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In this paper we present an open source framework developed in Python and consisting of three distinct classes designed to manipulate in a simple and intuitive way both symbolic representations of neutrosophic sets over universes of various types as well as mappings between them. The capabilities offered by this framework extend and generalize previous attempts to provide software solutions to the manipulation of neutrosophic sets such as those proposed by Salama et al., Saranya et al., El-Ghareeb, Topal et al. and Sleem. The code is described in detail and many examples and use cases are also provided., Comment: 38 PAGES

In this paper we present not only some properties related to bi-warped product submanifolds of locally conformal almost cosymplectic manifolds, but also we show how the squared norm of the second fundamental form and the bi-warped product's warping functions are related when the bi-warped product submanifold has a proper slant submanifold as a base or fiber., Comment: 21 pages

We derive the general formulas for a special configuration of the sequential warped product semi-Riemannian manifold to be Einstein, where the base-manifold is the product of two manifolds both equipped with a conformal metrics. Subsequently we study the case in which these two manifolds are conformal to a $n_1$-dimensional and $n_2$-dimensional pseudo-Euclidean space, respectively. For the latter case, we prove the existence of a family of solutions that are invariant under the action of a $(n_1-1)$-dimensional group of transformations to the case of positive constant Ricci curvature ($\lambda>0$)., Comment: Latest version has minor changes and added references. Accepted for publication in: Journal of Geometric Mechanics (AIMS - America Institute of Mathematical Sciences)

We introduce a new geometric/topological approach to the emerging braneworld scenario in the context of D-branes using partially negative dimensional product (PNDP) manifolds. The working hypothesis is based on the fact that the orientability of PNDP manifolds can be arbitrary, and starting from this, we propose that gravitational interaction can derive naturally from the non-orientability. According to this hypothesis, we show that topological defects can emerge from non-orientability and they can be identified as gravitational interaction at macroscopic level. In other words, the orientability of fundamental PNDPs can be related to the appearance of curvature at low energy scales., Comment: 11 pages. Version 2 has minor changes to match version accepted for publication in Int. J. Geom. Methods Mod. Phys

We provide a possible way of constructing new kinds of manifolds which we will call Partially Negative Dimensional Product manifold (PNDP-manifold for short). In particular a PNDP-manifold is an Einstein warped product manifold of special kind, where the base-manifold $B$ is a Remannian (or pseudo-Riemannian) product-manifold $B=\Pi_{i=1}^{q'}B_i \times \Pi_{i=(q'+1)}^{\widetilde q} B_i$, with $\Pi_{i=(q'+1)}^{\widetilde q} B_i$ an Einstein-manifold, and the fiber-manifold $F$ is a derived-differential-manifold (i.e., $F$ is the form: smooth manifold ($\mathbb{R}^d$)+ obstruction bundle, so it can admit negative dimension). Since the dimension of a PNDP-manifold is not related with the usual geometric concept of dimension, from the speculative and applicative point of view, we try to define this relation using the concept of desuspension to identify the PNDP with another kind of "object", introducing a new kind of hidden dimensions., Comment: Fixed misprint

For the studied cases in [10], the author showed that having the {\textit {$f$-curvature-Base}} ($R_{f_B}$) is equal to requiring a flat metric on the base-manifold. In [11] the authors introduced a new kind of Einstein warped product manifold, composed by positive-dimensional manifold and negative-dimensional manifold, the so called \textit{PNDP-manifolds} The aim of this paper is to extend the work done in [10] to $m$-dimensional fiber showing if the value of $m$ can influence the result, i.e., finding base-manifolds with non-flat metric for $dimF \neq 2$, and doing some considerations of the $(2, m)$-PNDP manifolds with $R_{f_B}$. As a result, we find out that the dimension of fiber-manifold does not change the result of [10]., Comment: Accepted in: Differential Geometry - Dynamical Systems (DGDS-2020)

Finite-time optimal feedback control for flow networks under information constraints is studied. By utilizing the framework of multi-parametric linear programming, it is demonstrated that when cost/constraints can be modeled or approximated by piecewise-affine functions, the optimal control has a closed-form state-feedback realization. The optimal feedback control law, however, has a centralized structure and requires instantaneous access to the state of the entire network that may lead to prohibitive communication requirements in large-scale complex networks. We subsequently examine the design of a decentralized optimal feedback controller with a one-hop information structure, wherein the optimum outflow rate from each segment of the network depends only on the state of that segment and the state of the segments immediately downstream. The decentralization is based on the relaxation of constraints that depend on state variables that are unavailable according to the information structure. The resulting decentralized control scheme has a simple closed-form representation and is scalable to arbitrary large networks; moreover, we demonstrate that, with respect to certain meaningful performance indexes, the performance loss due to decentralization is zero; namely, the centralized optimal controller has a decentralized realization with a one-hop information structure and is obtained at no computational/communication cost.

We consider continuous-time, finite-horizon, optimal quadratic control of semi-Markov jump linear systems (S-MJLS), and develop principled approximations through Markov-like representations for the holding-time distributions. We adopt a phase-type approximation for holding times, which is known to be consistent, and translates a S-MJLS into a specific MJLS with partially observable modes (MJLSPOM), where the modes in a cluster have the same dynamic, the same cost weighting matrices and the same control policy. For a general MJLSPOM, we give necessary and sufficient conditions for optimal (switched) linear controllers. When specialized to our particular MJLSPOM, we additionally establish the existence of optimal linear controller, as well as its optimality within the class of general controllers satisfying standard smoothness conditions. The known equivalence between phase-type distributions and positive linear systems allows to leverage existing modeling tools, but possibly with large computational costs. Motivated by this, we propose matrix exponential approximation of holding times, resulting in pseudo-MJLSPOM representation, i.e., where the transition rates could be negative. Such a representation is of relatively low order, and maintains the same optimality conditions as for the MJLSPOM representation, but could violate non-negativity of holding-time density functions. A two-step procedure consisting of a local pulling-up modification and a filtering technique is constructed to enforce non-negativity.