Pseudostarlike and pseudoconvex solutions of a differential equation with exponential coefficients

Dirichlet series $F(s)=e^{s}+\sum_{k=1}^{\infty}f_ke^{s\lambda_k}$ with the exponents $1<\lambda_k\uparrow+\infty$ and the abscissa of absolute convergence $\sigma_a[F]\ge 0$ is said to be pseudostarlike of order $\alpha\in [0,\,1)$ and type $\beta \in (0,\,1]$ if$\left|\dfrac{F'(s)}{F(s)}-1\right|<\beta\left|\dfrac{F'(s)}{F(s)}-(2\alpha-1)\right|$\ for all\ $s\in \Pi_0=\{s\colon \,\text{Re}\,s<0\}$. Similarly, the function $F$ is said to be pseudoconvex of order $\alpha\in [0,\,1)$ and type $\beta \in (0,\,1]$ if$\left|\dfrac{F''(s)}{F'(s)}-1\right|<\beta\left|\dfrac{F''(s)}{F'(s)}-(2\alpha-1)\right|$\ for all\ $s\in \Pi_0$. Some conditions are found on the parameters $b_0,\,b_1,\,c_0,\,c_1,\,\,c_2$ and the coefficients $a_n$, under which the differential equation $\dfrac{d^2w}{ds^2}+(b_0e^{s}+b_1)\dfrac{dw}{ds}+(c_0e^{2s}+c_1e^{s}+c_2)w=\sum\limits_{n=1}^{\infty}a_ne^{ns}$has an entire solution which is pseudostarlike or pseudoconvex of order $\alpha\in [0,\,1)$ and type $\beta \in (0,\,1]$. It is proved that by some conditions for such solution the asymptotic equality holds $\ln\,\max\{|F(\sigma+it)|\colon t\in {\mathbb R}\}=\dfrac{1+o(1)}{2}\left(|b_0|+\sqrt{|b_0|^2+4|c_0|}\right)$ as $\sigma \to+\infty$.

Existence and nonexistence of entire k-convex radial solutions to Hessian type system

In this paper, a Hessian type system is studied. After converting the existence of an entire solution to the existence of a fixed point of a continuous mapping, the existence of entire k-convex radial solutions is established by the monotone iterative method. Moreover, a nonexistence result is also obtained.

Implementation of the Digital COVID-19 Vaccination Passport based on Blockchain Protecting Privacy

The paper discusses proposals for implementing the COVID-19 digital Vaccination Passport based on Blockchain that protects privacy. Since the end of the last year, after the commencement of vaccination against COVID-19, there has been an intense discussion on the form of introducing such a tool and the consequences of its implementation. This discussion is taking place in many European countries. One element of this discussion was the safety and anonymity of the massively verified data of persons on vaccinations in various areas of society functioning. These issues are being resolved by the proposed digital Vaccination Passport system. This system uses two major methods: Blockchain and hash functions, which allow you to maintain security, privacy, and anonymity at the same time. To improve the intuitiveness and simplicity of the system operation, the QR code technology was proposed in the passport verification process. The system has been implemented and tested in the Amazon AWS cloud computing environment. A reference architecture based on Blockchain for the AWS environment was proposed, dedicated to large and demanding application solutions. In addition, the cloud environment offers access to many tools that were used in the system’s implementation, significantly increasing the security of the entire solution.

Wrapper based Feature Selection using Integrative Teaching Learning Based Optimization Algorithm

The performance of the machine learning models mainly relies on the key features available in the training dataset. Feature selection is a significant job for pattern recognition for finding an important group of features to build classification models with a minimum number of features. Feature selection with optimization algorithms will improve the prediction rate of the classification models. But, tuning the controlling parameters of the optimization algorithms is a challenging task. In this paper, we present a wrapper-based model called Feature Selection with Integrative Teaching Learning Based Optimization (FS-ITLBO), which uses multiple teachers to select the optimal set of features from feature space. The goal of the proposed algorithm is to search the entire solution space without struck in the local optima of features. Moreover, the proposed method only utilizes teacher count parameter along with the size of the population and a number of iterations. Various classification models have been used for finding the fitness of instances in the population and to estimate the effectiveness of the proposed model. The robustness of the proposed algorithm has been assessed on Wisconsin Diagnostic Breast Cancer (WDBC) as well as Parkinson’s Disease datasets and compared with different wrapper-based feature selection techniques, including genetic algorithm and Binary Teaching Learning Based Optimization (BTLBO). The outcomes have confirmed that FS-ITLBO model produced the best accuracy with the optimal subset of features

Pareto Explorer for Finding the Knee for Many Objective Optimization Problems

Optimization problems where several objectives have to be considered concurrently arise in many applications. Since decision-making processes are getting more and more complex, there is a recent trend to consider more and more objectives in such problems, known as many objective optimization problems (MaOPs). For such problems, it is not possible any more to compute finite size approximations that suitably represent the entire solution set. If no users preferences are at hand, so-called knee points are promising candidates since they represent at least locally the best trade-off solutions among the considered objective values. In this paper, we extend the global/local exploration tool Pareto Explorer (PE) for the detection of such solutions. More precisely, starting from an initial solution, the goal of the modified PE is to compute a path of evenly spread solutions from this point along the Pareto front leading to a knee of the MaOP. The knee solution, as well as all other points from this path, are of potential interest for the underlying decision-making process. The benefit of the approach is demonstrated in several examples.

Streamline-Based Simulation of Nanoparticle Transport in Field-Scale Heterogeneous Subsurface Systems

Nanoparticle (NP) transport is increasingly relevant to subsurface engineering applications such as aquifer characterization, fracture electromagnetic imaging and environmental remediation. An efficient field-scale simulation framework is critical for predicting NP performance and designing subsurface applications. In this work, for the first time, a streamline-based model is presented to simulate NP transport in field-scale subsurface systems. It considers a series of behaviors exhibited by engineered nanoparticles (NPs), including time-triggered encapsulation, retention, formation damage effects and variable nanofluid viscosity. The key methods employed by the algorithm are streamline-based simulation (SLS) and an operator-splitting (OS) technique for modeling NP transport. SLS has proven to be efficient for solving transport in large and heterogeneous systems, where the pressure and velocity fields are firstly solved on underlying grids using finite-difference (FD) methods. After tracing streamlines, one-dimensional (1D) NP transport is solved independently along each streamline. The adoption of OS enhances flexibility for the entire solution procedure by allowing different numerical schemes to solve different governing equations efficiently and accurately. For the NP transport model, an explicit FD scheme is used to solve the advection term, an implicit FD scheme is used for the diffusion term and an adaptive numerical integration is used to solve the retention terms. The model is implemented in an in-house streamline-based code, which is verified against analytical solutions, a commercial FD reservoir simulator (ECLIPSE) and an academic FD colloid transport code (MNMs). For a 1D homogeneous case, the effluent breakthrough curves (BTC) produced by the in-house simulator are in good agreement with the analytical solution and MNMs, respectively. For a two-dimensional (2D) heterogeneous case, the BTC and concentration pattern of the in-house simulator all match well with the solution produced by commercial simulator. Simulations on a synthetic three-dimensional (3D) nanocapsule application engineering design case, are performed to investigate the effect of fluid and NP properties on the displacement pattern of an existing subsurface fluid.

Half-space theorems for the Allen–Cahn equation and related problems

In this paper we obtain rigidity results for a non-constant entire solution u of the Allen–Cahn equation in {\mathbb{R}^{n}}, whose level set {\{u=0\}} is contained in a half-space. If {n\leq 3}, we prove that the solution must be one-dimensional. In dimension {n\geq 4}, we prove that either the solution is one-dimensional or stays below a one-dimensional solution and converges to it after suitable translations. Some generalizations to one phase free boundary problems are also obtained.

Estimating the Density of States of Boolean Satisfiability Problems on Classical and Quantum Computing Platforms

Given a Boolean formula ϕ(x) in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly e clauses, for all values of e. Thus, the density of states is a histogram of the number of unsatisfied clauses over all possible assignments. This computation generalizes both maximum-satisfiability (MAX-SAT) and model counting problems and not only provides insight into the entire solution space, but also yields a measure for the hardness of the problem instance. Consequently, in real-world scenarios, this problem is typically infeasible even when using state-of-the-art algorithms. While finding an exact answer to this problem is a computationally intensive task, we propose a novel approach for estimating density of states based on the concentration of measure inequalities. The methodology results in a quadratic unconstrained binary optimization (QUBO), which is particularly amenable to quantum annealing-based solutions. We present the overall approach and compare results from the D-Wave quantum annealer against the best-known classical algorithms such as the Hamze-de Freitas-Selby (HFS) algorithm and satisfiability modulo theory (SMT) solvers.

Anisotropic problems with unbalanced growth

The main purpose of this paper is to study a general class of (p, q)-type eigenvalues problems with lack of compactness. The reaction is a convex-concave nonlinearity described by power-type terms. Our main result establishes a complete description of all situations that can occur. We prove the existence of a critical positive value λ* such that the following properties hold: (i) the problem does not have any entire solution in the case of low perturbations (that is, if 0 < λ < λ*); (ii) there is at least one solution if λ = λ*; and (iii) the problem has at least two entire solutions in the case of high perturbations (that is, if λ > λ*). The proof combines variational methods, analytic tools, and monotonicity arguments.

Single-Molecule Mechanics in Ligand Concentration Gradient

Single-molecule experiments provide unique insights into the mechanisms of biomolecular phenomena. However, because varying the concentration of a solute usually requires the exchange of the entire solution around the molecule, ligand-concentration-dependent measurements on the same molecule pose a challenge. In the present work we exploited the fact that a diffusion-dependent concentration gradient arises in a laminar-flow microfluidic device, which may be utilized for controlling the concentration of the ligand that the mechanically manipulated single molecule is exposed to. We tested this experimental approach by exposing a λ-phage dsDNA molecule, held with a double-trap optical tweezers instrument, to diffusionally-controlled concentrations of SYTOX Orange (SxO) and tetrakis(4-N-methyl)pyridyl-porphyrin (TMPYP). We demonstrate that the experimental design allows access to transient-kinetic, equilibrium and ligand-concentration-dependent mechanical experiments on the very same single molecule.