Subject Classification Research Articles

Artificial intelligence-enhanced opportunistic screening of osteoporosis in CT scan: a scoping Review.

This scoping review aimed to assess the current research on artificial intelligence (AI)--enhanced opportunistic screening approaches for stratifying osteoporosis and osteopenia risk by evaluating vertebral trabecular bone structure in CT scans. PubMed, Scopus, and Web of Science databases were systematically searched for studies published between 2018 and December 2023. Inclusion criteria encompassed articles focusing on AI techniques for classifying osteoporosis/osteopenia or determining bone mineral density using CT scans of vertebral bodies. Data extraction included study characteristics, methodologies, and key findings. Fourteen studies met the inclusion criteria. Three main approaches were identified: fully automated deep learning solutions, hybrid approaches combining deep learning and conventional machine learning, and non-automated solutions using manual segmentation followed by AI analysis. Studies demonstrated high accuracy in bone mineral density prediction (86-96%) and classification of normal versus osteoporotic subjects (AUC 0.927-0.984). However, significant heterogeneity was observed in methodologies, workflows, and ground truth selection. The review highlights AI's promising potential in enhancing opportunistic screening for osteoporosis using CT scans. While the field is still in its early stages, with most solutions at the proof-of-concept phase, the evidence supports increased efforts to incorporate AI into radiologic workflows. Addressing knowledge gaps, such as standardizing benchmarks and increasing external validation, will be crucial for advancing the clinical application of these AI-enhanced screening methods. Integration of such technologies could lead to improved early detection of osteoporotic conditions at a low economic cost.

An exactly divergence-free hybridized discontinuous Galerkin method for the generalized Boussinesq equations with singular heat source

The purpose of this work is to propose and analyze a hybridized discontinuous Galerkin (HDG) method for the generalized Boussinesq equations with singular heat source. We use polynomials of order k, k − 1 and k to approximate the velocity, the pressure and the temperature. By introducing Lagrange multipliers for the pressure, the approximate velocity field obtained by the HDG method is shown to be exactly divergence-free and H(div)-conforming. Under a smallness assumption on the problem data and solutions, we prove by Brouwer’s fixed point theorem that the discrete system has a solution in two dimensions. If the viscosity and thermal conductivity are further assumed to be positive constants, a priori error estimates with convergence rate O(h) and efficient and reliable a posteriori error estimates are derived. Finally numerical examples illustrate the theoretical analysis and show the performance of the obtained a posteriori error estimator.

Analysis and Application of Artificial Intelligence in Subject Classification Systems at the High School Level : Take the Qing Dao Hua Wei International Education College as an Example

Analysis and Application of Artificial Intelligence in Subject Classification Systems at the High School Level : Take the Qing Dao Hua Wei International Education College as an Example

On a Class of Analytic Univalent Functions Associated with (H-R) Fractional Derivative

In this paper, we introduced a class of analytic functions defined by (H–R) fractional derivative defined in the unit disk, we obtained coefficient bounded, so we obtained some theorems of this class. 2000Mathematics Subject classification: 30C45.

Refinement of Jensen Mercer and Hermite–Hadamard-Mercer type inequalities for generalized convex functions on co-ordinates with their computational analysis

In the current study, the Jensen-Mercer inequality is extended to co-ordinated h-convex functions. Additionally, a novel inequality is employed to derive Hermite–Hadamard-Mercer type inequalities for h-convex functions defined on the co-ordinates of a rectangle in the plane. These developments not only reinforce the core tenets of convex analysis but also expand the applicability of Hermite-Hadamard-Mercer type inequalities to generalized convex functions on co-ordinates. This provides valuable tools for data analysis and optimization problem-solving. The practical utility and efficacy of this generalized inequality in real-world scenarios involving co-ordinates are demonstrated through a computational study. Mathematics Subject Classification: 26D10, 26D15, 26A51, 34A08.

On Certain Applications via (𝜑, ℘) -Suzuki type Fixed Point Results in 𝐴𝑏-Metric Spaces

Objective: In this study, we establish the existence and uniqueness of the common coupled fixed point theorem on complete - metric space. Method: We have used the - type Suzuki contraction on two mappings. Findings: For two mappings on the complete -Metric Space, we were able to obtain and prove a unique common coupled fixed point theorem and justify it with a suitable example. Novelty: A unique common coupled fixed point is obtained by using -type Suzuki contraction on two mappings and application of Suzuki contractive fixed point solutions of - type to integral equations in the setup of -Metric Space. Subject classification for mathematics in 2000. 54E50, 47H10, and 54H25. Keywords: Ab -Metric Space; -Type Suzuki Contraction; -Compatible; Ab -Completeness; Coupled Fixed Point

CLASSIFICATION OF SUBJECTS OF ADMINISTRATIVE LAW AND THE PLACE OF A LAWYER IN IT

The relevance of the studied topic is that subjects of administrative law are one of the most important elements of the legal system, since we are talking about such participants in admin­istrative-legal relations who solve tasks and perform the functions of executive power, who co­ordinate administrative and control-supervisory powers in branches of state administration and local self-government, consider cases of administrative offenses committed by individuals and legal entities in various spheres of public life, etc. It is important to clearly classify the place of each element of the system of administrative legal relations, in order to understand the direct powers and duties assigned to it. Without a deep understanding of the assigned role by each participant in administrative and legal relations, the very functioning of such a system is at risk. The main problems that need to be considered and solved at the new stage of the develop­ment of modern science and practice include the definition of subjects of administrative law, the analysis of their essence and features, as well as the outline of the main criteria for clas­sification. A necessary condition for the successful reform of administrative law as a fundamental branch of Ukrainian state law is the updating of the provisions of the theoretical and method­ological base of administrative and legal science. The article examines the systems of classification of subjects of administrative law exist­ing in modern legal science. The essence and content of the concept of “subject of administra­tive law”, as well as generally accepted definitions of this term, were studied. An attempt was made to establish the place of a lawyer in the system of subjects of admin­istrative law of Ukraine. A comprehensive approach to distinguishing and classifying a lawyer as a subject of administrative law is applied, taking into account the peculiarities of legal status, organizational and legal form of activity and the scope of public powers. However, the analysis of special literature shows that only a few researchers tried to con­sider the lawyer as a subject of administrative law or to determine his place in the accepted classifications.

Distribution of the Joint Survival Function of an Archimedean Copula

Suppose a random vector [Formula: see text] with values in the unit cube has a joint survival function: [Formula: see text] given by an Archimedean copula [Formula: see text] with generator [Formula: see text], a smooth decreasing convex function such that [Formula: see text]. In this article, we provide a formula for the distribution of [Formula: see text] where [Formula: see text] is an independent copy of [Formula: see text] and a method to simulate values from the distribution of Z in the bivariate case, that is, when d = 2. The case d > 2 does not seem to be tractable. As an application, we show how our result can be used to compute the limiting covariance of the empirical Kendall process corresponding to [Formula: see text]. AMS Subject Classification: 62H05

Right $\pi$-Regular Semirings

We prove the following results (1) If $R$ is a right and left $\pi$-regular semiring then $R$ is a $\pi$-regular semiring. (2) If $R$ is an additive cancellative semiprime, right Artinian or right $\pi$-regular right Noetherian semiring then $R$ is semisimple. (3) Let $I$ be a partitioning ideal of a semiring $R$ such that $Q=(R-I)\cup \{0\}$. If $I$ is a right regular ideal and the quotient semiring $R/I$ is right $\pi$-regular then $R$ is a right $\pi$-regular semiring. 2000 Mathematics Subject Classification. 16Y60

Semi-slant Submanifolds of Trans-Sasakian Manifolds

The purpose of the present paper is to study semi-slant submanifolds of a trans-Sasakian manifold. 2000 Mathematics Subject Classification. 53C40, 53B25

On Foci and Asymptotes of Conics in the Isotropic Plane

The paper shows that every conic with foci in the isotropic plane can be represented by the equation of the form $y^2=\epsilon x^2+x$, where $\epsilon \in \{-1, 0, 1\}$ for an ellipse, a parabola and a hyperbola with foci respectively. Using this equation some important properties of the foci are proved. According to duality the properties of asymptotes of the hyperbola in the isotropic plane are valid as well. 2000 Mathematics Subject Classification. 51N25

The Kontorovich - Lebedev Transformation on Sobolev Type Spaces

The Kontorovich-Lebedev transformation $$(KLf)(x)=\int_0^\inftyK_{i\tau}(x)f(\tau)d\tau, \;\, x \in {\mathbf R}_+$$ is consideredas an operator, which maps the weighted space $L_p(\mathbf R_+;$$\omega(\tau)d\tau), \;\, 2 \le p \le \infty$ into the Sobolevtype space $S_p^{N, \alpha}({\mathbf R}_+)$ with the finite norm$$||u||_{S_p^{N,\alpha}({\mathbf R}_+)}= \biggl( \sum_{k= 0}^N\int_0^\infty |A_x^k u|^p x^{\alpha_k p -1} dx\biggr)^{1/p} <\infty,$$where $\alpha= (\alpha_0, \alpha_1, \dots, \alpha_N), \alpha_k \in{\mathbf R}, k=0, \dots, N$, and $ A_x$ is the differentialoperator of the form$$A_x u= x^2u(x) - x\frac{d}{dx}\biggl[x\frac{du}{dx }\biggr], $$and $A_x^k$ means $k$-th iterate of $A_x, \ A_x^0u= u$. Elementary properties for the space $S_p^{N, \alpha} ({\mathbf R}_+)$ are derived. Boundedness and inversion properties for the Kontorovich-Lebedev transform are studied. In the Hilbert case ($p=2$) the isomorphism between these spaces is established for the special type of weights and Plancherel's type theorem is proved. 2000 Mathematics Subject Classification. 44A15, 46E35, 26D10

Dual Feuerbach Theorem in an Isotropic Plane

The dual Feuerbach theorem for an allowable triangle in an isotropic plane is proved analytically by means of the so-called standard triangle. A number of statements about relationships between some concepts of the triangle and their dual concepts are also proved. 2000 Mathematics Subject Classification. 51N25

Basins of Attraction of Equilibrium Points of Monotone Difference Equations

We investigate the global character of the difference equation of the form $$ x_{n+1} = f(x_n, x_{n-1},\ldots, x_{n-k+1}), \quadn=0,1, \ldots $$ with several equilibrium points, where $f$ is increasing in all its variables. We show that a considerable number of well known difference equations can be embeded into this equation through the iteration process. We also show that a negative feedback condition can be used to determine a part of the basin of attraction of different equilibrium points, and that the boundaries of the basins of attractions of different locally asymptotically stable equilibrium points are in fact the global stable manifolds of neighboring saddle or non-hyperbolic equilibrium points. 2000 Mathematics Subject Classification. 39A10, 39A11

Curvature of the Focal Conic in the Isotropic Plane

It is shown in \cite{beba} that every focal conic $\mathcal{C}$ in the isotropic plane can be represented by the equation $y^2=\epsilon x^2+x$, $\epsilon \in \{-1,0,1\}$ and a parametrization. This paper gives the equation of the circle of curvature at the point $T$ of the focal conic $\mathcal{C}$. The radius of curvature $\rho$ at the point $T$ of the focal conic $\mathcal{C}$ is given as well as its relation to the span $\delta $ from the center of $\mathcal{C}$ to the tangent $\lijepot$ at the point $T$ and to the length of the half diameter of $\mathcal{C}$ on the diameter parallel to the $\textup{tangent}$. 2000 Mathematics Subject Classification. 51N25

On the Boundedness of Solutions of a Non-autonomous Differential Equation of Second Order

We study the boundedness of the solutions to a non-autonomous differential equation of second order. With this work, we improve some stability results in the literature of boundedness of the solutions. We give two examples to illustrate the theoretical analysis in this work. 2000 Mathematics Subject Classification. 34C11, 34D20

Enhancing Systematic Reviews in Health Science Using Integrated Search Interfaces, Discovery Layers and Federated Searching

ABSTRACT This article highlights the importance of integrated search interfaces (ISI) in systematic reviews and examines the current guidelines on their use. ISI can help researchers determine the scope of their review topic and identify relevant search terms and subject headings. They can also assist in developing and documenting search strategies, as well as rapidly expanding searches to additional databases, registers, and gray literature. ISI can also be used for ongoing literature surveillance and the identification of retractions and errata. Limitations and challenges associated with the use of ISI in systematic reviews include; difficulties in translating search syntax between databases, limitations in the extensibility of controlled subject classifications, the need to select relevant databases, the commercialization of ISI hindering scientific reproducibility, challenges in maintaining the reproducibility of search strategies over time, and skills and knowledge deficits in the workforce. This article also discusses opportunities for vendors to enhance ISI to better support systematic review workflows. Features to improve ISI may include duplicate citation identification, cross-platform integration with citation management tools and screening platforms, transparency of search interface configuration, integration of bibliometrics and semantic mapping, and the use of artificial intelligence (AI) to enhance search strategies. Advancements in Large Language Models in the realm of AI, along with APIs designed to incorporate these models into various software tools, have the capability to significantly enhance the effectiveness and comprehensiveness of systematic reviews.

The protective role of cognitive reserve: an empirical study in mild cognitive impairment

BackgroundMild cognitive impairment (MCI) describes an aging profile characterized by a cognitive decline that is worse than expected in normal aging but less pervasive and critical than full-blown dementia. In the absence of an effective treatment strategy, it is important to identify factors that can protect against progression to dementia. In this field, it is hypothesized that one aspect that may be a protective factor against the neurotypical outcome of dementia is cognitive reserve (CR). Cognitive reserve is the ability to maintain cognitive functionality despite accumulating brain pathology.ObjectivesThe present study aimed to identify and analyze the differences in CR between healthy adults and patients with MCI. Specifically, it is hypothesized that (i) healthy older adult people have higher CR than older adult people diagnosed with MCI, and (II) CR could predict the classification of subjects into people with or without MCI.MethodsTwo hundred forty-three adults (mean age = 60.4, SD = 7.4) participated in the present study and were classified into three groups based on Petersen’s MCI criteria: healthy controls (HC), amnestic MCI (aMCI), and non-amnestic MCI (naMCI). The Cognitive Reserve Index questionnaire (CRIq) was administered to assess the level of CR,FindingsResults showed that HC had significantly higher CR scores than participants diagnosed with aMCI and naMCI. Moreover, a binomial logistic regression suggested that low CR was a significant risk factor for the MCI diagnosis.ConclusionsThe clinical picture that emerged from the results showed that lower CR could be considered a characteristic of pathological aging, such as MCI.Public significance statement, Since the brain attempts to cope with life-related changes or pathologies, it is fundamental for both clinicians and researchers to investigate further the factors that contribute to brain resilience. As an indirect expression of brain reserve, cognitive reserve may be both a marker and a predictor of adaptive aging.

MONTE CARLO AND NUMERICAL METHODS TO SOLVE THE TIME SERIES MODEL

In this paper we will solve the nonlinear system of equations in the parameters of the time series model by Monte Carlo methods and by numerical methods. When we identify the variance and the inter-covariances of time series, we obtain, dividing by variance, a quadratic nonlinear system of equation that does not contain the variance of wihite noise. We use only the autocorrelation function. AMS Subject Classification: 62M10, 91B84, 65C05.

On Micro Pre-Neighborhoods in Micro Topological Spaces

Objective: The basic objective of this article is to introduce and investigate the properties of micro pre-neighborhoods, micro pre-interior, micro pre-closure and micro pre-limit points. Methods: Using the concept of micro pre-open, micro pre-closed and micro pre-derived sets the result of the paper is obtained. Findings: In this article the properties and characterization of pre-open sets and pre-closed sets were opted on Micro topological space. Novelty: The relation between the characterization of micro pre-open sets, micro pre-closed sets and micro pre-derived sets were shown. AMS Subject Classifications: 54B05 Keywords: Micro topology, Micro pre-interior, Micro pre-closure, Micro pre-neighborhoods, Micro pre-limit points