A Proof of Riemann Hypothesis Based on MacLaurin Expansion of the Completed Zeta Function

The basic idea is to expand the completed zeta function $\xi(s)$ in MacLaurin series. Thus, $\xi(s)=0$ corresponds to an algebraic equation with real coefficients and infinite degree. In addition, by $\xi(s)=\xi(1-s)$, another formally equivalent algebraic equation exists, i.e., $\xi(1-s)=0$. Then these two simultaneous algebraic equations share the common solution, thus a proof of Riemann Hypothesis (RH) can be obtained.

Creativity and Complexity: Creative Solutions are Complex and Need Time

To create art means to be creative, but how creativity is gained, how we can induce and train creativity and how we can validly measure creative potential is a matter of still unsolved research. In our exploratory study, 49 participants had to create figures by using a double set of Tangram puzzles — so to say: to create something with an infinite degree of freedoms but that is still based on just a few defined and simple basic elements. In total, participants created 708 different figures. Creativity and complexity of these creations were then assessed in a subsequent study by five further raters in two randomly ordered blocks. We observed a strong correlation between the ratings of creativity and complexity on basis of average as well as individual data level. Interestingly, highly productive people, sometimes misinterpreted as ‘creatives’ due to their sheer quantitative output, actually produced simpler scenes that were also evaluated as less creative. We could also reveal that the level of creativity in the produced items remained very similar over the course of the test, pointing to relatively stable creativity traits (at least during the study phase). Our approach could lead to a deeper and more differentiated understanding of the concept of creativity and creative potential, specifically by combining it with qualitative analyses of the complexity of the created figures.

Dynamical Simulation of A CNC Turning Centre (Survey Paper)

This paper shows the most common rotor systems which can be used to analyse a CNC turning center. Starting with the simplest rotor system representation (single-degree-offreedom) up to analysing multi-degree-of-freedom and infinite-degree-of-freedom rotor systems using the TMM (Transfer Matrix Method) when it comes to cases like multi desk rotors and Jeffcott-rotors.

Dynamic Control of Soft Robots Using Reinforcement Learning

Soft robots made from soft materials recently attracted tremendous research owing to their unique softness compared with rigid robots, making them suitable for applications such as manipulation and locomotion. However, also due to their softness, the modeling and control of soft robots present a significant challenge because of the infinite degree of freedom. In this case, although analytic solutions can be derived for control, they are too computationally intensive for real-time application. In this paper, we aim to leverage reinforcement learning to approach the control problem. We gradually increase the complexity of the control problems to learn. We also test the effectiveness and efficiency of reinforcement learning techniques to the control of soft robots for different tasks. Simulation results show that the control commands to be computed in milliseconds, allowing effective control of soft manipulators, up to trajectory tracking.

Julia Robinson numbers

We construct an infinite family of totally real algebraic extensions of [Formula: see text] whose ring of integers has a Julia Robinson number distinct from [Formula: see text] and [Formula: see text]. In fact, the set of Julia Robinson numbers obtained is unbounded. This gives new examples of algebraic extensions of [Formula: see text] of infinite degree whose ring of integers has undecidable first-order theory.

The First Cut—The Intrinsic Modes of Being

Chapter 4 argues for the intrinsic modes of being (e.g., infinite/finite, necessary/contingent) as ultimate differences in Scotus’s expanded sense of the term. The first section begins with an account of what Scotus means by an intrinsic mode and the modal distinction. This is followed up in the second section with a discussion of the modes of being finite and infinite. Whereas Scotus identifies other modes, the chapter argues why these are his preferred terms. The third section links the modes of finite and infinite to what Scotus, following Augustine and others, calls “a transcendental magnitude.” The fourth section explains how Scotus understands the categories as finite transcendental magnitudes and infinitumas the transcendental magnitude of the divine essence. The chapter then establishes the connection between transcendental magnitudes and intensity and argues for a uniquely “non-additive” account of intensity (the fifth section). The chapter shows the diversity of differential degrees of being, which can nevertheless be measured on a scale of intensity reaching to, but never touching, the infinite degree.

Dynamic Focusing of Electrospinning Process With Quadrupole Traps

Electrospinning is the most widely used production method for polymer fibers formed from an electrified fluid jet. This method is very versatile, relatively inexpensive and simple. When the sufficiently high electric potential (about 20kV) is applied to the polymer solution, the electrostatic forces overcome the surface tension of the polymer and a thin liquid jet is ejected from the nozzle. However, after short straight distance of the motion of the fiber it rapidly grows into an electric charge driven bending instability and results in a 3D spiraling trajectory leading to a very random deposition on the grounded collector. This significantly reduces the positive qualities of the fiber and its use in biomechanical engineering like a production of tissue scaffolds mimicking the structure of the extracellular matrix or a delivery of expandable chemo- and radio-therapeutic stents. In this work we present the initial results from investigating the feasibility of using dynamic focusing of the electrified jet in a linear quadrupole trap. This is a new alternative to the more generally used mechanical approach with rotating mandrel, could in principle lead to the ability to control the deposition location without the use of any moving components. The proposed approach was originally developed for trapping and transporting individual charged ions. In contrast to ions, an electrified continuous fiber represents an infinite degree of freedom system, with potentially much richer dynamics and unknown stability regions in the parameter space. In order to understand the dynamics of the fiber, we present a discretized 2D reduced-order mathematical model which is investigated numerically. The resulting ODEs represent multi-dimensional form of a non-linear Mathieu’s and Meissner’s differential equations for harmonic, and step excitation functions, respectively. The model parameters were obtained from static experiments with electrodes compressing the fibers in a single plane. Finite-element model of the electrodes resulted in detailed potential maps, which were used to develop estimates of the required strength of the electrostatic field needed to steer the fibers. The estimated parameters were used to obtain stable solutions of the reduced-order approximate of a spring-mass-charged dumbbell model of the fiber.