Algorithmic Method for the Design of Sequential Circuits with the Use of Logic Elements

This article presents issues related to the design of sequential control systems. The algorithmic design method of sequential control systems is discussed, which allows the design of a diagram of any sequential system. The algorithmic method uses the description in the form of a connection formula. The connection formula defines the order of actuations of driver elements, in this case actuators. The algorithmic method is used, among others, for systems with actuators cooperating with distributors controlled electrically on both sides. The process of creating a system graph has been characterized. The operation of the system has been shown graphically. On the basis of the created graph describing the functions of signal processing, a method for rapid programming of sequential electro-pneumatic systems with the use of logic elements has been provided. A separate dedicated timing unit has been used to perform memory functions. Its operation is based on successive states, in such a way that the next state deletes the previous one. Graph-based systems have been validated through simulation using Festo’s FluidSim computer-aided design software.

Levi-Civita connections for conformally deformed metrics on tame differential calculi

Given a tame differential calculus over a noncommutative algebra [Formula: see text] and an [Formula: see text]-bilinear metric [Formula: see text] consider the conformal deformation [Formula: see text] [Formula: see text] being an invertible element of [Formula: see text] We prove that there exists a unique connection [Formula: see text] on the bimodule of one-forms of the differential calculus which is torsionless and compatible with [Formula: see text] We derive a concrete formula connecting [Formula: see text] and the Levi-Civita connection for the metric [Formula: see text] As an application, we compute the Ricci and scalar curvatures for a general conformal perturbation of the canonical metric on the noncommutative [Formula: see text]-torus as well as for a natural metric on the quantum Heisenberg manifold. For the latter, the scalar curvature turns out to be a negative constant.

Global Analysis of GG Systems

This paper deals with some analytic aspects of GG system introduced by I.M. Gelfand and M.I. Graev: we compute the dimension of the solution space of GG system over the field of meromorphic functions periodic with respect to a lattice. We describe the monodromy invariant subspace of the solution space. We provide a connection formula between a pair of bases consisting of $\Gamma $-series solutions of GG system associated with a pair of regular triangulations adjacent to each other in the secondary fan.

Assessing the Accuracy of the SCAN Functional for Water Through a Many-Body Analysis of the Adiabatic Connection Formula

<div> <div> <div> <p>We present a systematic analysis of the accuracy of a series of SCANα functionals for water, with varying fractions (α) of exact exchange, which are constructed through the adiabatic connection formula. Our results indicate that that all SCANα functionals exhibit substantial errors in the representation of the water 2-body energies. Importantly, the inclusion of exact exchange is found to have opposite effects on the ability of the SCANα functionals to describe the interaction energies of water clusters with 2-dimensional and 3-dimensional hydrogen-bonding arrangements. These errors are found to directly affect the ability of the SCANα functionals to describe the structure of liquid water at ambient conditions, which is investigated using explicit many-body models (MB-SCANα) derived from the corresponding SCANα data. In particular, it is found that all MB-SCANα models predict a more compact first hydration shell, which results in a denser liquid with a more ice-like structure. These ap- parent opposite trends can be explained by the inability of all SCANα functionals to provide a balanced description of the water 2B and 3B energies at the fundamental level. The analyses presented in this study provide new insights that can guide future developments of improved exchange-correlation functionals for water.</p> </div> </div> </div>

Assessing the Accuracy of the SCAN Functional for Water Through a Many-Body Analysis of the Adiabatic Connection Formula

<div> <div> <div> <p>We present a systematic analysis of the accuracy of a series of SCANα functionals for water, with varying fractions (α) of exact exchange, which are constructed through the adiabatic connection formula. Our results indicate that that all SCANα functionals exhibit substantial errors in the representation of the water 2-body energies. Importantly, the inclusion of exact exchange is found to have opposite effects on the ability of the SCANα functionals to describe the interaction energies of water clusters with 2-dimensional and 3-dimensional hydrogen-bonding arrangements. These errors are found to directly affect the ability of the SCANα functionals to describe the structure of liquid water at ambient conditions, which is investigated using explicit many-body models (MB-SCANα) derived from the corresponding SCANα data. In particular, it is found that all MB-SCANα models predict a more compact first hydration shell, which results in a denser liquid with a more ice-like structure. These ap- parent opposite trends can be explained by the inability of all SCANα functionals to provide a balanced description of the water 2B and 3B energies at the fundamental level. The analyses presented in this study provide new insights that can guide future developments of improved exchange-correlation functionals for water.</p> </div> </div> </div>

Assessing the Accuracy of the SCAN Functional for Water Through a Many-Body Analysis of the Adiabatic Connection Formula

<div> <div> <div> <p>We present a systematic analysis of the accuracy of a series of SCANα functionals for water, with varying fractions (α) of exact exchange, which are constructed through the adiabatic connection formula. Our results indicate that that all SCANα functionals exhibit substantial errors in the representation of the water 2-body energies. Importantly, the inclusion of exact exchange is found to have opposite effects on the ability of the SCANα functionals to describe the interaction energies of water clusters with 2-dimensional and 3-dimensional hydrogen-bonding arrangements. These errors are found to directly affect the ability of the SCANα functionals to describe the structure of liquid water at ambient conditions, which is investigated using explicit many-body models (MB-SCANα) derived from the corresponding SCANα data. In particular, it is found that all MB-SCANα models predict a more compact first hydration shell, which results in a denser liquid with a more ice-like structure. These ap- parent opposite trends can be explained by the inability of all SCANα functionals to provide a balanced description of the water 2B and 3B energies at the fundamental level. The analyses presented in this study provide new insights that can guide future developments of improved exchange-correlation functionals for water.</p> </div> </div> </div>

On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle

In this contribution, we propose an algorithm to compute holonomic second-order differential equations satisfied by some families of orthogonal polynomials. Such algorithm is based in three properties that orthogonal polynomials satisfy: a recurrence relation, a structure formula, and a connection formula. This approach is used to obtain second-order differential equations whose solutions are orthogonal polynomials associated with some spectral transformations of a measure on the unit circle, as well as orthogonal polynomials associated with coherent pairs of measures on the unit circle.

Bott–Chern harmonic forms on complete Hermitian manifolds

Let [Formula: see text] be a Hermitian manifold of complex dimension [Formula: see text]. Assume that the torsion of the Chern connection [Formula: see text] is bounded, and that there exists a [Formula: see text]exhausting function [Formula: see text] such that [Formula: see text] are bounded. We characterize [Formula: see text] Bott–Chern harmonic forms, extending the usual result that holds on compact Hermitian manifolds. Finally, if [Formula: see text] is Kähler complete, [Formula: see text], with [Formula: see text] bounded, and the sectional curvature is bounded, then we get a vanishing theorem for [Formula: see text] Bott–Chern harmonic [Formula: see text]-forms, if [Formula: see text].

Sheaf lines of Yang–Mills instanton sheaves

We calculate a sheaf line in [Formula: see text] which is the real line supporting sheaf points on [Formula: see text] of [Formula: see text] Yang–Mills (YM) instanton (or [Formula: see text] complex YM instanton) sheaves for some given ADHM data we obtained previously. We found that this sheaf line is indeed a special jumping line over [Formula: see text] spacetime. In addition, we calculate the singularity structure of the connection [Formula: see text] and the field strength [Formula: see text] at the corresponding singular point on [Formula: see text] of this sheaf line. We found that the order of singularity at the singular point on [Formula: see text] associated with the sheaf line in [Formula: see text] is higher than those of other singular points associated with normal jumping lines. We conjecture that this is a general feature for sheaf lines among jumping lines.