s theorem.

Some Classes of Bazilevič-Type Close-to-Convex Functions Involving a New Derivative Operator

In the present paper, we are merging two interesting and well-known classes, namely those of Bazilevič and close-to-convex functions associated with a new derivative operator. We derive coefficient estimates for this broad category of analytic, univalent and bi-univalent functions and draw attention to the Fekete–Szegö inequalities relevant to functions defined within the open unit disk. Additionally, we identify several specific special cases of our results by specializing the parameters.

Flat model structures and Gorenstein objects in functor categories

We construct a flat model structure on the category ${_{\mathcal {Q},\,R}\mathsf {Mod}}$ of additive functors from a small preadditive category $\mathcal {Q}$ satisfying certain conditions to the module category ${_{R}\mathsf {Mod}}$ over an associative ring $R$ , whose homotopy category is the $\mathcal {Q}$ -shaped derived category introduced by Holm and Jørgensen. Moreover, we prove that for an arbitrary associative ring $R$ , an object in ${_{\mathcal {Q},\,R}\mathsf {Mod}}$ is Gorenstein projective (resp., Gorenstein injective, Gorenstein flat, projective coresolving Gorenstein flat) if and only if so is its value on each object of $\mathcal {Q}$ , and hence improve a result by Dell'Ambrogio, Stevenson and Šťovíček.

A new strategy based on the logarithmic Chebyshev cardinal functions for Hadamard time fractional coupled nonlinear Schrödinger–Hirota equations

In this research, the Hadamard fractional derivative is used to define the time fractional coupled nonlinear Schrödinger–Hirota equations. The logarithmic Chebyshev cardinal functions, as a new category of cardinal functions, are introduced to build a numerical method to solve this system. To do this, the Hadamard fractional differentiation matrix of these functions is obtained. In the developed method, by considering a hybrid approximation of the problem’s solution using the logarithmic Chebyshev cardinal functions (for the temporal variable) and classical Chebyshev cardinal polynomials (for the spatial variable), and employing the interpolation property of these basis functions, along with the expressed derivative matrix, solving the fractional system turns into obtaining the solution of an algebraic system of equations. Two numerical examples are investigated to acknowledge the high accuracy of the introduced procedure.

Second Hankel Determinant and Fekete–Szegö Problem for a New Class of Bi-Univalent Functions Involving Euler Polynomials

Second Hankel Determinant and Fekete–Szegö Problem for a New Class of Bi-Univalent Functions Involving Euler Polynomials

The Miller-Ross Poisson distribution and its applications to certain classes of bi-univalent functions related to Horadam polynomials

Within the scope of this research, we introduce a novel category of bi-univalent functions. Horadam polynomials are utilized to characterize these functions by utilizing series from the Poisson distribution of the Miller-Ross type. Functions from these new categories have been used to construct estimates for the Fekete-Szego functional, as well as estimates of the Taylor-Maclaurin coefficients |l2| and |l3|. These projections were created for the methods in each of these brand-new subclasses. We made some additional discoveries after, focusing on the traits that contributed to our initial findings.

Properties for Certain Class of p- Valent Functions Related to Jackson’s Operator

An inspiration from the fundamentals of (r,q) calculus to introduce an innovative subclass within the T(p) category of multivalent analytic functions, located within the confines of the open unit disk, is subjected to examination. The establishment of the subclass was achieved by employing Jackson's derivative operator to enhance the comprehension of these analytical functions. This article began by investigating and establishing adequate criteria that dictate the inclusion of functions within this recently introduced subclass. To achieve this, a comprehensive coefficient characterization to facilitate a deeper comprehension of the subclass's properties and behavior is derived. Further, various pertinent results that contribute to the broader understanding of the functions belonging to this subclass are explored. The findings and implications of these results are elucidated, underscoring the potential significance of this work in advancing the field of multivalent analytic functions and their applications. In conclusion, this paper broadens the scope of T(p) and sheds light on the distinct characteristics exhibited by the functions in this newly introduced subclass. This work sets the stage for further exploration and applications of (r,q) calculus and Jackson's derivative operator in the domain of multivalent analytic functions.

Outer functors and a general operadic framework

For O an operad in k-vector spaces, FO is defined to be the category of k-linear functors from the PROP associated to O to k-vector spaces. Given a binary operation μ∈O(2) that satisfies a right Leibniz condition, the full subcategory FOμ⊂FO is introduced here and its properties studied.This is motivated by the case of the Lie operad Lie, where μ is taken to be the generator. By previous results of the author, when k=Q, FLie is equivalent to the category of analytic functors on the opposite grop of the category gr of finitely-generated free groups. The main result shows that FLieμ identifies with the category of outer analytic functors on grop, as introduced in earlier work of the author with Vespa.Using this identification, this theory has applications to the study of the higher Hochschild homology functors related to work of Turchin and Willwacher.

A Specific Category of Harmonic Functions Characterized By A Generalized Komatu Operator in Conjunction With The (R-K) Integral Operator and Applications to Neutrosophic Complex Field

In our work, we introduced a distinct subclass of univalent harmonic functions referred to as a subclass of chiral functions. These functions are defined by combining the generalized Komatu operator with the integral operator (R − K), which has positive coefficients within the unit disc A. Also, we generalize the same subclass into neutrosophic complex numbers. Throughout our investigation, we establish several properties associated with these functions, including coefficient estimates, the convex formula, the integral operator, and the Hadamard product. On the other hand, we present the Neutrosophic convex formula and the neutrosophic integral operator.

Functions of one-time occurrence verbs in I. Bunin’s short stories “Dark Alleys”

The article presents the results of the study of modern Russian verbs with the person subject based on the cycle of stories “Dark Alleys” by I. Bunin. The purpose of the article is a one-time occurrence verbs’ multi–level analysis taking into account several aspects, lexico-semantic and grammatical ones, through the prism of functional grammar. This analysis will reveal the features of the use of verbs with the meaning of one-time occurrence in I. Bunin’s idiostyle, and their role in revealing the main conceptual space of the author’s stories. The novelty of our research is the fact that we have taken into account the morphological and syntactic characteristics of the verbs, their features of compatibility with the circumstances of time, mode of action, measure and degree. We have established that the category of one-time occurrence functions in two groups (marked and unmarked one-time use), which have their own specific morphological characteristics, however, they are characterized by the fact that, as a rule, they are combined with time constants. The most frequent group of one-act verbs has been identified, namely: verbs with the suffix – nu (ну) -. This interpretation has made it possible to analyze in more detail the linguistic phenomenon of I. Bunin, to reveal the author’s individual picture of the world. The analysis of the linguistic material allowed us to conclude that the functioning of the verbs with the meaning of one-time occurrence in fictional discourse helps to identify the author’s perception of reality based on the unity of rational and emotional elements.

A new type of radial basis functions for problems governed by partial differential equations.

The aim of this paper is to introduce a novel category of radial basis functions that incorporate smoothing techniques. Initially, we employ the power augmented and shape parameter schemes to create the radial basis functions. Subsequently, we apply the newly-constructed radial basis functions using the traditional collocation method and singular values decomposition algorithm to solve the corresponding linear system equations. Finally, we analyze several pairs of radial basis functions in depth to address physical problems linked to thermal science that are governed by partial differential equations. The numerical results demonstrate that the radial basis functions constructed using the power augmented and shape parameter schemes exhibit remarkable performance.

Concerning a Novel Integral Operator and a Specific Category of Starlike Functions

In this study, a novel integral operator that extends the functionality of some existing integral operators is presented. Specifically, the integral operator acts as the inverse operator to the widely recognized Opoola differential operator. By making use of the integral operator, a certain subclass of analytic univalent functions defined in the unit disk is proposed and investigated. This new class encompasses some familiar subclasses, like the class of starlike and the class of convex functions, while some new ones are introduced. The investigation thereafter covers coefficient inequality, distortion, growth, covering, integral preserving, closure, subordinating factor sequence, and integral means properties. Furthermore, the radii problems associated with this class are successfully addressed. Additionally, a few remarks are provided, to show that the novel integral operator and the new class generalize some existing ones.

Nilpotent Category of Abelian Category and Self-adjoint Functors

Nilpotent Category of Abelian Category and Self-adjoint Functors

T-Structures with Grothendieck hearts via functor categories

We study when the heart of a t-structure in a triangulated category mathcal {D} with coproducts is AB5 or a Grothendieck category. If mathcal {D} satisfies Brown representability, a t-structure has an AB5 heart with an injective cogenerator and coproduct-preserving associated homological functor if, and only if, the coaisle has a pure-injective t-cogenerating object. If mathcal {D} is standard well generated, such a heart is automatically a Grothendieck category. For compactly generated t-structures (in any ambient triangulated category with coproducts), we prove that the heart is a locally finitely presented Grothendieck category. We use functor categories and the proofs rely on two main ingredients. Firstly, we express the heart of any t-structure in any triangulated category as a Serre quotient of the category of finitely presented additive functors for suitable choices of subcategories of the aisle or the co-aisle that we, respectively, call t-generating or t-cogenerating subcategories. Secondly, we study coproduct-preserving homological functors from mathcal {D} to complete AB5 abelian categories with injective cogenerators and classify them, up to a so-called computational equivalence, in terms of pure-injective objects in mathcal {D}. This allows us to show that any standard well generated triangulated category mathcal {D} possesses a universal such coproduct-preserving homological functor, to develop a purity theory and to prove that pure-injective objects always cogenerate t-structures in such triangulated categories.

Rehabilitation clinical trials in global registries: reporting of participant inclusion by sex, age, race and ethnicity

Purpose Registries of clinical trials exist in part to standardize data for the scientific community. Studies in the United States demonstrated gaps in reporting on ClinicalTrials.gov. The purpose of this cross-sectional study was to evaluate clinical trial participation among global registries. Methods This study identified registries with results reported and assessed available results for physical and rehabilitation medicine (PRM) diagnosis, intervention, primary outcome, and the International Classification of Functioning, Disability and Health (ICF) categories. Participant characteristics including sex, age, and race/ethnicity were assessed. Results A total of 93 rehabilitation trials from eight registries met inclusion criteria. Most trials included persons with musculoskeletal disorders (50.5%), technology such as robotics (25.8%) and outcomes in ICF category of body functions and structures (54.7%). Sex was reported in 61.3% of trials and varied among registries (0 to 100%). Participation of women in trials showed variability from 0 to 75%. Reporting of age of the participants was not uniform and six registries did not include age in all trials. Information about race/ethnicity was absent in most trials and registries. Conclusions Based on trials registered with accessible results, these findings may reveal either a gap in reporting results or a lack of trials investigating important PRM diagnoses, interventions, and outcomes. Implications for Rehabilitation This study contributes to the growing body of evidence that there are gaps in standardization of rehabilitation results reported on clinical trials registries. The uniform reporting of results is an important component of advancing rehabilitation science and may be a factor in high-quality study design and improved transparency.

Generalized tilting theory in functor categories

AbstractThis paper is devoted to the study of generalized tilting theory of functor categories in different levels. First, we extend Miyashita’s proof (Math Z 193:113–146,1986) of the generalized Brenner–Butler theorem to arbitrary functor categories $\mathop{\textrm{Mod}}\nolimits\!(\mathcal{C})$ with $\mathcal{C}$ an annuli variety. Second, a hereditary and complete cotorsion pair generated by a generalized tilting subcategory $\mathcal{T}$ of $\mathop{\textrm{Mod}}\nolimits \!(\mathcal{C})$ is constructed. Some applications of these two results include the equivalence of Grothendieck groups $K_0(\mathcal{C})$ and $K_0(\mathcal{T})$ , the existences of a new abelian model structure on the category of complexes $\mathop{\textrm{C}}\nolimits \!(\!\mathop{\textrm{Mod}}\nolimits\!(\mathcal{C}))$ , and a t-structure on the derived category $\mathop{\textrm{D}}\nolimits \!(\!\mathop{\textrm{Mod}}\nolimits \!(\mathcal{C}))$ .