Franciscan Books and their Readers

The book explores the manuscripts written, read, and studied by Franciscan friars from the thirteenth to the fifteenth centuries in Northern Italy, and specifically Padua, assessing four key aspects: ideal, space, form and readership. The ideal is studied through the regulations that determined what manuscripts should aim for. Space refers to the development and role of Franciscan libraries. The form is revealed by the assessment of the physical configuration of a set of representative manuscripts read, written, and manufactured by the friars. Finally, the study of the readership shows how Franciscans were skilled readers who employed certain forms of the manuscript as a portable, personal library, and as a tool for learning and pastoral care. By comparing the book collections of Padua’s reformed and unreformed medieval Franciscan libraries for the first time, this study reveals new features of the ground-breaking cultural agency of medieval friars.

Extended Fractional Singular Kalman Filter

Effective and accurate state estimation is a staple of modern modeling. On the other hand, nonlinear fractional-order singular (FOS) systems are an attractive modeling tool as well since they can provide accurate descriptions of systems with complex dynamics. Consequently, developing accurate state estimation methods for such systems is highly relevant since it provides vital information about the system including related memory effects and long interconnection properties with constraint elements. However, missing features in transforming structures such as violation of constraints in non-singular versions of such systems may affect the performance of the estimation result. This paper proposes the state estimation algorithm design for the original and non-transformed stochastic nonlinear FOS system. We introduce a deterministic data-fitting based framework which helps us to take steps directly towards Kalman filter (KF) derivation of the system, called extended fractional singular KF (EFSKF). Using stochastic reasoning, we demonstrate how to construct recursive form of the filter. Analysis of the filter shows how the proposed algorithm reduces to the nominal nonlinear filters when the system is in its usual state-space form making said algorithm highly flexible. Finally, simulation results verify that the estimation of nonlinear states can be accomplished with the proposed EFSKF algorithm with a reasonable performance.

A certain η-parallelism on real hypersurfaces in a nonflat complex space form

In this paper, we give the complete classification of real hypersurfaces in a nonflat complex space form from the viewpoint of the η-parallelism of the tensor field h(= (1/2)𝓛 ξ ϕ). In addition we investigate real hypersurfaces whose tensor h is either Killing type or transversally Killing tensor. In particular, we shall determine Hopf hypersurfaces whose tensor h is transversally Killing tensor by using an application of the classification of real hypersurfaces admitting η-parallelism with respect to the tensor h.

Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms

The purpose of this article is to establish some inequalities concerning the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of totally real spacelike submanifolds in statistical manifolds of the type para-Kähler space form. Moreover, this study is focused on the equality cases in these inequalities. Some examples are also provided.

Periodic solutions of Hilbert’s fourth problem

It is shown that a possibly irreversible [Formula: see text] Finsler metric on the torus, or on any other compact Euclidean space form, whose geodesics are straight lines is the sum of a flat metric and a closed [Formula: see text]-form. This is used to prove that if [Formula: see text] is a compact Riemannian symmetric space of rank greater than one and [Formula: see text] is a reversible [Formula: see text] Finsler metric on [Formula: see text] whose unparametrized geodesics coincide with those of [Formula: see text], then [Formula: see text] is a Finsler symmetric space.

Netosis in the pathogenesis of antiphospholipid syndrome and systemic lupus erythematosus

Antiphospholipid syndrome (APS) and systemic lupus erythematosus (SLE) are autoimmune diseases. In recent years, APS has been considered as an autoimmune thrombo-inflammatory disease. It has been established that clinical manifestations of APS can persist, progress over time, or debut during an adequate anticoagulant therapy and, in some cases, require administration of immunosuppressive drugs, which indicates the role of autoimmune inflammation in their development. The formation of extracellular neutrophil traps (neutrophil extracellular traps, NETs) is one of the connecting links of inflammation and thrombosis. Netosis is the process by which activated neutrophils in the extracellular space form netlike structures (NETs). This review examines the role of neutrophils and netosis in the pathogenesis of APS and SLE.

Some Eigenvalues Estimate for the ϕ -Laplace Operator on Slant Submanifolds of Sasakian Space Forms

This paper is aimed at establishing new upper bounds for the first positive eigenvalue of the ϕ -Laplacian operator on Riemannian manifolds in terms of mean curvature and constant sectional curvature. The first eigenvalue for the ϕ -Laplacian operator on closed oriented m -dimensional slant submanifolds in a Sasakian space form M ~ 2 k + 1 ε is estimated in various ways. Several Reilly-like inequalities are generalized from our findings for Laplacian to the ϕ -Laplacian on slant submanifold in a sphere S 2 n + 1 with ε = 1 and ϕ = 2 .

Chen-Ricci Inequalities with a Quarter Symmetric Connection in Generalized Space Forms

In this article, we obtain improved Chen-Ricci inequalities for submanifolds of generalized space forms with quarter-symmetric metric connection, with the help of which we completely characterized the Lagrangian submanifold in generalized complex space form and a Legendrian submanifold in a generalized Sasakian space form. We also discuss some geometric applications of the obtained results.